Q.What is orbital velocity? Find the value of orbital velocity of a satellite orbiting around earth very near to the surface of earth.

Orbital velocity is the speed needed for a stable circular orbit; near Earth's surface it works out to about 7.92 km/s.

Definition: Orbital velocity is the minimum (horizontal) velocity that must be given to a satellite so that it moves in a stable circular orbit around a planet, i.e. the gravitational pull of the planet exactly supplies the centripetal force needed to keep it in that circular path.

Derivation for a satellite orbiting close to Earth's surface:

For a satellite of mass m orbiting at radius r (≈ R, Earth's radius, since it is very near the surface) with orbital speed v, gravity provides the centripetal force:

$\dfrac{GMm}{R^2} = \dfrac{mv^2}{R}$

$v^2 = \dfrac{GM}{R}$

$v = \sqrt{\dfrac{GM}{R}}$

Using the relation between g (acceleration due to gravity at the surface) and GM: $g = \dfrac{GM}{R^2} \Rightarrow GM = gR^2$. Substituting:

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