Orbital velocity is the velocity given to artificial satellite so that it may start revolving around the earth.

Expression for orbital velocity:
Suppose 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 radius of the earth.
∴ r = R + h
    To revolve the satellite, centripetal force of  is required (where  is orbital velocity)  which is provided by gravitational force  between the earth and the satellite.
∴               
or             

or               
But GM=gR² where g is the acceleration due to gravity.

Let g' be the acceleration due to gravity in the orbit i.e. at a height h from the surface.
∴       
or            
∴                

Escape velocity is minimum velocity with which a body must be thrown upward so that it may just escape.
Expression for escape velocity:
Let a body of mass m be escaped from gravitational field of the earth. During the course of motion, let at any instant body be at a distance r from the centre of the earth.

The gravitational force between body and the earth is,
                               
and work done to raise the body by distance dr is,
                             
   Total work done W in raising the body from the surface of the earth to infinity is,
                             
                                 

If we throw the body upward with a velocity v_e, then work done to raise the body from surface of the earth to infinity is done by kinetic energy,
                                 
or                                
or                                 
Substituting the values, g = 9.81m/sec and R = 6.4 x 10⁶m, we have,
  
       

(i) Escape velocity is independent of the mass of body projected and is same for all the bodies.

i.e., 11.2 km/s, therefore, both must be projected with equal velocity. 

(ii) Momentum of body of mass m₁ is,
                       

Momentum of the body of mass  is, 

                       

Since     

∴              

That is, a heavy body must be thrown with greater momentum. 

(iii) Kinetic energy of mass  is, 

            

Kinetic energy of mass  is,

                 

Since m₁ > m₂, therefore K₁ > K_2.

That is, i.e., heavy body must be thrown with greater kinetic energy.