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Home » Let us assume that our galaxy consists of stars each of one solar mass. How long will a star at a distance of ly from the galactic centre take to complete one revolution? Take the diameter of the Milky Way to be .
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 \mathbf{5 0 , 0 0 0} ly from the galactic centre take to complete one revolution? Take the diameter of the Milky Way to be 10^{5} \mathrm{ly}.
CBSE | Class 11 | Gravitation | NCERT | Physics
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 \mathbf{5 0 , 0 0 0} ly from the galactic centre take to complete one revolution? Take the diameter of the Milky Way to be 10^{5} \mathrm{ly}.

Mass of our galaxy is given as M=2.5 \times 10^{11} solar mass

1 Solar mass as we know is, Mass of Sun =2 \times 10^{30} \mathrm{~kg}

Mass of our galaxy as we know is M=2.5 \times 10^{11} \times 2 \times 10^{30}=5 \times 10^{41} \mathrm{~kg}

Radius of Milky Way is r=5 \times 10^{4} \mathrm{ly}

1 \mathrm{ly}=9.46 \times 10^{15} \mathrm{~m}

So, r=5 \times 104 \times 9.46 \times 10^{15}=4.73 \times 10^{20} \mathrm{~m}

The following relation gives the time it takes for a star to circle around the galactic centre,

\mathrm{T}=\left(4 \pi^{2} \mathrm{r}^{3} / \mathrm{G} \mathrm{M}\right)^{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} \mathrm{~s}

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

=3.55 \times 10^{8} years

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