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)

Question

Philoid · Accepted Answer

Given radius of Earth = 6400Km

Let M be the mass of earth and m be the mass of the satellite.

Let us assume, at height h, the force on the satellite due to earth is reduce to half.

We know gravitational force between two mass of objects,

Where,

G = universal gravitation constant =

m_{1 =}_mass of first object = M

m₂ = mass of second object = m

r = distance between the objects

On Earth surface, the force on the satellite due to the earth is given by –

On reaching a height h, the force on the satellite due to the earth is given by –

From question,

Taking square root on both sides –