Define orbital velocity. Derive the expression for it.

Expression for orbital velocity: 
Consider, a satellite of mass 'm' is revolving around the earth in a circular orbit of radius 'r', at a height 'h' from the surface of the earth.
Let 'M' be the mass of the earth and 'R' be the radius of the earth. 
Therefore,
                  r = R + h
The centripetal force that is required to revolve the satellite =   
where,
  is orbital velocity.
Orbital velocity is produced by the gravitational force between the earth and the satellite =   

Therefore, 
                

                 
                  
But,
                      GM=gR² 
where,

g is the acceleration due to gravity.
So, 
 
Let g' be the acceleration due to gravity in the orbit i.e. at a height h from the surface. 
Therefore,
                
          
∴               , is the required orbital velocity.