# Why do satellites orbit around the centre of a planet?

Why can satellites not orbit around the North or South Pole, instead of orbiting about the centre of the earth?

• On the chance that the answers are misinterpreting, highly inclined orbits are a thing. This means that the satelight orbits in a plane that includes the goemetric center of the Earth but also passes near the goemetric poles. Useful for mapping, global surface observations and spying. Such orbits are not stable in the long term due to high order moments of the planet, but they last for years. Commented Nov 19, 2019 at 1:03
• @dmckee, "Such orbits are not stable in the long term...", "...but they last for years." : Could you please explain how polar orbits being unstable last for years? Further, what does this statement mean "...high order moments of the planet..."? Thank you. Commented Nov 27, 2019 at 7:17

The gravitational force $$\vec F$$ can be split into two components $$\vec {F'}$$ and $$\vec {F''}$$ such that $$\vec {F}=\vec {F'} + \vec {F''}$$.
The component in the plane of the orbit $$\vec {F'}$$ provides the centripetal acceleration around the North Pole $$r\omega^2$$.
However there is still the component $$\vec {F''}$$ to deal with as otherwise there will also be an acceleration of the satellite in the direction of this force.
One would need to have the satellite equipped with a rocket engine continuously providing a force equal in magnitude but opposite in direction to force $$\vec {F''}$$ to keep the satellite in the required orbit.