1. Homework Statement
Suppose that we send a spaceship on a trip to Alpha Centauri, 4 light years away. The space ship travels at a constant speed of .5c, it stops at Alpha C. for 1 year and then it returns to the Earth at constant speed .5c.
a. Draw a spacetime Diagram with axes x,ct and plot the worldine of the spaceship.
b. suppose that 1 year after the departure of the spaceship we send a radio message from earth to the spaceship. Plot the worldline of the radio signal.
c. At what time does it reach the spaceship?

2. Homework Equations

3. The Attempt at a Solution
a.
ct
|\
| .\
| .. \
| ... |
| .. /
| ./
|/________________x
where the angle between the ct and x axis is given by

theta = arctan(.5)

b.)I drew a cone with an angle of 45 between the ct and x axis.
c.) this is what i'm confused about. I'm not sure if I have to take relativity into account since c is the same in all reference frames. So, my answer is 1 year after the message is sent.

Can anyone please tell me if any of this is right? Any help will be greatly appreciated.