Question

An earth satellite in a circular orbit a height of 200km above the
earth's surface has a period of 80minutes. Calculate the mass of
the earth from this data, Radius of the earth=6400km.​

Answer 1

Answer:

earth,s surface has a period of 80 minutes. calculate the mass of the earth from this data radius of the earth =6400km.

Answer 2

The mass of  the earth is $7.38\times10^2^4kg$.

Explanation:

The time period of Earth satellite is given as

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

Here R is the radius of the of the circular motion and M is the mass of the earth and G is the gravitational constant.

So, the mass of the earth,

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

Given R = 200 km + r (radius of earth) = 200 km + 6400 km = 6600 km.

We know, $G = 6.67\times10^-^1^1Nm^2/kg^2$

Substitute the values, we get

$M=4\times(3.14)^2[\frac{(6600\times10^3)^3}{ 6.67\times10^-^1^1Nm^2/kg^2\times(4800s)^2} ]$

$M=7.38\times10^2^4kg$

Thus, the mass of  the earth is $7.38\times10^2^4kg$

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