The kinetic energy of an object in orbit can easily be found from
the following equations:

Centripetal force on a satellite of mass m moving at velocity v in
an orbit of radius r = mv^{2}/r

But this is equal to the gravitational force (F)
between the planet (mass M) and the satellite:

F =GMm/r^{2} and
so mv^{2} = GMm/r

But kinetic energy = ½mv^{2} and so:

kinetic
energy of the satellite = ½ GMm/r

All satellites have to be given a tangential velocity (v) to maintain their orbit position and this process is called orbit injection.

However the total energy **INPUT** required to put a satellite into an orbit of
radius r around a planet of mass M and radius R is therefore the sum of the
gravitational potential energy (GMm[1/R-1/r]) and the kinetic energy of the
satellite ( ½GMm/r).

Energy of launch = GMm[1/R – 1/2r]

Calculate the total energy required to place the space shuttle in orbit.

Orbit radius = 6.76x10

Mass of space shuttle = 1.18x10

Gravitational constant G = 6.67x10

Mass of the Earth = 6x10

Velocity in this orbit: v = √GM/r = √[6.67x10

Total energy required = GMm[1/R –1/2r] = 3.9x10

Note: this is very much simplified calculation. The mass used is just that of the shuttle orbiter. To raise the orbiter into its orbit requires rockets and fuel and these in turn need energy to lift them off the ground. The actual total energy required for the mission is therefore much larger than the result quoted above.