The center of our Milky Way galaxy is about 23000 ly away a

The center of our Milky Way galaxy is about 23,000 ly away.

(a) To eight significant figures, at what constant speed parameter would you need to travel exactly 23,000 ly (measured in the Galaxy frame) in exactly 28 y (measured in your frame)?


(b) Measured in your frame and in light-years, what length of the Galaxy would pass by you during the trip?
ly

Solution

dt = d/v = dto/(sqrt(1-(v/c)^2)

d = 23000 ly = 23000 c y

dto = 28 y

23000c/v = 28/(sqrt(1-(v/c)^2))

v = 0.99c <<-----answer

L = lo/sqrt(1-(v/c)^2)

L = 23000*sqrt(1-0.99^2)

L = 3244.5 ly