On his 30th birthday, a twin gets on a spaceship travelling at 4/5c which takes him to a distance star system. When he arrives he immediately turns around and comes home at the same speed. His twin sister stays behind on the Earth. Then first twin arrives home on his 48th birthday (by his own watch).

a) How old is his twin sister?

b) How far away is the star as measured in the Earth's frame?

c) What is the distance from the Earth to the star as seen from the rocket's reference frame?

d) Draw a spacetime diagram in the Earth's frame with the rocket launch at the origin. Show the path followed by the twin sister and the path followed by the twin brother?

e) The twin sister sends a radio message to her brother on her 35th birthday (as measured by her watch). Show the path of that signal on the spacetime diagram. How much time has passed by her watch when he receives the signal? How old is the twin brother (again measured by his own watch) when he receives it? What is the invariant length of the path of the signal on the spacetime diagram?