time to travel light from moon to earth

Shop Our Online Science Store

3-in-1 alternative energy car diy stem kit.

• $19.99 $14.95

Hand-Crank Generator DIY STEM Kit

• $9.99 $5.95

Solar & Battery Fan DIY STEM Kit

Flashing led circuit diy electronics kit.

• $4.99 $2.59

Battery-Powered Balancing Robot DIY STEM Kit

• $8.99 $4.95

Solar + Battery Car DIY STEM Kit

• $11.99 $5.95

Wire Maze Electricity DIY STEM Kit

Solar micro car kit diy stem kit.

• $7.99 $4.95
• Privacy Policy
• Cookie Policy

The speed of light is torturously slow, and these 3 simple animations by a scientist at NASA prove it

• The speed of light in a vacuum is about 186,282 miles per second (299,792 kilometers per second).
• A scientist at NASA animated how long it takes light to travel around Earth, as well as between the planet, its moon, and Mars.
• The physics animations show just how fast (and slow) the speed limit of the universe can be.

A series of new animations by a NASA scientist show just how zippy — and also how torturously slow — the speed of light can be.

Light speed is the fastest that any material object can travel through space. That is, of course, barring the existence of theoretical shortcuts in the fabric of space called wormholes (and the ability to go through them without being destroyed).

In a perfectly empty vacuum, a particle of light, which is called a photon, can travel 186,282 miles per second (299,792 kilometers per second), or about 670.6 million mph (1.079 billion kilometers per hour).

This is incredibly fast. However, light speed can be frustratingly slow if you're trying to communicate with or reach other planets, especially any worlds beyond our solar system.

Read more : Astronomers found a 'cold super-Earth' less than 6 light-years away — and it may be the first rocky planet we'll photograph beyond the solar system

To depict the speed limit of the cosmos in a way anyone could understand, James O'Donoghue , a planetary scientist at NASA's Goddard Space Flight Center, took it upon himself to animate it.

"My animations were made to show as instantly as possible the whole context of what I'm trying to convey," O'Donoghue told Business Insider via Twitter . "When I revised for my exams, I used to draw complex concepts out by hand just to truly understand, so that's what I'm doing here."

O'Donoghue said he only recently learned how to create these animations — his first were for a NASA news release about Saturn's vanishing rings . After that, he moved on to animating other difficult-to-grasp space concepts, including a video illustrating the rotation speeds and sizes of the planets. He said that one "garnered millions of views" when he posted it on Twitter .

O'Donoghue's latest effort looks at three different light-speed scenarios to convey how fast (and how painfully slow) photons can be.

How fast light travels relative to Earth

One of O'Donoghue's first animations shows how fast light moves in relation to Earth.

Earth is 24,901 miles around at its center. If our world had no atmosphere (air refracts and slows down light a little bit), a photon skimming along its surface could lap the equator nearly 7.5 times every second.

In this depiction , the speed of light seems pretty fast — though the movie also shows how finite it is.

How fast light travels between Earth and the moon

A second animation by O'Donoghue takes a big step back from Earth to include the moon.

Related stories

On average, there is about 238,855 miles (384,400 kilometers) of distance between our planet and its large natural satellite.

This means all moonlight we see is 1.255 seconds old, and a round-trip between the Earth and moon at light speed takes about 2.51 seconds.

This timing is growing every day, however, as the moon is drifting farther from Earth at a rate of about 1.5 inches (3.8 centimeters) per year. (The moon is constantly sapping Earth's rotational energy via ocean tides , boosting its orbit to a greater and greater distance.)

How fast light travels between Earth and Mars

O'Donoghue's third speed-of-light animation illustrates the challenge that many planetary scientists deal with on a daily basis.

When NASA tries to talk to or download data from a spacecraft, such as the InSight probe on Mars , it can do so only at the speed of light. This is much too slow to operate a spacecraft in "live mode" as you would a remote-controlled car. So, commands must be carefully thought out, prepackaged, and aimed at the precise location in space at the precise time so that they don't miss their target.

Read more : NASA can hear the 'haunting' sound of dust devils tearing across Mars with its new $830 million lander

The fastest a conversation could ever happen between Earth and Mars is when the planets are at their nearest point to one another, an event called closest approach that happens once roughly every two years. On average, that best-case-scenario distance is about 33.9 million miles (54.6 million kilometers).

As that 60-second clip of O'Donoghue's full movie on YouTube shows, light takes 3 minutes 2 seconds to travel between Earth and Mars at closest approach. That's six minutes and four seconds for a light-speed round-trip.

But on average, Mars is about 158 million miles from Earth — so the average round-trip communication takes about 28 minutes and 12 seconds.

The speed of light gets more depressing the farther you go

The hurdle of light's finite speed gets even more challenging for spacecraft such as New Horizons, which is now more than 4 billion miles from Earth , and the Voyager 1 and 2 spacecraft, each of which have reached the space between stars .

The situation gets downright depressing when you start looking outside the solar system. The closest-known exoplanet , called Proxima b, is about 4.2 light-years away from us (a distance of about 24.7 trillion miles or 39.7 trillion kilometers).

However, the fastest any spacecraft has ever gone is NASA's Parker Solar Probe at about 213,200 mph ; at that speed, it'd take 13,211 years to reach Proxima b.

A Russian-American billionaire's Breakthrough Starshot project envisions a way to address this speed problem. The multidecade plan is to build and fly tiny "nanocraft" past such exoplanets via ultrapowerful laser blasts , ideally at a planned cruise velocity of 20% of the speed of light. Yet the entire concept is still theoretical, may end up not working, and would operate at a fraction of light-speed.

Space is impossibly vast. Although the universe is about 13.77 billion years old, its edge is about 45.34 billion light-years away in any direction and is increasing due to expansion .

That's far too big to illustrate in a simple animation. One illustration comes close, though: this image created by musician Pablo Carlos Budassi , which combines logarithmic maps of the universe from Princeton and images from NASA to capture it all in one picture.

This story has been updated.

Watch: What humans will look like on Mars

• Main content

Chapter 15: Galaxies

Chapter 1 how science works.

• The Scientific Method
• Measurements
• Units and the Metric System
• Measurement Errors
• Mass, Length, and Time
• Observations and Uncertainty
• Precision and Significant Figures
• Errors and Statistics
• Scientific Notation
• Ways of Representing Data
• Mathematics
• Testing a Hypothesis
• Case Study of Life on Mars
• Systems of Knowledge
• The Culture of Science
• Computer Simulations
• Modern Scientific Research
• The Scope of Astronomy
• Astronomy as a Science
• A Scale Model of Space
• A Scale Model of Time

Chapter 2 Early Astronomy

• The Night Sky
• Motions in the Sky
• Constellations and Seasons
• Cause of the Seasons
• The Magnitude System
• Angular Size and Linear Size
• Phases of the Moon
• Dividing Time
• Solar and Lunar Calendars
• History of Astronomy
• Ancient Observatories
• Counting and Measurement
• Greek Astronomy
• Aristotle and Geocentric Cosmology
• Aristarchus and Heliocentric Cosmology
• The Dark Ages
• Arab Astronomy
• Indian Astronomy
• Chinese Astronomy
• Mayan Astronomy

Chapter 3 The Copernican Revolution

• Ptolemy and the Geocentric Model
• The Renaissance
• Copernicus and the Heliocentric Model
• Tycho Brahe
• Johannes Kepler
• Elliptical Orbits
• Kepler's Laws
• Galileo Galilei
• The Trial of Galileo
• Isaac Newton
• Newton's Law of Gravity
• The Plurality of Worlds
• The Birth of Modern Science
• Layout of the Solar System
• Scale of the Solar System
• The Idea of Space Exploration
• History of Space Exploration
• Moon Landings
• International Space Station
• Manned versus Robotic Missions
• Commercial Space Flight
• Future of Space Exploration
• Living in Space
• Moon, Mars, and Beyond
• Societies in Space

Chapter 4 Matter and Energy in the Universe

• Matter and Energy
• Rutherford and Atomic Structure
• Early Greek Physics
• Dalton and Atoms
• The Periodic Table
• Structure of the Atom
• Heat and Temperature
• Potential and Kinetic Energy
• Conservation of Energy
• Velocity of Gas Particles
• States of Matter
• Thermodynamics
• Laws of Thermodynamics
• Heat Transfer
• Thermal Radiation
• Radiation from Planets and Stars
• Internal Heat in Planets and Stars
• Periodic Processes
• Random Processes

Chapter 5 The Earth-Moon System

• Earth and Moon
• Early Estimates of Earth's Age
• How the Earth Cooled
• Ages Using Radioactivity
• Radioactive Half-Life
• Ages of the Earth and Moon
• Geological Activity
• Internal Structure of the Earth and Moon
• Basic Rock Types
• Layers of the Earth and Moon
• Origin of Water on Earth
• The Evolving Earth
• Plate Tectonics
• Geological Processes
• Impact Craters
• The Geological Timescale
• Mass Extinctions
• Evolution and the Cosmic Environment
• Earth's Atmosphere and Oceans
• Weather Circulation
• Environmental Change on Earth
• The Earth-Moon System
• Geological History of the Moon
• Tidal Forces
• Effects of Tidal Forces
• Historical Studies of the Moon
• Lunar Surface
• Ice on the Moon
• Origin of the Moon
• Humans on the Moon

Chapter 6 The Terrestrial Planets

• Studying Other Planets
• The Planets
• The Terrestrial Planets
• Mercury's Orbit
• Mercury's Surface
• Volcanism on Venus
• Venus and the Greenhouse Effect
• Tectonics on Venus
• Exploring Venus
• Mars in Myth and Legend
• Early Studies of Mars
• Mars Close-Up
• Modern Views of Mars
• Missions to Mars
• Geology of Mars
• Water on Mars
• Polar Caps of Mars
• Climate Change on Mars
• Terraforming Mars
• Life on Mars
• The Moons of Mars
• Martian Meteorites
• Comparative Planetology
• Incidence of Craters
• Counting Craters
• Counting Statistics
• Internal Heat and Geological Activity
• Magnetic Fields of the Terrestrial Planets
• Mountains and Rifts
• Radar Studies of Planetary Surfaces
• Laser Ranging and Altimetry
• Gravity and Atmospheres
• Normal Atmospheric Composition
• The Significance of Oxygen

Chapter 7 The Giant Planets and Their Moons

• The Gas Giant Planets
• Atmospheres of the Gas Giant Planets
• Clouds and Weather on Gas Giant Planets
• Internal Structure of the Gas Giant Planets
• Thermal Radiation from Gas Giant Planets
• Life on Gas Giant Planets?
• Why Giant Planets are Giant
• Ring Systems of the Giant Planets
• Structure Within Ring Systems
• The Origin of Ring Particles
• The Roche Limit
• Resonance and Harmonics
• Tidal Forces in the Solar System
• Moons of Gas Giant Planets
• Geology of Large Moons
• The Voyager Missions
• Jupiter's Galilean Moons
• Jupiter's Ganymede
• Jupiter's Europa
• Jupiter's Callisto
• Jupiter's Io
• Volcanoes on Io
• Cassini Mission to Saturn
• Saturn's Titan
• Saturn's Enceladus
• Discovery of Uranus and Neptune
• Uranus' Miranda
• Neptune's Triton
• The Discovery of Pluto
• Pluto as a Dwarf Planet
• Dwarf Planets

Chapter 8 Interplanetary Bodies

• Interplanetary Bodies
• Early Observations of Comets
• Structure of the Comet Nucleus
• Comet Chemistry
• Oort Cloud and Kuiper Belt
• Kuiper Belt
• Comet Orbits
• Life Story of Comets
• The Largest Kuiper Belt Objects
• Meteors and Meteor Showers
• Gravitational Perturbations
• Surveys for Earth Crossing Asteroids
• Asteroid Shapes
• Composition of Asteroids
• Introduction to Meteorites
• Origin of Meteorites
• Types of Meteorites
• The Tunguska Event
• The Threat from Space
• Probability and Impacts
• Impact on Jupiter
• Interplanetary Opportunity

Chapter 9 Planet Formation and Exoplanets

• Formation of the Solar System
• Early History of the Solar System
• Conservation of Angular Momentum
• Angular Momentum in a Collapsing Cloud
• Helmholtz Contraction
• Safronov and Planet Formation
• Collapse of the Solar Nebula
• Why the Solar System Collapsed
• From Planetesimals to Planets
• Accretion and Solar System Bodies
• Differentiation
• Planetary Magnetic Fields
• The Origin of Satellites
• Solar System Debris and Formation
• Gradual Evolution and a Few Catastrophies
• Chaos and Determinism
• Extrasolar Planets
• Discoveries of Exoplanets
• Doppler Detection of Exoplanets
• Transit Detection of Exoplanets
• The Kepler Mission
• Direct Detection of Exoplanets
• Properties of Exoplanets
• Implications of Exoplanet Surveys
• Future Detection of Exoplanets

Chapter 10 Detecting Radiation from Space

• Observing the Universe
• Radiation and the Universe
• The Nature of Light
• The Electromagnetic Spectrum
• Properties of Waves
• Waves and Particles
• How Radiation Travels
• Properties of Electromagnetic Radiation
• The Doppler Effect
• Invisible Radiation
• Thermal Spectra
• The Quantum Theory
• The Uncertainty Principle
• Spectral Lines
• Emission Lines and Bands
• Absorption and Emission Spectra
• Kirchoff's Laws
• Astronomical Detection of Radiation
• The Telescope
• Optical Telescopes
• Optical Detectors
• Adaptive Optics
• Image Processing
• Digital Information
• Radio Telescopes
• Telescopes in Space
• Hubble Space Telescope
• Interferometry
• Collecting Area and Resolution
• Frontier Observatories

Chapter 11 Our Sun: The Nearest Star

• The Nearest Star
• Properties of the Sun
• Kelvin and the Sun's Age
• The Sun's Composition
• Energy From Atomic Nuclei
• Mass-Energy Conversion
• Examples of Mass-Energy Conversion
• Energy From Nuclear Fission
• Energy From Nuclear Fusion
• Nuclear Reactions in the Sun
• The Sun's Interior
• Energy Flow in the Sun
• Collisions and Opacity
• Solar Neutrinos
• Solar Oscillations
• The Sun's Atmosphere
• Solar Chromosphere and Corona
• The Solar Cycle
• The Solar Wind
• Effects of the Sun on the Earth
• Cosmic Energy Sources

Chapter 12 Properties of Stars

• Star Properties
• The Distance to Stars
• Apparent Brightness
• Absolute Brightness
• Measuring Star Distances
• Stellar Parallax
• Spectra of Stars
• Spectral Classification
• Temperature and Spectral Class
• Stellar Composition
• Stellar Motion
• Stellar Luminosity
• The Size of Stars
• Stefan-Boltzmann Law
• Stellar Mass
• Hydrostatic Equilibrium
• Stellar Classification
• The Hertzsprung-Russell Diagram
• Volume and Brightness Selected Samples
• Stars of Different Sizes
• Understanding the Main Sequence
• Stellar Structure
• Stellar Evolution

Chapter 13 Star Birth and Death

• Star Birth and Death
• Understanding Star Birth and Death
• Cosmic Abundance of Elements
• Star Formation
• Molecular Clouds
• Young Stars
• T Tauri Stars
• Mass Limits for Stars
• Brown Dwarfs
• Young Star Clusters
• Cauldron of the Elements
• Main Sequence Stars
• Nuclear Reactions in Main Sequence Stars
• Main Sequence Lifetimes
• Evolved Stars
• Cycles of Star Life and Death
• The Creation of Heavy Elements
• Horizontal Branch and Asymptotic Giant Branch Stars
• Variable Stars
• Magnetic Stars
• Stellar Mass Loss
• White Dwarfs
• Seeing the Death of a Star
• Supernova 1987A
• Neutron Stars and Pulsars
• Special Theory of Relativity
• General Theory of Relativity
• Black Holes
• Properties of Black Holes

Chapter 14 The Milky Way

• The Distribution of Stars in Space
• Stellar Companions
• Binary Star Systems
• Binary and Multiple Stars
• Mass Transfer in Binaries
• Binaries and Stellar Mass
• Nova and Supernova
• Exotic Binary Systems
• Gamma Ray Bursts
• How Multiple Stars Form
• Environments of Stars
• The Interstellar Medium
• Effects of Interstellar Material on Starlight
• Structure of the Interstellar Medium
• Dust Extinction and Reddening
• Groups of Stars
• Open Star Clusters
• Globular Star Clusters
• Distances to Groups of Stars
• Ages of Groups of Stars
• Layout of the Milky Way
• William Herschel
• Isotropy and Anisotropy
• Mapping the Milky Way

Chapter 15 Galaxies

• The Milky Way Galaxy
• Mapping the Galaxy Disk
• Spiral Structure in Galaxies
• Mass of the Milky Way
• Dark Matter in the Milky Way
• Galaxy Mass
• The Galactic Center
• Black Hole in the Galactic Center
• Stellar Populations
• Formation of the Milky Way
• The Shapley-Curtis Debate
• Edwin Hubble
• Distances to Galaxies
• Classifying Galaxies
• Spiral Galaxies
• Elliptical Galaxies
• Lenticular Galaxies
• Dwarf and Irregular Galaxies
• Overview of Galaxy Structures
• The Local Group

Light Travel Time

• Galaxy Size and Luminosity
• Mass to Light Ratios
• Dark Matter in Galaxies
• Gravity of Many Bodies
• Galaxy Evolution
• Galaxy Interactions
• Galaxy Formation

Chapter 16 The Expanding Universe

• Galaxy Redshifts
• The Expanding Universe
• Cosmological Redshifts
• The Hubble Relation
• Relating Redshift and Distance
• Galaxy Distance Indicators
• Size and Age of the Universe
• The Hubble Constant
• Large Scale Structure
• Galaxy Clustering
• Clusters of Galaxies
• Overview of Large Scale Structure
• Dark Matter on the Largest Scales
• The Most Distant Galaxies
• Black Holes in Nearby Galaxies
• Active Galaxies
• Radio Galaxies
• The Discovery of Quasars
• Types of Gravitational Lensing
• Properties of Quasars
• The Quasar Power Source
• Quasars as Probes of the Universe
• Star Formation History of the Universe
• Expansion History of the Universe

Chapter 17 Cosmology

• Early Cosmologies
• Relativity and Cosmology
• The Big Bang Model
• The Cosmological Principle
• Universal Expansion
• Cosmic Nucleosynthesis
• Cosmic Microwave Background Radiation
• Discovery of the Microwave Background Radiation
• Measuring Space Curvature
• Cosmic Evolution
• Evolution of Structure
• Mean Cosmic Density
• Critical Density
• Dark Matter and Dark Energy
• Age of the Universe
• Precision Cosmology
• The Future of the Contents of the Universe
• Fate of the Universe
• Alternatives to the Big Bang Model
• Particles and Radiation
• The Very Early Universe
• Mass and Energy in the Early Universe
• Matter and Antimatter
• The Forces of Nature
• Fine-Tuning in Cosmology
• The Anthropic Principle in Cosmology
• String Theory and Cosmology
• The Multiverse
• The Limits of Knowledge

Chapter 18 Life On Earth

• Nature of Life
• Chemistry of Life
• Molecules of Life
• The Origin of Life on Earth
• Origin of Complex Molecules
• Miller-Urey Experiment
• Pre-RNA World
• From Molecules to Cells
• Extremophiles
• Thermophiles
• Psychrophiles
• Acidophiles
• Alkaliphiles
• Radiation Resistant Biology
• Importance of Water for Life
• Hydrothermal Systems
• Silicon Versus Carbon
• DNA and Heredity
• Life as Digital Information
• Synthetic Biology
• Life in a Computer
• Natural Selection
• Tree Of Life
• Evolution and Intelligence
• Culture and Technology
• The Gaia Hypothesis
• Life and the Cosmic Environment

Chapter 19 Life in the Universe

• Life in the Universe
• Astrobiology
• Life Beyond Earth
• Sites for Life
• Complex Molecules in Space
• Life in the Solar System
• Lowell and Canals on Mars
• Implications of Life on Mars
• Extreme Environments in the Solar System
• Rare Earth Hypothesis
• Are We Alone?
• Unidentified Flying Objects or UFOs
• The Search for Extraterrestrial Intelligence
• The Drake Equation
• The History of SETI
• Recent SETI Projects
• Recognizing a Message
• The Best Way to Communicate
• The Fermi Question
• The Anthropic Principle
• Where Are They?

