In our Universe the orbits of planets are generally elliptical and ellipses are a type of conic shape as they can be formed by cutting out a cross section from a cone. Circles and ellipses are the only conical shapes that a planet could have as an actual orbit as parabolas and hyperbolas don't curve back in on themselves like circles and ellipses and so if a planet had a parabolic or hyperbolic orbit then it would move towards the star and then move away from the star without moving back towards the star? While ellipses including circles are the only conic shape that curves back in on itself there are other non conic shapes that curve back in on themselves.
If a circle would be the only conic shape that would be stable as an orbit in dimensions greater than 3d could there still be none conic shapes that would be stable as orbits?