Mass of the object m = m
Mass of the planet M = M
Radius of the planet R = R
Height h = h
Total energy at height h is E = Potential energy at height h
= -GMm/(R+h)
Total energy at the surface of the planet E ' = [-GMm/R] + ( 1/ 2)
mv 2
From law of conservation of energy , E = E '
-GMm/(R+h) = [-GMm/R] + ( 1/ 2) mv 2
( 1/ 2) mv 2 = [-GMm/(R+h) ] +[GMm/R]
v 2 = [-2GM/(R+h) ] +[2GM/R]
= [-2GMR +2GM(R+h)]/[(R+h)R]
= 2GMh / [(R+h) R ]
v = √ {2GMh / [(R+h) R ]}
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