Do you want to travel to another planet? Or perhaps even another star system?

Then you can use this calculator to work out how long it will take you, how much energy your spacecraft needs and what your maximum velocity will be. If you travel close to the speed of light, you can also see how much time it will take from your point of view and from the point of view of the people on earth. You can also see how the length of your spacecraft will shorten for observers watching it from earth, if only they had powerful enough telescopes.

This is the simplest way to use the space travel calculator:

Enter a distance to a planet or star. Don't know any? Then type
Pr and press the down arrow. The distance to Proxima Centauri appears. Select it and the distance will be filled in. Try other places in space.

Click Calculate. The calculator determines the remaining
unfilled values.

Click Run. Watch the space rocket travel from earth to your destination. Also watch the clocks of the observer and the traveler.

Known problems

The animation spacecraft is at a different scale to the distance between
the observer and destination. Even for the shortest space travel
distances, for example the earth to the moon, the spacecraft would
occupy less than a pixel. This problem will not be fixed.

As an object moves further into the distance it appears smaller to
an observer. This change in perspective distance is not represented in
the animation. The reduction in the spacecraft length from the
observer's framework at velocities approaching the speed of light is
an entirely different concept to perspective distance.

If you set the iterations on the animation to a low number,
e.g. less than 20, the animation's spaceship time will not be
calculated accurately if the observer and traveler times diverge
substantially.

The code is old and the user interface needs to be refreshed. (Also the PHP
component is overkill and was only used for learning purposes.) You're
encouraged to improve the code and place the travel calculator on your own
website; it's FLOSS.

A bug fix was made in June 2016. The calculation for the fuel needed for the
trip did not take into account conservation of momentum. These two webpages
helped me correct the error and I am grateful to the various people contributed
the notes that helped me fix this (Physics Stack Exchange users user2096078,
Qmechanic and udrv, Don Koks for the Relativistic Rocket, and John F who emailed
me) :

This is the distance from earth to your destination. Either enter a
value or search the database for a distance to a space object by typing
the first few letters of its name. All objects in the database matching
that start with the letters you have typed will appear. Select the one
you want. Distances are approximate because the planets' positions
change continuosly relative to the earth. If you leave distance blank,
it will be calculated --if you enter the observer time elapsed and the
traveler's maximum velocity-- using this equation:

$\frac{\mathit{cvt}}{c+\sqrt{({c}^{2}-{v}^{2})}}$

where
c = the speed of light,
v = maximum velocity,
t = time elapsed in observer timeframe.

where
s = distance,
v = maximum velocity and
t = time elapsed in observer timeframe

This is increasingly inaccurate as you approach the speed of light, so
for large distances, such as to the nearest stars, it is better to enter
the acceleration manually.

If a spacecraft accelerates constantly at 1g --or 9.8m/s-- the travelers
on board can experience earth-like gravity. Unfortunately interstellar
travel at this acceleration will likely never be achieved because of the
huge amount of energy required. It is not possible to travel to the
nearest stars at this acceleration if the fuel must be carried onboard
the spacecraft, no matter what kind of fuel is used.

This is the maximum velocity the spacecraft will reach, from the
perspective of an observer on earth. This occurs when the spacecraft is
half way to its destination. This is calculated using this
equation:

Note that if this field is blanked out it is not calculated.
This field must have a value if you want energy and
fuel mass to be calculated.

Also note that if the fuel mass is calculated to be more than the
mass of your spacecraft, then your trip cannot be done unless you
extract fuel from space. If your fuel mass is more than half the mass of
your spacecraft, you're probably on a one way trip, so take enough food,
books and episodes of Star Trek to last the rest of your life.

This is the amount of energy your spacecraft's payload will need to constantly
accelerate to half way to your destination and then decelerate at the
same rate until you reach your destination. This is calculated using
this equation:

The fuel conversion rate is the the efficiency with which your
spacecraft's fuel is converted into energy. At today's fuel
conversion rates there is no prospect of sending a spacecraft to another
star in a reasonable period of time. Advances in technologies such as
nuclear fusion are needed first.

The default fuel conversion rate of 0.008 is for hydrogen into helium
fusion. David Oesper explains that this rate assumes 100% of the fuel
goes into propelling the spacecraft, but there will be energy losses
which will require a greater amount of fuel than this.

If you leave this field blank but enter the fuel mass, it is calculated by
dividing the given fuel mass by what the fuel mass would be if it were perfectly
efficient (i.e. a conversion rate of 1.0).

This is the mass of the fuel needed to for your journey.
This is calculated using this equation:

$\frac{M}{m}=\frac{2\frac{v}{c}}{1-\frac{v}{c}}$

v = maximum velocity and
c = speed of light.

Source: The Relativistic Rocket and Physics Stack
Exchange. (Thanks to users user2096078,
Qmechanic and udrv. Also thanks to John F for informing me of a bug that has
now hopefully been corrected.)

This is the length of the spacecraft at the beginning of the journey.
Note that the spacecraft length always stays the same for the people in it.
This is calculated using this equation:

This is the length of the spacecraft from the observer on earth's
perspective. Of course spacecrafts are small, so it would be impossible
to see a spacecraft from earth on an interstellar voyage. This is
calculated using this equation:

$l={l}_{0}\sqrt{1-\frac{{v}^{2}}{{c}^{2}}}$

where
l_{0} = original length of spacecraft on earth,
v = maximum velocity of traveler and
c = speed of light.