[VadeRetro]

The behavior of hovering above either pole is inconsistent with orbiting Earth. Think of how geosynchronous works: the earth rotates under you at a rate that matches your orbital speed. Neither pole rotates in the manner required. An orbit at or near the equator is needed.

Just in general, when you orbit the earth, your orbit is either in the plane of the ecliptic or has to cross the plane of the ecliptic. You're orbiting the earth's center of mass. The center of mass must by Kepler's (pick one from "First," "Second," or "Third") Law be at one of the foci of your ellipse and thus in the plane of the orbit.

Same problem if the center of the orbit is the sun. You're still in the plane of the ecliptic or crossing it. The center of mass about which you are orbiting is going to be in the plane of your orbit. There's no stable orbit about Earth or sun which tracks the earth and hovers over one pole.

[RadioAstronomer]

Think of how geosynchronous works: the earth rotates under you at a rate that matches your orbital speed. Neither pole rotates in the manner required. An orbit at or near the equator is needed.

Geostationary. :-)

A geosynchronous orbit need not be over the equator.

[RadioAstronomer]

You're orbiting the earth's center of mass

Well kinda. :-)

Both objects are orbiting a COMMON center of mass. Just so happens with small satellites, the mass is so tiny compared to the Earth it is negligible.