On ground the gravitational force on satalite is W what is the gravitational force when the satellite is at the height of R/50 (R is radius of Earth)?

1 Answer
Jun 28, 2018

F=2500/2601W(=(50/51)^2W)

Explanation:

The gravitational force between two objects due to their masses is

F=G(m_1m_2)/r^2

where
F=force in newtons
m_1=mass of first object in kilograms
m_2=mass of second object in kilograms
r=distance between centres of the objects in metres
G=the "gravitational constant", approximately equal to 6.674xx10^(-11)Nkg^(-2)m^2

This idea was first formulated by Isaac Newton, and published by him in 1686.

In this problem, let m_1=m_E=mass of the earth; let m_2=m_S=mass of the satellite.

On the ground:
W=G(m_Em_S)/R^2, where R is the radius of the earth.

In orbit:
F=G(m_Em_S)/(R+R/50)^2=G(m_Em_S)/((51R)/50)^2
where F is the force we're looking for.

Put the two together:

F((51R)/50)^2=WR^2
F(51/50)^2=W

F=2500/2601W