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A geostationary satellite orbits the Ear...

A geostationary satellite orbits the Earth at a height of nearly `36,000 km` from the surface of earth. What is the potential due to earth's gravity at the site of this satllite ? (Take the potential energy at infinity to be zero). Mass of the Earth `= 6.0 xx 10^(24) kg`, radius `= 6400 km, G = 6.67 xx 10^(-11) Nm^(2)//kg^(2)`.

Text Solution

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Mass of the Earth `= 6.0 xx 10^(24) kg`
Radius of the Earth, (R ) = 6,400 km
Distance of satellite from the surface of the Earth (h) = 36,000 km
The potential due to earth.s gravity at the site of the satellite.
`V = -(GM)/((R + h))`
`= -(6.67 xx 10^(-11) xx (6 xx 10^(24)))/((6,400 + 36,000) xx 10^(3))`
`= -9.43 xx 10^(6)J kg^(-1)`.
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