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Assuming the distance of the Moon from t...

Assuming the distance of the Moon from the Earth `R=3.84xx10^(8)m` and Moon's period of revolution as 27.3 days, calculate the mass of the Moon.

Text Solution

Verified by Experts

We know that,
`M_(E)=(4pi^(2)R^(3))/(GT^(2))" i.e., M_(E)=(4xx3xx142^(2)xx(3.84)^(3)xx10^(24))/(6.64xx10^(-11)xx(27.3xx8.64xx10^(4))^(2))`
i.e., `M_(E) = 6.02xx10^(24)kg. ` where 1 day = 86400s.
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If 'R' is the distance of the Moon from the Earth and 'T ' is the period of revolution of the Moon , then obtain the formula to calculate the mass of the Earth.

Weighing the Earth : You are given the following data: g = 9.81 ms^(-2) , R_(E) = 6.37 ×x 10^(6) m, the distance to the moon R = 3.84 ×x 10^(8) m and the time period of the moon’s revolution is 27.3 days. Obtain the mass of the Earth M_(E) in two different ways.

Knowledge Check

  • Two satellites revolve around the earth at distances 3R and 6R from the centre of earth. Their periods of revolutions will be in the ratio:

    A
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    B
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    C
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    D
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