Relative Orbital Physics

alpha1714

When a moon orbits around a planet, its centripetal force is balanced against the gravity of the planet, keeping it in a stable orbit. If all motion is relative, then the moon in perfect orbit could be said to be standing still while the planet rotates under it. The major difference I see is that if the moon is 'still' while the planet rotates, there would be no centripetal outward force to balance against the planet's gravity! Wouldn't it fall into the rotating planet?

Does a moon have angular momentum even if it is considered 'still' and the planet rotates? What am I missing?

I suppose the core question here is whether or not this scenario is evidence for a static 'aether', or space-time as a fabric within which absolute motion is truly applicable. Most contemporary theories reject any 'absolute' position or motion, so I'd be interested how relative motion can account for the seeming lack of congruent forces between perspectives within the physical system.

Thanks,

-alpha1714

Matterwave

Centripetal force IS the gravitational force. The gravitational force supplies the centripetal force in this scenario to keep the Moon from shooting off into space.

The reason the Moon doesn't fly into the Earth is not because the forces are balanced, but because it has sufficient velocity to escape a collision with Earth. In a sense, it is constantly falling towards the Earth, but it's "horizontal" speed is sufficient that it clear's Earth's curvature.

See this picture for example:
http://en.wikipedia.org/wiki/File:Newton_Cannon.svg

As for relative motion; since the Moon is constantly falling towards Earth, it is undergoing constant (approximately) acceleration. Thus, the Moon's reference frame is accelerated, and not inertial. Therefore, the principle of special relativity doesn't apply to the Moon. One must use general relativity to discuss these reference frames...a subject I'm not sufficiently proficient in to make further discussion.

TurtleMeister

The inertial frame of reference for bodies in orbit about each other is the center of mass, or barycenter. For the earth moon orbit, that center is located within the earth itself. The reason for this is that the earth is more massive than the moon. The earth does orbit the moon, but because the center is located within the earth itself, the earth only appears to wobble.

Go to this wikipedia page and scroll down to the section labeled "animations".
http://en.wikipedia.org/wiki/Center_of_mass

alpha1714

Thanks everyone for your replies. After considering your posts and a lot of further pondering, I think I understand what I was missing.

From the perspective of the planet, it is standing still while the moon is revolving around it. From the moon's point of view, it is still while the planet spins beneath. In both cases, however, the gravitational acceleration toward each other is balanced against a feeling of opposite acceleration in exactly the other direction. From the perspective of the moon, it is falling toward the planet while the planet is moving directly away from the moon at the same speed, and vice versa. This accounts for the feeling of mutual attraction while remaining at a fixed distance. It's like a speedboat dragging a water skier behind, both always feeling the tug of attraction but remaining the same distance apart.

Thanks again for your help, keep up the good thinking.

-alpha1714