Question

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.

Answer 1

The mass of the earth,
`M=6.023* 10^(24)\ kg`

Step-by-step 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* 10^6\ m`

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

`T^2=(4\pi^2)/(GM)r^3`

`M=(4\pi^2r^3)/(T^2G)`

`M=(4\pi^2* (384* 10^6)^3)/((2358720)^2* 6.67* 10^(-11))`

`M=6.023* 10^(24)\ kg`

So, the mass of the earth is
`6.023* 10^(24)\ kg`. Hence, this is the required solution.