In the everyday world, as perceived by the human senses, light seems to travel instantaneously from one place to another. In fact, the speed of light is not infinite, and light doesn't instantly jump from your ceiling light to your desk and then to your eye. We perceive light as moving instantly because its actual velocity is almost unimaginably high; light travels at 300,000 km/s, denoted c. Using the equation Rate × Time = Distance, you can divide any distance by this number to figure out the time it would take light to cross that distance. In this way, we can see that light takes 1.5 × 10 8 / 3 × 10 5 = 500 seconds to reach Earth from the Sun, or just over 8 minutes. It takes light about 40 times longer ( Pluto at a distance of 39.4 A.U.) to leave the Solar System or about 5 hours.

The speed of light is a built-in quality of our universe . All evidence to date indicates that light has always traveled at this speed, that the speed is exact, and that the same speed is observed for all observers. The vast size of the universe, coupled with the finite (albeit large) speed of light, means that as we look out in space, we look back in time. Distant light is old light.

The 5 hours it takes light to travel across our Solar System may seem like a short period to cross such a large distance, but we have to think about scale. While distances within the Solar System are large to us, they are dwarfed by the distances between the stars. Considering larger regions of the Milky Way, a natural distance unit is the distance light travels in one year. This is called a light year. We can easily calculate the size of this unit by remembering that distance has the units of velocity times time. So:

D ly = vt = c x 1 year = 3 × 10 5 x (3600 × 24 × 365) = 9.5 × 10 12 km

A light year is the typical distance between stars in the neighborhood of the Sun. It is nearly 10 trillion kilometers or 6 trillion miles! The fundamental unit of distance defined by geometry is the 13 km; defined as the distance corresponding to a parallax of 1 second of arc.">parsec , equal to 3.1 × 10 13 km. This is described in more detail in the article on parallax . Geometrically, one parsec is the height of a right triangle with an angle of 1 arcsec describing its apex , and a distance of 1 AU describing its base. The units are related by a small numerical constant D ly = 3.26 D pc . So to roughly convert from parsecs to light years, multiply by 3.3.

The following list gives the distance to various points within the Milky Way and beyond, both in terms of parsecs and the light travel time in years (which is also the distance in light years or 3.3 times the distance in parsecs). To fully appreciate how isolated we are in space, remember that light is the fastest thing we know of. The fastest spacecraft can not reach 1% of the speed of light. So you would have to multiply the numbers on the right-hand side of the table by at least 100 to estimate how long it would take to send a probe through the Milky Way and into the Local Group with current technology.

• Nearest star (α Centauri) - 1.3 pc, 4.2 years • Sirius - 2.7 pc, 8.8 years • Vega - 8.1 pc, 26 years • Hyades cluster - 42 pc, 134 years • Pleiades cluster - 125 pc, 411 years • Orion nebula - 460 pc, 1500 years • Nearest spiral arm - 1200 pc, 3900 years • Center of the 8 to 10 13 solar masses.">galaxy - 8500 pc, 29,000 years • Far edge of the galaxy - 24,000 pc, 78,000 years • Large Magellanic Cloud - 50,000 pc, 163,000 years • Andromeda galaxy (M31) - 670,000 pc, 2.2 million years

What does Andromeda look like now? Nobody knows. Since nothing travels faster than light (and this applies to all the colors of light across the electromagnetic spectrum ), there is no quicker way to send information from one place to another. We are stuck with collecting and measuring "old" light. While this seems like a limitation, scientists actually find that it turns out that light travel time is a wonderful tool. By looking further out in space we look further back in time. In this way, astronomers get to explore the earlier stages of the universe seeing firsthand (with a delay) what the early universe looked like.

How far away is the Moon?

What is the distance between the Earth and the Moon? The answer is not as simple as you think...

The Moon is the most recognisable object in the night sky, and has an enormous impact on life here on Earth. But what is the exact distance between the Earth and the Moon? And why is that question not as simple as it sounds? Royal Observatory astronomer Affelia Wibisono explains all...

How far away is the Moon from the Earth?

The  average  distance between the Earth and the Moon is 384 400 km (238 855 miles) . 

How far is that in light-seconds?

Light travels at 300,000 kilometres per second, so it takes about 1.3 seconds for light to travel from the Moon back to the Earth. In other words, the Moon is 1.3 light-seconds away from the Earth .

Visit the Insight Investment Astronomy Photographer of the Year exhibition

What is a light year, the moon's elliptical orbit.

No orbit is perfectly circular. Some are very close, but they are all at least slightly elliptical in shape. Astronomers can measure how near to a perfect circle an orbit is by calculating its 'eccentricity'.

This is expressed by a number that is between 0 and 1. The closer the eccentricity is to 0, the closer the orbit is to a circle. In fact, a circle can be thought of as a special kind of ellipse that has an eccentricity of 0.

Venus’ orbit is the least eccentric out of all of the planets in our Solar System and closest to a circle, with a value of 0.007. Mercury’s is the most eccentric with a value of 0.2.

The eccentricity of the Moon’s orbit is 0.05 . Furthermore, the Earth is not at the very centre of the Moon’s orbit either. It is located at one of the foci of the Moon’s elliptical orbit, so is closer to one edge of the orbit than the other.

Apogee, perigee and average distance - the distance to the Moon explained

Astronomers tend to talk about three different numbers when talking about the distance between the Earth and the Moon.

At its furthest point from the Earth, the Moon is about 405 696 km (252 088 miles) away and astronomers say that the Moon is at apogee (‘apo’ means ‘away’).

On the other hand, when the Moon is at perigee (‘peri’ means ‘near’), the Moon is at its closest approach to the Earth . The distance between them is only 363 104 km (225 623 miles).

These two figures differ by 42 592 km (26 465 miles) - more than three times larger than the diameter of the Earth! The average distance between the Earth and the Moon is 384 400 km (238 855 miles) .

The Moon’s elliptical orbit with the distances at apogee and perigee. Note that the Earth is not at the very centre of the orbit and that the eccentricity of the orbit has been exaggerated here! Credit: NASA/Luc Viator/Affelia Wibisono.

The supermoon and micromoon

But do the two distances affect us in any way? Not really. The full Moon will look slightly bigger if it occurs during perigee (sometimes called a supermoon) and slightly smaller at apogee (a micromoon). However, the difference won’t be easily noticeable to the naked eye and a side by side photographic comparison is the only way to really see it.

Find out more about supermoons

Comparison between a micromoon and a supermoon. Supermoons appear to be 14% larger and 30% brighter than a micromoon. Credit: Marcoaliaslama.

How does the Moon affect the tides?

Our tides are caused by the gravitational pull of the Moon and the Sun and the Earth’s rotation . High tides are highest and low tides are lowest when it is a full moon or a new moon because of the gravitational pull of our natural satellite and star add up. These tides are called spring tides, as the tides spring out and spring back, they do not have anything to do with the spring season. At perigee, the Moon’s gravitational pull will be slightly stronger than usual and so the difference between high and low tides would be larger – but only by about 5cm! Similarly, when the Moon is at apogee, the difference between high and low tides will only be about 5cm smaller than usual.

The biggest tides occur when the Sun, Moon and Earth align because the gravitational pull of the Sun and Moon combine. Neap tides are smaller and occur when the Sun and Moon are perpendicular to each other. Credit: NASA/Luc Viator/HalloweenNight/Affelia Wibisono.

How far is the Moon from the sun?

Since the Moon orbits the Earth and the Earth orbits the Sun, both the Moon and the Earth are the same average distance away from the Sun. On average, the Earth and Moon are about 150 million kilometres (or 93 million miles) from the Sun!

That distance is so large that it takes light eight minutes to reach us (remember that light travels at 300,000 kilometres per second). That means that if the Sun were to stop shining right now, we wouldn’t know for another eight minutes.

How long does it take to get to the Moon from the Earth?

On average it would take three days , but it depends on how fast you are travelling and the exact route you take. It also depends on what you want to do – passing by the Moon does not require you to slow down to enter its orbit, minimising the time it would take to get there.

8 hours and 35 minutes

The record for the shortest journey time to the Moon is currently held by the New Horizons spacecraft with a time of 8 hours and 35 minutes.

1 day 10 hours

The first spacecraft to attempt to reach the Moon was the Soviet Union's   Luna 1 in 1959. Unfortunately, it did not slow down enough to complete its mission, but it did reach the vicinity of the Moon within 34 hours (1 day 10 hours).

13.5 months

SMART 1 , a European Space Agency spacecraft powered by an ion engine, was launched in 2003. It was very fuel efficient but did take 13.5 months to complete its journey!

How long did it take the Apollo missions to reach the Moon?

Human space travel will usually take longer than robotic ones. On average, the nine crewed missions to the Moon, (including Apollo 8, Apollo 10, Apollo 13 and the six that landed on the surface) took just over 78 hours (3 days 6 hours) to enter lunar orbit. The quickest was Apollo 8 which took 2 days, 21 hours and 8 minutes, while Apollo 17 took the longest with a time of 3 days, 14 hours and 41 minutes (times include the time spent in Earth orbit).

How long would it take to drive to the moon?

If you were driving at a speed of 40mph it would take approximately 5,791.375 hours to get to the Moon. However, this depends on whether the Moon is in apogee or perigee - and what kind of rocket car you have of course. 

How long does it take the Moon to orbit the Earth?

The lunar phase cycle takes 29.5 days to complete , and is directly connected to the orbit of the Moon around the Earth. However this is not how long it takes for one orbit to complete. Instead the Moon takes 27.3 days to orbit the Earth once .

This difference comes from how you measure the motions of objects in space. As there are no truly fixed points in space to measure against, you are forced to use objects that are considered not to move to within a reasonable level of uncertainty. 

Very distant stars and galaxies, while all technically in motion, don’t noticeably move in the sky on human timescales. Therefore they can be considered fixed. 

If you measure how the Moon orbits compared to these distant stars you get 27.3 days, the true orbital period of the Moon. However, the phases of the Moon are dependent on how the Moon, Earth and Sun are placed. During the time the Moon orbits the Earth, the Earth has moved on in its orbit around the Sun. In effect, the Moon needs a couple of extra days to catch up and return to the same point in space relative to the Sun. Hence the 29.5 day lunar phase cycle.

How long is a day on the Moon?

You may have noticed that the full Moon always looks about the same. You always see the same pattern of craters, hills, valleys and mare (seas) on the full Moon. In fact if you look at any phase of the Moon, it will always show the same features, though not all of the features will be lit up.

This is because the Moon spins at the same rate as it orbits around the Earth, with the exception of a couple of minor wobbles (known as libration) that brings a little more of the Moon into view. This means we only ever see the near side of the Moon from Earth, and never the far side. This is sometimes known as the “dark side” of the Moon - not because it actually is dark, but because it was mysterious and unknown until humans explored it.

The result is a very slowly rotating Moon: it takes 29.5 days to go from midday to midday on the Moon. Daylight lasts about two weeks and night time another two weeks. That, coupled with the lack of an atmosphere on the Moon, means the temperature changes wildly from over 100°C during the day to around -150°C at night. 

Is the Moon moving away from the Earth?

Astronomers have discovered that the Moon is currently moving away from the Earth by 3.8 cm every year!

Astronauts from the Apollo 11, 14 and 15 missions and the two Soviet Union rovers, Lunokhod 1 and Lunokhod 2 , left a total of five mirrors on the surface of the Moon. Astronomers on Earth can reflect laser beams off these mirrors and record the time it takes for the laser to return. We know how fast the laser beam is travelling (the speed of light) so we can easily calculate the distance that the laser beam has travelled. The Earth-Moon distance would then be half of this value.

This would mean that in the far future, total  solar eclipses  would be a thing of the past as the Moon will appear to be smaller: therefore, its disc will not be large enough to completely obscure the Sun. It will eventually stop receding from the Earth in about 50 billion years’ time according to theory. However, the Sun would have already entered the next stage of its life long before that happens. As it expands into a red giant star in 5 billion years or so, it will push the Moon back towards the Earth causing it to disintegrate due to strong tidal forces.

This article has been written by an astronomer at the Royal Observatory, Greenwich

01/06/2018: Affelia Wibisono

Accessible astronomy guides

Explore space from the comfort of home. Introducing Illuminates, accessible guides on space written by Royal Observatory astronomers

Time Travel: Observing Cosmic History

By observing light from faraway cosmic objects, the Hubble Space Telescope is like a time machine. Light takes time to reach Hubble, because it travels great distances. That means images captured by Hubble today, show what the objects looked like years ago!

The Hubble Space Telescope is many things. It’s an observatory, a satellite, and an icon of cultural and scientific significance – but perhaps most interestingly, Hubble is also a time machine.

Hubble isn’t that far away, locked in a low-Earth orbit just a few hundred miles up that takes about 90 minutes to complete. But with its position just above Earth’s murky atmosphere, Hubble’s transformative view of our universe literally lets us witness our universe’s past.  It allows us to effectively travel back in time.

How does that work? After all, Hubble doesn’t travel beyond our solar system, or even our home planet’s gravity. It certainly doesn’t have any sci-fi elements you might find in Doctor Who or Back to the Future.

Light Travel

The answer is simply light.

The term “light-year” shows up a lot in astronomy. This is a measure of distance that means exactly what it says – the distance that light travels in one year. Given that the speed of light is 186,000 miles (299,000 kilometers) per second, light can cover some serious ground over the course of 365 days. To be precise, almost 6 trillion miles (9.5 trillion kilometers)!

Traveling Back in Time: 8 minutes

Hubble works by gathering light from objects in our universe – some as close as our Moon, and some as distant as galaxy clusters that are billions of light-years away. All that light takes time to reach the telescope, just as it takes time for light to travel from its source to our eyes. For example, our Sun is located about 93 million miles (150 million kilometers) from Earth. That means that it takes roughly eight minutes for its light to reach us here on our planet, so when we look at the Sun (though directly is never recommended!) we see it exactly as it was eight minutes in the past.

Cosmically speaking, the 93 million miles between us and the Sun are nothing. We orbit around just one of billions of stars in the Milky Way Galaxy, which is one of countless trillions of galaxies in the universe.

With that in mind, time travel gets more intense when Hubble observes objects beyond our star system.

Traveling Back in Time: 4 years

Aside from our Sun, the next closest star to us is named Proxima Centauri. It’s about four light-years away, which makes it a close neighbor on a universal scale. But even with Hubble’s sharp, powerful vision, Proxima Centauri remains a point-like object – demonstrating our universe’s unfathomably large size.

Traveling Back in Time: 700 years

Another stellar target of Hubble’s is named Betelgeuse, which is about 700 light-years from Earth. Again, this means that when Hubble looks at Betelgeuse, the star appears exactly as it was 700 years ago. As one of the brightest stars in our sky, astronomers believe it’s likely that even the earliest humans knew of it, as this star appears in stories from several cultures.

This red supergiant star began to dim significantly in the fall of 2019, losing about 60% of its brightness within months. But by April 2020, its regular brightness returned. Hubble studied Betelgeuse and found out that the star “blew its top” – it went through a surface mass ejection, in which the star spewed out a large amount of its surface material into space. When that material in space cooled down, it became a dust cloud that temporarily blocked some of the star’s light.

Hubble’s unique ability to observe in ultraviolet light helped reveal the details of this dimming event and its aftermath. In this range of light, Hubble can better observe the hot layers of atmosphere above a star’s surface.

The telescope continues to be the go-to observatory for scientists who study Betelgeuse. Because it’s taken this long for the light from Betelgeuse to reach us, only in very recent history have we witnessed a cosmic event unfolding that really occurred about 700 years ago!

Scientists also believe that Betelgeuse is on the verge of going supernova – dying in an explosive event. In fact, it may have already done so, but the light from the explosion still hasn’t reached us. There’s a good chance that Betelgeuse no longer exists, though we can still see it today from Earth.

Traveling Back in Time: 6,500 years

Nebulae are clouds of gas and dust where stars are birthed, or the remnants of a dead or dying star itself. These beautiful, ethereal cosmic objects are the subject of some of Hubble’s most iconic images, but they can also teach us more about how our universe behaves and evolves.

For example, a favorite target for Hubble is the Crab Nebula, located about 6,500 light-years away. There are records from 1054 CE written by Chinese astronomers noting the new presence of a shockingly bright “guest” star in the sky, visible even during the daytime. Turns out, they actually saw a supernova – a star’s explosive death – which became the Crab Nebula, made up by the remnants of this violent event. Of course, those Chinese astronomers witnessed a supernova explosion that occurred about 5446 BCE, but it took the light from the explosion 6,500 years to reach Earth in the year 1054.

Traveling Back in Time: 2.5 million years

When Hubble looks beyond our own galaxy, we can watch cosmic history unfold over eons.

The Andromeda Galaxy is a whopping 2.5 million light-years away, but that’s just the closest major galaxy to us here in the Milky Way. Observing Andromeda is like staring into a vision from 2.5 million years ago – back during the Paleolithic period on Earth, when very early humans existed.

And if Andromeda is the closest major galaxy to us, it’s difficult to comprehend just how far the light from the most distant observed galaxies has traveled.

Traveling Back in Time: 12.9 billion years

Another Hubble record is for observing the most distant individual star ever detected, named Earendel. This faraway star emitted its light within the first billion years of the universe, which is about 13.8 billion years old, so it took quite a while to reach Hubble! In fact, that observation was only made possible by nature’s magnifying glass – an astronomical phenomenon known as gravitational lensing. When a massive cosmic object has enough gravity, its gravitational field can magnify and bend light coming from objects located behind it. The gravity of a galaxy cluster located between Hubble and Earendel magnified the star’s light, making it detectable.  The type of star that Earendel seems to be typically have brief lives, only surviving about half a billion years. That means Earendel has ceased to exist for over 12 billion years, yet we are able to look back in time and watch Earendel during its short life.

Traveling Back in Time: 13.4 billion years

Perhaps some of Hubble’s most legendary observations are its deep field images, which collect light from thousands of galaxies that are billions of light-years away.

With this type of imagery, we can better understand how our universe changes over time by puzzling out how galaxies evolve. The farther back we look with Hubble, the closer we get to the the big bang, when the universe began – so the most distant galaxies observed by Hubble often appear to us as the “youngest” ones – giving us a sneak peek at the universe in its infancy. Because these galaxies emitted their light when they were young, we get to witness them in their early stages. These early galaxies often appear simpler and smaller than the grandiose spiral galaxies and merged galaxies we see closer to us in distance, and therefore in time. These young galaxies are actually old galaxies now as they have evolved over the time this light has taken to reach us.

Hubble’s farthest observation is of a galaxy named GN-z11, observed as it was 13.4 billion years in the past! This places it within just 400 million years of the big bang itself.

Watching Our Universe Over Time

Observations of the most distant objects, like GN-z11 and Earendel, give astronomers exciting insight into the environment of our early universe. The light we see literally traveled from all the way back then!

Our universe remains mysterious, mind-bendingly large, and ever-expanding, but by gathering light from near and far – from the recent past to the dawn of the universe itself – Hubble helps answer questions about where we are and how the universe works.

At its core, astronomy is really just archaeology. Cosmic objects give off light, letting us learn more about their lives. It can take a long, long time for light to reach Hubble – just one telescope orbiting just one planet in just one solar system in just one galaxy. Scientists use Hubble like the time machine that it is to piece together the history and mystery of the cosmos, giving us all a glimpse right up to the edge of the universe – and time itself.

Explore More Hubble

The Lost Universe

NASA's Hubble Space Telescope has vanished from Earth’s timeline. Only an ambitious crew of adventurers can uncover what was lost. Are you up to the challenge?

Hubble Science Highlights

Hubble has affected every area of astronomy. Its most notable scientific discoveries reflect the broad range of research and the breakthroughs it has achieved.

Hubble's Cultural Impact

Even if you don't know anything about the Hubble Space Telescope, its pictures have been a part of your life.

What is Hubble Observing?

See the area of sky Hubble is currently investigating or explore its upcoming and past targets.

Hubble E-books

Investigate the mysteries of the universe with Hubble. Learn Hubble's history and dive deeper into its discoveries by downloading our e-books.

• Anatomy & Physiology
• Astrophysics
• Earth Science
• Environmental Science
• Organic Chemistry
• Precalculus
• Trigonometry
• English Grammar
• U.S. History
• World History

... and beyond

• Socratic Meta
• Featured Answers

How long does it take for light to get to Earth from the Moon?

Space Travel Calculator

Table of contents

Ever since the dawn of civilization, the idea of space travel has fascinated humans! Haven't we all looked up into the night sky and dreamed about space?

