## The Cosmic Travel Planner

### Christian Bär, July 14, 2018

This cosmic travel planner allows you to compute your travel time to destinations anywhere in the universe.
The scenario is the following:
You are flying a space ship which travels with constant acceleration.
The value of the acceleration is precisely that of acceleration due to gravity on earth.
This does not only make your space ship faster but also simulates gravity on board thus avoiding all problems that come with zero gravity in conventional space travel.

More precisely, the space ship accelerates during the first half of the trip and then decelerates during the second half, with the same absolute value of acceleration.
So maximum speed relative to the earth is achieved at half time.
At the end of the trip, when you arrive at your destination, the speed relative to the earth is again zero.

The travel planner computes the total time required for your journey and the maximal speed relative to the earth encountered during the trip.
It does so in two ways:
it first uses classical mechanics due to Newton ignoring all relativistic effects, and then uses Einstein's relativity theory.
In the latter case there are two values for the duration of the journey; the one experienced by the crew on board the space ship and the one experienced by those left on earth.
For short trips, e.g. those within our solar system, all values will be roughly the same.
Relativistic effects are negligible.
For trips to remote destinations however, crew time will be a lot shorter than earth time; classical Newtonian time will lie somewhere in between.
Hence the crew can reach destinations thousands of lightyears away within their lifetime.
They just should not expect to meet their friends again after returning to earth.

How do you use the cosmic travel planner?
Here is an example.
Suppose you want to travel to Dubhe, the second brightest star in the constellation of Ursa Major.
The distance from earth to this star is 38 parsec.
Choose parsec for the physical length unit and insert 38 in the distance field.
Choose the time and velocity units in which you want to obtain the results, e.g. year and speed of light (c).
Hit "Update".

Alternatively, you can choose one of the predefined destinations from the drop-down menu.
Then a reasonable choice of physical units will be made and the distance will be inserted automatically.

This page is based on the open-source computer algebra system SageMath.
The computations are carried out on the sage cell server.