The orbit of cruithne?

[Zylstra]

so, I'm looking at this site, and I don't grasp how this orbit works. I mean, I can see how the 'kidney bean' shape might come about as it speeds between Earth and Sol, but how does that work when it's on the opposite side of the sun as earth?

I'm confused

 

[Master_Ghost_Knight]

I believe it is using a normalized frame of reference for a 3 body problem. It is basically a frame of reference that spins with the earths motion arround the sun, to it both earth and sol are standing still while everyhing else is moving. The shape is due to a combination of the motion of the earth arround the sun and the asteroid own motion.
And because the periods of the obits are very close if the asteroid starts at the oposite end of the sun, as it closes in trough one side, the earth slips away to the other, and so from earth you will never see the asteroid from this side of the sun. The transformation of this particular orbit on this reference makes it necessarily that the shape looks like a kidney bean.
A similar patern will ocur if the starting point is somewhere else (but the position f the bean differs).

The periods are not precisely the same, and It does apear tht te asteroid is disturbed as he falls behind and picks up again to the position of the earth.

In a usual frame of reference, it would look like this

 

[Artsysiridean]

So it's orbit is like that of a hula hoop?

 

[Master_Ghost_Knight]

So it's orbit is like that of a hula hoop?

As a first aproximation it is an elipse, whit a better aproximation it is an elipse the changes the position slowly over time.
The truth is it is neither, it is just close aproximation, the real shape doesn't follow any perfect patern at all.