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 ? Taken the diameter of the Milky way to be ${10}^5$ ly.

Answer 1

Number of stars in our galaxy $=2.5\times {10}^{30}$ Mass of each star = 1 solar mass

$\Rightarrow$ Mass of our galaxy

$2.5\times {10}^{11}2\times {10}^{36}kg$

$=5\times {10}^{41}$

Diameter of milky way ${10}^5\times 3\times {10}^{8}m{s}^{-1}\times 1yr$

The distance of the star = radius of its orbit = $5\times {10}^4$ nly. Therefore , the time period of the revolving star is given by ,

$T^2=\frac{4{\pi }^2{R}^3}{GM}$

$=\frac{4{\pi }^2}{GM}\times \frac{d^3}{8}$

$T^2=$

$\frac{{\pi }^2\times (3\times {10}^3\times 365\times 24\times 60\times 60)}{2\times 6.67\times {10}^{-11}\times 5\times {10}^{{}^{41}}}y{r}^2$

$T^2=1.259\times {10}^{17}y{r}^2$

$T=3.549\times {10}^{8}yrs$it takes about $3.55\times {10}^8$ years to complete one revolution for a star around the milky way