Elliptical orbit question

Reposting with corrections ("centrifugal force" is what was meant):

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It might help to think of two-body orbit dynamics in a way that most people don't think of it:

A satellite going around a planet acts like a mass hanging on the end of a spring.

Basic diagram:
https://i.ytimg.com/vi/lZPtFDXYQRU/maxresdefault.jpg

Gravity pulls down on the mass, but the mass can move down and up in an oscillation. The spring is pulling up on the mass, and this is how the centrifugal force works, pulling the satellite up and away from the Earth. The centrifugal force is a manifestation of the inertial property of the satellite's mass.

When gravity and the centrifugal force are in equilibrium, the mass remains at a constant altitude from the Earth. Circular orbits are static in this respect, in a reference frame that rotates at the same rate as the satellite is orbiting. And this is why you can bolt your DirecTV dish pointing to one point in the sky and the geometry does not change. The satellite is as still as the mass hanging on the end of the spring.

Elliptical orbits are not still. They have a continual tradeoff of Potential Energy & Kinetic Energy.

This is the situation you have in the lab, with the mass bobbing up and down on the end of the spring.

Hopefully this makes it clear exactly what is causing the altitude changes with the satellite. When the mass moves down past what would be the static equilibrium point, it has plenty of kinetic energy. And that is getting packed into "the spring" of inertia. It bottoms out at perigee when the spring force finally overcomes the motion from the gravitational force, and the direction reverses.

So yes, it is the inertia of the velocity that has built up during this downward part of the cycle that causes the altitude reversal. You can think of it as a spring that has been pulling on this satellite. You stretch the spring all the way down to perigee, and then its force will finally reverse the direction that the force of gravity was pulling in.

But from every moment that the mass was below the point of equilibrium - the altitude of the circular orbit - that spring force was greater than the force of gravity. The satellite's velocity toward the Earth was decelerating the entire time since it had passed that equilibrium point.

That equates to a flight path angle, gamma, with respect to the horizon, that was continually shallowing ever since passing that circular altitude equilibrium point. And upon passing perigee, the satellite's flight path angle goes through zero and turns from negative to positive and it starts climbing again.

Just like the mass on the spring.

~ CT
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(Originally posted at https://groups.google.com/d/msg/sci....k/HxefrAHiBgAJ)