How will you .weigh the Sun., that is estimate its mass? You will need to know the period of one of its planets and the radius of the planetary orbit. The mean orbital radius of the Earth around the Sun is 1.5 xx 10^8km. Estimate the mass of the Sun.

How will you .weigh the Sun., that is estimate its mass? You will need

1.	How will you .weigh the Sun., that is estimate its mass? You will need to know the period of one of its planets and the radius of the planetary orbit. The mean orbital radius of the Earth around the Sun is 1.5 xx 10^8km. Estimate the mass of the Sun.
Answer» SOLUTION :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 gravitationalforce 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 `