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.

Answers (1)

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