Question

define critical velocity? derive an expression for critical velocity of satellite.​

Answer 1

CRITICAL VELOCITY OF SATELLITE:

• It is also known as the orbital velocity of a satellite orbiting around the planet.

• It is the stable velocity with which a satellite revolves around the planet in a circular trajectory.

DERIVATION OF THE EXPRESSION:

• When a satellite is revolving around the planet, gravitational force provides the centripetal component of the circular trajectory.

Let mass of planet be M and mass of satellite be m. Radius of trajectory be R+h , where R is the radius of planet.

$F_{g} = F_{c}$

$\implies \: \dfrac{GMm}{{(R + h)}^{2} } = \dfrac{m {v}^{2} }{R + h}$

$\implies \: \dfrac{GM}{(R + h)} = {v}^{2}$

$\implies \: v = \sqrt{\dfrac{GM}{(R + h)} }$

[Hence derived].