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As you have learnt in the text a geostat...

 As you have learnt in the text a geostationary satellite orbits the earth at a height of nearly 36,000 km from the surface of the earth. What is the potential due to earth's gravity at the site of this satellite ? (Take the potential energy at infinity to be zero). 
Mass of the earth ` 6.0xx 10^(24(kg)` ,
Radius = 6400 km .

Text Solution

Verified by Experts

`implies` Mass of the earth `M_(E) 6.0 xx 10^(24) kg,`
Radius of earth `R_(E) = 6400 km = 6.4 xx 10^(7)m`
Distance of geo stationary satellite from the surface of earth h `= 3600 km = 3.6 xx 10^(7) m`
Gravitational potential due to earth.s gravity at height h, 
`phi= (-GM_E)/(R_(E)+h)`
`=-(6.67 xx10^(-11)xx6xx10^(24))/(6.4 xx10^(6)+36 xx 10^(6))`
`=-(40.02xx 10^(13))/(4.24xx10^(7))`
`=-9.43 xx10^(6)Jkg`
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