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. 

