A rocket is constructed on Earth with the following specifications: 96 m long, with a mass of 4.5 x 10^3 kg. a) On a trip to visit a nearby star...

Hello!

This question is about the special relativity theory. It states (and there are many experiments confirming it) that the speed of light in a vacuum is a constant, denoted `c,` regardless of the frame of reference. This gives some paradoxical results.

Denote the given speed of a rocket as `v.` Then the Lorentz factor `gamma = sqrt(1-(v^2)/(c^2))`  describes the changes in observed length, time and mass of a moving object. Namely, length is contracted, time is dilated and mass is increased with this factor. In numbers it is `sqrt(1-(0.68)^2) approx0.73` (dimensionless).

Therefore

a) the length will be `96*gamma approx 70.4 (m),`

b) the apparent mass will be `(4.5*10^3)/gamma approx6139 (kg),`

c) the dilated time is given to be `15` years, so the time for astronauts will be less by `gamma,` i.e. `15*gamma approx 11 (years).` Note that it is a simplification, because to return a rocket must change its velocity.