With the successful return of the first all-civilian crew of SpaceX's Inspiration4 mission after orbiting the Earth for three days, the dream of space travel looks more and more realistic now.

While traveling deep into space is still something out of science fiction movies like Star Trek and Star Wars, the tremendous progress made by private space companies so far seems very promising. Someday, space travel (or even interstellar travel) might be accessible to everyone!

It's never too early to start planning for a trip of a lifetime (or several lifetimes). You can also plan your own space trip and celebrate World Space Week in your own special way!

This space travel calculator is a comprehensive tool that allows you to estimate many essential parameters in theoretical interstellar space travel . Have you ever wondered how fast we can travel in space, how much time it will take to get to the nearest star or galaxy, or how much fuel it requires? In the following article, using a relativistic rocket equation, we'll try to answer questions like "Is interstellar travel possible?" , and "Can humans travel at the speed of light?"

Explore the world of light-speed travel of (hopefully) future spaceships with our relativistic space travel calculator!

If you're interested in astrophysics, check out our other calculators. Find out the speed required to leave the surface of any planet with the escape velocity calculator or estimate the parameters of the orbital motion of planets using the orbital velocity calculator .

One small step for man, one giant leap for humanity

Although human beings have been dreaming about space travel forever, the first landmark in the history of space travel is Russia's launch of Sputnik 2 into space in November 1957. The spacecraft carried the first earthling, the Russian dog Laika , into space.

Four years later, on 12 April 1961, Soviet cosmonaut Yuri A. Gagarin became the first human in space when his spacecraft, the Vostok 1, completed one orbit of Earth.

The first American astronaut to enter space was Alan Shepard (May 1961). During the Apollo 11 mission in July 1969, Neil Armstrong and Buzz Aldrin became the first men to land on the moon. Between 1969 and 1972, a total of 12 astronauts walked the moon, marking one of the most outstanding achievements for NASA.

In recent decades, space travel technology has seen some incredible advancements. Especially with the advent of private space companies like SpaceX, Virgin Galactic, and Blue Origin, the dream of space tourism is looking more and more realistic for everyone!

However, when it comes to including women, we are yet to make great strides. So far, 566 people have traveled to space. Only 65 of them were women .

Although the first woman in space, a Soviet astronaut Valentina Tereshkova , who orbited Earth 48 times, went into orbit in June 1963. It was only in October 2019 that the first all-female spacewalk was completed by NASA astronauts Jessica Meir and Christina Koch.

Women's access to space is still far from equal, but there are signs of progress, like NASA planning to land the first woman and first person of color on the moon by 2024 with its Artemis missions. World Space Week is also celebrating the achievements and contributions of women in space this year!

In the following sections, we will explore the feasibility of space travel and its associated challenges.

How fast can we travel in space? Is interstellar travel possible?

Interstellar space is a rather empty place. Its temperature is not much more than the coldest possible temperature, i.e., an absolute zero. It equals about 3 kelvins – minus 270 °C or minus 455 °F. You can't find air there, and therefore there is no drag or friction. On the one hand, humans can't survive in such a hostile place without expensive equipment like a spacesuit or a spaceship, but on the other hand, we can make use of space conditions and its emptiness.

The main advantage of future spaceships is that, since they are moving through a vacuum, they can theoretically accelerate to infinite speeds! However, this is only possible in the classical world of relatively low speeds, where Newtonian physics can be applied. Even if it's true, let's imagine, just for a moment, that we live in a world where any speed is allowed. How long will it take to visit the Andromeda Galaxy, the nearest galaxy to the Milky Way?

We will begin our intergalactic travel with a constant acceleration of 1 g (9.81 m/s² or 32.17 ft/s²) because it ensures that the crew experiences the same comfortable gravitational field as the one on Earth. By using this space travel calculator in Newton's universe mode, you can find out that you need about 2200 years to arrive at the nearest galaxy! And, if you want to stop there, you need an additional 1000 years . Nobody lives for 3000 years! Is intergalactic travel impossible for us, then? Luckily, we have good news. We live in a world of relativistic effects, where unusual phenomena readily occur.

Can humans travel at the speed of light? – relativistic space travel

In the previous example, where we traveled to Andromeda Galaxy, the maximum velocity was almost 3000 times greater than the speed of light c = 299,792,458 m/s , or about c = 3 × 10 8 m/s using scientific notation.

However, as velocity increases, relativistic effects start to play an essential role. According to special relativity proposed by Albert Einstein, nothing can exceed the speed of light. How can it help us with interstellar space travel? Doesn't it mean we will travel at a much lower speed? Yes, it does, but there are also a few new relativistic phenomena, including time dilation and length contraction, to name a few. The former is crucial in relativistic space travel.

Time dilation is a difference of time measured by two observers, one being in motion and the second at rest (relative to each other). It is something we are not used to on Earth. Clocks in a moving spaceship tick slower than the same clocks on Earth ! Time passing in a moving spaceship T T T and equivalent time observed on Earth t t t are related by the following formula:

where γ \gamma γ is the Lorentz factor that comprises the speed of the spaceship v v v and the speed of light c c c :

where β = v / c \beta = v/c β = v / c .

For example, if γ = 10 \gamma = 10 γ = 10 ( v = 0.995 c v = 0.995c v = 0.995 c ), then every second passing on Earth corresponds to ten seconds passing in the spaceship. Inside the spacecraft, events take place 90 percent slower; the difference can be even greater for higher velocities. Note that both observers can be in motion, too. In that case, to calculate the relative relativistic velocity, you can use our velocity addition calculator .

Let's go back to our example again, but this time we're in Einstein's universe of relativistic effects trying to reach Andromeda. The time needed to get there, measured by the crew of the spaceship, equals only 15 years ! Well, this is still a long time, but it is more achievable in a practical sense. If you would like to stop at the destination, you should start decelerating halfway through. In this situation, the time passed in the spaceship will be extended by about 13 additional years .

Unfortunately, this is only a one-way journey. You can, of course, go back to Earth, but nothing will be the same. During your interstellar space travel to the Andromeda Galaxy, about 2,500,000 years have passed on Earth. It would be a completely different planet, and nobody could foresee the fate of our civilization.

A similar problem was considered in the first Planet of the Apes movie, where astronauts crash-landed back on Earth. While these astronauts had only aged by 18 months, 2000 years had passed on Earth (sorry for the spoilers, but the film is over 50 years old at this point, you should have seen it by now). How about you? Would you be able to leave everything you know and love about our galaxy forever and begin a life of space exploration?

Space travel calculator – relativistic rocket equation

Now that you know whether interstellar travel is possible and how fast we can travel in space, it's time for some formulas. In this section, you can find the "classical" and relativistic rocket equations that are included in the relativistic space travel calculator.

There could be four combinations since we want to estimate how long it takes to arrive at the destination point at full speed as well as arrive at the destination point and stop. Every set contains distance, time passing on Earth and in the spaceship (only relativity approach), expected maximum velocity and corresponding kinetic energy (on the additional parameters section), and the required fuel mass (see Intergalactic travel — fuel problem section for more information). The notation is:

• a a a — Spaceship acceleration (by default 1   g 1\rm\, g 1 g ). We assume it is positive a > 0 a > 0 a > 0 (at least until halfway) and constant.
• m m m — Spaceship mass. It is required to calculate kinetic energy (and fuel).
• d d d — Distance to the destination. Note that you can select it from the list or type in any other distance to the desired object.
• T T T — Time that passed in a spaceship, or, in other words, how much the crew has aged.
• t t t — Time that passed in a resting frame of reference, e.g., on Earth.
• v v v — Maximum velocity reached by the spaceship.
• K E \rm KE KE — Maximum kinetic energy reached by the spaceship.

The relativistic space travel calculator is dedicated to very long journeys, interstellar or even intergalactic, in which we can neglect the influence of the gravitational field, e.g., from Earth. We didn't include our closest celestial bodies, like the Moon or Mars, in the destination list because it would be pointless. For them, we need different equations that also take into consideration gravitational force.

Newton's universe — arrive at the destination at full speed

It's the simplest case because here, T T T equals t t t for any speed. To calculate the distance covered at constant acceleration during a certain time, you can use the following classical formula:

Since acceleration is constant, and we assume that the initial velocity equals zero, you can estimate the maximum velocity using this equation:

and the corresponding kinetic energy:

Newton's universe — arrive at the destination and stop

In this situation, we accelerate to the halfway point, reach maximum velocity, and then decelerate to stop at the destination point. Distance covered during the same time is, as you may expect, smaller than before:

Acceleration remains positive until we're halfway there (then it is negative – deceleration), so the maximum velocity is:

and the kinetic energy equation is the same as the previous one.

Einstein's universe — arrive at the destination at full speed

The relativistic rocket equation has to consider the effects of light-speed travel. These are not only speed limitations and time dilation but also how every length becomes shorter for a moving observer, which is a phenomenon of special relativity called length contraction. If l l l is the proper length observed in the rest frame and L L L is the length observed by a crew in a spaceship, then:

What does it mean? If a spaceship moves with the velocity of v = 0.995 c v = 0.995c v = 0.995 c , then γ = 10 \gamma = 10 γ = 10 , and the length observed by a moving object is ten times smaller than the real length. For example, the distance to the Andromeda Galaxy equals about 2,520,000 light years with Earth as the frame of reference. For a spaceship moving with v = 0.995 c v = 0.995c v = 0.995 c , it will be "only" 252,200 light years away. That's a 90 percent decrease or a 164 percent difference!

Now you probably understand why special relativity allows us to intergalactic travel. Below you can find the relativistic rocket equation for the case in which you want to arrive at the destination point at full speed (without stopping). You can find its derivation in the book by Messrs Misner, Thorne ( Co-Winner of the 2017 Nobel Prize in Physics ) and Wheller titled Gravitation , section §6.2. Hyperbolic motion. More accessible formulas are in the mathematical physicist John Baez's article The Relativistic Rocket :

• Time passed on Earth:
• Time passed in the spaceship:
• Maximum velocity:
• Relativistic kinetic energy remains the same:

The symbols sh ⁡ \sh sh , ch ⁡ \ch ch , and th ⁡ \th th are, respectively, sine, cosine, and tangent hyperbolic functions, which are analogs of the ordinary trigonometric functions. In turn, sh ⁡ − 1 \sh^{-1} sh − 1 and ch ⁡ − 1 \ch^{-1} ch − 1 are the inverse hyperbolic functions that can be expressed with natural logarithms and square roots, according to the article Inverse hyperbolic functions on Wikipedia.

Einstein's universe – arrive at destination point and stop

Most websites with relativistic rocket equations consider only arriving at the desired place at full speed. If you want to stop there, you should start decelerating at the halfway point. Below, you can find a set of equations estimating interstellar space travel parameters in the situation when you want to stop at the destination point :

Intergalactic travel – fuel problem

So, after all of these considerations, can humans travel at the speed of light, or at least at a speed close to it? Jet-rocket engines need a lot of fuel per unit of weight of the rocket. You can use our rocket equation calculator to see how much fuel you need to obtain a certain velocity (e.g., with an effective exhaust velocity of 4500 m/s).

Hopefully, future spaceships will be able to produce energy from matter-antimatter annihilation. This process releases energy from two particles that have mass (e.g., electron and positron) into photons. These photons may then be shot out at the back of the spaceship and accelerate the spaceship due to the conservation of momentum. If you want to know how much energy is contained in matter, check out our E = mc² calculator , which is about the famous Albert Einstein equation.

Now that you know the maximum amount of energy you can acquire from matter, it's time to estimate how much of it you need for intergalactic travel. Appropriate formulas are derived from the conservation of momentum and energy principles. For the relativistic case:

where e x e^x e x is an exponential function, and for classical case:

Remember that it assumes 100% efficiency! One of the promising future spaceships' power sources is the fusion of hydrogen into helium, which provides energy of 0.008 mc² . As you can see, in this reaction, efficiency equals only 0.8%.

Let's check whether the fuel mass amount is reasonable for sending a mass of 1 kg to the nearest galaxy. With a space travel calculator, you can find out that, even with 100% efficiency, you would need 5,200 tons of fuel to send only 1 kilogram of your spaceship . That's a lot!

So can humans travel at the speed of light? Right now, it seems impossible, but technology is still developing. For example, a photonic laser thruster is a good candidate since it doesn't require any matter to work, only photons. Infinity and beyond is actually within our reach!

How do I calculate the travel time to other planets?

To calculate the time it takes to travel to a specific star or galaxy using the space travel calculator, follow these steps:

• Choose the acceleration : the default mode is 1 g (gravitational field similar to Earth's).
• Enter the spaceship mass , excluding fuel.
• Select the destination : pick the star, planet, or galaxy you want to travel to from the dropdown menu.
• The distance between the Earth and your chosen stars will automatically appear. You can also input the distance in light-years directly if you select the Custom distance option in the previous dropdown.
• Define the aim : select whether you aim to " Arrive at destination and stop " or “ Arrive at destination at full speed ”.
• Pick the calculation mode : opt for either " Einstein's universe " mode for relativistic effects or " Newton's universe " for simpler calculations.
• Time passed in spaceship : estimated time experienced by the crew during the journey. (" Einstein's universe " mode)
• Time passed on Earth : estimated time elapsed on Earth during the trip. (" Einstein's universe " mode)
• Time passed : depends on the frame of reference, e.g., on Earth. (" Newton's universe " mode)
• Required fuel mass : estimated fuel quantity needed for the journey.
• Maximum velocity : maximum speed achieved by the spaceship.

How long does it take to get to space?

It takes about 8.5 minutes for a space shuttle or spacecraft to reach Earth's orbit, i.e., the limit of space where the Earth's atmosphere ends. This dividing line between the Earth's atmosphere and space is called the Kármán line . It happens so quickly because the shuttle goes from zero to around 17,500 miles per hour in those 8.5 minutes .

How fast does the space station travel?

The International Space Station travels at an average speed of 28,000 km/h or 17,500 mph . In a single day, the ISS can make several complete revolutions as it circumnavigates the globe in just 90 minutes . Placed in orbit at an altitude of 350 km , the station is visible to the naked eye, looking like a dot crossing the sky due to its very bright solar panels.

How do I reach the speed of light?

To reach the speed of light, you would have to overcome several obstacles, including:

Mass limit : traveling at the speed of light would mean traveling at 299,792,458 meters per second. But, thanks to Einstein's theory of relativity, we know that an object with non-zero mass cannot reach this speed.

Energy : accelerating to the speed of light would require infinite energy.

Effects of relativity : from the outside, time would slow down, and you would shrink.

Why can't sound travel in space?

Sound can’t travel in space because it is a mechanical wave that requires a medium to propagate — this medium can be solid, liquid, or gas. In space, there is no matter, or at least not enough for sound to propagate. The density of matter in space is of the order 1 particle per cubic centimeter . While on Earth , it's much denser at around 10 20 particles per cubic centimeter .

Dreaming of traveling into space? 🌌 Plan your interstellar travel (even to a Star Trek destination) using this calculator 👨‍🚀! Estimate how fast you can reach your destination and how much fuel you would need 🚀

