Question

The Milky Way has a diameter (proper length) of about 1.2×10^5 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

Time taken by the spacecraft to cross milky way,
`T = 6.147* 10^(4) years`

Given:

Actual length, l =
`1.2* 10^(5) ly`

speed of the aircraft, v =0.890 c

Solution:

From the Einstein's theory of relativity, using length contraction:

`l' = l\sqrt(1 - (v^(2))/(c^(2)))`

`l' = 1.2* 10^(5)\sqrt(1 - ((0.890 c)^(2))/(c^(2)))`

l' =
`5.472* 10^(4) ly = 5.472* 10^(4)c yrs`

Time taken by the spacecraft to cross milky way, T:

`T = (l')/(v)`

`T = ( 5.472* 10^(4)c)/(0.890 c)`

`T = 6.147* 10^(4) years`