Relativistic Einstein's Star Ship Calculator

distance: Light Years Astronomical Units
acceleration: Earth G's Meters/sec/sec
time on earth: Years Days
time on board: Years Days
maximum speed: fraction of c

maximum kinetic energy: (y - 1)·c mega joules per kilogram


The star ship accelerates continuously from the origin to the midpoint of the mission.
At the midpoint, the ship turns its thrusters to face the destination.
The ship decelerates continuously from the midpoint to the destination.
The Relativistic Star Ship Calculator is a Java Script calculator that computes the times to reach distant points with a space vehicle that can accelerate continuously.
Such a vehicle can approach but never exceed the speed of light in vacuum,
The calculator computes travel times for this mission profile:
The observed elapsed time of the mission is computed for two cases:
for the astronauts in the star ship who are in the moving frame
for the clocks at the origin and destination which are in the rest frame
 The maximum velocity, of the star ship is reached at the midpoint of the mission.
The calculator shows this as the ratio of maximum velocity to the speed of light.
Some representative distances
Special Theory of Relativity.
Basically, an object in motion undergoes 3 relativistic changes:
An increase in mass
A contraction in the direction of travel (Lorentz Transformation)
A "slowing down" of time. (Time Dilation)
Velocities in ordinary life which to us might seem incredibly fast have only a
miniscule relativistic effect.
For example, orbital velocity (5 miles per second) produces a relativistic factor of change of only 1.000000000360219.
Traveling at 93,141.1985 miles per second (half the speed of light)
produces a factor of 1.1547005383792517.
Here the velocity is incredibly fast and yet the change is still quite small.
At .9 times the speed of light, the factor becomes 2.294157338705618.
Finally, the effects of relativity become significant.
What does this factor mean though?
If you were in a spaceship traveling at .9 times the speed of light:
 the ship's mass (and you) would increase by a factor of 2.294
the ship (and you) would contract in the direction of travel by 2.294,
meaning a 300 foot ship would shrink to 130.77 feet.
Perhaps the most interesting change is that 1 year to you would seem
to be 2.294 years for someone, back on Earth.