.css-slt4t3.css-slt4t3{color:#2B3148;background-color:transparent;font-family:"Roboto","Helvetica","Arial",sans-serif;font-size:20px;line-height:24px;overflow:visible;padding-top:0px;position:relative;}.css-slt4t3.css-slt4t3:after{content:'';-webkit-transform:scale(0);-moz-transform:scale(0);-ms-transform:scale(0);transform:scale(0);position:absolute;border:2px solid #EA9430;border-radius:2px;inset:-8px;z-index:1;}.css-slt4t3 .js-external-link-button.link-like,.css-slt4t3 .js-external-link-anchor{color:inherit;border-radius:1px;-webkit-text-decoration:underline;text-decoration:underline;}.css-slt4t3 .js-external-link-button.link-like:hover,.css-slt4t3 .js-external-link-anchor:hover,.css-slt4t3 .js-external-link-button.link-like:active,.css-slt4t3 .js-external-link-anchor:active{text-decoration-thickness:2px;text-shadow:1px 0 0;}.css-slt4t3 .js-external-link-button.link-like:focus-visible,.css-slt4t3 .js-external-link-anchor:focus-visible{outline:transparent 2px dotted;box-shadow:0 0 0 2px #6314E6;}.css-slt4t3 p,.css-slt4t3 div{margin:0px;display:block;}.css-slt4t3 pre{margin:0px;display:block;}.css-slt4t3 pre code{display:block;width:-webkit-fit-content;width:-moz-fit-content;width:fit-content;}.css-slt4t3 pre:not(:first-child){padding-top:8px;}.css-slt4t3 ul,.css-slt4t3 ol{display:block margin:0px;padding-left:20px;}.css-slt4t3 ul li,.css-slt4t3 ol li{padding-top:8px;}.css-slt4t3 ul ul,.css-slt4t3 ol ul,.css-slt4t3 ul ol,.css-slt4t3 ol ol{padding-top:0px;}.css-slt4t3 ul:not(:first-child),.css-slt4t3 ol:not(:first-child){padding-top:4px;} .css-4okk7a{margin:auto;background-color:white;overflow:auto;overflow-wrap:break-word;word-break:break-word;}.css-4okk7a code,.css-4okk7a kbd,.css-4okk7a pre,.css-4okk7a samp{font-family:monospace;}.css-4okk7a code{padding:2px 4px;color:#444;background:#ddd;border-radius:4px;}.css-4okk7a figcaption,.css-4okk7a caption{text-align:center;}.css-4okk7a figcaption{font-size:12px;font-style:italic;overflow:hidden;}.css-4okk7a h3{font-size:1.75rem;}.css-4okk7a h4{font-size:1.5rem;}.css-4okk7a .mathBlock{font-size:24px;-webkit-padding-start:4px;padding-inline-start:4px;}.css-4okk7a .mathBlock .katex{font-size:24px;text-align:left;}.css-4okk7a .math-inline{background-color:#f0f0f0;display:inline-block;font-size:inherit;padding:0 3px;}.css-4okk7a .videoBlock,.css-4okk7a .imageBlock{margin-bottom:16px;}.css-4okk7a .imageBlock__image-align--left,.css-4okk7a .videoBlock__video-align--left{float:left;}.css-4okk7a .imageBlock__image-align--right,.css-4okk7a .videoBlock__video-align--right{float:right;}.css-4okk7a .imageBlock__image-align--center,.css-4okk7a .videoBlock__video-align--center{display:block;margin-left:auto;margin-right:auto;clear:both;}.css-4okk7a .imageBlock__image-align--none,.css-4okk7a .videoBlock__video-align--none{clear:both;margin-left:0;margin-right:0;}.css-4okk7a .videoBlock__video--wrapper{position:relative;padding-bottom:56.25%;height:0;}.css-4okk7a .videoBlock__video--wrapper iframe{position:absolute;top:0;left:0;width:100%;height:100%;}.css-4okk7a .videoBlock__caption{text-align:left;}@font-face{font-family:'KaTeX_AMS';src:url(/katex-fonts/KaTeX_AMS-Regular.woff2) format('woff2'),url(/katex-fonts/KaTeX_AMS-Regular.woff) format('woff'),url(/katex-fonts/KaTeX_AMS-Regular.ttf) format('truetype');font-weight:normal;font-style:normal;}@font-face{font-family:'KaTeX_Caligraphic';src:url(/katex-fonts/KaTeX_Caligraphic-Bold.woff2) format('woff2'),url(/katex-fonts/KaTeX_Caligraphic-Bold.woff) format('woff'),url(/katex-fonts/KaTeX_Caligraphic-Bold.ttf) format('truetype');font-weight:bold;font-style:normal;}@font-face{font-family:'KaTeX_Caligraphic';src:url(/katex-fonts/KaTeX_Caligraphic-Regular.woff2) format('woff2'),url(/katex-fonts/KaTeX_Caligraphic-Regular.woff) format('woff'),url(/katex-fonts/KaTeX_Caligraphic-Regular.ttf) format('truetype');font-weight:normal;font-style:normal;}@font-face{font-family:'KaTeX_Fraktur';src:url(/katex-fonts/KaTeX_Fraktur-Bold.woff2) format('woff2'),url(/katex-fonts/KaTeX_Fraktur-Bold.woff) format('woff'),url(/katex-fonts/KaTeX_Fraktur-Bold.ttf) format('truetype');font-weight:bold;font-style:normal;}@font-face{font-family:'KaTeX_Fraktur';src:url(/katex-fonts/KaTeX_Fraktur-Regular.woff2) format('woff2'),url(/katex-fonts/KaTeX_Fraktur-Regular.woff) format('woff'),url(/katex-fonts/KaTeX_Fraktur-Regular.ttf) format('truetype');font-weight:normal;font-style:normal;}@font-face{font-family:'KaTeX_Main';src:url(/katex-fonts/KaTeX_Main-Bold.woff2) format('woff2'),url(/katex-fonts/KaTeX_Main-Bold.woff) format('woff'),url(/katex-fonts/KaTeX_Main-Bold.ttf) format('truetype');font-weight:bold;font-style:normal;}@font-face{font-family:'KaTeX_Main';src:url(/katex-fonts/KaTeX_Main-BoldItalic.woff2) format('woff2'),url(/katex-fonts/KaTeX_Main-BoldItalic.woff) format('woff'),url(/katex-fonts/KaTeX_Main-BoldItalic.ttf) format('truetype');font-weight:bold;font-style:italic;}@font-face{font-family:'KaTeX_Main';src:url(/katex-fonts/KaTeX_Main-Italic.woff2) format('woff2'),url(/katex-fonts/KaTeX_Main-Italic.woff) format('woff'),url(/katex-fonts/KaTeX_Main-Italic.ttf) format('truetype');font-weight:normal;font-style:italic;}@font-face{font-family:'KaTeX_Main';src:url(/katex-fonts/KaTeX_Main-Regular.woff2) format('woff2'),url(/katex-fonts/KaTeX_Main-Regular.woff) format('woff'),url(/katex-fonts/KaTeX_Main-Regular.ttf) format('truetype');font-weight:normal;font-style:normal;}@font-face{font-family:'KaTeX_Math';src:url(/katex-fonts/KaTeX_Math-BoldItalic.woff2) format('woff2'),url(/katex-fonts/KaTeX_Math-BoldItalic.woff) format('woff'),url(/katex-fonts/KaTeX_Math-BoldItalic.ttf) format('truetype');font-weight:bold;font-style:italic;}@font-face{font-family:'KaTeX_Math';src:url(/katex-fonts/KaTeX_Math-Italic.woff2) format('woff2'),url(/katex-fonts/KaTeX_Math-Italic.woff) format('woff'),url(/katex-fonts/KaTeX_Math-Italic.ttf) format('truetype');font-weight:normal;font-style:italic;}@font-face{font-family:'KaTeX_SansSerif';src:url(/katex-fonts/KaTeX_SansSerif-Bold.woff2) format('woff2'),url(/katex-fonts/KaTeX_SansSerif-Bold.woff) format('woff'),url(/katex-fonts/KaTeX_SansSerif-Bold.ttf) format('truetype');font-weight:bold;font-style:normal;}@font-face{font-family:'KaTeX_SansSerif';src:url(/katex-fonts/KaTeX_SansSerif-Italic.woff2) format('woff2'),url(/katex-fonts/KaTeX_SansSerif-Italic.woff) format('woff'),url(/katex-fonts/KaTeX_SansSerif-Italic.ttf) format('truetype');font-weight:normal;font-style:italic;}@font-face{font-family:'KaTeX_SansSerif';src:url(/katex-fonts/KaTeX_SansSerif-Regular.woff2) format('woff2'),url(/katex-fonts/KaTeX_SansSerif-Regular.woff) format('woff'),url(/katex-fonts/KaTeX_SansSerif-Regular.ttf) format('truetype');font-weight:normal;font-style:normal;}@font-face{font-family:'KaTeX_Script';src:url(/katex-fonts/KaTeX_Script-Regular.woff2) format('woff2'),url(/katex-fonts/KaTeX_Script-Regular.woff) format('woff'),url(/katex-fonts/KaTeX_Script-Regular.ttf) format('truetype');font-weight:normal;font-style:normal;}@font-face{font-family:'KaTeX_Size1';src:url(/katex-fonts/KaTeX_Size1-Regular.woff2) format('woff2'),url(/katex-fonts/KaTeX_Size1-Regular.woff) format('woff'),url(/katex-fonts/KaTeX_Size1-Regular.ttf) format('truetype');font-weight:normal;font-style:normal;}@font-face{font-family:'KaTeX_Size2';src:url(/katex-fonts/KaTeX_Size2-Regular.woff2) format('woff2'),url(/katex-fonts/KaTeX_Size2-Regular.woff) format('woff'),url(/katex-fonts/KaTeX_Size2-Regular.ttf) format('truetype');font-weight:normal;font-style:normal;}@font-face{font-family:'KaTeX_Size3';src:url(/katex-fonts/KaTeX_Size3-Regular.woff2) format('woff2'),url(/katex-fonts/KaTeX_Size3-Regular.woff) format('woff'),url(/katex-fonts/KaTeX_Size3-Regular.ttf) format('truetype');font-weight:normal;font-style:normal;}@font-face{font-family:'KaTeX_Size4';src:url(/katex-fonts/KaTeX_Size4-Regular.woff2) format('woff2'),url(/katex-fonts/KaTeX_Size4-Regular.woff) format('woff'),url(/katex-fonts/KaTeX_Size4-Regular.ttf) format('truetype');font-weight:normal;font-style:normal;}@font-face{font-family:'KaTeX_Typewriter';src:url(/katex-fonts/KaTeX_Typewriter-Regular.woff2) format('woff2'),url(/katex-fonts/KaTeX_Typewriter-Regular.woff) format('woff'),url(/katex-fonts/KaTeX_Typewriter-Regular.ttf) format('truetype');font-weight:normal;font-style:normal;}.css-4okk7a .katex{font:normal 1.21em KaTeX_Main,Times New Roman,serif;line-height:1.2;text-indent:0;text-rendering:auto;}.css-4okk7a .katex *{-ms-high-contrast-adjust:none!important;border-color:currentColor;}.css-4okk7a .katex .katex-version::after{content:'0.13.13';}.css-4okk7a .katex .katex-mathml{position:absolute;clip:rect(1px, 1px, 1px, 1px);padding:0;border:0;height:1px;width:1px;overflow:hidden;}.css-4okk7a .katex .katex-html>.newline{display:block;}.css-4okk7a .katex .base{position:relative;display:inline-block;white-space:nowrap;width:-webkit-min-content;width:-moz-min-content;width:-webkit-min-content;width:-moz-min-content;width:min-content;}.css-4okk7a .katex .strut{display:inline-block;}.css-4okk7a .katex .textbf{font-weight:bold;}.css-4okk7a .katex .textit{font-style:italic;}.css-4okk7a .katex .textrm{font-family:KaTeX_Main;}.css-4okk7a .katex .textsf{font-family:KaTeX_SansSerif;}.css-4okk7a .katex .texttt{font-family:KaTeX_Typewriter;}.css-4okk7a .katex .mathnormal{font-family:KaTeX_Math;font-style:italic;}.css-4okk7a .katex .mathit{font-family:KaTeX_Main;font-style:italic;}.css-4okk7a .katex .mathrm{font-style:normal;}.css-4okk7a .katex .mathbf{font-family:KaTeX_Main;font-weight:bold;}.css-4okk7a .katex .boldsymbol{font-family:KaTeX_Math;font-weight:bold;font-style:italic;}.css-4okk7a .katex .amsrm{font-family:KaTeX_AMS;}.css-4okk7a .katex .mathbb,.css-4okk7a .katex .textbb{font-family:KaTeX_AMS;}.css-4okk7a .katex .mathcal{font-family:KaTeX_Caligraphic;}.css-4okk7a .katex .mathfrak,.css-4okk7a .katex .textfrak{font-family:KaTeX_Fraktur;}.css-4okk7a .katex .mathtt{font-family:KaTeX_Typewriter;}.css-4okk7a .katex .mathscr,.css-4okk7a .katex .textscr{font-family:KaTeX_Script;}.css-4okk7a .katex .mathsf,.css-4okk7a .katex .textsf{font-family:KaTeX_SansSerif;}.css-4okk7a .katex .mathboldsf,.css-4okk7a .katex .textboldsf{font-family:KaTeX_SansSerif;font-weight:bold;}.css-4okk7a .katex .mathitsf,.css-4okk7a .katex .textitsf{font-family:KaTeX_SansSerif;font-style:italic;}.css-4okk7a .katex .mainrm{font-family:KaTeX_Main;font-style:normal;}.css-4okk7a .katex .vlist-t{display:inline-table;table-layout:fixed;border-collapse:collapse;}.css-4okk7a .katex .vlist-r{display:table-row;}.css-4okk7a .katex .vlist{display:table-cell;vertical-align:bottom;position:relative;}.css-4okk7a .katex .vlist>span{display:block;height:0;position:relative;}.css-4okk7a .katex .vlist>span>span{display:inline-block;}.css-4okk7a .katex .vlist>span>.pstrut{overflow:hidden;width:0;}.css-4okk7a .katex .vlist-t2{margin-right:-2px;}.css-4okk7a .katex .vlist-s{display:table-cell;vertical-align:bottom;font-size:1px;width:2px;min-width:2px;}.css-4okk7a .katex .vbox{display:-webkit-inline-box;display:-webkit-inline-flex;display:-ms-inline-flexbox;display:inline-flex;-webkit-flex-direction:column;-ms-flex-direction:column;flex-direction:column;-webkit-align-items:baseline;-webkit-box-align:baseline;-ms-flex-align:baseline;align-items:baseline;}.css-4okk7a .katex .hbox{display:-webkit-inline-box;display:-webkit-inline-flex;display:-ms-inline-flexbox;display:inline-flex;-webkit-flex-direction:row;-ms-flex-direction:row;flex-direction:row;width:100%;}.css-4okk7a .katex .thinbox{display:-webkit-inline-box;display:-webkit-inline-flex;display:-ms-inline-flexbox;display:inline-flex;-webkit-flex-direction:row;-ms-flex-direction:row;flex-direction:row;width:0;max-width:0;}.css-4okk7a .katex .msupsub{text-align:left;}.css-4okk7a .katex .mfrac>span>span{text-align:center;}.css-4okk7a .katex .mfrac .frac-line{display:inline-block;width:100%;border-bottom-style:solid;}.css-4okk7a .katex .mfrac .frac-line,.css-4okk7a .katex .overline .overline-line,.css-4okk7a .katex .underline .underline-line,.css-4okk7a .katex .hline,.css-4okk7a .katex .hdashline,.css-4okk7a .katex .rule{min-height:1px;}.css-4okk7a .katex .mspace{display:inline-block;}.css-4okk7a .katex .llap,.css-4okk7a .katex .rlap,.css-4okk7a .katex .clap{width:0;position:relative;}.css-4okk7a .katex .llap>.inner,.css-4okk7a .katex .rlap>.inner,.css-4okk7a .katex .clap>.inner{position:absolute;}.css-4okk7a .katex .llap>.fix,.css-4okk7a .katex .rlap>.fix,.css-4okk7a .katex .clap>.fix{display:inline-block;}.css-4okk7a .katex .llap>.inner{right:0;}.css-4okk7a .katex .rlap>.inner,.css-4okk7a .katex .clap>.inner{left:0;}.css-4okk7a .katex .clap>.inner>span{margin-left:-50%;margin-right:50%;}.css-4okk7a .katex .rule{display:inline-block;border:solid 0;position:relative;}.css-4okk7a .katex .overline .overline-line,.css-4okk7a .katex .underline .underline-line,.css-4okk7a .katex .hline{display:inline-block;width:100%;border-bottom-style:solid;}.css-4okk7a .katex .hdashline{display:inline-block;width:100%;border-bottom-style:dashed;}.css-4okk7a .katex .sqrt>.root{margin-left:0.27777778em;margin-right:-0.55555556em;}.css-4okk7a .katex .sizing.reset-size1.size1,.css-4okk7a .katex .fontsize-ensurer.reset-size1.size1{font-size:1em;}.css-4okk7a .katex .sizing.reset-size1.size2,.css-4okk7a .katex .fontsize-ensurer.reset-size1.size2{font-size:1.2em;}.css-4okk7a .katex .sizing.reset-size1.size3,.css-4okk7a .katex .fontsize-ensurer.reset-size1.size3{font-size:1.4em;}.css-4okk7a .katex .sizing.reset-size1.size4,.css-4okk7a .katex .fontsize-ensurer.reset-size1.size4{font-size:1.6em;}.css-4okk7a .katex .sizing.reset-size1.size5,.css-4okk7a .katex .fontsize-ensurer.reset-size1.size5{font-size:1.8em;}.css-4okk7a .katex .sizing.reset-size1.size6,.css-4okk7a .katex .fontsize-ensurer.reset-size1.size6{font-size:2em;}.css-4okk7a .katex .sizing.reset-size1.size7,.css-4okk7a .katex .fontsize-ensurer.reset-size1.size7{font-size:2.4em;}.css-4okk7a .katex .sizing.reset-size1.size8,.css-4okk7a .katex .fontsize-ensurer.reset-size1.size8{font-size:2.88em;}.css-4okk7a .katex .sizing.reset-size1.size9,.css-4okk7a .katex .fontsize-ensurer.reset-size1.size9{font-size:3.456em;}.css-4okk7a .katex .sizing.reset-size1.size10,.css-4okk7a .katex .fontsize-ensurer.reset-size1.size10{font-size:4.148em;}.css-4okk7a .katex .sizing.reset-size1.size11,.css-4okk7a .katex .fontsize-ensurer.reset-size1.size11{font-size:4.976em;}.css-4okk7a .katex .sizing.reset-size2.size1,.css-4okk7a .katex .fontsize-ensurer.reset-size2.size1{font-size:0.83333333em;}.css-4okk7a .katex .sizing.reset-size2.size2,.css-4okk7a .katex .fontsize-ensurer.reset-size2.size2{font-size:1em;}.css-4okk7a .katex .sizing.reset-size2.size3,.css-4okk7a .katex .fontsize-ensurer.reset-size2.size3{font-size:1.16666667em;}.css-4okk7a .katex .sizing.reset-size2.size4,.css-4okk7a .katex .fontsize-ensurer.reset-size2.size4{font-size:1.33333333em;}.css-4okk7a .katex .sizing.reset-size2.size5,.css-4okk7a .katex .fontsize-ensurer.reset-size2.size5{font-size:1.5em;}.css-4okk7a .katex .sizing.reset-size2.size6,.css-4okk7a .katex .fontsize-ensurer.reset-size2.size6{font-size:1.66666667em;}.css-4okk7a .katex .sizing.reset-size2.size7,.css-4okk7a .katex .fontsize-ensurer.reset-size2.size7{font-size:2em;}.css-4okk7a .katex .sizing.reset-size2.size8,.css-4okk7a .katex .fontsize-ensurer.reset-size2.size8{font-size:2.4em;}.css-4okk7a .katex .sizing.reset-size2.size9,.css-4okk7a .katex .fontsize-ensurer.reset-size2.size9{font-size:2.88em;}.css-4okk7a .katex .sizing.reset-size2.size10,.css-4okk7a .katex .fontsize-ensurer.reset-size2.size10{font-size:3.45666667em;}.css-4okk7a .katex .sizing.reset-size2.size11,.css-4okk7a .katex .fontsize-ensurer.reset-size2.size11{font-size:4.14666667em;}.css-4okk7a .katex .sizing.reset-size3.size1,.css-4okk7a .katex .fontsize-ensurer.reset-size3.size1{font-size:0.71428571em;}.css-4okk7a .katex .sizing.reset-size3.size2,.css-4okk7a .katex .fontsize-ensurer.reset-size3.size2{font-size:0.85714286em;}.css-4okk7a .katex .sizing.reset-size3.size3,.css-4okk7a .katex .fontsize-ensurer.reset-size3.size3{font-size:1em;}.css-4okk7a .katex .sizing.reset-size3.size4,.css-4okk7a .katex .fontsize-ensurer.reset-size3.size4{font-size:1.14285714em;}.css-4okk7a .katex .sizing.reset-size3.size5,.css-4okk7a .katex .fontsize-ensurer.reset-size3.size5{font-size:1.28571429em;}.css-4okk7a .katex .sizing.reset-size3.size6,.css-4okk7a .katex .fontsize-ensurer.reset-size3.size6{font-size:1.42857143em;}.css-4okk7a .katex .sizing.reset-size3.size7,.css-4okk7a .katex .fontsize-ensurer.reset-size3.size7{font-size:1.71428571em;}.css-4okk7a .katex .sizing.reset-size3.size8,.css-4okk7a .katex .fontsize-ensurer.reset-size3.size8{font-size:2.05714286em;}.css-4okk7a .katex .sizing.reset-size3.size9,.css-4okk7a .katex .fontsize-ensurer.reset-size3.size9{font-size:2.46857143em;}.css-4okk7a .katex .sizing.reset-size3.size10,.css-4okk7a .katex .fontsize-ensurer.reset-size3.size10{font-size:2.96285714em;}.css-4okk7a .katex .sizing.reset-size3.size11,.css-4okk7a .katex .fontsize-ensurer.reset-size3.size11{font-size:3.55428571em;}.css-4okk7a .katex .sizing.reset-size4.size1,.css-4okk7a .katex .fontsize-ensurer.reset-size4.size1{font-size:0.625em;}.css-4okk7a .katex .sizing.reset-size4.size2,.css-4okk7a .katex .fontsize-ensurer.reset-size4.size2{font-size:0.75em;}.css-4okk7a .katex .sizing.reset-size4.size3,.css-4okk7a .katex .fontsize-ensurer.reset-size4.size3{font-size:0.875em;}.css-4okk7a .katex .sizing.reset-size4.size4,.css-4okk7a .katex .fontsize-ensurer.reset-size4.size4{font-size:1em;}.css-4okk7a .katex .sizing.reset-size4.size5,.css-4okk7a .katex .fontsize-ensurer.reset-size4.size5{font-size:1.125em;}.css-4okk7a .katex .sizing.reset-size4.size6,.css-4okk7a .katex .fontsize-ensurer.reset-size4.size6{font-size:1.25em;}.css-4okk7a .katex .sizing.reset-size4.size7,.css-4okk7a .katex .fontsize-ensurer.reset-size4.size7{font-size:1.5em;}.css-4okk7a .katex .sizing.reset-size4.size8,.css-4okk7a .katex .fontsize-ensurer.reset-size4.size8{font-size:1.8em;}.css-4okk7a .katex .sizing.reset-size4.size9,.css-4okk7a .katex .fontsize-ensurer.reset-size4.size9{font-size:2.16em;}.css-4okk7a .katex .sizing.reset-size4.size10,.css-4okk7a .katex .fontsize-ensurer.reset-size4.size10{font-size:2.5925em;}.css-4okk7a .katex .sizing.reset-size4.size11,.css-4okk7a .katex .fontsize-ensurer.reset-size4.size11{font-size:3.11em;}.css-4okk7a .katex .sizing.reset-size5.size1,.css-4okk7a .katex .fontsize-ensurer.reset-size5.size1{font-size:0.55555556em;}.css-4okk7a .katex .sizing.reset-size5.size2,.css-4okk7a .katex .fontsize-ensurer.reset-size5.size2{font-size:0.66666667em;}.css-4okk7a .katex .sizing.reset-size5.size3,.css-4okk7a .katex .fontsize-ensurer.reset-size5.size3{font-size:0.77777778em;}.css-4okk7a .katex .sizing.reset-size5.size4,.css-4okk7a .katex .fontsize-ensurer.reset-size5.size4{font-size:0.88888889em;}.css-4okk7a .katex .sizing.reset-size5.size5,.css-4okk7a .katex .fontsize-ensurer.reset-size5.size5{font-size:1em;}.css-4okk7a .katex .sizing.reset-size5.size6,.css-4okk7a .katex .fontsize-ensurer.reset-size5.size6{font-size:1.11111111em;}.css-4okk7a .katex .sizing.reset-size5.size7,.css-4okk7a .katex .fontsize-ensurer.reset-size5.size7{font-size:1.33333333em;}.css-4okk7a .katex .sizing.reset-size5.size8,.css-4okk7a .katex .fontsize-ensurer.reset-size5.size8{font-size:1.6em;}.css-4okk7a .katex .sizing.reset-size5.size9,.css-4okk7a .katex .fontsize-ensurer.reset-size5.size9{font-size:1.92em;}.css-4okk7a .katex .sizing.reset-size5.size10,.css-4okk7a .katex .fontsize-ensurer.reset-size5.size10{font-size:2.30444444em;}.css-4okk7a .katex .sizing.reset-size5.size11,.css-4okk7a .katex .fontsize-ensurer.reset-size5.size11{font-size:2.76444444em;}.css-4okk7a .katex .sizing.reset-size6.size1,.css-4okk7a .katex .fontsize-ensurer.reset-size6.size1{font-size:0.5em;}.css-4okk7a .katex .sizing.reset-size6.size2,.css-4okk7a .katex .fontsize-ensurer.reset-size6.size2{font-size:0.6em;}.css-4okk7a .katex .sizing.reset-size6.size3,.css-4okk7a .katex .fontsize-ensurer.reset-size6.size3{font-size:0.7em;}.css-4okk7a .katex .sizing.reset-size6.size4,.css-4okk7a .katex .fontsize-ensurer.reset-size6.size4{font-size:0.8em;}.css-4okk7a .katex .sizing.reset-size6.size5,.css-4okk7a .katex .fontsize-ensurer.reset-size6.size5{font-size:0.9em;}.css-4okk7a .katex .sizing.reset-size6.size6,.css-4okk7a .katex .fontsize-ensurer.reset-size6.size6{font-size:1em;}.css-4okk7a .katex .sizing.reset-size6.size7,.css-4okk7a .katex .fontsize-ensurer.reset-size6.size7{font-size:1.2em;}.css-4okk7a .katex .sizing.reset-size6.size8,.css-4okk7a .katex .fontsize-ensurer.reset-size6.size8{font-size:1.44em;}.css-4okk7a .katex .sizing.reset-size6.size9,.css-4okk7a .katex .fontsize-ensurer.reset-size6.size9{font-size:1.728em;}.css-4okk7a .katex .sizing.reset-size6.size10,.css-4okk7a .katex .fontsize-ensurer.reset-size6.size10{font-size:2.074em;}.css-4okk7a .katex .sizing.reset-size6.size11,.css-4okk7a .katex .fontsize-ensurer.reset-size6.size11{font-size:2.488em;}.css-4okk7a .katex .sizing.reset-size7.size1,.css-4okk7a .katex .fontsize-ensurer.reset-size7.size1{font-size:0.41666667em;}.css-4okk7a .katex .sizing.reset-size7.size2,.css-4okk7a .katex .fontsize-ensurer.reset-size7.size2{font-size:0.5em;}.css-4okk7a .katex .sizing.reset-size7.size3,.css-4okk7a .katex .fontsize-ensurer.reset-size7.size3{font-size:0.58333333em;}.css-4okk7a .katex .sizing.reset-size7.size4,.css-4okk7a .katex .fontsize-ensurer.reset-size7.size4{font-size:0.66666667em;}.css-4okk7a .katex .sizing.reset-size7.size5,.css-4okk7a .katex .fontsize-ensurer.reset-size7.size5{font-size:0.75em;}.css-4okk7a .katex .sizing.reset-size7.size6,.css-4okk7a .katex .fontsize-ensurer.reset-size7.size6{font-size:0.83333333em;}.css-4okk7a .katex .sizing.reset-size7.size7,.css-4okk7a .katex .fontsize-ensurer.reset-size7.size7{font-size:1em;}.css-4okk7a .katex .sizing.reset-size7.size8,.css-4okk7a .katex .fontsize-ensurer.reset-size7.size8{font-size:1.2em;}.css-4okk7a .katex .sizing.reset-size7.size9,.css-4okk7a .katex .fontsize-ensurer.reset-size7.size9{font-size:1.44em;}.css-4okk7a .katex .sizing.reset-size7.size10,.css-4okk7a .katex .fontsize-ensurer.reset-size7.size10{font-size:1.72833333em;}.css-4okk7a .katex .sizing.reset-size7.size11,.css-4okk7a .katex .fontsize-ensurer.reset-size7.size11{font-size:2.07333333em;}.css-4okk7a .katex .sizing.reset-size8.size1,.css-4okk7a .katex .fontsize-ensurer.reset-size8.size1{font-size:0.34722222em;}.css-4okk7a .katex .sizing.reset-size8.size2,.css-4okk7a .katex .fontsize-ensurer.reset-size8.size2{font-size:0.41666667em;}.css-4okk7a .katex .sizing.reset-size8.size3,.css-4okk7a .katex .fontsize-ensurer.reset-size8.size3{font-size:0.48611111em;}.css-4okk7a .katex .sizing.reset-size8.size4,.css-4okk7a .katex .fontsize-ensurer.reset-size8.size4{font-size:0.55555556em;}.css-4okk7a .katex .sizing.reset-size8.size5,.css-4okk7a .katex .fontsize-ensurer.reset-size8.size5{font-size:0.625em;}.css-4okk7a .katex .sizing.reset-size8.size6,.css-4okk7a .katex .fontsize-ensurer.reset-size8.size6{font-size:0.69444444em;}.css-4okk7a .katex .sizing.reset-size8.size7,.css-4okk7a .katex .fontsize-ensurer.reset-size8.size7{font-size:0.83333333em;}.css-4okk7a .katex .sizing.reset-size8.size8,.css-4okk7a .katex .fontsize-ensurer.reset-size8.size8{font-size:1em;}.css-4okk7a .katex .sizing.reset-size8.size9,.css-4okk7a .katex .fontsize-ensurer.reset-size8.size9{font-size:1.2em;}.css-4okk7a .katex .sizing.reset-size8.size10,.css-4okk7a .katex .fontsize-ensurer.reset-size8.size10{font-size:1.44027778em;}.css-4okk7a .katex .sizing.reset-size8.size11,.css-4okk7a .katex .fontsize-ensurer.reset-size8.size11{font-size:1.72777778em;}.css-4okk7a .katex .sizing.reset-size9.size1,.css-4okk7a .katex .fontsize-ensurer.reset-size9.size1{font-size:0.28935185em;}.css-4okk7a .katex .sizing.reset-size9.size2,.css-4okk7a .katex .fontsize-ensurer.reset-size9.size2{font-size:0.34722222em;}.css-4okk7a .katex .sizing.reset-size9.size3,.css-4okk7a .katex .fontsize-ensurer.reset-size9.size3{font-size:0.40509259em;}.css-4okk7a .katex .sizing.reset-size9.size4,.css-4okk7a .katex .fontsize-ensurer.reset-size9.size4{font-size:0.46296296em;}.css-4okk7a .katex .sizing.reset-size9.size5,.css-4okk7a .katex .fontsize-ensurer.reset-size9.size5{font-size:0.52083333em;}.css-4okk7a .katex .sizing.reset-size9.size6,.css-4okk7a .katex .fontsize-ensurer.reset-size9.size6{font-size:0.5787037em;}.css-4okk7a .katex .sizing.reset-size9.size7,.css-4okk7a .katex .fontsize-ensurer.reset-size9.size7{font-size:0.69444444em;}.css-4okk7a .katex .sizing.reset-size9.size8,.css-4okk7a .katex .fontsize-ensurer.reset-size9.size8{font-size:0.83333333em;}.css-4okk7a .katex .sizing.reset-size9.size9,.css-4okk7a .katex .fontsize-ensurer.reset-size9.size9{font-size:1em;}.css-4okk7a .katex .sizing.reset-size9.size10,.css-4okk7a .katex .fontsize-ensurer.reset-size9.size10{font-size:1.20023148em;}.css-4okk7a .katex .sizing.reset-size9.size11,.css-4okk7a .katex .fontsize-ensurer.reset-size9.size11{font-size:1.43981481em;}.css-4okk7a .katex .sizing.reset-size10.size1,.css-4okk7a .katex .fontsize-ensurer.reset-size10.size1{font-size:0.24108004em;}.css-4okk7a .katex .sizing.reset-size10.size2,.css-4okk7a .katex .fontsize-ensurer.reset-size10.size2{font-size:0.28929605em;}.css-4okk7a .katex .sizing.reset-size10.size3,.css-4okk7a .katex .fontsize-ensurer.reset-size10.size3{font-size:0.33751205em;}.css-4okk7a .katex .sizing.reset-size10.size4,.css-4okk7a .katex .fontsize-ensurer.reset-size10.size4{font-size:0.38572806em;}.css-4okk7a .katex .sizing.reset-size10.size5,.css-4okk7a .katex .fontsize-ensurer.reset-size10.size5{font-size:0.43394407em;}.css-4okk7a .katex .sizing.reset-size10.size6,.css-4okk7a .katex .fontsize-ensurer.reset-size10.size6{font-size:0.48216008em;}.css-4okk7a .katex .sizing.reset-size10.size7,.css-4okk7a .katex .fontsize-ensurer.reset-size10.size7{font-size:0.57859209em;}.css-4okk7a .katex .sizing.reset-size10.size8,.css-4okk7a .katex .fontsize-ensurer.reset-size10.size8{font-size:0.69431051em;}.css-4okk7a .katex .sizing.reset-size10.size9,.css-4okk7a .katex .fontsize-ensurer.reset-size10.size9{font-size:0.83317261em;}.css-4okk7a .katex .sizing.reset-size10.size10,.css-4okk7a .katex .fontsize-ensurer.reset-size10.size10{font-size:1em;}.css-4okk7a .katex .sizing.reset-size10.size11,.css-4okk7a .katex .fontsize-ensurer.reset-size10.size11{font-size:1.19961427em;}.css-4okk7a .katex .sizing.reset-size11.size1,.css-4okk7a .katex .fontsize-ensurer.reset-size11.size1{font-size:0.20096463em;}.css-4okk7a .katex .sizing.reset-size11.size2,.css-4okk7a .katex .fontsize-ensurer.reset-size11.size2{font-size:0.24115756em;}.css-4okk7a .katex .sizing.reset-size11.size3,.css-4okk7a .katex .fontsize-ensurer.reset-size11.size3{font-size:0.28135048em;}.css-4okk7a .katex .sizing.reset-size11.size4,.css-4okk7a .katex .fontsize-ensurer.reset-size11.size4{font-size:0.32154341em;}.css-4okk7a .katex .sizing.reset-size11.size5,.css-4okk7a .katex .fontsize-ensurer.reset-size11.size5{font-size:0.36173633em;}.css-4okk7a .katex .sizing.reset-size11.size6,.css-4okk7a .katex .fontsize-ensurer.reset-size11.size6{font-size:0.40192926em;}.css-4okk7a .katex .sizing.reset-size11.size7,.css-4okk7a .katex .fontsize-ensurer.reset-size11.size7{font-size:0.48231511em;}.css-4okk7a .katex .sizing.reset-size11.size8,.css-4okk7a .katex .fontsize-ensurer.reset-size11.size8{font-size:0.57877814em;}.css-4okk7a .katex .sizing.reset-size11.size9,.css-4okk7a .katex .fontsize-ensurer.reset-size11.size9{font-size:0.69453376em;}.css-4okk7a .katex .sizing.reset-size11.size10,.css-4okk7a .katex .fontsize-ensurer.reset-size11.size10{font-size:0.83360129em;}.css-4okk7a .katex .sizing.reset-size11.size11,.css-4okk7a .katex .fontsize-ensurer.reset-size11.size11{font-size:1em;}.css-4okk7a .katex .delimsizing.size1{font-family:KaTeX_Size1;}.css-4okk7a .katex .delimsizing.size2{font-family:KaTeX_Size2;}.css-4okk7a .katex .delimsizing.size3{font-family:KaTeX_Size3;}.css-4okk7a .katex .delimsizing.size4{font-family:KaTeX_Size4;}.css-4okk7a .katex .delimsizing.mult .delim-size1>span{font-family:KaTeX_Size1;}.css-4okk7a .katex .delimsizing.mult .delim-size4>span{font-family:KaTeX_Size4;}.css-4okk7a .katex .nulldelimiter{display:inline-block;width:0.12em;}.css-4okk7a .katex .delimcenter{position:relative;}.css-4okk7a .katex .op-symbol{position:relative;}.css-4okk7a .katex .op-symbol.small-op{font-family:KaTeX_Size1;}.css-4okk7a .katex .op-symbol.large-op{font-family:KaTeX_Size2;}.css-4okk7a .katex .op-limits>.vlist-t{text-align:center;}.css-4okk7a .katex .accent>.vlist-t{text-align:center;}.css-4okk7a .katex .accent .accent-body{position:relative;}.css-4okk7a .katex .accent .accent-body:not(.accent-full){width:0;}.css-4okk7a .katex .overlay{display:block;}.css-4okk7a .katex .mtable .vertical-separator{display:inline-block;min-width:1px;}.css-4okk7a .katex .mtable .arraycolsep{display:inline-block;}.css-4okk7a .katex .mtable .col-align-c>.vlist-t{text-align:center;}.css-4okk7a .katex .mtable .col-align-l>.vlist-t{text-align:left;}.css-4okk7a .katex .mtable .col-align-r>.vlist-t{text-align:right;}.css-4okk7a .katex .svg-align{text-align:left;}.css-4okk7a .katex svg{display:block;position:absolute;width:100%;height:inherit;fill:currentColor;stroke:currentColor;fill-rule:nonzero;fill-opacity:1;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1;}.css-4okk7a .katex svg path{stroke:none;}.css-4okk7a .katex img{border-style:none;min-width:0;min-height:0;max-width:none;max-height:none;}.css-4okk7a .katex .stretchy{width:100%;display:block;position:relative;overflow:hidden;}.css-4okk7a .katex .stretchy::before,.css-4okk7a .katex .stretchy::after{content:'';}.css-4okk7a .katex .hide-tail{width:100%;position:relative;overflow:hidden;}.css-4okk7a .katex .halfarrow-left{position:absolute;left:0;width:50.2%;overflow:hidden;}.css-4okk7a .katex .halfarrow-right{position:absolute;right:0;width:50.2%;overflow:hidden;}.css-4okk7a .katex .brace-left{position:absolute;left:0;width:25.1%;overflow:hidden;}.css-4okk7a .katex .brace-center{position:absolute;left:25%;width:50%;overflow:hidden;}.css-4okk7a .katex .brace-right{position:absolute;right:0;width:25.1%;overflow:hidden;}.css-4okk7a .katex .x-arrow-pad{padding:0 0.5em;}.css-4okk7a .katex .cd-arrow-pad{padding:0 0.55556em 0 0.27778em;}.css-4okk7a .katex .x-arrow,.css-4okk7a .katex .mover,.css-4okk7a .katex .munder{text-align:center;}.css-4okk7a .katex .boxpad{padding:0 0.3em 0 0.3em;}.css-4okk7a .katex .fbox,.css-4okk7a .katex .fcolorbox{box-sizing:border-box;border:0.04em solid;}.css-4okk7a .katex .cancel-pad{padding:0 0.2em 0 0.2em;}.css-4okk7a .katex .cancel-lap{margin-left:-0.2em;margin-right:-0.2em;}.css-4okk7a .katex .sout{border-bottom-style:solid;border-bottom-width:0.08em;}.css-4okk7a .katex .angl{box-sizing:border-box;border-top:0.049em solid;border-right:0.049em solid;margin-right:0.03889em;}.css-4okk7a .katex .anglpad{padding:0 0.03889em 0 0.03889em;}.css-4okk7a .katex .eqn-num::before{counter-increment:katexEqnNo;content:'(' counter(katexEqnNo) ')';}.css-4okk7a .katex .mml-eqn-num::before{counter-increment:mmlEqnNo;content:'(' counter(mmlEqnNo) ')';}.css-4okk7a .katex .mtr-glue{width:50%;}.css-4okk7a .katex .cd-vert-arrow{display:inline-block;position:relative;}.css-4okk7a .katex .cd-label-left{display:inline-block;position:absolute;right:calc(50% + 0.3em);text-align:left;}.css-4okk7a .katex .cd-label-right{display:inline-block;position:absolute;left:calc(50% + 0.3em);text-align:right;}.css-4okk7a .katex-display{display:block;margin:1em 0;text-align:center;}.css-4okk7a .katex-display>.katex{display:block;white-space:nowrap;}.css-4okk7a .katex-display>.katex>.katex-html{display:block;position:relative;}.css-4okk7a .katex-display>.katex>.katex-html>.tag{position:absolute;right:0;}.css-4okk7a .katex-display.leqno>.katex>.katex-html>.tag{left:0;right:auto;}.css-4okk7a .katex-display.fleqn>.katex{text-align:left;padding-left:2em;}.css-4okk7a body{counter-reset:katexEqnNo mmlEqnNo;}.css-4okk7a table{width:-webkit-max-content;width:-moz-max-content;width:max-content;}.css-4okk7a .tableBlock{max-width:100%;margin-bottom:1rem;overflow-y:scroll;}.css-4okk7a .tableBlock thead,.css-4okk7a .tableBlock thead th{border-bottom:1px solid #333!important;}.css-4okk7a .tableBlock th,.css-4okk7a .tableBlock td{padding:10px;text-align:left;}.css-4okk7a .tableBlock th{font-weight:bold!important;}.css-4okk7a .tableBlock caption{caption-side:bottom;color:#555;font-size:12px;font-style:italic;text-align:center;}.css-4okk7a .tableBlock caption>p{margin:0;}.css-4okk7a .tableBlock th>p,.css-4okk7a .tableBlock td>p{margin:0;}.css-4okk7a .tableBlock [data-background-color='aliceblue']{background-color:#f0f8ff;color:#000;}.css-4okk7a .tableBlock [data-background-color='black']{background-color:#000;color:#fff;}.css-4okk7a .tableBlock [data-background-color='chocolate']{background-color:#d2691e;color:#fff;}.css-4okk7a .tableBlock [data-background-color='cornflowerblue']{background-color:#6495ed;color:#fff;}.css-4okk7a .tableBlock [data-background-color='crimson']{background-color:#dc143c;color:#fff;}.css-4okk7a .tableBlock [data-background-color='darkblue']{background-color:#00008b;color:#fff;}.css-4okk7a .tableBlock [data-background-color='darkseagreen']{background-color:#8fbc8f;color:#000;}.css-4okk7a .tableBlock [data-background-color='deepskyblue']{background-color:#00bfff;color:#000;}.css-4okk7a .tableBlock [data-background-color='gainsboro']{background-color:#dcdcdc;color:#000;}.css-4okk7a .tableBlock [data-background-color='grey']{background-color:#808080;color:#fff;}.css-4okk7a .tableBlock [data-background-color='lemonchiffon']{background-color:#fffacd;color:#000;}.css-4okk7a .tableBlock [data-background-color='lightpink']{background-color:#ffb6c1;color:#000;}.css-4okk7a .tableBlock [data-background-color='lightsalmon']{background-color:#ffa07a;color:#000;}.css-4okk7a .tableBlock [data-background-color='lightskyblue']{background-color:#87cefa;color:#000;}.css-4okk7a .tableBlock [data-background-color='mediumblue']{background-color:#0000cd;color:#fff;}.css-4okk7a .tableBlock [data-background-color='omnigrey']{background-color:#f0f0f0;color:#000;}.css-4okk7a .tableBlock [data-background-color='white']{background-color:#fff;color:#000;}.css-4okk7a .tableBlock [data-text-align='center']{text-align:center;}.css-4okk7a .tableBlock [data-text-align='left']{text-align:left;}.css-4okk7a .tableBlock [data-text-align='right']{text-align:right;}.css-4okk7a .tableBlock [data-vertical-align='bottom']{vertical-align:bottom;}.css-4okk7a .tableBlock [data-vertical-align='middle']{vertical-align:middle;}.css-4okk7a .tableBlock [data-vertical-align='top']{vertical-align:top;}.css-4okk7a .tableBlock__font-size--xxsmall{font-size:10px;}.css-4okk7a .tableBlock__font-size--xsmall{font-size:12px;}.css-4okk7a .tableBlock__font-size--small{font-size:14px;}.css-4okk7a .tableBlock__font-size--large{font-size:18px;}.css-4okk7a .tableBlock__border--some tbody tr:not(:last-child){border-bottom:1px solid #e2e5e7;}.css-4okk7a .tableBlock__border--bordered td,.css-4okk7a .tableBlock__border--bordered th{border:1px solid #e2e5e7;}.css-4okk7a .tableBlock__border--borderless tbody+tbody,.css-4okk7a .tableBlock__border--borderless td,.css-4okk7a .tableBlock__border--borderless th,.css-4okk7a .tableBlock__border--borderless tr,.css-4okk7a .tableBlock__border--borderless thead,.css-4okk7a .tableBlock__border--borderless thead th{border:0!important;}.css-4okk7a .tableBlock:not(.tableBlock__table-striped) tbody tr{background-color:unset!important;}.css-4okk7a .tableBlock__table-striped tbody tr:nth-of-type(odd){background-color:#f9fafc!important;}.css-4okk7a .tableBlock__table-compactl th,.css-4okk7a .tableBlock__table-compact td{padding:3px!important;}.css-4okk7a .tableBlock__full-size{width:100%;}.css-4okk7a .textBlock{margin-bottom:16px;}.css-4okk7a .textBlock__text-formatting--finePrint{font-size:12px;}.css-4okk7a .textBlock__text-infoBox{padding:0.75rem 1.25rem;margin-bottom:1rem;border:1px solid transparent;border-radius:0.25rem;}.css-4okk7a .textBlock__text-infoBox p{margin:0;}.css-4okk7a .textBlock__text-infoBox--primary{background-color:#cce5ff;border-color:#b8daff;color:#004085;}.css-4okk7a .textBlock__text-infoBox--secondary{background-color:#e2e3e5;border-color:#d6d8db;color:#383d41;}.css-4okk7a .textBlock__text-infoBox--success{background-color:#d4edda;border-color:#c3e6cb;color:#155724;}.css-4okk7a .textBlock__text-infoBox--danger{background-color:#f8d7da;border-color:#f5c6cb;color:#721c24;}.css-4okk7a .textBlock__text-infoBox--warning{background-color:#fff3cd;border-color:#ffeeba;color:#856404;}.css-4okk7a .textBlock__text-infoBox--info{background-color:#d1ecf1;border-color:#bee5eb;color:#0c5460;}.css-4okk7a .textBlock__text-infoBox--dark{background-color:#d6d8d9;border-color:#c6c8ca;color:#1b1e21;}.css-4okk7a .text-overline{-webkit-text-decoration:overline;text-decoration:overline;}.css-4okk7a.css-4okk7a{color:#2B3148;background-color:transparent;font-family:"Roboto","Helvetica","Arial",sans-serif;font-size:20px;line-height:24px;overflow:visible;padding-top:0px;position:relative;}.css-4okk7a.css-4okk7a:after{content:'';-webkit-transform:scale(0);-moz-transform:scale(0);-ms-transform:scale(0);transform:scale(0);position:absolute;border:2px solid #EA9430;border-radius:2px;inset:-8px;z-index:1;}.css-4okk7a .js-external-link-button.link-like,.css-4okk7a .js-external-link-anchor{color:inherit;border-radius:1px;-webkit-text-decoration:underline;text-decoration:underline;}.css-4okk7a .js-external-link-button.link-like:hover,.css-4okk7a .js-external-link-anchor:hover,.css-4okk7a .js-external-link-button.link-like:active,.css-4okk7a .js-external-link-anchor:active{text-decoration-thickness:2px;text-shadow:1px 0 0;}.css-4okk7a .js-external-link-button.link-like:focus-visible,.css-4okk7a .js-external-link-anchor:focus-visible{outline:transparent 2px dotted;box-shadow:0 0 0 2px #6314E6;}.css-4okk7a p,.css-4okk7a div{margin:0px;display:block;}.css-4okk7a pre{margin:0px;display:block;}.css-4okk7a pre code{display:block;width:-webkit-fit-content;width:-moz-fit-content;width:fit-content;}.css-4okk7a pre:not(:first-child){padding-top:8px;}.css-4okk7a ul,.css-4okk7a ol{display:block margin:0px;padding-left:20px;}.css-4okk7a ul li,.css-4okk7a ol li{padding-top:8px;}.css-4okk7a ul ul,.css-4okk7a ol ul,.css-4okk7a ul ol,.css-4okk7a ol ol{padding-top:0px;}.css-4okk7a ul:not(:first-child),.css-4okk7a ol:not(:first-child){padding-top:4px;} Spaceship and destination 👩‍🚀👨‍🚀

