A spaceship travels at a constant speed from earth to a plan

A spaceship travels at a constant speed from earth to a planet orbiting another star. When the spacecraft arrives, 14 years have elapsed on earth, and 8.4 years have elapsed on board the ship. How far away (in meters) is the planet, according to observers on earth?

Solution

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

So, gamma = 14/8.4 = 1.67

gamma factor = 1/sqr(1-v^2/c^2)

v=.8c=2.4*10^8m/sec

Distance: Time*Velocity= 14*365*24*60*60*2.4*10^8m = 1.06*10^17m