Question

Let us assume that our galaxy consists of $2.5\times {10}^{11}$ stars each of one solar mass. How long will a star at a distance of 50,000 ly from the galactic centre take to complete one revolution ? Take the diameter of the Milky Way to be ${10}^5$ ly.

Answer 1

Mass of our galaxy Milky Way,$M=2.5\times {10}^{11}solarmass$
1 Solar mass = Mass of Sun$=2\times {10}^{30}kg$
Mass of our galaxy,$M=2.5\times {10}^{11}\times 2\times {10}^{30}=5\times {10}^{41}kg$

Diameter of Milky Way,$d={10}^{5}ly$
Radius of Milky Way,$r=5\times {10}^{4}ly$
$1ly=9.46\times {10}^{15}m$

$\therefore r=5\times {10}^4\times 9.46\times {10}^{15}$

$=4.73\times {10}^{20}$

Since a star revolves around the galactic centre of the Milky Way, its time period is given by the relation:
$T=(4{\pi }^2{r}^3/GM{)}^{1/2}$

$=\sqrt{\frac{4\times {3.14}^2\times {4.73}^3\times {10}^{60}}{6.67\times {10}^{-11}\times 5\times {10}^{41}}}$

$=1.12\times {10}^{16}s$

$=\frac{1.12\times {10}^{16}}{365\times 24\times 60\times 60}years$

$=3.55\times {10}^{8}years$