The orbital velocity of a satellite body and its escape velocity to escape out of Earth's gravitational field are equal.
the orbital (linear) velocity of a body revolving around the Earth, in a circular orbit of radius R.
Kinetic energy = 1/2 m v
₀², Potential energy in Earth's gravitational field at distance R = - G Me m / R
where, m = mass of the body (or satellite),
Me = mass of Earth, G = Universal Gravitational ConstantThe centripetal force for the body in the orbit is supplied by the gravitational force. Hence,
₀² / R = G Me m / R² => v₀² = G Me / R ---- equation 1
=> K.E. = 1/2 m v
₀² = G Me m / 2 R = - P.E./ 2
Total energy at radius R = KE+PE = - G Me M / 2 R --- equation 2
Suppose now, this body is given an additional velocity v (perpendicular to the orbit and along the radius) such that it goes to a distance d from center of Earth. Since the total mechanical energy is conserved
by the gravitational force, the energy at a distance d from the
center of Earth is given by:
The escape velocity of a satellite is the velocity (along radius) required to send it away into the space, just manages
to travel to infinite distance. It is equal to the orbital velocity.