Question

Our Milky Way galaxy is 100,000 ly in diameter. A spaceship crossing the galaxy measures the galaxy's diameter to be a mere 1 ly. What is the speed of the spaceship relative to the galaxy? and How long is the crossing time as measured in the galaxy's reference frame?

Answer 1

Answer:

t= 100000.000005 years

Explanation:

Our Milky Way galaxy is 100,000 ly in diameter.

the galaxy's diameter to be a mere 1 ly.

We know that

$L=L_0\sqrt{1-\frac{v^2}{c^2} }$

L= 1 ly

L_0= 100,000 ly

$1=100,000\sqrt{1-\frac{v^2}{c^2} }$

v= 0.99999999995 c

so time t= $\frac{d}{v} = \frac{100000c}{0.99999999995c}$

t= 100000.000005 years