If a mission is only interested in a single polar region of a planet, what kind of orbit would be most fitted for the satellite.
The first things that comes to mind is a polar orbit, but then it seems that there is no way to avoid huge amount of wasted time for the satellite.
Maybe you can reduce this by using a Molniya orbit, but isn't there anything better ? Do you have to go highly elliptical ?
Because of the way orbits work you can't have a satellite in a stationary orbit over the poles. I think a Molniya orbit would work best, that's what the Soviets (and now Russia) used for communications satellites.
The previous comment and answer are correct if you assume a Keplerian orbit. But if you have a propulsion system that allows a non-Keplerian orbit for a sufficient duration to achieve the objectives, then indeed there is a kind of orbit that allows such continuous observation of one pole. It's called a "pole-sitter" orbit, an idea that goes back at least to Johnie M. Driver's 1980 paper in the Journal of Spacecraft and Rockets, "Analysis of an Arctic Polesitter", unfortunately not available for freebie download. Another paper, by Ceriotti et al., is available for freebie download at https://pdfs.semanticscholar.org/7c2b/2fceb1830133a0cdba092a188f4d697976e6.pdf . In that paper they consider solar sail and electric propulsion, even both together on a single spacecraft. Usually for these orbits the distances to the pole are fairly large (tens of thousands of km or more), so you might need some moderately powerful optics to get good spatial resolution. Also they're significantly offset from directly above the pole, in the anti-sun direction, so there's some foreshortening, and possibly some specular reflections from areas on the sunward side of the pole.
