Question

What is the minimum orbital velocity?

Answer 1

The velocity with which a body should revolve around the other body is called the orbital velocity. This orbital velocity depends on the two forces and are gravitational force and the centripetal force. The orbital velocity is different for different orbits.

Complete answer:
The centripetal force is a force that acts on the body/object to keep it moving or revolving along a circular path. The gravitational force holds the body/object on the surface, that is, the force between 2 objects/bodies that form an action reaction pair.
This orbital velocity depends on these two forces, that is, the centripetal force and the gravitational force. When the centripetal force equals the gravitational force, the orbital velocity is said to occur. Because, the centripetal force is responsible for the circular motion, whereas, the gravitational force is responsible for the existence of the orbiting.
Consider a satellite of mass $m$ revolving around the Earth in a circular orbit of radius $r$ at a height $h$ from the surface of the Earth. Suppose $M$ and $R$ are the mass and radius of the Earth respectively, then $r=R+h$.
The equation of the centripetal force is, ${{F}_{c}}=\dfrac{m{{v}^{2}}}{r}$
The equation of the gravitational force is, ${{F}_{G}}=\dfrac{GMm}{{{r}^{2}}}$
Equate both of the above equations.

& \dfrac{m{{v}^{2}}}{r}=\dfrac{GMm}{{{r}^{2}}} \\\ & {{v}^{2}}=\dfrac{GM}{r} \\\ & v=\sqrt{\dfrac{GM}{r}} \\\ \end{aligned}$$ Or $$v=\dfrac{2\pi r}{T}$$ Considering the object is revolving around the orbit of the planet earth, then the orbiting velocity is computed as 7.8 km/s. $$\therefore $$The minimum orbital velocity considering the earth at the centre of the orbit is about 7.8 km/s. **Note:** The orbital velocity of the objects revolving around the different orbits will be different. The reason being, the different orbits have different values of the radius. The escape velocity is different from the orbital velocity. The escape velocity is the speed needed to escape an object’s gravitational pull.