Question

A spaceship travels at a constant speed from earth to a planet orbiting another star. When the spacecraft arrives, 11 years have elapsed on earth, and 9.7 years have elapsed on board the ship. How far away (in meters) is the planet, according to observers on earth?

Answer 1

T = t*gamma where T = time past on earth, and t = time past on the ship. So

gamma = 11/9.7 = 1.13402

Now the gamma factor is 1.13402, and the gamma factor = 1/sqr(1-v^2/c^2)

Rearrange this and you get v = 0.471*c where c is the speed of light

To get a velocity in m/s remember that c = 3*10^8 m/s and you get

v = 1.414*10^8 m/s

Since you want the distance, simply multiply the velocity by the number of seconds in 11 years

11 * 365 * 24 * 60 * 60 = 3468496000 seconds

the required distance = 1.414*10^8 m/s * 3468496000 s = 4.905*10^16 meters