can a satellite coast in a stable orbit in a plane that doesn't intersect the Earth's center?

Question

Can a satellite coast in a stable orbit in a plane that doesn't intersect the Earth's center? Why or why not?

Answer 1

No. Gravity will always pull the satellite toward the center of the earth. If you have a satellite orbiting in a plane that does not contain the center of the earth, then you will have a component of gravity that points perpendicular to that orbiting plane. The in-plane component or gravity will keep the satellite moving in a circle. However, the out-of-plane component of gravity will pull the satellite away from the plane that it is originally orbiting toward a plane that contains the center of the earth. So if you somehow released a satellite with a fly-by space ship into an orbit with a plane that does not containe the center of the earth, it will end up actually traveling in a corkscrew path, drifting toward an orbit plane that will contain the center of the earth. Assuming your orbit is significantly larger than the radius of the earth and there is no resistance to motion, it will overshoot, slow down, then corkscrew back in the other direction. The oscillation about the two ends of the corkscrew orbit will actually be a form of simple harmonic motion, all the while with the satellite circling the earth in a circular fashion perpendicular to the axis of the corkscrew.

Answer 2

No. If you go through the math, you can model the entire earth as having all its mass concentrated at its center. Anything that orbints must be in a plane that intersects it.