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8.5 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 Milk Way to be 10⁵ ly.

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Vishal Baghel | Contributor-Level 10

4 months ago

Mass of our galaxy Milky Way, M = 2.5 $\times 10^{11}$ solar mass

Solar mass = Mass of the Sun = 2.0 $\times 10^{30}$ kg

Mass of our galaxy = 2.5 $\times 10^{11} \times$ 2.0 $\times 10^{30}$ = 5 $\times 10^{41}$ kg

Diameter of the Milky Way, d = 10⁵ ly

Radius of the Milky Way = 5 $\times 10^{4}$ ly

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

r = 5 $\times 10^{4} \times$ 9.46 $\times 10^{15}$ m = 4.73 $\times 10^{20}$ m

As a star revolves around the galactic centre of the Milky Way, its time period is given by the relation: $τ$ = ( ${\frac{4 π^{2} r^{3}}{G M})}^{\frac{1}{2}}$ = ( ${\frac{4 \times {3.14}^{2} {\times 4.73}^{3} \times 10^{60}}{6.67 \times 10^{- 11} \times 5 \times 10^{41}})}^{\frac{1}{2}}$ = 1.12 $\times 10^{16} s$ = 3.55 x $10^{8}$ years

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8.5 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 Milk Way to be 10⁵ ly.

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8.5 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 Milk Way to be 105 ly.

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8.5 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 Milk Way to be 10⁵ ly.