Question

Twins Abby and Bill separate. Abby travels at a uniform speed (except the brief turn around perion) to a star 4 light years away and, upon returning, finds that she is 5 years younger than Bill. How fast was Abby traveling By how much has Bill aged during the period Abby was traveling? Answer in units of year

Answer 1

d = 4 light years, t = 5 years

The speed of Abby is v.

The vojage lasted for time Tb = 2d/v

from the point of view of Bill.

v = 2d/Tb

The vojage lasted for time Ta = Tb(1-v^2)^0.5 = Tb (1-(2d/Tb)^2)^0.5

from the point of view of Abby.

The difference in ages

ΔT =Tb - Ta = Tb((1-(2d/Tb)^2)^0.5

1- ΔT/Tb = (1-(2d/Tb)^2)^0.5

(Tb - ΔT)^2 = Tb^2 - (2d)^2

2ΔT*Tb = ΔT^2 +(2d)^2

Tb = ΔT/2 +(2d^2/ΔT)

Tb = (5/2) +(2*4^2/5)

Tb = 8.9 years