What is the difference between orbital velocity and critical velocity? Are their values similar or not?

Question

As critical velocity is the minimum velocity required to put a satellite into orbit. And orbital velocity is the velocity required to keep a satellite moving in an orbit.The value of critical velocity I found is 7.9km/s.On various sites it is written that there is a difference between orbital velocity and critical velocity ,but when I found the value of orbital velocity by formula v equals square root GM/R it comes 7.9km/s by putting standard values for G,M AND R .As these values are same can anyone tell me, why is there a difference between two?

Answer 1

I have not used the term critical velocity so have used your definitions of orbital and critical velocity.

orbital velocity is the velocity required to keep a satellite moving in an orbit

For a circular orbit this is found by using Newton's second law with the gravitational attractive force $\frac {GMm}{R^2}$ producing the centripetal acceleration $\frac{v_{\rm orbital}^2}{R}$ for a satellite of mass $m$.

$\frac {GMm}{R^2} = m \frac{v_{\rm orbital}^2}{R} \Rightarrow v_{\rm orbital} = \sqrt{\frac{GM}{R}}$

critical velocity is the minimum velocity required to put a satellite into orbit

Ignoring the rotation of the Earth and any effects due to the atmosphere you will need to give a satellite enough kinetic energy $\frac 12 mv^2_{\rm critical}$ at launch to enable it to increase its gravitational potential energy $\frac{GMm}{R_{\rm Earth}} - \frac{GMm}{R }$ and then have enough kinetic energy left $\frac 12 m v^2_{\rm orbital}$ to go into orbit.

Answer 2

Orbital velocity depends upon height of satellite It is given by v= square root of (ghR) where h is the height of satellite and R is the radius of earth Critical velocity is a constant value and its value on earth is 7.9km/s It does not depends upon altitude It gives the velocity of smallest possible orbit given that there is no air friction and other retarding factors

Answer 3

The orbital velocity is given by, V(orbital) = $\sqrt{GMe/R}$ , Where R is the sum of radius of earth and the altitude at which the sattelite is revolving. R = Radius + Altitude, So its value will be always greater than or equal to critical velocity. Critical velocity is the minimum velocity required to put a sattelite to orbit while orbital velocity can be any velocity greater than critical velocity.Orbital velocity can be equal to or greater than the critical velocity.I hope you understood.