I am not a mathematician and it may even take me weeks to understand the math involved but I have an odd question on orbital mechanics that I hope will be worth the experts' time. I am a hobbyist programmer just getting my feet wet in the concepts 3D graphics and (by extension) orbital mechanics.
As I understand it a polar orbit allows a satellite to efficiently see the entire surface of a planet because the planet rotates on its axis while the satellite orbits at an inclination of 90 degrees to the equator. This theoretically makes polar orbits very efficient (few to no course corrections required) for mapping the surface of planets.
But -- hypothetically -- what if the planet does not rotate at all? What kind of orbit would be needed to map the planet's surface in an efficient way (few to no course corrections once the satellite's orbital path was initiated)? Is there a name for such an orbital type? Can this even be done or would a non-rotating planet need to be orbited with constant course corrections to map the entire surface?
Since this is about virtual space go ahead and assume a perfect sphere and uniform gravity to keep the math simple. On the other hand, how different would the math be if this was a perfect ellipsoid instead of a perfect sphere?
Thanks for indulging my self-directed education on this subject.