Spaceship acceleration

Spaceship mass

Mass of spaceship excluding fuel.

Destination

Select a destination from the list or type in distance by hand.

Which star/galaxy?

If you want to input your own distance, select the 'Custom destination' option in the 'Which star/galaxy?' field.

Calculation options

Do you want to stop at destination point? If yes, the spaceship will start decelerating once it reaches the halfway point.

Calculations mode

You can compare Einstein's special relativity with non-relativistic Newton's physics. Remember that at near-light speeds only the former is correct!

Travel details 🚀

Time passed in spaceship

Time passed on Earth

Time passed in the resting frame of reference. It could be an observer on Earth.

Required fuel mass

Assuming 100% efficiency.

Maximum velocity

Note that our calculator may round velocity to the speed of light if it is really close to it.

Additional parameters

Space Travel Calculator

Calculate how long it would take to reach planets, stars, or galaxies, as well as fuel mass, velocity and more, journey details.

Science in School

To the moon and back: reflecting a radio signal to calculate the distance teach article.

Author(s): Richard Middelkoop

Using a simple calculation, measure the distance between Earth and the Moon with the help of a local amateur radio station.

Inspired by an earlier article in Science in School that used photography to measure the distance to the Moon ( Cenadelli et al., 2016 ), we set up an experiment with groups of scouts around the globe to do the same with radio signals. With help from a qualified radio user, the groups sent radio signals from their transmitter stations to the Moon. The signals bounce off the surface of the Moon and back to Earth, where they are detected by a receiver. This radio transmission technique, which is known as ‘moon bounce’ or ‘Earth-Moon-Earth’ communication, was used extensively for military communication in the days before satellites.

Since radio waves are a type of electromagnetic radiation, they travel at the speed of light. Due to the travel time between Earth and the Moon, the reflected radio signal is delayed typically by a few seconds. Using this time delay, the groups calculated the distance that the radio wave travelled and successfully measured the distance to the Moon.

Measuring the distance from Earth to the Moon

In this article, we describe how to conduct the activity at your school, beginning with contacting a radio amateur (a person licensed by the relevant authorities to transmit high-power radio signals) for help. We then explain how to transmit and measure the radio signal, and carry out the final calculation. The experiment, which must be carried out when the Moon is above the horizon w1 is suitable for students aged 11 and above and will take around 1.5–2 hours, including set-up time.

For the teacher

The use of an amateur radio station is essential to send the radio signal to the Moon, so you will need to ask your local or national radio amateur club w2 (most countries have one) for their assistance. People with an interest in radio transmission can take an examination to obtain a licence that allows them to transmit radio signals at amateur radio frequencies.

This requires:

• An antenna capable of being pointed at the Moon to convert the signal into radio waves, and vice versa (figure 1)
• A radio transmitter/receiver (figure 2) to transmit the radio waves and receive the bounced waves from the Moon
• A dual-channel oscilloscope (figure 3) to show the time delay between transmitting and receiving the radio waves (figure 4)

Your radio amateur will be able to provide the equipment, if necessary with the help of a local amateur radio club. If the radio amateur sends the signals from the amateur radio station, the returning signals can be streamed via the internet to be viewed at your school (see ‘A louder alternative’ section).

For the radio amateur

• Set up the transmitter/receiver and connect it to the antenna.. The antenna and radio transmitter should be within line of sight of the Moon, and the receiver should not be disturbed by interference signals, such as large electric installations nearby. You can find out where exactly the Moon is positioned in the sky, as seen from your location at the time of the experiment, by looking on the Sky Live website w3 .
• Select an appropriate frequency in a VHF or UHF amateur radio band.
• Point the antenna towards the Moon.
• Connect the oscilloscope to the sound input of the transmitter so that it shows the signal being transmitted.
• Connect the output of the transmitter/receiver to the second channel of the oscilloscope.
• Transmit a signal in Morse code or as a series of pulses that easily show on the oscilloscope.
• On the receiver, listen for the reflection of your signal and watch it on the oscilloscope.
• Set the transmitter/receiver in the ‘break-in mode’ to quickly switch between transmitting and receiving.
• Adjust the antenna direction if needed.
• Align the two signals seen on the oscilloscope and read the time delay between them from the screen.

For the students

Using the time delay, calculate the distance d to the Moon using the following equation

d = ( c x t ) / 2

d = distance of Earth to Moon in metres

c = the speed of light, 3 x 10 8 metres per second

t =time delay in seconds

The radio signal covers the same distance twice (Earth to the Moon, and back), hence the need to divide by 2

For example, with a delay time of 2.56 seconds:

d = [(3 x 10 8 ) x 2.56] / 2

d = 348 000 000 m

Extension options

• Radio-amatorul ar putea trimite şi recepţiona semnale multiple, astfel încât elevii să poată obţină mai multe măsurători ale timpului de întârziere, pentru a calcula o medie a valorilor şi respectiv o deviaţie standard, cu scopul de a creşte precizia rezultatului.
• Înregistraţi pe suport digital semnalele transmise şi recepţionate, folosind un dispozitiv audio simplu, precum smart-phone-ul, pentru a le putea analiza ulterior. Aceasta ar permite elevilor să deruleze activitatea şi în absenţa radio-amatorului.

Why does the distance to the Moon vary slightly depending on the observation point on Earth?

Due to the curvature of Earth, the simple formula introduces a small error: the distance to the Moon is slightly different depending on where the observation point is on Earth – close to the equator or closer to one of the poles (see figure 5). This error is very small compared to the huge distance from Earth to the Moon, so it is ignored for this experiment

The experiment to measure the distance to the Moon and back was carried out by several scout groups during their annual event, called Jamboree-On-The-Airi w4 (JOTA) in October. The groups were scattered all over the globe, so the aspect angle between their observation points and the Moon were all different.

Why would the result vary if you repeated the experiment two weeks later?

The distance from Earth to the Moon is not completely fixed. The Moon’s orbit around Earth is not a perfect circle, so the distance varies slightly (figure 6). The experiment was carried out in the same weekend so the distance variation had little to no influence.

What other sources of small errors are there in your experiment?

• Delays in streaming the signals over the internet introduces a small error in the calculated distance. This extra delay is typically an order of magnitude smaller than the delay caused by the signal travel time between Earth and the Moon and is therefore ignored in this experiment.
• The accuracy of the oscilloscope, which depends on the time base (the number of seconds per screen division), can also introduce errors. Typically, the reading can be accurate up to one-tenth of the time base setting. The lower the time base is set, the higher the sweep frequency and the more accurate the result.
• A weak signal (one that is only just visible above background noise) is more difficult to read on the oscilloscope screen. Identifying the time delay is open to errors, and variations of up to several hundreds of milliseconds can easily occur. Taking multiple measurements and using the average can reduce the error margin.
• Objects that partially block the path of the radio wave can cause the signal to scatter. This is more likely to occur in urban areas than in open fields and can result in multiple echoes that are visible on the oscilloscope, which in some cases can be stronger than the directly reflected signal from the Moon. As a result, students may mistakenly use the wrong echo to read the time delay.

A louder alternative

If the signal is not strong enough to carry out the activity using the method described for the radio amateur, or you wish to stream the radio signals via the internet, you can use this alternative method instead.

To determine whether the signal will be strong enough, the radio amateur should check the equipment sensitivity and find out exactly where the Moon is positioned in the sky prior to the activity. If they can’t hear the reflected signal, or if the visual signal is lost amongst background noise on the oscilloscope, they can use a large astronomy radio telescope at the Dwingeloo Radio Observatory in the Netherlands as the receiver (figure 7). The radio telescope has been refurbished and is operated by a group of radio amateurs. It receives the radio signal and converts it into a visible signal, which is streamed online and is available for anyone to view w5 .

• In preparation, use the C A Muller Radio Astronomie Station (CAMRAS) website w6 to check for planned activities at the Dwingeloo Radio Observatory. If the telescope is unavailable, you can find an alternative receiver listed on the WebSDR website w7 . Anyone – not just radio amateurs – can use the website at any time. Check that the Moon will be visible from the observatory at the time of your planned experiment w3 .
• Follow steps 1–4 of the original procedure
• On the CAMRAS webpage showing the WebSDR stream w5 , shift the yellow slider to the same frequency that will be used to transmit your signal to the Moon (see figure 8).
• Transmit a signal in Morse code or as a series of pulses that easily show on an oscilloscope connected to your computer.
• On the computer, listen for the audio signal of the reflected radio wave and watch it on the oscilloscope. Students could also view the signals on separate computers.

• Cenadelli D et al (2016) Geometry can take you to the Moon . Science in School 35 .

Web References

• w1 – To find out the positions and times that the Moon rises and sets, visit the Heavens Above website .
• w2 ­– Find your radio amateur using the International Amateur Radio Union website. .
• w3 – Find out exactly where the Moon is in the sky from your location at the time of your experiment using the Sky Live website .
• w4 – Jamboree-On-The-Air (JOTA) is an international event of the World Organization of the Scout Movement w8 (WOSM), encouraging scouts around the world to communicate with one another using amateur radio and the internet.
• w5 – Visit the CAMRAS WebSDR stream to hear radio signals received by the Dwingeloo Radio Observatory amateur telescope in The Netherlands.
• w6 – Find out whether the Dwingeloo Radio Observatory telescope will be available at the time of your experiment by visiting the CAMRAS website .
• w7 – To see a list of available radio receivers and to stream signals via the internet, visit the WebSDR .
• w8 – The World Organization of the Scout Movement (WOSM) is an independent, non-political, non-governmental organisation that is made up of 164 National Scout Organisations (NSOs) from 224 countries and territories around the world. With over 40 million members, WOSM is one of the largest youth movements in the world.
• Iscra A, Quaglini MT, Rossi G (2006) Introducing radio transmission with a simple experiment . Science in School 3: 39–42.
• Pössel M (2017) Parallax: reaching the stars with geometry . Science in School 39: 40–44.

Richard Middelkoop has a bachelor’s degree in electrical engineering and a master’s degree in telecommunications from the Eindhoven University of Technology in The Netherlands. He volunteers at the World Organization of the Scout Movement w8 (WOSM) to lead a team that organises an annual get-togetheă w4 for 1 million young people around the globe, by means of radio and internet connections

This activity can provide students with a unique opportunity to take a peek into the world of the experts, observe them while working and understand the science behind the instruments used. It is a fantastic way to put some of the theory learned about radio waves into practice, by calculating the distance of the Moon from different locations, and to investigate the Moon’s orbital pattern. It would also be a great opportunity to collaborate with another school on the other side of the globe and share results and experiences.

Catherine Cutajar, physics teacher, St. Martin’s College Sixth Form, Malta

Download this article as a PDF

Share this article

Subscribe to our newsletter.

How far is the moon from Earth?

Answering the question "how far is the moon from Earth?", can change depending on when you ask it.

• Shortest distance
• Greatest distance
• Travel time
• Drifting away

Additional Resources

It's the brightest object in our night sky, but how far is the moon from Earth?

The moon 's distance from Earth affects the strength of ocean tides and the appearance of solar eclipses in our skies.

The average distance between the blue planet and its only natural satellite is about 238,855 miles (384,400 kilometers), according to NASA . 

The moon does not orbit Earth in a perfect circle, so there are places along its trip when it is either closer or farther away from our planet than this average distance. 

Shortest distance between the moon and Earth: Perigee

When the moon reaches its shortest distance to Earth — known as perigee — it is about 226,000 miles (363,300 km) away. 

If perigee coincides with a full moon phase, this is generally called a supermoon . The term is not a scientific one, but it is used by the skywatching community when the full moon appears within 90% of perigee. 

Supermoons appear roughly 17% bigger and 30% brighter than the faintest moon of the year. Since the moon's gravity exerts a pulling force on Earth's oceans to produce tides, the moon's closer proximity to Earth around perigee can also trigger higher-than-usual tides. 

Greatest distance between the moon and Earth: Apogee

When the moon is at its farthest distance from Earth, known as apogee, it is about 251,000 miles (405,500 km) from our planet. One of the clearest natural visuals for apogee are annular, or "ring of fire," solar eclipses . 

A remarkable quality of solar eclipses is the serendipity of their existence. For the next 600 million years , the moon's proximity to Earth will be about 400 times greater than the sun's distance to Earth. Since the star's diameter is also approximately 400 times greater than that of the moon, the disks of both objects tend to match almost perfectly during solar eclipses. This produces moments of totality when just the solar corona peeks out from behind the moon. 

Related: Solar eclipses 2023: When, where & how to see them

But if the new moon phase that produces solar eclipses coincides with apogee, the moon's longer distance from Earth means that the lunar disk will appear much smaller in the sky. While still spectacular, annular solar eclipses do not completely block out the sun, Instead, they leave a ring of the solar disk visible to spectators.

How long does it take to get to the moon?

A range of factors determines how long it takes to reach the moon. Human missions, for instance, tend to take longer than passenger-free satellites. Whether or not an object stops at the moon or just zips by also comes into play.

The USSR launched the first mission to the moon,  Luna 1 , in 1959. With no propulsion system, the sphere-shaped satellite was hurled into space and took only 34 flight hours to make the trip. After its flyby, the satellite went into orbit around the sun, between the orbits of Earth and Mars . This remains one of the fastest trips to the moon.

In 2003, the European Space Agency launched SMART-1, the first successful European spacecraft to the moon. Rather than travel a direct path, SMART-1 spiraled around Earth to reach its satellite, arriving more than a year after launch. Instead of propellant, SMART-1 made the first use of an ion engine, in combination with gravity assist maneuvers, to reach the moon making it extremely fuel efficient. The extended path provided significant insight into the Earth-moon system

– How big is the moon?

– How was the moon formed?

– What is a blood moon?

– What is a Blue Moon?

"Operating SMART-1 has been an extremely complex but rewarding task," Octavio Camino-Ramos, ESA SMART-1 Spacecraft Operations Manager said in a  statement . "The long spiraling trajectory around Earth to test solar electric propulsion (a low-thrust approach), the long exposure to radiation, the strong perturbations of the gravity fields of the Earth-moon system and then the reaching of a lunar orbit optimized for the scientific investigations, have allowed us to gain valuable expertise in navigation techniques for low-thrust propulsion." He called the findings "a remarkable benchmark for the future."

NASA sent eight crewed Apollo missions to the moon, six of which landed successfully. (Apollo 8 was the first mission to orbit another body and Apollo 13's infamous disaster resulted in a journey around the moon rather than a landing on its surface.) Each spent about three days traveling through space.

Apollo 8  took 69 hours and 8 minutes to enter orbit around the moon.  Apollo 11 , which placed the first humans on the moon, took 75 hours and 56 minutes to enter orbit around the moon. Long before they entered orbit, however, both spacecraft entered the moon's sphere of influence, a region 33,823 nautical miles (62,630 km) from the moon. For Apollo 11, this occurred after 61 hours and 56 minutes, while for Apollo 8 it took only 55 hours 40 minutes.

But the quickest trip to the moon was the  New Horizons  probe, which zipped past the moon in just 8 hours 35 minutes. The spacecraft didn't even slow down or approach lunar orbit but instead flew by on its way to Pluto .

The moon is getting further away

The moon was once much closer to Earth. During the infancy of the solar system just as planets were finalizing their formation , a protoplanetary Earth collided with a Mars-sized object that may have formed farther away from the sun. Known as Theia , its impact produced the material that would eventually coalesce to form the moon. 

The distance between the Earth and the moon grew as time passed. Currently, the moon drifts away from our planet at a rate of approximately 1.5 inches (3.8 cm) a year, roughly the same rate at which your fingernails grow !

Explore the distance to the moon in more detail with this article from Royal Museums Greenwich . Learn how to measure the distance to the moon using a lunar eclipse or a parallax with this feature from Universe Today . Continue exploring moon to Earth distance measurements with the educational website Earth How .

If you're looking to take the best photos of the moon that you can, our  how to photograph the moon  guide is full of expert tips on techniques, times and tools to help you start taking the most impressive lunar photos you can. Our  best cameras for astrophotography  and  best lenses for astrophotography  can also help you take the best moon images you can, no matter your skill level.

Fancy taking a more in-depth moonlit tour of our rocky companion? Our  ultimate guide to observing the moon  will help you plan your next skywatching venture whether it be exploring the lunar seas, mountainous terrain, or the many craters that blanket the landscape. You can also see where astronauts, rovers and landers have ventured with our  Apollo landing sites observing guide . 

Bibliography

Ahrens, Caitlin. " Origin of the Moon, Impactor Theory ." Encyclopedia of Lunar Science (2021). 

Cano, Erick J., Zachary D. Sharp, and Charles K. Shearer. " Distinct oxygen isotope compositions of the Earth and Moon ." Nature Geoscience 13.4 (2020): 270-274. 

Jones, Andrea, et al. " Overview | Inside & Out – Moon: NASA Science." Public Engagement  Team at NASA Goddard's Solar System Exploration Division. Accessed 31 January 2022.

Jones, Andrea, et al. " Eclipses | Moon in Motion ." Public Engagement Team at NASA Goddard's Solar System Exploration Division. Accessed 31 January 2022.

Jones, Andrea, et al. " Supermoons | Moon in Motion ." Public Engagement Team at NASA Goddard's Solar System Exploration Division. Accessed 31 January 2022.

