Thanks Tony,
I found your program very good for visualising these orbits, especially lagrange.gsim. (Is lagrange.gsim an accurate simulation of what the actual orbit of a lagrange captured object would be?) If that's the case, then I just need to work out how to convert your orbitsimulator parameters into Celestia's ElipticalOrbit definitions.
In laymans terms, the way I think of this orbit, in order to visualise it, is to think of an object initially at the L5 position in an orbit modelled on the Moon's orbit: It's orbit will be modified or perturbed by the Sun''s influence as the object orbits the Earth, such that when it is travelling towards the Sun it's orbital velocity relative to Earth will be increased by the Sun's influence, thereby moving it into a lower Earth orbit and ahead of the L-point; As it reaches the point between Earth and Sun it will be at it's closest approach to Earth, and the Sun's influence is reversed, such that it is now being slowed by the Sun, therefore it's orbit widens and slows again, and as it continues it's outward journey from the Sun, it is slowed further so that it now passes outside and behind the L-point. It will be at it's slowest and widest (apogee??) when it reaches the far side of the Earth from the Sun.
To me, this equates to an elliptical orbit modelled on the Moon's but with a much greater eccentricity. (This can definitely be modelled to some approximation within Celestia). It seems to me that this ellipse's axis must also advance as the Earth orbits the Sun, so that (perigee?? periapsis??) always occurs at the conjunction between Sun and Earth. (Not sure how to model that in Celestia)
All this means that the object orbits around the L-point in the opposite direction to it's orbit around the earth. ie. Clockwise rather than anti-clockwise. (This is confirmed by your simulation)
The thing I haven't grasped yet, is how to extend this conceptual model to
many objects following each other around L5, but I think that would equate to varying their individual Epoch or MeanAnomaly/MeanLongitude's (in Celestia terminology), but I think that would have to include a corresponding variation in the axis alignment as well, to ensure each object reaches perigee at the appropriate time for it's epoch.
Am I thinking about all this in the right way?
Sorry if my thinking is a little simplistic, but I'm no planetary scientist.
PS. The other thing I haven't worked out, is why it's effective orbit around the L-point is 89 days as reported on some websites, but I'm thinking this may be to do with the fact that it's effective motion around the point, is retrograde to it's orbital motion.
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