Question

Astronaut rachel leaves earth in a spaceship at a speed of 0.960c relative to an observer on earth. rachel's destination is a star system 14.4 light-years away (one light-year is the distance light travels in one year). according to rachel, how long does the trip take?

Answer 1

Utilizing Lorentz factor;

Lorentz factor = Sqrt (1-u^2/c^2), where u = initial velocity, c = speed of light

But, u/c = 0.960

Therefore,
Lorentz factor = Sqrt (1-0.960^2) = 0.28

For an observer,
t = (Distance to the star*Lorentz factor)/ (u/c) = (14.4*0.28)/0.96 = 4.2 years