Jones, Andrea, et al. " Moon Phases | Moon in Motion ." Public Engagement Team at NASA Goddard's Solar System Exploration Division. Accessed 31 January 2022.

Join our Space Forums to keep talking space on the latest missions, night sky and more! And if you have a news tip, correction or comment, let us know at: [email protected].

Get the Space.com Newsletter

Breaking space news, the latest updates on rocket launches, skywatching events and more!

Satellites watch as 4th global coral bleaching event unfolds (image)

Happy Earth Day 2024! NASA picks 6 new airborne missions to study our changing planet

Watch 2 cosmonauts conduct spacewalk outside the ISS today

Most Popular

• 2 Watch China launch 3 astronauts to Tiangong space station today
• 3 Buried in the Cat's Paw Nebula lies one of the largest space molecules ever seen
• 4 Netflix releases official trailer for Jennifer Lopez mech combat sci-fi film 'Atlas' (video)
• 5 Ancient rocks hold proof of Earth's magnetic field. Here's why that's puzzling

• Subscribe to BBC Science Focus Magazine
• Previous Issues
• Future tech
• Everyday science
• Planet Earth
• Newsletters

How long does it take to get to the Moon?

From Apollo to Artemis, here's how long it takes to get to the Moon.

Toby Saunders

How long does it take to get to the Moon ? If you’re planning your next weekend break to spend time on the lunar surface, you’ll need to know exactly how long it will take to get there.

While we’re a ways off building bases on the Moon , NASA’s Artemis mission is taking people back onto the lunar surface for the first time since Apollo 17 in 1972. The aim of the Artemis mission is to build the Lunar Gateway , which will place a space station in lunar orbit to act as a staging post for future trips to the Moon.

Artemis 3 is set to bring people back onto the Moon for the first time in over 50 years. This mission is likely to take place in 2026 at the earliest – but how long will it take the astronauts to get to the Moon?

Read on to find out how far away the Moon is from the Earth, how long it takes to get to the Moon, how long it took Apollo 11, and how long it takes a probe to get there.

How far away is the Moon?

The Moon doesn’t have a fixed distance away from the Earth. Just as the Earth’s orbit isn’t 100 per cent circular around the Sun, the Moon’s orbit isn’t around the Earth. It gets closer and further away over time.

The Moon is 363,104km from Earth at its closest point (perigee) and 405,696km away at its farthest (apogee). Taking these measurements, the average distance between the Earth and the Moon is around 384,400km.

The elliptical nature of the Moon’s orbit of the Earth is just one of many factors scientists need to take into account when planning missions up there.

It’s difficult to give a definitive answer on how long it takes to get to the Moon but it should take just over three days . There are a multitude of factors to account for, including the changing distance between us and the Moon, take-off trajectory, whether the craft is manned or unmanned, choice of propulsion system, and whether it’s landing, orbiting, or flying by.

During NASA’s Apollo program, the fastest mission was Apollo 8, which took 69 hours and eight minutes to enter the lunar orbit insertion burn. This was the quickest of NASA's Apollo missions – each mission after this had flight durations of 74 hours and over. The final Moon-landing mission, Apollo 17, took 86 hours and 14 minutes to reach the Moon.

The Artemis 1, an uncrewed craft, took five days in 2022 to reach the Moon’s orbit. Travelling to the Moon has become slower in the years since the 'one small step for man and a giant leap for mankind' took place, mainly because we have moved on from a direct transfer trajectory to save on fuel and costs.

How long did it take to get to the Moon in 1969?

The Apollo 11 Moon-landing mission in 1969 took astronauts Neil Armstrong , Buzz Aldrin , and Michael Collins 75 hours and 49 minutes to get to and land on the Moon. That’s just over three days. This is the time it took for them to actually land on the Moon, not just entering its orbit.

According to NASA, an entire Apollo mission, from leaving Earth and landing back at home took a total of eight days, three hours, 18 minutes, and 35 seconds. Here is the full list of Apollo missions to the Moon and how long they took:

• Apollo 8: 69 hours, 8 minutes (1968)
• Apollo 10: 75 hours, 55 minutes (1969)
• Apollo 11: 75 hours, 49 minutes (1969)
• Apollo 12: 83 hours, 25 minutes (1969)
• Apollo 13: 76 hours (1970)
• Apollo 14: 81 hours, 56 minutes (1971)
• Apollo 15: 78 hours, 31 minutes (1971)
• Apollo 16: 74 hours, 28 minutes (1972)
• Apollo 17: 86 hours, 14 minutes (1972)

How long does it take a probe to get to the Moon?

A probe can get to the Moon in around eight and a half hours.

The New Horizons probe took eight hours and 35 minutes to reach the moon. It eventually reached Pluto after nine years in 2015.

Other probes can take far longer to reach the Moon, however, and the time taken is dependent on different factors including fuel used and more. The European Space Agency’s Smart-1 probe in 2003, for example, took one year and six weeks to get to the Moon. Its use of electric-ion propulsion (using up just 82kg of Xenon fuel), the reason behind its slow speed.

• What's the largest planet in the Universe?
• When is the next full Moon? Your lunar astronomy guide
• Why does the Sun produce so much radiation?

Share this article

• Terms & Conditions
• Privacy policy
• Cookies policy
• Code of conduct
• Magazine subscriptions
• Manage preferences

How long does it take to travel to the Moon?

Last Updated: November 23, 2022

Humans have always been fascinated by the prospect of visiting the Moon – our closest celestial neighbor, and the first stepping stone in the exploration of the solar system. Even with the use of modern technology and advanced propulsion systems, reaching the Moon remains a very difficult and very expensive endeavour.

So how long does it take to get to the Moon? The short answer is that it takes an average of 3 days to reach the Moon. 

Between 1969 and 1972, NASA sent 18 astronauts to the Moon as part of the Apollo space program . In addition, five nations and two political unions have successfully landed unmanned spacecraft on the lunar surface or placed them into lunar orbit.

The last Moon landing occurred almost 40 years ago! In fact, humans have not set foot on the lunar ground since December 14, 1972. That being said, NASA’s new “Artemis” mission is generating a great deal of public interest. The next Moon landing is scheduled for 2024!

So, what are the factors that can influence the duration of this incredible journey? Let’s dive in! Or should I say, let’s take off?

Cargo load is one of the many factors that can influence the time it takes to travel to the Moon.

Does the Moon's orbit affect the time it takes to get there?

We know that the Moon is located at an average distance of 238,855 miles from Earth. However, the trajectory of the Moon’s orbit around the Earth is elliptical, with one side closer to the Earth than the other and an average eccentricity of 0.0549.

Since its path is not perfectly circular, there is a moment when the Moon is as close as possible to the Earth (lunar perigee) at 221,500 miles, and another moment when it is as far away as possible (lunar apogee) at 252,700 miles.

While the distance between the Moon and Earth is an important factor to consider when planning a spacecraft’s trajectory, other considerations come into play regarding the duration of the flight to the Moon.

Related reading : How Far Away is The Moon From Earth Right Now?

The duration of a journey to the Moon varies according to the following factors:

• The chosen itinerary;
• The selected type of propulsion system ;
• The presence or the absence of crew members aboard the spacecraft;
• Whether the spacecraft is scheduled to land on the surface, orbit around the Moon, or just fly by the Moon while heading towards a more distant target.

For example, if the space probe “New Horizons” was travelling at its maximum speed of 36,400 mph while the Moon is at perigee (221,500 miles), the probe would reach the Moon in only 6 hours and 15 minutes! If the Moon was at apogee (252,700 miles), the space probe would take about 6 hours and 50 minutes to pass by the Moon.

How long does it take to fly a manned spacecraft to the moon?

The most popular lunar mission is undoubtedly Apollo 11, during which the astronauts Neil Amstrong, Buzz Aldrin and Michael Collins travelled to the Moon for the first time. After blasting off from the Kennedy Space Center on July 16, 1969, the astronauts landed on the lunar surface on July 20, 1969, and the journey took 75 hours and 49 minutes. 

To date, the Apollo 8 mission still holds the record for the shortest travel time ever achieved by a spacecraft carrying astronauts on board (69 hours et 8 minutes). In total, NASA conducted 6 lunar landings during the Apollo program.

Although other countries have conducted orbital placements as well as landings of unmanned spacecraft, the United States remains to this day the only country to have successfully landed astronauts on the Lunar surface.

As you can see in the table below, the time taken to reach the Moon is different for each Apollo mission. There are several explanations for this:

• The purpose of some missions was only to orbit the Moon rather than land on it.
• NASA was constantly researching and testing for the best possible trajectory.
• Some missions involved transporting very heavy equipment, such as the lunar rover.

The Apollo 12 mission arrived on the Moon after a voyage that took three and a half days.

How long does it take to send an unmanned spacecraft to the moon?

Even for unmanned space probes, there is no such thing as a consistent travel time… It all depends on whether the spacecraft is just passing by the Moon, whether it is intended to be placed into orbit or to land on the surface. New Horizons holds the record for the shortest trip to the Moon: 8 hours and 35 minutes! 

The record for the longest journey to the Moon is held by SMART-1, a space probe engineered by the European Space Agency: it took a full year to reach the Moon! Although SMART-1 is the slowest spacecraft to ever reach the Moon, it remains the most fuel-efficient spacecraft in history.

How long did it take Artemis 1 to reach the Moon?

Artemis 1 was launched on November 16 2022, at 6:47 am GMT (1:47 EST). This flight was the first in a series of missions planned by NASA as part of its Artemis program, which aims to land the first woman and next man on the moon by 2024. The launch vehicle used for the mission was the SLS (Space Launch System), carrying the Orion spacecraft into space.

After a relatively smooth journey, Orion officially entered lunar orbit on November 21, at 7:57 am ET (12:57 UTC). In total, Artemis took 5 days, 1 hour, and 10 minutes to travel from Earth to the Moon. It is not the quickest flight we’ve seen, but the main goals were:

• Test the flight systems
• Test the new technology that was developed for the mission
• Provide data on how the SLS performed, as well as insights into the health of Orion’s systems and overall performance.
• Prepare for crewed missions starting next year.

Related Article: How Much of Space Have We Explored So Far?

In summary, the time it takes to reach the Moon is about 3 days on average for manned spacecraft. On the other hand, for unmanned spacecraft, the travel time can vary considerably depending on the mission objectives. They usually reach their destination much faster.

I eagerly look forward to the launch of the next lunar mission scheduled for 2024.  Mankind will return to the lunar surface for the first time in 40 years! And this time, a woman will be part of the crew! How amazing!

Is it possible that 40 years of technological progress will significantly reduce the time it takes to reach the Moon? Perhaps the new private space companies, such as SpaceX, Virgin Galactic and Blue Origin, will beat all previous records? We’ll find out the answer in a few years…!

Written by Tom Urbain

I’ve been fascinated by space and astronomy from a very young age. When I’m not watching space-themed documentaries, movies or TV series, I spend most of my free time in my backyard admiring the planets and galaxies with my telescope.

Explore more space travel stories 🚀

This moon-related story is part of our collection of astronomy articles . If this piece sparked your interest, you’re sure to enjoy the fascinating insights offered in our subsequent articles.

The Duration of a Voyage to Mars: A Detailed Analysis

How long does it take to reach the Uranus?

Countdown to Saturn: The Travel Time Involved

Traveling to Jupiter: How Long is the Journey?

How Long Does it Take to Get to The Sun?

Advertisement

How Long Does It Take to Get to the Moon?

• Share Content on Facebook
• Share Content on LinkedIn
• Share Content on Flipboard
• Share Content on Reddit
• Share Content via Email

Boldly glowing in the night sky, the moon has long been an object of fascination. It's not just a pretty face in our solar system; it's a natural satellite that affects the tides , animal sleep cycles (including humans !) and hormones .

But how long does it take to get to the moon ? Humans have long been inspired to look up and reach beyond the atmosphere of our own planet — that's part of why President John F. Kennedy set his sights on NASA's mission objective to travel to the moon in the 1960s — so it's only natural to wonder how long the journey takes.

So far, American astronauts have made nine journeys to the moon — six of which landed on the lunar surface. NASA, other governments, and other private companies are now planning crewed missions back to the moon, which will give us even more data about how long it takes to make the trip.

The Moon's Distance: Not Just a Straight Line

Travel time to the moon, a flashback to apollo 11, what lies ahead: new missions and new hopes.

The moon doesn't just lazily hover around Earth in a perfectly circular path. The moon's orbit is, in fact, elliptical .

This causes the moon to be sometimes closer to Earth (a point known as perigee) and sometimes further (known as apogee). This is why you might have heard the term " supermoon " thrown around.

Taking advantage of lunar orbit mechanics, astrophysicists can plan lunar missions to coincide with those times when the moon's elliptical orbit is at its closest point to Earth.

Based on past missions, we know that it usually takes about three days for a manned spacecraft to reach the moon when the average distance from Earth to the moon is 240,000 miles (386,243 kilometers) . This translates to a spacecraft's speed of about 3,333 mph (5,364 kph).

Yet, the duration isn't always set in stone. Some uncrewed missions, in a bid to be more fuel efficient, might move a lot slower. For instance, China's Chang'e missions took around four to five days .

But, want to hear something astonishing? The 1959 Luna 1, launched by a powerful rocket, made its journey to the moon in just 36 hours , traveling at a speed of about 6,500 mph (10,500 kph). However, it failed to land on the moon's surface.

The Luna 2, which launched only a few months later, not only succeeded in becoming the first spacecraft to land on the moon, but it also made the trip in 34 hours. And let's not forget the 2006 New Horizons, which breezed past the moon in a mere eight and a half hours en route to Pluto, reaching speeds of up to 36,373 mph (58,536 kph).

The Apollo missions, headed by NASA from the Kennedy Space Center, were monumental in unraveling the mysteries of our lunar neighbor. The Apollo 11 mission showcases the wonders of orbital mechanics.

While it took Neil Armstrong, Buzz Aldrin and their team three days, three hours and 49 minutes to reach the moon and set foot on its surface, they returned to Earth in just two days, 22 hours and 56 minutes .

Why the time difference? As Armstrong and Aldrin were hopping around on the lunar surface, Earth and the moon grew slightly closer — an effect of that elliptical orbit we mentioned earlier. moon

With advancements in propulsion system and launch vehicle technologies, both governmental bodies and private enterprises are gearing up for future crewed missions to the moon. The European Space Agency, in collaboration with NASA's Orion spacecraft, aims to achieve newer milestones.

So, the next time you look up and see that silvery orb in the sky, just remember: A new chapter in our relationship with the moon is about to unfold with another crewed mission to its surface likely on the way.

This article was updated in conjunction with AI technology, then fact-checked and edited by a HowStuffWorks editor.

Frequently Asked Questions

What's the average distance from earth to the moon, i've heard of a "distant retrograde orbit." what is it, how long does it take to travel to the moon.

Please copy/paste the following text to properly cite this HowStuffWorks.com article:

• How Long Does it Take To Get to the Moon?

For us to fully grasp how long it takes to get to the Moon, it is vital to understand the distance between the Moon and the Earth. The average distance between the Moon and the Earth is 238,857 miles. The figures give the average distance because different variables make the distance between the Earth and the Moon to differ from one phase to another, hence affecting how long it takes to get to the Moon. The Moon naturally orbits the Earth in an elliptical path, because of this, sometimes Moon is closer or farther away from Earth, which in turn greatly affects how long it may take to get to the Moon. Different countries have organized missions and traveled to the Moon and the time taken for all the missions have varied considerably.

Unmanned Missions

These are endeavors to the Moon without the physical presence of people onboard to control the movements of the spacecraft. One of the slowest yet advanced missions to the Moon was by the ESA’s SMART-1 which took the longest time ever recorded of one year, one month and two weeks using an ion-propelled engine. The second unmanned mission was the Chang’e-1 which took five days. Chang’e-2 followed on October 1st, 2010 taking four days and 16 hours before arriving in lunar orbit. The next mission launch took place at the end of 2013 becoming the fastest Change mission arriving in the lunar orbit after only four days and 12 hours and 23 minutes.

Manned Missions

With the presence of people onboard, manned missions have been taking a relatively short time to reach the Moon from the Earth's surface. The Apollo mission is the only Moon mission that was manned with renowned astronauts being the first beings to ever set foot on the lunar surface. The Apollo 11 mission took 51 hours and 49 minutes to arrive on the lunar surface back on July 19th, 1969, hence becoming the fastest spacecraft mission to the Moon that had astronauts who then took 1,376 minutes to return.

Fastest Recorded Missions to Date

NASA’s New Horizons Pluto mission was the fastest ever mission that went past the Moon. With a speedy launch that utilized the advanced technological systems, it took the New Horizon 515 minutes to arrive on the lunar surface before venturing on to Pluto and the Kuiper Belt. A mission was in 2014 undertaken using a device called ‘Orion Capsule.' It managed to reach different orbits of the Earth and return in 270 minutes breaking significant records. Through calculations, this showed that the Orion mission could reach the lunar in approximately 12 hours after covering an average distance of 238,857 miles. As plans are underway for the creation of space tourism in future, taking into consideration how long it will take to reach the Moon is vital and the type of technologies that will be utilized to make the journey and experience enjoyable and safe.

• World Facts

More in World Facts

The Largest Countries In Asia By Area

The World's Oldest Civilizations

Is England Part of Europe?

Olympic Games History

Southeast Asian Countries

How Many Countries Are There In Oceania?

Is Australia A Country Or A Continent?

Is Turkey In Europe Or Asia?

• For the best experience possible, please upgrade your browser. Upgrade now.
• Javascript must be enabled to use Cool Cosmos. Learn how.

• NGC 1097 (Spitzer)
• Helix (Spitzer)
• Flame Nebula (WISE)
• Galactic Center (2MASS)
• Cool Andromeda (Herschel)

• Why does the Moon follow me when I move?
• How fast does the Moon travel around Earth?
• How long is a day on the Moon?

How long does it take to travel to the Moon?

• What is a blue moon?
• What causes a ring around the Moon?
• How much would I weigh on the Moon?
• How does the Moon shine?
• How many astronauts have walked on the Moon?
• What is the temperature on the Moon?
• How small is the Moon compared to Earth?
• How far away is the Moon?

It takes about 3 days for a spacecraft to reach the Moon. During that time a spacecraft travels at least 240,000 miles (386,400 kilometers) which is the distance between Earth and the Moon. The specific distance depends on the specific path chosen.

April 19, 2024

How to See the Lunar Far Side Right Here on Earth

Perspective and subtle motion allows us to peek over the moon’s edge and into its far side

By Phil Plait

The moon's appearance changes throughout the month—not only via its well-known cycling through phases, but also in a subtle wobble called libration that brings a small fraction of its far side into view from Earth.

NASA's Scientific Visualization Studio

In my most recent article for Scientific American , I may have lied to you.

In my defense, I didn’t so much lie as maybe oversimplify a tiny bit. I wrote that because of the effects of the tidal force from Earth, “the moon always shows one face to Earth.” That turns out to be only mostly true. We actually see more like 59 percent of the moon’s total surface from Earth , not strictly half, as you might expect. What I didn’t get into last week was the slow rocking and nodding motion our satellite makes with respect to Earth, which together we call libration. (That shouldn’t be confused with libations, which can cause similar motions in people.)

As I explained in that article, the moon spins once for every one time it orbits Earth. This is the outcome of the inexorable force of our planet’s gravity, which has slowed the moon’s spin and moved our satellite farther and farther from Earth until both angular rates matched. (We sometimes call this spin-orbit resonance, if you want to get technical.)

On supporting science journalism

If you're enjoying this article, consider supporting our award-winning journalism by subscribing . By purchasing a subscription you are helping to ensure the future of impactful stories about the discoveries and ideas shaping our world today.

Some people have a misconception that the moon doesn’t spin at all, but this is easily debunked: Take a spherical object such as an orange and place it on a table—this will be our model moon—and put some small object near it to represent Earth. Now move the orange around the other object. If you don’t spin the orange, you’ll find that someone on the ersatz Earth will see the entire surface of the orange over the course of one orbit. You have to carefully spin the orange once per revolution to ensure only one side is seen, thus proving that the moon does indeed spin and that this rotation takes the same amount of time as its orbital period.

The overall effect is that the moon is apparently split into two halves: the hemisphere that always faces Earth, which we call the near side, and the half that always points away, known as the far side. Another misconception is that the far side is literally the dark side, but the sun shines for half the time on the lunar far side, giving it two weeks of light and two of darkness , just as on the near side. I’m willing to give some metaphorical ground here because “dark” can mean unknown or unexplored; most of the moon’s far side is forever hidden from Earth, so the metaphor is apt. It wasn’t until the former Soviet Union sent the spacecraft Luna 3 around the moon in 1959 that the first images of the far side were ever seen by human eyes.

