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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

Verified by Experts

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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A geostationary satellite orbits the earth at a height of nearly 36000 km. What is the potential due to earth's gravity at the site of this satellite (take the potential energy at oo to be zero). Mass of earth is 6xx10^(24)kg , radius of earth is 6400 km.

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Knowledge Check

  • A geostationary satellite is orbiting the earth at a height of 6R above the surface of the earth, where R is the radius of the earth. What is the time period of another satellite orbiting at a height of 2.5 R from the surface of the earth ?

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