Question

Two stars z and p, are exactly in the opposite directions from the Earth.

The distance to 'z' from earth is 80 light-years. The distance to 'p' is 90 light-years.

Zerah takes off in the direction of z, at a speed of 0.8 c, while Perez takes off in the direction of p at the speed 0.9c.

(distance between two stars in earth frame = 170c*y)

(time to each star in earth frame = 100 years, simultaneous events in earth's frame)

Answer these questions in the reference frame of Zerah (still moving at the same speed)

a) How long does it take for Zerah to reach z?

b) What is the time difference between his time of arrival to z, and Perez time of

arrival to p? Who arrives later?

c) How far apart is Perez from Zerah when he arrives at p?

d) What is Perez velocity? What is Zerah velocity?

Answer these questions in the reference frame of Perez spaceship (still moving at the same speed).

e) How long does it take for Zerah to reach z?

f) What is the time difference between Perez’s time of arrival at p, and Zerah’s time of

arrival at z? Who arrives later?

g) How far apart is Perez from Zerah when he arrives at p?

Answer 1

I have used the concept of special theory of relativity and used the necessary formulae regarding that. Thus, I found out the answers.