Question

Define Orbital Velocity. Obtain the relation between orbital velocity and

acceleration due to gravity g, for a satellite orbiting very close to the surface of the earth.​

Answer 1

Orbital Velocity of a satellite is the minimum velocity it has to maintain to continue its circular motion in its orbit. We know for a circular motion to continue, a force called centripetal force is required to work upon the object in circular motion. And this force is a real and acts towards the centre of the circle. As this is a real force it’s to be supplied by a real mechanism or system. A satellite moves in a circular track and the centripetal force acting on it is supplied by the gravitational force acting between the earth and the satellite. Orbital Velocity formula:With the help of this concept or information we can easily go for the derivation of Orbital Velocity. We will derive this expression(2 sets) and later will find out the expression of Orbital Velocity for a nearby orbit. (so you get total 3 sets of equations)

Derivation of Orbital Velocity

Deriving the expression or formula #1

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

Answer 2

Answer:

Orbital Velocity is the minimum velocity of a satellite required to escape from the gravitational field.

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