Question

Define the term orbital velocity. Establish a relation for the orbital velocity of a satellite very close to the surface of the earth. Find the ratio of orbital velocity and escape velocity.

Answer 1

Orbital velocity is the minimum velocity that is needed to put the satellite into a given orbit around Earth. Consider a satellite of mass ‘m’ moving around in an orbit at height ‘h’ above the ground. Let M be mass of Earth, R be the radius of earth and the orbital velocity be V_o.

We know that, F_g = \(\frac{GMm}{(R+h)^2}\)

and centrifugal force F_C = \(\frac{GV_o^2}{(R+h)}\)

In equilibrium i.e., while rotating around the orbit

(Since, h << R ; R + h = R)

\(\frac{V_o}{V_{esc}} \) \(\frac {\sqrt {gR}}{\sqrt {2gR}} = \frac {1} {\sqrt2}\).