Question

Twins who are 19.0 years of age leave the earth and travel to a distant planet 12.0 light-years away. Assume that the planet and earth are at rest with respect to each other. The twins depart at the same time on different spaceships. One twin travels at a speed of 0.912c, and the other twin travels at 0.445c.

(a) According to the theory of special relativity, what is the difference between their ages when they meet again at the earliest possible time?

A₂ - A₁ =

Answer 1

a) Twin A1 take a time T_A1 as viewed from earth, to reach the other planet

  

Given D=12 ly, V_A1=0.912c

Time dilation give the time T'_A1 that twin A1 sees passing:

Twin A2 take a time T_A2 as viewed from earth, to reach the other planet

Time dilation give the time T'_A2 that twin A2 sees passing:

Twin A1 aged 5.394+(24.14-13.15) = 16.38 y, when twin A2 joins A1 at distant planet. Twin A2 aged 24.14 y.

(b) A2-A1 = 24.14y - 16.38y = 7.76 y,

Twin A2 will be 7.76 y older.