Ncert Exercises & Solutions

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 Milky Way to be 105 ly.

G i v e n,

r = 50000 l y = 50000 \times 9.46 \times 10^{15} m

= 4.73 \times 10^{20} m

M = 2.5 \times 10^{11} s o l a r m a s s = 2.5 \times 10^{11} \times 2 \times 10^{30} k g

= 5 \times 10^{41} k g

W e k n o w t h a t,

T = {(\frac{4 π^{2} r^{3}}{G M})}^{\frac{1}{2}}

= {[\frac{4 \times {(3.14)}^{2} \times {(4.73 \times 10^{20})}^{3}}{6.67 \times 10^{- 11} \times (5 \times 10^{41})}]}^{\frac{1}{2}}

= 1.12 \times 10^{16} s .

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

= 3.55 \times 10^{8} y e a r s .

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