Circular orbits

  • First of all, I'm studying orbits for a hobby: world building. Unfortunately, my mathematical abilities approach a ridiculous low threshold, which means I am stuck with reading the simplest explanations, which in turn leave me asking tons of fairly basic questions.

    Allow me to start with a simple point. I know that Kepler's Laws state that planetary orbits must always be elliptical. I also know that Earth's orbit varies from more elliptical to less elliptical, and that its less elliptical stage is nearly circular.

    So... what would happen if Earth did have a circular orbit? Why is it impossible for any planet (or moon, by the way) to orbit another body in a perfectly circular path?

    Some moons do have as good a circular orbit as can be measured. Triton of Neptune) has an eccentricity of 0.0000 and I think that is to the precision it has been measured. That of Earth is 0.0167. And Triton is almost as large as our Moon. Triton's interaction with smaller moons is believed to have circularized its orbit. A circle is a special case of an ellipse, and one which is naturally strived for, if there's other junk around to take the hit.

    @LocalFluff: Oh. That makes my whole question particularly dumb, I suppose.

    Hey, no, don't say that!

    @LocalFluff - has Triton's eccentricity at 0.000016, not 0.

    @LocalFluff: Dumb questions can have amazingly enlightening answers. One can be embarrassed, but should never be ashamed of them. :)

    Some of the biggest breakthroughs come from very simple questions.

  • You've been given an answer, and it's perfectly valid, but here's something from a different perspective (less strict).

    A circle is really just a particular case of an ellipse. Take an ellipse, and change it, by moving its focal points closer together. When those two points coincide, what you get is a circle. It's still an ellipse, technically - one that happens to have both focal points in the same place, is all.

    enter image description here

    So yes, you can actually have planetary orbits, or any orbits, circular. There's nothing forbidding that. It's just pretty unlikely that this will occur via a natural process.

    As indicated elsewhere, in the real world, all orbits and trajectories are a bit imperfect due to perturbations - whether they be elliptical, circular, parabolic or hyperbolic, they are always a bit perturbed by external factors. In many cases, perturbations are so tiny that you can ignore them.

    When a planet is orbiting the Sun, and the orbit is elliptical, the Sun will be in one of those two focal points; the other point has no particular signification. If you could circularize that orbit, then the Sun would be in the center of the circle, of course.

    Kepler's laws remain valid for a circular orbit:

    1. The orbit of every planet is an ellipse with the Sun at one of the two foci.

    Still true. A circle is an ellipse where the foci coincide.

    1. A line joining a planet and the Sun sweeps out equal areas during equal intervals of time.

    Still true. On a circular orbit, the planet moves at constant speed, so the swept area remains constant per time.

    1. The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit.

    Still true. The semi-major axis becomes the radius of the circle.

    You must understand that Kepler's laws now have more of a historic interest. They are not exactly at the bleeding edge of science anymore. During Kepler's time, it seemed reasonable to state that all orbits must be elliptical (in the strict sense of the term), but now we know that trajectories (including orbits, or closed trajectories) can be circular, elliptical, parabolic or hyperbolic, depending on a few factors.

    We also know that perturbations actually deflect all these trajectories a little bit from ideal shapes (but it's usually a very tiny effect).

    We also know that relativity makes all "elliptical" orbits more complex - they remain close to elliptic, but the whole ellipse keeps turning around the central star very slowly.

    All this stuff was not known during Kepler's time, so take his laws for what they are - a snapshot of the development of our understanding in time.

    Just to clarify, though both answers were helpful, this one gives a very clear, step-by-step explanation. So I've chosen it.

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Content dated before 7/24/2021 11:53 AM

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