Work-energy theorem for elliptical orbits

[ZedCar]

Homework Statement

I was reading in a book a little section about orbital velocities.

It states:

For elliptical orbits, consider a body moving from point A to point B. The total work done by the force on the body is given by

W = KE (for B) - KE (for A)

Homework Equations

The Attempt at a Solution

Since W=Fd, does the KE simply represent the kinetic energy?

Thank you.

 

[tiny-tim]

Hi ZedCar!

Yes, the work energy theorem says that the change in energy equals the work done.

Since the only energy that changes for an orbiting body is the kinetic energy, and the only force is gravity, that means the change in kinetic energy equals the work done by gravity.

(We ignore the gravitational potential energy, since it is defined as minus the work done by a conservative force, such as gravity … and we cannot count it twice! )