Space Lan

How do I find the speed of the spaceship relative to the Earth?

A spaceship flies from Earth to a distant star at a constant speed. Upon arrival, a clock on board the spaceship shows a total elapsed time of 8 years for the trip. An identical clock on the Earth shows that the total elapsed time for the trip was 10 years. What was the speed of the spaceship relative to the Earth?

Public Comments

1. Apparently, you're supposed to treat this as a problem in special relativity. The clocks start when the ship passes Earth with velocity v, relative to Earth; the clock stops when the ship passes the distant star. So clocks are slowed by the factor gamma = 1/0.8 = 1.25. gamma = 1/sqrt(1- (v/c)^2) = 1.25 sqrt(1- (v/c)^2) = .8 1- (v/c)^2 = .8^2 = .96 v/c = sqrt(1- .96 ) = sqrt(.04) = .2 v = .2c