Not sure where to ask this. It's for an interdisciplinary honors seminar:
I believe the first part is a trick question, time dilation does not take noticeable effect until you are at subliminal speeds. So he would wait 50 years on Alderaan for 50 years to elapse on Earth from t=1 onward. The second part is more difficult: if Han has a ship that travels 1 c, it would take 65 years to travel from Alderaan to Earth.1. Han and Leia are on Alderaan, a planet orbiting Aldebaran, 65 light years from Earth. At t=0, Leia travels from Alderaan to Earth in a ship with velocity 65 light years per hour, and arrives at t=1. Assuming Alderaan and Earth are identical in every respect,
a) If Han also has a ship that also travels 65 light years per hour, how long must he wait on Alderaan before leaving such that 50 years pass on Earth?
b) If Han leaves Alderaan immediately and discovers 50 years have passed on Earth while he was traveling, how much has he aged, and how fast was he going?
1/65 = x/50
x = .76923
So Han would have to have a spaceship that is traveling .76923c, which would age him 50 years. But here's where the problem occurs. Time dilation would take effect at anything <1c with these distances, so less time would pass on Han's ship than on Earth. But that's as far as I know, I know my simple calculation is right, and I don't know how to model this problem properly. I've had some exposure to differential equations but I'm not equipped for anything like this!