Imagine that we have an object of mass m in a circular orbit around an object of mass M. An example could be a satellite orbiting the Earth. What is the total energy associated with this object in its circular orbit?

As usual, E = U + K.

U

=

- G m M R

and         K = ½ mv2

The only force acting on the object is the force of gravity. Applying Newton's Second Law gives:

SF = ma

G m M r2

=

mv2 r

Therefore:   mv2

=

G m M r

and   K

=

½ mv2

=

G m M 2r

The kinetic energy is positive, and half the size of the potential energy.

E

=

-G m M r

+

G m M 2r

=

-G m M 2r

A negative total energy tells us that this is a bound system. Much like an electron is bound to a proton in a hydrogen atom with a negative binding energy, the satellite is bound to the Earth - energy would have to be added to each system to remove the electron or the satellite.