Libration is the reason this near- and far-side dichotomy isn’t quite so clear-cut. The phenomenon chiefly arises because the moon’s orbit isn’t a perfect circle but is instead quite elliptical (oval-shaped). Perigee, the closest point in the moon’s orbit to Earth, is about 356,000 kilometers distant, while apogee, its farthest point, is 407,000 km, a difference of roughly 13 percent. This means that from Earth, the moon can appear about 13 percent larger at perigee than apogee—but this also has orbital implications as well.

The speed at which, say, a moon orbits a planet depends on its distance from that planet. The farther out it is, the slower it moves along its trajectory, and conversely, the closer it is, the faster it moves. Because the moon is a huge, massive object, however, its spin doesn’t change at all; it always rotates at the same rate.

This means that when the moon is at apogee, its spin rate is a bit faster than its actual orbital rate, and vice versa at perigee. At apogee it rotates its western side a little bit more into our view, and at perigee we see a little bit more of its eastern side. The amount of extra lunar territory we see is about 7.5 degrees on each side.

So we can, in effect, peek over the edges of the moon’s near side—but only a little. An odd geometric effect makes this difficult to discern: on the moon’s edge, that extra rotation is mostly in a direction straight toward Earth, so the actual extra surface we see is hugely foreshortened and difficult to spot. The effect is greatest for landmarks near the meridian, the moon’s central line that divides east from west. There we see features rock back and forth by 15 degrees, which is quite easy to spot in photographs. When I was in high school, I shot a lot of photographs of the moon using my telescope and camera, and I remember seeing Mare Crisium , a dark impact feature near the moon’s eastern limb, clearly closer to the moon’s edge in one shot than the other. I had discovered libration!

And I found it only 330 years after astronomer Johannes Hevelius first explained it . I will accept partial credit.

This effect is called longitudinal libration, the libration seen east to west. But there’s also latitudinal libration north to south as well. This is because the moon’s orbit is not directly above Earth’s equator but is instead tilted by about five degrees. (The technical term for this is inclination.) When the moon is at the northernmost point in its orbit, we can see a little bit more surface past its south pole, and at its southernmost orbital point we can see farther into the far side at the north.

Together this means we can see 59 percent more moon than if the orbit were perfectly circular and aligned with Earth’s equator. Over the course of the monthlong lunar orbit, the moon appears to wobble east to west and nod north to south. This effect can be seen quite clearly in a video NASA puts out every year showing the moon’s physical motion and phase; the resulting animation is quite mesmerizing .

I’ve known about libration a long time, but it can still surprise me. I’ve always heard that from the moon, spin-orbit resonance means Earth never moves in the sky, as if nailed to a single spot. But libration means that can’t be true: the effect, in fact, makes Earth move in the moon’s sky up to 15 degrees! That would be very noticeable if you were at the extreme eastern or western moon edge of the moon; you could actually see Earth slowly rise and sink back down below the horizon over the course of a few hours every month. That wouldn’t be a bad place to set up a tourist spot. How much would you pay for a cozy spot from which to watch earthrise?

In astronomy—in everything —we take mental shortcuts, such as saying we only see half of the moon, to simplify situations. In general these are fine; they help us grasp what can be complex situations. But we need to be careful not to let these be over simplifications because there can be very cool science, and poetic beauty, in discovering the details.

NASA is giving the moon its own time zone. Why the clock is ticking.

It’s going to start getting crowded on the moon, and we’ll soon need a precise lunar timekeeping system, a shared clock , to coordinate missions and prevent disasters.

Time moves a bit faster on the moon than on Earth because the moon's mass is smaller than that of Earth and its gravity is weaker. That means the moon is going to get its own time zone .

NASA has been asked to establish a unified standard time for the moon and other celestial bodies by the end of 2026. That request came from the White House – specifically the Office of Science and Technology Policy – on April 2.

"The same clock that we have on Earth would move at a different rate on the moon ," said Kevin Coggins, NASA's space communications and navigation chief, in an interview with Reuters.

The difference is slight: 58.7 microseconds per Earth day. (A microsecond is one-millionth of a second.) Microseconds are often used as measurements in electronics, computing and telecommunication applications.

On Earth, Coordinated Universal Time, or UTC , is the standard used to set all time zones around the world. Eastern Time is four hours behind UTC.

The new lunar time zone will be known as Coordinated Lunar Time, or LTC . It's not yet determined whether the moon will have one or multiple time zones.

Why do we need precise time on the moon?

That 58.7 microseconds may not sound like much to worry about. An eye blink, for example, takes 0.1 to 0.4 seconds , or 100,000 to 400,000 microseconds.

But the time discrepancy becomes crucial in space missions, which require perfect precision for communication, tracking and navigation.

Unable to view our graphics? Click here to see them.  

LTC is also needed for secure data transfers between spacecraft and for matched communication among Earth, lunar satellites, bases and astronauts, Reuters reported.

And because future missions will be multinational, all participants will need to be synchronized.

Nations have been using their own standard time in space missions. NASA, for example, used Mission Elapsed Time, or the amount of time from the moment of liftoff, to coordinate space missions.

Where will Coordinated Lunar Time be used?

LTC will be used in operations in cislunar space , the region around the Earth that extends to the moon and past its orbit. It includes:

• The lunar surface.
• Lunar orbits.
• Earth-moon Lagrange points.

Lagrange points are gravity balanced positions in space between two bodies – the Earth and moon, in this example – in which objects such as spacecraft can stay in position. Lagrange points are easy to reach, and many spacecraft use them to perform observations , Space.com says.

Will the moon's time system be similar to that of Earth?

It could be. Earth's UTC uses a group of 450 highly precise atomic clocks in 85 time laboratories around the world. The Office of Science and Technology Policy directive suggests "an ensemble of clocks" on the moon could be used to set up the moon's LTC.

The White House directive also says LTC must have:

• Traceability or a calculated connection to Earth's Coordinated Universal Time.
• Specificity and accuracy to measure very short spans of time, necessary for precise scientific study and spacecraft landings.
• Self-sufficiency , in case connection with Earth is lost.
• Scalability , so other celestial objects or space environments could use it.

NASA will work with the departments of Commerce, Defense, State and Transportation to create and implement the lunar time zone.

NASA also will need to consult the 36 nations that have signed the Artemis Accords , an agreement that spells out countries' activities in space and on the moon.

China and Russia, the two main U.S. rivals in space, have not signed the agreement.

SOURCE USA TODAY Network reporting and research; NASA; Office of Science and Technology Policy; European Space Agency; space.com ; itu.int; Florida Today; Center for Strategic and International Studies

NASA’s Deep Space Optical Comm Demo Sends, Receives First Data

NASA’s Psyche spacecraft is shown in a clean room at the Astrotech Space Operations facility near the agency’s Kennedy Space Center in Florida on Dec. 8, 2022. DSOC’s gold-capped flight laser transceiver can be seen, near center, attached to the spacecraft.

DSOC, an experiment that could transform how spacecraft communicate, has achieved ‘first light,’ sending data via laser to and from far beyond the Moon for the first time.

NASA’s Deep Space Optical Communications ( DSOC ) experiment has beamed a near-infrared laser encoded with test data from nearly 10 million miles (16 million kilometers) away – about 40 times farther than the Moon is from Earth – to the Hale Telescope at Caltech’s Palomar Observatory in San Diego County, California. This is the farthest-ever demonstration of optical communications.

Riding aboard the recently launched Psyche spacecraft, DSOC is configured to send high-bandwidth test data to Earth during its two-year technology demonstration as Psyche travels to the main asteroid belt between Mars and Jupiter. NASA’s Jet Propulsion Laboratory in Southern California manages both DSOC and Psyche.

The tech demo achieved “first light” in the early hours of Nov. 14 after its flight laser transceiver – a cutting-edge instrument aboard Psyche capable of sending and receiving near-infrared signals – locked onto a powerful uplink laser beacon transmitted from the Optical Communications Telescope Laboratory at JPL’s Table Mountain Facility near Wrightwood, California. The uplink beacon helped the transceiver aim its downlink laser back to Palomar (which is 100 miles, or 130 kilometers, south of Table Mountain) while automated systems on the transceiver and ground stations fine-tuned its pointing.

Learn more about how DSOC will be used to test high-bandwidth data transmission beyond the Moon for the first time – and how it could transform deep space exploration.

“Achieving first light is one of many critical DSOC milestones in the coming months, paving the way toward higher-data-rate communications capable of sending scientific information, high-definition imagery, and streaming video in support of humanity’s next giant leap: sending humans to Mars ,” said Trudy Kortes, director of Technology Demonstrations for the Space Technology Mission Directorate at NASA Headquarters in Washington.

Test data also was sent simultaneously via the uplink and downlink lasers, a procedure known as “closing the link” that is a primary objective for the experiment. While the technology demonstration isn’t transmitting Psyche mission data, it works closely with the Psyche mission-support team to ensure DSOC operations don’t interfere with those of the spacecraft.

“Tuesday morning’s test was the first to fully incorporate the ground assets and flight transceiver, requiring the DSOC and Psyche operations teams to work in tandem,” said Meera Srinivasan, operations lead for DSOC at JPL. “It was a formidable challenge, and we have a lot more work to do, but for a short time, we were able to transmit, receive, and decode some data.”

Before this achievement, the project needed to check the boxes on several other milestones, from removing the protective cover for the flight laser transceiver to powering up the instrument. Meanwhile, the Psyche spacecraft is carrying out its own checkouts, including powering up its propulsion systems and testing instruments that will be used to study the asteroid Psyche when it arrives there in 2028.

First Light and First Bits

With successful first light, the DSOC team will now work on refining the systems that control the pointing of the downlink laser aboard the transceiver. Once achieved, the project can begin its demonstration of maintaining high-bandwidth data transmission from the transceiver to Palomar at various distances from Earth. This data takes the form of bits (the smallest units of data a computer can process) encoded in the laser’s photons – quantum particles of light. After a special superconducting high-efficiency detector array detects the photons, new signal-processing techniques are used to extract the data from the single photons that arrive at the Hale Telescope.

Get the Latest JPL News

The DSOC experiment aims to demonstrate data transmission rates 10 to 100 times greater than the state-of-the-art radio frequency systems used by spacecraft today. Both radio and near-infrared laser communications utilize electromagnetic waves to transmit data, but near-infrared light packs the data into significantly tighter waves, enabling ground stations to receive more data. This will help future human and robotic exploration missions and support higher-resolution science instruments.

The flight laser transceiver operations team for NASA’s Deep Space Optical Communications (DSOC) technology demonstration works in the Psyche mission support area at JPL in the early hours of Nov. 14, when the project achieved “first light.”

DSOC ground laser transmitter operators pose for a photo at the Optical Communications Telescope Laboratory at JPL’s Table Mountain Facility near Wrightwood, California, shortly after the technology demonstration achieved “first light” on Nov. 14.

“Optical communication is a boon for scientists and researchers who always want more from their space missions, and will enable human exploration of deep space,” said Dr. Jason Mitchell, director of the Advanced Communications and Navigation Technologies Division within NASA’s Space Communications and Navigation (SCaN) program. “More data means more discoveries.”

While optical communication has been demonstrated in low Earth orbit and out to the Moon , DSOC is the first test in deep space. Like using a laser pointer to track a moving dime from a mile away, aiming a laser beam over millions of miles requires extremely precise “pointing.”

The demonstration also needs to compensate for the time it takes for light to travel from the spacecraft to Earth over vast distances: At Psyche’s farthest distance from our planet, DSOC’s near-infrared photons will take about 20 minutes to travel back (they took about 50 seconds to travel from Psyche to Earth during the Nov. 14 test). In that time, both spacecraft and planet will have moved, so the uplink and downlink lasers need to adjust for the change in location.

“Achieving first light is a tremendous achievement. The ground systems successfully detected the deep space laser photons from DSOC’s flight transceiver aboard Psyche,” said Abi Biswas, project technologist for DSOC at JPL. “And we were also able to send some data, meaning we were able to exchange ‘bits of light’ from and to deep space.”

More About the Mission

DSOC is the latest in a series of optical communication demonstrations funded by the Technology Demonstration Missions ( TDM ) program within NASA’s Space Technology Mission Directorate and SCaN program within the agency’s Space Operations Mission Directorate.

The Psyche mission is led by Arizona State University. JPL is responsible for the mission’s overall management, system engineering, integration and test, and mission operations. Psyche is the 14th mission selected as part of NASA’s Discovery Program under the Science Mission Directorate, managed by the agency’s Marshall Space Flight Center in Huntsville, Alabama. NASA’s Launch Services Program, based at the agency’s Kennedy Space Center, managed the launch service. Maxar Technologies in Palo Alto, California, provided the high-power solar electric propulsion spacecraft chassis.

For more information about DSOC, visit:

https://www.jpl.nasa.gov/missions/dsoc

News Media Contact

Ian J. O’Neill

Jet Propulsion Laboratory, Pasadena, Calif.

818-354-2649

[email protected]

Why does NASA want a time zone on the moon?

NASA has been tasked with determining a standard time zone for the moon, but it’s more complicated than you might think.

The United States government has tasked its space agency, NASA, with establishing a standard time zone for the moon, which will be known as Coordinated Lunar Time (CLT).

In a memo issued on April 2, the US Office of Science and Technology Policy (OSTP) stated: “Federal agencies will develop celestial time standardisation with an initial focus on the lunar surface and missions operating in Cislunar space [the area within the moon’s orbit], with sufficient traceability to support missions to other celestial bodies.” “Traceability” means that CLT can be kept in sync with time zones on Earth.

Keep reading

Russia’s angara a5 rocket blasts off into space after two aborted launches, photos: mexico, us, canada mesmerised by rare total solar eclipse, moment total solar eclipse occurs in north america, millions across north america await total solar eclipse.

The memo outlined the following features for the new CLT:

• Traceability to Coordinated Universal Time (UTC – a compromise for both English and French speakers);
• Accuracy sufficient to support precision navigation and science;
• Resilience to loss of contact with Earth (meaning CLT can operate independently of Earth); and
• Scalability to space environments beyond the Earth-moon system (meaning other space stations beyond the moon would be able to use CLT as well).

Don’t expect your favourite time zone and calendar apps to have CLT as an option yet; NASA has until the end of 2026 to establish CLT.

Why does the moon need its own time zone?

In layman’s terms, we need a reliable “lunar time” earth-syncing system because lower gravity on the moon causes time to move slightly faster there than on Earth – by just 58.7 microseconds (there are 1 million microseconds in a single second) faster within every 24 Earth hours.

This is not science fiction, even though it is a main feature of Hollywood blockbusters such as Interstellar. Known as “gravitational time dilation”, the passage of time is impacted by gravity.

Although small, these time discrepancies can cause issues with syncing satellites and space stations in lunar orbit.

An unnamed OSTP official told Reuters: “Imagine if the world wasn’t syncing their clocks to the same time – how disruptive that might be and how challenging everyday things become.”

How would we tell time on the moon?

Earth uses UTC or Coordinated Universal Time to sync time zones around the world. UTC is determined by more than 400 atomic clocks that are maintained in national “time laboratories” in about 30 countries around the world. An atomic clock uses the vibrations of atoms to achieve extreme precision in keeping track of time.

Similar atomic clocks would be placed on the moon to get an accurate time reading.

Known as Positioning, Navigation and Timing (PNT), this precision-timing system allows communications systems to measure and keep accurate timing. The Ordnance Survey, the British organisation that has been producing maps since 1791, explains that PNT has three core elements:

• Positioning – the ability to precisely determine one’s location and orientation, predominantly two dimensionally on a printed map, although three-dimensional orientation can be determined when required.
• Navigation – the ability to determine both the current and desired position (either relative or absolute), and apply corrections to course, orientation and speed to reach a desired position from anywhere in the world, from sub-surface (below the Earth’s surface) to surface, and from surface to space.
• Timing – the ability to maintain accurate and precise time from anywhere in the world.

Does NASA have plans for time zones in other parts of outer space?

Although there has been no mention of time zones on other planets, in 2019, NASA’s Deep Space Atomic Clock (DSAC) mission tested an atomic clock to improve spacecraft navigation in deep space. The DSAC mission, on SpaceX’s Falcon Heavy rocket, was launched on June 22, 2019. The rocket tested the atomic clock in Earth’s orbit for one year.

Typically, spacecraft keep accurate time by bouncing signals to atomic clocks on Earth and then the signal is sent back to the spacecraft. In this mission, the on-board atomic clock was tested to keep precise time without relying on this two-way communication between the spacecraft and the atomic clocks on Earth. The accuracy of the timing is tied to getting accurate positioning, while helping the spacecraft reach the intended location in space successfully.

As NASA’s Jet Propulsion Laboratory, the centre for robotic exploration of the solar system, explains: “A two-way system that sends a signal from Earth to a spacecraft, back to Earth and then to the spacecraft again would take an average of 40 minutes. Imagine if the GPS on your phone took 40 minutes to calculate your position. You might miss your turn or be several exits down the highway before it caught up with you. If humans travel to the Red Planet [Mars], it would be better if the system was one-way, allowing the explorers to immediately determine their current position rather than waiting for that information to come back from Earth.”

The mission successfully ended in 2021, with the on-board atomic clock maintaining the correct timing and navigational positioning.

NASA Is Giving the Moon Its Own Standard Time Zone — Why?

A memo from Washington directs NASA to establish a standard time zone for the moon.

According to the  memo  issued on April 2, NASA has until late 2026 to set a "Coordinated Lunar Time (LTC)," a deadline that coincides the Artemis III, which will be mankind's first mission on course to land at the lunar South Pole.

Taking into account the difference in gravity between Earth and the moon, which causes lunar time to move 58.7 microseconds faster every day, this new standardization is set to make space travel more precise.

Why Is NASA Establishing a Standard Time Zone for the Moon?

Space travel is a precise endeavor. As experts at  NASA  put it: "Without proper and accurate measurements, none of NASA's missions could be successfully accomplished."

This new directive from the US Office of Science and Technology (OSTP) emphasizes that the new CLT will have the following features:

Traceability to Coordinated Universal Time (UTC)

The promising Artemis mission is not solely run by the Americans. According to the  Artemis Accords , the space program currently has 36 countries signed as partners, with Uruguay being the most recent signee.

Being in sync with the Coordinated Universal Time means the US and all of its partners from around the world now have a distinct and uniform reference time to keep track of the events of the Artemis mission. 

Accuracy sufficient to support precision navigation and science

CLT, taking into consideration the slight  time dilation  caused by the difference in gravity and removing the need to rely on a signal from Earth to reach a spacecraft and vice versa, can help spacecraft achieve more accurate timing and positioning. 

Read Also:  NASA Solves Mystery of Space Debris That Crashed into Florida Home-Origins Revealed!

(Photo : LAURENT EMMANUEL/AFP via Getty Images)

Topshot - a photo taken on may 13, 2019 shows a view of the moon in cannes, southern france. - the moon is steadily shrinking, causing wrinkling on its surface and quakes, according to an analysis of imagery captured by nasa's lunar reconnaissance orbiter (lro) published monday may 13, 2019., resilience to loss of contact with earth).

Instruments and people losing contact with Earth can operate independently thanks to CLT.

Scalability to space environments beyond the Earth-moon system.

NASA's Jet Propulsion Laboratory explains (via Aljazeera): "A two-way system that sends a signal from Earth to a spacecraft, back to Earth and then to the spacecraft again would take an average of 40 minutes. Imagine if the GPS on your phone took 40 minutes to calculate your position. You might miss your turn or be several exits down the highway before it caught up with you."

If humans travel to the Red Planet [Mars], it would be better if the system was one-way, allowing the explorers to immediately determine their current position rather than waiting for that information to come back from Earth," JPL adds.

As stated in the memo, "NASA will also include consideration of Coordinated Lunar Time (LTC), as described in this memorandum, as part of its annual Moon-to-Mars Architecture Concept Review cycle no later than December 31, 2024." 

Related Article:  NASA Roman Space Telescope's Eyes Are One Step Closer in Peering Through the Galaxy's Mysteries

LA Metro Buses to Soon Use AI-Powered Cameras to Battle Illegal Parking

President biden hails economic revival with micron technology investment in upstate new york, microsoft q3 2024: xbox, surface revenue down; office, cloud bring biggest business, high school gym teacher arrested for using ai voice cloning to frame principal.