Trojan asteroids aren't doing correct tadpole orbits

[charliewhitfield]

They currently go around Jupiter's L4 and L5 in, well, some other way -- not tadpole orbits as they should.

Tadpole and horseshoe orbits are well-approximated by existing equations (see Solar System Dynamics, Murray & Dermott, ch. 3). But I currently lack mathematical competence to implement some parts of it. Imaginary eigenvalues! Oh my!

Anyway, I'll figure it out eventually, if no one else does before me...

[charliewhitfield]

I've come to realize that this issue will never be closed. There are no closed form solutions, and good approximations are too expensive to do for 1000s of asteroids.

However, v0.0.14 goes a long way towards less inaccuracy! The amplitude of axial and longitudinal librations is now correct, I believe.

So, we will never close this issue. But we will continue to progress towards a less inaccurate state!