Question

PLEASE solve this


what is orbital velocity of a satellite and derive v = √GM/R+h​

Answer 1

For orbital velocity, the force due to gravity will be equal to centrifugal force.

Thus equating GMm/r^2 and mv^2/r

Here v will be orbital velocity, M is mass of planet, r is distance from planet, m is mass of object, G is universal gravitational constant.

Moving variables around and cancelling, we get

v=√(GM/r)

Answer 2

Orbital Velocity of a satellite is the minimum velocity it has to maintain to continue its circular motion in its orbit.

Deriving the expression

The Gravitational Force between the earth and the satellite = Fg = (G.M.m)/r2 ……………… (1)

The centripetal force acting on the satellite = Fc = mV2/r ……………………….. (2)

Here, M is the mass of earth and m is the mass of the satellite which is having a uniform circular motion in a circular track of radius r around the earth. V is the linear velocity of the satellite at a point on its circular track.

Now this r is the sum of the radius of the earth(R) and the height(h) of the satellite from the surface of the earth.

r = R + h

Now equating, equation 1 and 2 we get,

Fg = Fc

=> (G.M.m)/r2 = mV2/r

V = [(GM)/r]1/2 ……………………………….. (3)

This is the first equation or expression of Orbital Velocity of a satellite. Here r = R +h

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