What is the orbital velocity of a satellite? Derive its equation.

(N/A) The velocity required by a satellite to revolve around the Earth in a given orbit is known as the orbital velocity of the satellite.
Consider a satellite of mass $m$ at a height $h$ from the surface of the Earth,revolving around the Earth as shown in the figure. Its distance from the center of the Earth is $r = R_E + h$. Let the orbital velocity of the satellite be $v_0$.
The gravitational force exerted on the satellite by the Earth is:
$F = \frac{G M_E m}{r^2}$
The necessary centripetal force for the circular motion of the satellite is provided by the Earth's gravitational force:
$F_c = \frac{m v_0^2}{r}$
Equating the centripetal force to the gravitational force:
$\frac{m v_0^2}{r} = \frac{G M_E m}{r^2}$
Simplifying the equation:
$v_0^2 = \frac{G M_E}{r}$
Substituting $r = R_E + h$:
$v_0 = \sqrt{\frac{G M_E}{R_E + h}}$
This equation indicates that as the height $h$ increases,the orbital velocity $v_0$ decreases.