What is orbital velocity? Obtain an expression for it.

Explanation

Orbital velocity `(V_(@))` : Velocity of a satellite moving in orbit is called orbital velocity `(V_(@))`.
Let a satellite of mass is revolving round the earth in a circular orbit at a height 'h' above the ground.
Radius of the orbit =R+h where R is radius of earth.
In orbit motion is " The centrifugal and centripetal forces acting on the satellite".
Centrifugal force `=(mV^2)/( r)=(mV_0^2)/(R+h)"........"(1)`
Centripetal force is the force acting towards the centre of the circle it is provided by gravitational force between the planet and satellite.
`:.F=(GM)/((R+h)^2)" "".............(2)`
`(1)=(2)(mV_0^2)/((R+h))=(GM)/((R+h)^2)`
`:.V_0^2=(GM)/(R+h)" or "V_(@)=sqrt((GM)/(R+h))`
When `h lt ltR` then orbital velocity.

`V_(@)=sqrt(gR)` is called orbital velocity. Its value is `7.92` km/sec.