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A satellite is orbiting in an orbit with...

A satellite is orbiting in an orbit with a velocity 4 km/s . Then find acceleration due to gravity at that height.

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As centripetal acceleration equal to acceleration due gravity at that height, then
`a = (V^(2))/(r) = g_(h)` and `V^(2) = (GM)/(r) = (gR^(2))/(r)`
`rArr r = (gR^(2))/(V^(2)) = (10 xx 6400 xx 6400 xx 10^(6))/(16 xx 10^(6))(g = 10 m//s^(2))`
= 25600 km
`therefore g_(h) = a = (V^(2))/(r) = (16 xx 10^(6))/(25600 xx 10^(3)) = (10)/(16)m//s^(2)`
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