Define orbital velocity of a satellite. Derive expressions for the orbital velocity of a body from the earth’s surface is root2 times its velocity in a circular orbit just above the earth’s surface.

Orbital velocity is the speed required to place a satellite in a stable orbit around the Earth.

When a satellite orbits the Earth, the gravitational force acting on it provides the necessary centripetal force to maintain its circular path. The gravitational force depends on the mass of the Earth, the mass of the satellite, and the distance between the Earth’s center and the satellite, which is the sum of the Earth’s radius and the satellite’s height above the surface.

At equilibrium, the gravitational pull balances the centripetal force required for the satellite’s circular motion. From this balance, we determine the orbital velocity of the satellite. For satellites orbiting close to the Earth’s surface, the orbital velocity is approximately 7.92 km/s, assuming Earth’s acceleration due to gravity is 9.8 m/s² and the Earth’s radius is about 6.4 × 10⁶ m.