Estimate the mass of the sun, assuming the orbit of Earth around the sun to be a circle. The distance between the sun and the Earth is `1.49 xx 10^(11) m`, and `G = 6.67 xx 10^(-11) Nm^(2) kg^(-2)`.

Explanation

To estimate the mass of the sun, we require, the time period of revolution `T` of one if its plants (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 graviational 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 centripetel
force acting on Earth is `F' = M_(e) r omega^(2) = M_(e) r(4 pi^(2))/(T^(2))`
As this centripetal force is provided by the graviational pull of sun on Earth, so
`(GM_(s)M_(e))/(r^(2)) = M_(e)r(4pi^(2))/(T^(2))` or `M_(s) = (4 pi^(2) r^(3))/(GT^(2))`
Knowing `r` and `T`, mass `M_(s)` of the sun can be estimated.
In this question, we are given, `r = 1.5xx 10^(8) km = 1.5 xx 10^(11) m, T = 365 days = 365 xx 24 xx 60 xx 60 s`
`:. 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`