Question

Distance to the moon from the earth
is 3.84 x 108 m and the time period of
the moon’s revolution is 27.3 days.
Obtain the mass of the earth.
(Gravitational constant
g=6.67 x 10-11 Nm2
kg-2
.)

Answer 1

Answer:use kepler's law

Explanation:use the following formulae

Answer 2

The mass of the earth is $6.01775286\times10^2^4kg$.

Explanation:

The period of the Moon’s orbit  about the Earth is given as

$T=2\pi\sqrt{\frac{R^3}{GM} }$

Here, M is the mass of the earth, R is the distance between moon from the earth and G is the gravitational constant.

Above formula can also write as

$M=4\pi^2\frac{R^3}{T^2G}$

Given $R=3.84\times10^8 m$,  T = 27.3 days = 2358720 s and $G = 6.67\times10^-^1^1Nm^2kg^-^2$.

Substitute the given values, we get

$M=4\times(3.14)^2[\frac{(3.84\times10^8)^3}{(2358720s)^2\times6.67\times10^-^1^1}]$

$M=6.01775286\times10^2^4kg$

Thus, the mass of the earth is $6.01775286\times10^2^4kg$.

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