Not to add to the heat (I hope). The curvature of space-time (or gravitational field if you prefer) allows orbits that are conic sections. This includes circles, ellipses, parabolas (parabolae? ) and hyperbolas. This is an effect of the inverse square nature of gravity, that is the strength of the field (or curvature of space-time) drops off as the square of the distance.

FWIW, this is true of any inverse-square law, so trajectories in an electric field also follow conic section paths.

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"I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind." - William Thompson, 1st Baron Lord Kelvin

"If it was so, it might be, and if it were so, it would be, but as it isn't, it ain't. That's logic!" - Tweedledee

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