Re: Some Physics Snacks
1) If you took the Earth away, "poof," and the Moon were at just that part of the orbit where it were moving in the same direction as the Earth, then it would continue in an Earthlike orbit around the Sun. Since both the Earth and the Moon are revolving around the Sun, at the same distance and speed, they both have a centrifugal force which exactly balances the Sun's gravitational pull on them. You could say they are both in orbit around the Sun together. Then, Earth + Moon is a system in orbit around the sun, and we can consider just the gravitional interaction between the Earth and the moon and disregard the Sun when computing lunar cycles.
2) A Geosynchronous satellite is defined as one whose orbit causes it to reside in exactly one spot above the Earth's surface. It is synchrozined with the Earth (Geo- means Earth; it comes from Greek.) The only place this occurs is when you're an exact distance above the equator. Here's why: First, the velocity of the orbit is determined by the distance from the center of the Earth. Geosynchronous satellites have to be just exactly the distance that gives them a 24 hour orbit. I forget what the exact distance is. You can compute it. Second, the satellite must be moving in the exact same direction that the earth is spinning, or else it will drift. Picture it: Say the satellite starts over the equator but is going north in it's orbit. After six hours, it is over the north pole. Well, it's not over the same spot anymore is it? So it's not geosynchronous. It may still have a 24 hour orbit and not be geosynchronous.
3) I don't know about 3. That's cool if it's true.
4) A flywheel could be any shape. (But it should be symmetric about the axis unless you want some serious vibration issues!) It depends mostly on the materials you're building it with and the factory methods you're using. Sorry, but it is all engineering. From a scientific point of view, the ideal flywheel is a ring of infinite diameter...
Basically, you want enough mass away from the axis to store gobs of rotational momentum, but you need enough mass close to the center so that when it spins up to 30,000 rpm, it doesn't fall apart because of the mechanical stresses (even hard steel can take only so much).
5) It does? I'm going to have to try that!