3D Map of the Trojans

[Krystman]

Hello. I'm not sure if this question fits in here or in physics.

Some time ago I did this nice interactive 3D map of the interplanetary neighborhood. It all very low-fi. I just used data from Wikipedia.
http://kisd.de/~krystian/starmap/

I would like to do a similar map of the asteroid belt of the solar system. But because they are on orbits and swarm around, I would like to focus on the Jupiter Trojans as they stick around in one "cloud".

What I would like to find out is how to determine the spatial the position of a Trojan relative to it's Lagrangian point if you have only the ephemeris to start with. I want to end up with a plot very much like this, only in 3D.
http://en.wikipedia.org/wiki/File:Inner ... tem-en.png

Can anybody please help me out with the math?

 

[eburacum45]

Hi, Krystman! I must congratulate you on your remarkable 3d maps. They are beautiful.

I'm sure you know that the Trojan Asteroids all move with respect to the Lagrangian points over time. Do you intend to make a map of a snapshot in time, perhaps?

 

[Krystman]

I'd love to make an animated map. But I realized that calculating the orbits may be quite difficult.

 

[MeteorWayne]

The Trojans do not remain at a fixed distance from Jupiter. The float around Near the L4 and L5 points, but their orbits constantly change, at a faster rate than the planet's orbits do. So as the orbital elements constantly change, the ephemeris will constatly change.