# Space Travel Calculator

Created by Dominik Czernia, PhD and Purnima Singh, PhD
Reviewed by Bogna Szyk and Jack Bowater
Last updated: Dec 23, 2022

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 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 .

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 × 108 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 $T$ and equivalent time observed on Earth $t$ are related by the following formula:

$T = \gamma\, t$

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

$\gamma = \frac{1}{1 - \beta^2} = \frac{1}{\sqrt{1 - v^2/c^2}}$

where $\beta = v/c$.

For example, if $\gamma = 10$ ($v = 0.995c$), 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 (if you turn on the advanced mode), and the required fuel mass (see Intergalactic travel – fuel problem section for more information). The notation is:

• $a$ — Spaceship acceleration (by default $1\rm\, g$). We assume it is positive $a > 0$ (at least until halfway) and constant.
• $m$ — Spaceship mass. It is required to calculate kinetic energy (and fuel).
• $d$ — Distance to the destination. Note that you can select it from the list or type in any other distance to the desired object.
• $T$ — Time that passed in a spaceship, or, in other words, how much the crew has aged.
• $t$ — Time that passed in a resting frame of reference, e.g., on Earth.
• $v$ — Maximum velocity reached by the spaceship.
• $\rm KE$ — 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 in the destination list our closest celestial bodies, like the Moon or Mars, 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, $T$ equals $t$ for any speed. To calculate the distance covered at constant acceleration during a certain time, you can use the following classical formula:

$d = \frac{1}{2}at^2$

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

$v = at,$

and the corresponding kinetic energy:

${\rm KE} = \frac{1}{2}mv^2$

Newton's universe – arrive at 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:

$d = \frac{1}{4}at^2$

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

$v = \frac{1}{2}at,$

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 $l$ is the proper length observed in the rest frame and $L$ is the length observed by a crew in a spaceship, then:

$L = \frac{l}{\gamma}$

What does it mean? If a spaceship moves with the velocity of $v = 0.995c$, then $\gamma = 10$, 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 $v = 0.995c$, 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 , section §6.2. Hyperbolic motion. More accessible formulas are in the mathematical physicist John Baez's article :

• Time passed on Earth:
$\small\qquad \begin{split} t &= \frac{c}{a}\sh\!\left(\frac{aT}{c}\right)\\[1.5em] &= \sqrt{(d/c)^2 + 2d/a} \end{split}$
• Time passed in the spaceship:
$\small\qquad \begin{split} T &= \frac{c}{a}\sh^{-1}\! \left(\frac{at}{c}\right)\\[1.5em] &= \frac{c}{a}\ch^{-1}(ad/c^2 + 1) \end{split}$
• Distance:
$\small\qquad \begin{split} d &= \frac{c^2}{a}\left(\ch\! \left(\frac{aT}{c}\right)-1\right)\\[1.5em] &= \frac{c^2}{a} \left(\sqrt{1 + (at/c)^2} - 1 \right) \end{split}$
• Maximum velocity:
$\small\qquad \begin{split} v &= c \th\! \left(\frac{aT}{c} \right)\\[1.5em] &= \frac{at}{\sqrt{1 + (at/c)^2}} \end{split}$
• Relativistic kinetic energy remains the same:
$\small\qquad {\rm KE_{rel}} = mc^2(\gamma -1)$

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

• Time passed on Earth:
$\small\qquad \begin{split} t &= 2\frac{c}{a}\sh\!\left(\frac{aT}{2c}\right)\\[1.5em] &= \sqrt{(d/c)^2 + 4d/a} \end{split}$
• Time passed in the spaceship:
$\small\qquad \begin{split} T &= \frac{2c}{a}\sh^{-1}\! \left(\frac{at}{2c}\right)\\[1.5em] &= \frac{2c}{a}\ch^{-1}(ad/2c^2 + 1) \end{split}$
• Distance:
$\small\qquad \begin{split} d &= \frac{2c^2}{a}\left(\ch\! \left(\frac{aT}{2c}\right)-1\right)\\[1.5em] &= \frac{2c^2}{a} \left(\sqrt{1 + (at/2c)^2} - 1 \right) \end{split}$
• Maximum velocity:
$\small\qquad \begin{split} v &= c \th\! \left(\frac{aT}{2c} \right)\\[1.5em] &= \frac{at}{2\sqrt{1 + (at/2c)^2}} \end{split}$
• Relativistic kinetic energy remains the same:
$\small\qquad {\rm KE_{rel}} = mc^2(\gamma -1)$

## 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:

$M = m(e^{aT/c} - 1),$

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

$M = \frac{mv^2}{2c^2} + \frac{mv}{c}$

Remember that it assumes 100% efficiency! One of the promising future spaceships' power sources is the fusion of hydrogen into helium, which provides . 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 is a good candidate since it doesn't require any matter to work, only photons. Infinity and beyond is actually within our reach!

Dominik Czernia, PhD and Purnima Singh, PhD
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 🚀.
Prepare for travel 👩‍🚀👨‍🚀
Spaceship acceleration
g
Spaceship mass
US ton
Destination
Star or galaxy
Which star/galaxy?
Select...
Distance
ly
Travel details
Aim
Arrive at destination and stop
Calculations mode
Einstein's universe
5-4-3-2-1-0 booster ignition and liftoff! 🚀
Time passed in spaceship
yrs
Time passed on Earth
yrs
Required fuel mass
US ton
Maximum velocity
c
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