Question

A satellite is projected vertically upwards from an earth station. AT what height above the earth's surface will the force on the satellite due to the earth be reduced to half its value at the earth station ? (Radius of the earth is 6400 km.)

Answer 1

Let the mass of earth = M

and mass of satellite = m

Then $F_1=\frac{GMm}{R^2}$

$F_2=\frac{GMm}{(R+h{)}^2}$

According to question,

$\frac{F_1}{F_2}=\frac{(R+h{)}^2}{R^2}$

$\Rightarrow 2=\frac{(R+h{)}^2}{R^2}$

$\Rightarrow \sqrt{2}=1+\frac{h}{R}$

$\Rightarrow h=(\sqrt{2}-1)R$

$=0.414\times 6400=2649.6km$