Celestial orbits question :)

[Kyriakos]

A sort-of orbit-centered question:

-Is there any (known or theorised) celestial object which is estimated/guessed as running a non-elliptic orbit around another? (planet or star, etc).

From what i read on comet orbits, they are bound to break off the local star once they reach a parabolic course (and i suppose soon having a hyperbolic course next to the old focus point).

I am not sure how much actually is established on what happens in the not charted out parts of a parabolic or hyperbolic course, but it seems an interesting issue; afaik Kepler did not originally try to assign ellipsis as the orbital type of the known moving planets, and i was wondering if in astronomy there have been attempts to theorise on other orbital types (set parabolic, or any kind of hyperbolic)

[Aulus]

Perhaps I'm not understanding your question in entirely the right way (and please correct me if I am interpreting it wrongly), but an object can't have a periodic orbit if it follows a parabolic or hyperbolic path. The 'not charted out' areas of these orbits isn't some blank other portion of the curve waiting to be discovered, because there is no connection between one side and the other. If the object starts at say -x, and travels to +x on a parabolic path, it will never get to the spot -x again. In the picture below, supposing the object moves from bottom to top, it won't circle around to the bottom if it follows the parabolic or hyperbolic path.

Once the object comes near the mass at the focus and passes it, it's gone, and it will not return to that area by any gravitational interaction between it and the focus mass. These are called open or escape trajectories, and comets are the prime example. What happens after the comet passes the sun depends on its trajectory and what other large masses are in that direction. Theoretically, if we say there is nothing else to interact with, it'll fly off in that direction for eternity. I suppose, theoretically, we could also say that if there were masses in the right spots, a comet could follow various parabolic or hyperbolic orbits around them and eventually get back to where it started, but that's chance and not something inherent to the nature of the orbit.

[Kyriakos]

Thank you for the answer

My question is indeed if there is any theory about kinds of orbit which would appear to be close to the known outer parts of the parabola and the hyperbola, and so would seem interesting in that manner. I know that comets are examined as having elliptic orbit and are bound to get away from the object they orbit (eg the Sun) if they start having parabolic (and soon over that in eccentricity) movement in regards to the old focus point (the star).

Another part of the question is if there is any theory as to whether something can move parabolically in orbit, and what would go on in the missing part of the conic section.

[Aulus]

Another part of the question is if there is any theory as to whether something can move parabolically in orbit, and what would go on in the missing part of the conic section.

This is the part I'm not quite understanding. What do you mean by missing part of the conic section? Circles and ellipses are obviously bounded, but parabolas and hyperbolas mathematically go on to infinity.

It sounds like, to me, you are wondering if there is a possibility that an object can follow a parabolic trajectory around the Sun, fly off towards another focus point that it too moves around in a parabolic trajectory and returns to the Sun in the form of a distorted ellipse? In that case, no, there is no theory that I know of that describes that. By definition, a parabolic conic is not an elliptical conic as they have different values of eccentricity.

[Kyriakos]

^Yes, it is just a question on whether anyone tried to come up with a similar theory, exactly due to the nature of the conic sections which have from eccentricity=1 and above that Basically whether anything was noted to orbit our own star in a way very close to the parabolic(or hyperbolic) course, then vanished, and after X period of time returned and followed again a parabolic(or hyperbolic) course (or just did so once, etc). Not basing this question on info it has ever happened, just seemed interesting to me

[Aulus]

Ahhh, ok. Well, there are many comets that have near-1 eccentricity, and thus have elliptical orbits. Here's a table of some comets with eccentricity between 1 and 0.99, and it's definitely possible to see that near-parabolic orbits do return, with a variety of periods (hundreds to millions of years). Although, I am not sure why there a few e = 1.0000 comets with orbital periods, so I suppose the most I can say is that, in general, once e = 1 the object won't return to the Sun. I hoped I helped a little bit at least!

http://ssd.jpl.nasa.gov/sbdb_query.cgi#x

EDIT:
Whoops, link is just to the search query form. I used parameters e<1 and e>.99 and outputted the period.

[Kyriakos]

^Thanks

Btw, is the eccentricity of the so-called 'Halley's comet' stable? (i know it is significantly below 0.99, but i wondered if it stays virtually the same).

I read that it is possible that the comet was first documented before the Chinese sighting, ie at around 460 BC when a meteorite fell near Aigos Potamoi (where 60 years later the Athenian empire was defeated by Sparta and Lysander).
Supposedly this influenced Anaxagoras in his theories at that time, about the Sun being a massive fiery sphere, very distant and extremely hot.