Understanding Time Dilation: How Do Clocks Differ in Space Travel?

[DespicableMe]

Homework Statement

At 3 pm a rocketship passes extremely close to the Earth with a speed of 0.800 c. Observers on the ship and on Earth agree that it is 3 pm. At 3:40 pm, as indicated on the rocketship clock, the ship passes a small space station that is fixed relative to the Earth and whose clocks read Earth time.

a) What time is it on the station clocks when the ship passes?
b) How far from Earth (in Earth coordinates) is the station?
c) At 3:40 pm rocketship time, the ship reports by radio back to earth.
When (by Earth time) does the Earth receive the signal?

I'm confused on time dilation. I've read the section several times but I'm still a little puzzled. At the concept and at this problem.

I'm not sure where to start.

 

[tiny-tim]

Welcome to PF!

Hi DespicableMe! Welcome to PF!

Call the rocketship's measurements x and t, and the Earth measurements x' and t'.

You know that, for the rocketship, both the Earth and the space station are moving with speed v = 0.800c, and that they go past the rocketship at positions x = 0 and t = 0 and 240 (I'm measuring t in seconds, starting at 3:00pm ).

(And the answers you need are all in x' and t')

Carry on from there. ​