Special Relativity - Twins sending light pulses

jinksys

1. The problem statement, all variables and given/known data
Twin A is on earth. Twin B is aboard a spacecraft that leaves earth toward a start 12LY away at 0.6c.
Both twins send light pulses every year according to their clocks.
How many pulses does A send and receive and how many does send and receive if B makes a round trip to the star and back?

2. Relevant equations



3. The attempt at a solution

For twin A I need to know how long it takes B to complete the round trip.

time = d/r = 24LY/0.6c = 40 years

Twin a would send 39 pulses since B would arrive at year 40.

For twin B, the universe is moving past him at 0.6c so I need to compute the length of the trip according to his point of reference.

L = [tex]L_{0}[/tex][tex]\sqrt{1 - 0.6^2}[/tex] = 9.6LY

t = d/r = 18.6LY/0.6c = 32 years

Twin b would send 31 pulses since b would arrive at year 32.