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Let us assume that our galaxy consists o...

Let us assume that our galaxy consists of `2.5xx10^(11)` stars each of one solar mass. How long will a star at a distance of 50.000 ly from the galacite centre take to complete one revolution? Take the diameter of the milky way to be `10^(8)`?

Text Solution

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`M = 2.5 xx 10^11 `solar mass
` = 2.5 xx 10^11 xx (2 xx 10^30 )kg = 5.0 xx 10^41 kg `
We know that `M = (4pi^2 r^3)/(GT^2) `
` r = 50,000ly = 50,000 xx 9.46 xx 10^15 m = 4.73 xx 10^20m`
` T = ((4pi^2 r^3)/(GM))^(1//2) = [(4 xx (22//7)^2 xx (4.73 xx 10^20)^3)/((6.67 xx 10^(-11)) xx (5.0 xx 10^41))]^(1/2) = 1.12 xx 10^16 s `
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