Energie van een satelliet in een cirkelvormige baan

Consider an artificial satellite orbiting the Earth in a perfectly circular orbit under the influence of the Earth's gravitational force.

Therefore, it orbits with critical velocity v_c, which is equal to the square root of the product of the gravitational constant and the Earth's mass, divided by its total distance from the Earth's center.

Now, squaring and multiplying the critical velocity equation with half times the satellite's mass, the kinetic energy of the satellite in a circular orbit is obtained.

Recall that the potential energy of the satellite is expressed as the negative product of the gravitational constant and the two masses, divided by the distance between them.

Therefore, the potential energy of the satellite equals minus two times its kinetic energy.

Since the total energy is a sum of kinetic and potential energy, it equals the negative of its kinetic energy for the satellite in circular orbit. The negative sign in the total energy equation indicates that the satellite is bound to the Earth.