# Homework Help: Constant energy in an elliptical orbit

1. Nov 15, 2013

### Sleepycoaster

1. The problem statement, all variables and given/known data

There's no specific question, but mostly a theory I wanted clarified. According to my textbook, the measurement of the total mechanical energy E of a mass orbiting a much larger mass in an ellipse is:

E = radial (change in radius) kinetic energy + rotational kinetic energy + potential energy

Or in other words,

E = (1/2)μ(dr/dt)2 + (1/2)(angular momentum)^2 / μr2 - GMm/r

But consider this: At both the apogee and perigee of the orbit the total energy should be constant and radial kinetic energy should be zero. Yet at these points the r is different and everything else is the same. How can energy be constant?

2. Relevant equations

r is the radius between the focus of the ellipse where the larger mass is and the smaller mass
μ is the reduced mass 1/(1/m + 1/M)

3. The attempt at a solution

None so far. It seems like a rather fundamental issue with a hopefully fundamental fix.

Last edited: Nov 15, 2013
2. Nov 15, 2013

### TSny

Hello, sleepycoaster.

Yes.

Note that r occurs in the denominator of two terms and the two terms have opposite signs.