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Relationship between orbiting velocity and acceleration due to gravity?
Wiki User
∙ 14y ago
If Vo is the orbital velocity then the centrifugal force is m Vo2/ R+h where R is the radius of the earth and h is height of the body of mass m orbiting around the earth.
The force of attraction between earth and body is G M m /(R+h)2 G is the universal gravitational constant and M is mass of the earth.
For equilibrium the gravitational force will be equal to the centrifugal force.
So Vo = sq root of GM/(R+h)
But GM = gR2 g is acceleration due to gravity.
So Vo = sq root of g R2/R+h
When h is very much smaller compared to R then neglecting h
we get Vo = sq root of gR
So orbital velocity is directly proportional to the square root of acceleration due to gravity.
Wiki User
∙ 14y ago
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