EXAMPLE
A satellite of mass is launched from the surface of the Earth into an orbit of radius , where
is the radius of the Earth. How much work is done to get it into orbit?The work done getting the satellite from one place to another is equal to the change in the
satellite’s potential energy. If its potential energy on the surface of the Earth is and its potential
energy when it is in orbit is , then the amount of work done is:
Energy of an Orbiting Satellite
Suppose a satellite of mass is in orbit around the Earth at a radius R. We know the kinetic
energy of the satellite is KE =^1 / 2 mv^2. We also know that we can express centripetal force, , as
= mv^2 /R. Accordingly, we can substitute this equation into the equation for kinetic energy andget:
Because is equal to the gravitational force, we can substitute Newton’s Law of Universal
Gravitation in for :
We know that the potential energy of the satellite is , so the total energy of the
satellite is the sum, E = KE + U:
Weightlessness
People rarely get to experience firsthand the phenomenon of weightlessness, but that doesn’t keep