If an ellipse has semi-major axis length a, and a circle has radius a, and you walked along their boundary, which one would be longer? A circle's circumference is calculated using $2\pi r$, but I don't know the equivalent for an ellipse. Probably involves integration. Is there a general rule or will it vary from case to case?
2026-04-12 21:37:59.1776029879
Does an ellipse or circle have greater circumference?
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If the semimajor axis of the ellipse is identical to the radius of the circle, then the perimeter of the ellipse is smaller. One way to see this is by continuously increasing the semiminor axis to match that radius as well. This will stretch your ellipse to a circle, and that stretching will only make things (lengths as well as areas) larger, never smaller.
Actually computing the perimeter of an ellipse involves elliptic integrals, which is the reason why there is no direct analogon to the simple $2\pi r$ you have for circles.
If that's what you are after, then likely the perimeter is of little interest. You should ask about this explicitely (but not in this question here, and only after checking existing answers). If you do so, make sure to be precise as to what you fix in your comparison. Is it the energy of the planet, or the perihelion distance, or the orbit period, or whatever.