I think you knew this but it wasn't obvious from how you wrote it. Your orbit is not required to be a circle. The diagrams we draw for children are nice circles, but most things that we know are orbiting something do not travel in a circle, e.g. the Earth -- if the orbit was circular our seasons would be slightly different†and the insight that the orbits can be non-circular ellipses was critical to the reasoning that eventually got us a heliocentric model of our solar system.
Geostationary communications satellites do have a basically circular orbit, as you said, but many other birds do not.
Russia has a bunch of stuff in orbits that "linger" very high over Russian territory for much of their orbital period then shoot right around close to the back side of the planet quickly and linger again, these are called Molniya orbits.
The US has a bunch of secret (presumably spy) satellites that fly less obvious orbits like this too, for presumably similar reasons.
†Edited: This post originally said "very" different, but in fact the difference would be modest since our orbit just isn't that elliptical. I wasn't able to find out how modest, but certainly if you think summer in New Zealand (in December) is pretty similar to summer in England (in June) then it's reasonable to say at least that similar.
Geostationary communications satellites do have a basically circular orbit, as you said, but many other birds do not.
Russia has a bunch of stuff in orbits that "linger" very high over Russian territory for much of their orbital period then shoot right around close to the back side of the planet quickly and linger again, these are called Molniya orbits.
The US has a bunch of secret (presumably spy) satellites that fly less obvious orbits like this too, for presumably similar reasons.
†Edited: This post originally said "very" different, but in fact the difference would be modest since our orbit just isn't that elliptical. I wasn't able to find out how modest, but certainly if you think summer in New Zealand (in December) is pretty similar to summer in England (in June) then it's reasonable to say at least that similar.