# A Coorbital question

#### mollwollfumble

Summary
Information wanted on three-body solvers, and on high inclination coorbitals
I was working on a proposal for a spacecraft, and suddenly realised that the ideal orbit may be a high inclination type of near-Earth coorbital called a "retrograde satellite" or RS orbit. Do you know of:

* A person who can compute 100 years of coorbital stability using three body (sun, earth, satellite) or four body (with moon) kinematics?

* A simple-to-use approximate 3-D calculator for the three body problem, simplified so the third body has negligible mass.

* Where I can find as much information as possible on RS orbits in general. eg. ellipticity vs inclination.

* Any information at all on periodic RS orbits with 1:1 resonance.

So far, all I know about RS orbits comes from "Coorbital Dynamics at Large Eccentricity and Inclination ", https://journals.aps.org/prl/pdf/10.1103/PhysRevLett.83.2506
The inclination range I'm most interested in is 15 to 45 degrees.

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#### mollwollfumble

These are the sort of orbits I'm hoping for. These are heliocentric orbits, but appear to circle the Earth. The Earth is at (0, 0). The L4 and L5 Lagrangian points are at +-60 degrees on the horizontal axis. In the background, contours of the intensity of the inner zodiacal light are drawn. These orbits see through the fringes of the inner zodiacal light at all points on the orbit and so, with luck and planning, could see faint galaxies and transient events on the far side of the Sun. They are closer than orbits around L4 or L5 and more stable than Earth- leading and Earth-trailing trajectories.

#### mollwollfumble

> A simple-to-use approximate 3-D calculator for the three body problem, simplified so the third body has negligible mass.

I think I've found one. http://www.fisica.edu.uy/~gallardo/atlas/
Program name atlas2bgeneral.f

It needs at least a slight modification in that it calculates number of resonances at assumed eccentricity and inclination. Whereas I want best (ie periodic orbit) eccentricity and inclination for a specific (Earth 1:1) resonance. I'm intrigued to know if its calculation of semimajor axis is correct, I don't think it can be because the semimajor axis has to depend on orbital inclination. The closer the inclination brings us to Earth, the larger the semimajor axis has to be, not by much, but by enough to make a difference as to whether the orbit is exactly 1:1 resonant.

"Coorbital question"

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