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How will you .weigh the Sun. to estimate...

How will you .weigh the Sun. to estimate its mass ? The mean orbital radius of the earth around the Sun is `1.5 x 10^(8)` km.

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To estimate the mass of the Sun, we require, the time period of revolution Tone of its planets (say the Earth). Let `M_s, M_e` be the masses of Sun and Earth respectively and r be the mean orbital radius of the Earth around the Sun. The gravitational force acting on Earth due to Sun is
`F = (GM_s.M_e)/(r^2)`
Let the Earth be moving in circular orbit around the Sun with a uniform angular velocity `omega`.
The centripetal force acting on Earth is `F. = M_e r omega^2 = M_e r (4pi^2)/(T^2)`.
As this centripetal force is provided by the gravitational pull of Sun on Earth, so
`(GM_sM_e)/(r^2) = M_e r (4pi^2)/(T^2) " or " M_s = (4pi^2 r^3)/(GT^2)`
Knowing r and T, mass `M_s` of the Sun can be estimated. In this equation.
we are given,
`r = 1.5 xx 10^8 km = 1.5 xx 10^11 m , T = 365 `days = `365 xx 24 xx 60 xx 60s `
`M_s = (4 xx (22//7)^2 xx (1.5 xx 10^11)^3)/((6.67 xx 10^(-11)) xx (365 xx 24 xx 60 xx 60)^2) = 2 xx 10^30 kg `
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