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Westkost [7]
3 years ago
13

The Moon orbits Earth in an average of p = 27.3 days at an average distance of a =384,000 kilometers. Using Newton’s version of

Kepler’s third law determine the mass of Earth. You may neglect the mass of the Moon in comparison to the mass of Earth.
Physics
1 answer:
Korvikt [17]3 years ago
7 0

Answer:

The mass of the earth, M=6.023\times 10^{24}\ kg

Explanation:

It is given that,

Time taken by the moon to orbit the earth, T=27.3\ days=2358720\ m

Distance between moon and the earth,r=384000\ km=384\times 10^6\ m

We need to find the mass of the Earth using Kepler's third law of motion as :

T^2=\dfrac{4\pi^2}{GM}r^3

M=\dfrac{4\pi^2r^3}{T^2G}

M=\dfrac{4\pi^2\times (384\times 10^6)^3}{(2358720)^2\times 6.67\times 10^{-11}}

M=6.023\times 10^{24}\ kg

So, the mass of the earth is 6.023\times 10^{24}\ kg. Hence, this is the required solution.

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