Question

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)?

Answer 1

`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`