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

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?

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.

• I want to know that ,critical and orbital velocities have same valuesthen why they are called different? I can't get my answer from your answer. – Rabik John May 10 '18 at 11:13
• @RabikJohn My answer shows that the values of critical speed and orbital speed are different. – Farcher May 10 '18 at 12:38
• But,I get the same values for both .The value of critical velocity is 7.9km/s and value for orbital velocity also comes 7.9km/s ,after putting values in formula v equals to square root GM/R – Rabik John May 11 '18 at 4:26
• @RabikJohn The only time the two speeds can be the same is for an orbit of radius equal to the radius of the Earth when there is no gain in gravitational potential energy. – Farcher May 11 '18 at 5:30
• @RabikJohn So I think that your question has been answered? – Farcher May 11 '18 at 7:13

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

• Please use MathJax to make formulas in your post readable. – flaudemus Feb 19 at 17:19