Let us assume that our galaxy consists of 2.5 × 1011 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 105ly.

Asked by Pragya Singh | 1 year ago |  107

Solution :-

Mass of our galaxy, M=2.5×10 11 solar mass

1 Solar mass = Mass of Sun =2×1030 kg

Mass of our galaxy, M=2.5×1011×2×10 30=5×1041kg

Diameter of Milky Way,d=105 ly

Radius of Milky Way,r=5×10ly

1 ly=9.46×1015m

Therefore, r=5×104×9.46×1015

=4.73×1020m

The time taken by the star to revolve around the galactic centre is given by the relation:

T=$$(\dfrac{4π^2r^3}{GM})$$1/2

$$\sqrt{\dfrac{4\times (3.14)^{2}\times (4.73)^{3}\times 10^{60}}{6.67\times 10^{-11}\times 5\times 10^{41}}}$$

= 1.12 x 1016 s

$$\dfrac{1.12\times 10^{16}}{365\times 24\times 60\times 60}\, years$$

= 3.55 x 108 years

Answered by Abhisek | 1 year ago

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