They do not. Artificial satellites are mostly close to the Earth, while the Moon is a quarter-million miles away.
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No, beacuse they stay at the same place.
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Stay above the same place on Earth "forever" ... thus they stay in the same place in our sky.
No, sometimes it is towards the Sun (at new moon), sometimes it is in the opposite direction (at full moon).
An isochronous satellite is one that orbits the earth in one day. So it orbits the earth as the same speed as the earth rotates. Most satellites that are isochronous are infact geostationary satellites as they also stay in the same position above the earth. However these satellites occupy a very specific orbit above the equator. It is possible to have isochronous satellites that aren't geostationary however getting them to remain in orbit would prove difficult.
There is no set inclination of a satellites orbit to the earth's equator. Once in space, the spin of the earth or where it's poles happen to be become irrelevant to the satellite. Many satellites like spy and weather satellites orbit over the two poles (north and south) while communication satellites are placed in orbit directly above the equator at a height that is synchronised with the earth's orbit. This way they stay permanently above the same place on the equator and do not APPEAR to move at all.
Yes because there are no forces on the moon to erode the foot step. That is that same reason we can leave the Apollo's on the moon.
No. The moon Is constantly revolving around the Earth, which is revolving the Sun.
The reason that satellites stay in orbit around Earth is because of two factors. Velocity and the gravitational pull between the satellite and the Earth.
Gravity and inertia.