# Q: 8.5  Let us assume that our galaxy consists of   $2.5\times 10^1^1$  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.

We know that one light year is $9.45\times 10^{15}\ m$.

The time period of rotation is given by :

$T\ =\ \left ( \frac{4 \pi r^3}{GM} \right )^\frac{1}{2}$

Putting all the value (in SI units) in the above equation we get :

$=\ \left ( \frac{4 \times \left ( 3.14 \right )^2\times (4.73)^3\times 10^{60}}{6.67\times 10^{-11} \times 5\times 10^{41}} \right )^\frac{1}{2}$

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

In years :

$=\ \frac{1.12\ \times 10^{16}}{365 \times 24 \times 60 \times 60}\ =\ 3.55\times 10^8\ years$

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