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You are given the following data :g=9.81...

You are given the following data `:g=9.81ms^(-2)`, radius of earth `=6.37xx10^(6)m` the distance the Moon from the earth `=3.84xx10^(8) m` and the time period of the Moon's revolution `=27.3days`. Obtain the mass of the earth in two different ways. `G=6.67xx10^(-11)Nm^(2)kg^(2)`.

Text Solution

Verified by Experts

(a) Mass of the earth can be given by
`M_(E) = (gR_(E)^(2))/(G) = (9.81 xx (6.37 xx 10^(6))^(2))/(6.67 xx 10^(-11))`
`= 5.97 xx 10^(24) kg`
(b) Also, from Kepler.s law of periods, mass of the earth is
`M_(E) = (4pi^(2)r^(3))/(G T^(2)) = (4 xx (3.14)^(2) xx (3.84 xx 10^(8))^(3))/(6.67 xx 10^(-11) xx (27.3 xx 24 xx 60 xx 60)^(2))`
`= 6.02 xx 10^(24) kg`
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