An alien pilot of an intergalactic spaceship on a mission to

An alien pilot of an intergalactic spaceship, on a mission to measure the sizes of galaxies, is traveling at 0.85c relative to the galaxy shown below. She determines the length of the short axis of the galaxy to be 3.7 × 1017 km. What would the length of this axis be as measured by an observer living on a planet within the galaxy?

Solution

l = l0*sqrt(1-v^2/c^2)

v^2/c^2 = 0.85^2c^2/c^2 = 0.85

l = 3.7*10^17*sqrt(1-0.85)

l = 1.433*10^17 km