# Total Energy of an orbiting satellite?

1. Feb 15, 2015

### YarnJunior

Hello!

So this is a rather stupid question, but I'm having trouble with gravitational fields, and can't exactly pinpoint what's going on. The total energy of an orbiting satellite is (due to ME = KE + GPE) (-GMm/2r), right? Well, I have found multiple statements that claim that the 'r' we use for GPE is the radius of the planetary object, whilst the 'R' we use for KE is the orbiting radius. How could this be? This means that the only possible way for ME to = -GMm/2r is for the r of the KE to match that of the GPE, which basically mean that the object MUST be on the surface, not orbiting.

Pardon my ignorance, but this is driving me insane. I'm quite certain I got the R's wrong, if so I'd be really grateful for any clarification. Thanks a lot!

2. Feb 15, 2015

### willem2

For the total energy to be: -GMm/(2r) = -GMm/r (potential) + GMm/(2r) (kinetic), you need the radius of the orbit in the expression for both kinetic and potential energy.
Kinetic energy depends on speed, which depends on the radius of the orbit, because the gravitational force must equal the acceleration:
GmM/r^2 = v^2/r.
The radius of the earth doesn't come into it. You'd get the same orbits and energies with a planet with a smaller radius and the same mass.

Note that potential energy here is 0 for an object at infinity, and is <0 at any other place.
If you want potential energy relative to the surface you get GMm/R - GMm/r, where R is the radius of the earth and r the radius of the orbit.