Question

The radius of our galaxy is about $3\times {10}^{20}m$. With what speed should a person travel so that he can reach from the centre of the galaxy to its edge in 20 years of his lifetime?

Answer 1

Let the speed of the person be v. As seen by the person, the edge of the galaxy is coming towards him at a speed v. In 20 years (as measured by the person), the edge moves (20 y) v and reaches the person. The radius of the galaxy as measured by the person is, therefore, (20 y) v. The rest length of the radius of the galaxy is $3\times {10}^{20}m$. Thus,
$\left(20y\right)v=(3\times {10}^{20}m)\sqrt{1-v^2/c^2}$
or, $(6.312\times {10}^{8}s{)}^2{v}^2=(9\times {10}^{40}{m}^2\left)\right(1-v^2/c^2)$.
Solving this,
$v=0.9999996c.$