Question

The Milky Way has a diameter (proper length) of about 1.2×10⁵ light-years. According to an astronaut, how many years would it take to cross the Milky Way if the speed of the spacecraft is 0.890 c?

Answer 1

Lenght would be contracted byfactor in the frame of reference of astronaut,where

= v{1 - (v/c)2} = v{ 1 - (0.89c / c)2}

= 0.456

Distance travelled byspacecarft according to astronaut

d = d0* , d0 beingproper distance

d = 1.2* 10^5 * 0.456 = 5.472* 10^4 ly

d = 5.472* 10^4 ly * 9.46 *10^15 = 5.176 *10^20 m

Timetaken = distance (d) / speed(v)

t = 5.176* 10^20 / 0.89c = 5.176 * 10^20 /0.89 * 3.0 * 10^8

t = 1.938*10^12 s = 1.938* 10^12 / 3.15 *10^7 years

t = 6.15* 10^4 years