Question

28.
Define orbital velocity of a satellite. Derive expressions for the orbital
velocity of a satellite. Show that the escape velocity of a body from the
earth's surface is (2)1/2 times its velocity in a circular orbit just above the earth surface​

Answer 1

Answer:

Orbital velocity is the velocity needed to achieve a balance between gravity's pull on the body and the inertia of the body's motion. For a satellite revolving around the Earth, the orbital velocity of the satellite depends on its altitude above Earth.

Explanation:

To derive the orbital velocity, we concern ourselves with the following two concepts:

Gravitational Force

Centripetal Force

It is important to know the gravitational force because it is the force that allows orbiting to exist. A central body exerts a gravitational force on the orbiting body to keep it in its orbit. Centripetal force is also important, as this is the force responsible for circular motion.

For the derivation, let us consider a satellite of mass m revolving around the Earth in a circular orbit of radius r at a height h from the surface of the Earth. Suppose M and R are the mass and radius of the Earth respectively, then r = R + h.