How Does Special Relativity Affect Space Travel and Communication?

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Homework Statement

Suppose that we send a spaceship on a trip to Alpha Centauri, 4 light years away. The spaceship 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?

Homework Equations

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.

 

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does anyone have any ideas? I'm still really confused about this one. The only things that we've gone over so far are the basic Gallilean transformations and Lorentz transformations. But, i just don't see how either of them would help here. Once again, if anyone could offer any guidance or feedback I would really appreciate it.