Hierax Posted June 16, 2009 Report Share Posted June 16, 2009 I need some help with some complex calculations involving conjunctions of moons in a 3-moon and 2 different 6-moon systems all with an orbital Laplace Resonances. Basically, I need to create paper charts (or computer charts and/or animations) of moon conjunctions based on the math of Jupiter's Io-Euorpa-Ganymede dynamics. If you have the skills and patience to figure these out and explain them, let me know (either here or by private message) and I'll explain exactly what I'm trying to create in detail. Thanks! Quote Link to comment Share on other sites More sharing options...
Cancer Posted June 16, 2009 Report Share Posted June 16, 2009 Re: Help with Orbit Laplace Resonance Calculations of Conjunctions Ummm ... a 6-moon system? Computing one of those right so that you know it really works is an exceedingly complex thing. Slapping together something that has a resonance pattern which may or may not be stable for any length of time (hint: bet on not) is something else. Quote Link to comment Share on other sites More sharing options...
Hierax Posted June 16, 2009 Author Report Share Posted June 16, 2009 Re: Help with Orbit Laplace Resonance Calculations of Conjunctions The difficulty of this is why I wanted to work with something where the calculations are already done in a real-universe system that already is stable and works, hence the Jupiter's Io-Euorpa-Ganymede. That is what would be used for the 3-moon system. The 2 different 6-moon systems would actually be just 2 variant combos of this 3-moon system for parallel planets - where there would be 3 pairs of 2 moons using the 1:2:4 resonance: one using 6 orbits with pairs with the same rotational rate in different orbital distances; and one using 3 orbits but with the pairs sharing the same orbit via opposite moons. I don't need to get it exactly realistically stable just enough that some space-science guy has to stop to think if it is possible at all rather than outright rejecting it. It was a long shot but I figured it couldn't hurt to ask. FWIW, it's for a Fantasy universe but there are some sci-fi elements and I hate just "hand waving" stuff away and like things to at least be strongly based on something that does work. One of these would be for the main planet and the other 2 for parallel dimension alternate "earths". Quote Link to comment Share on other sites More sharing options...
Cancer Posted June 16, 2009 Report Share Posted June 16, 2009 Re: Help with Orbit Laplace Resonance Calculations of Conjunctions Moons in the same orbit but 180 degrees apart is known not to be stable in the long term; that's a senior-level-undergrad homework problem to show that. Pairs of moons in general cannot share an orbit unless there's something else making serious perturbations in the system. In the Saturn system with co-orbital satellites, the co-orbitals are tiny and are perturbed continually by the other moons and by the ring systems. On a back-of-the-envelope basis, Kepler's 3rd Law tells you P^2/a^3 = constant for a given planet-moon system, where P is the orbital period and a is the orbital size. So if you want orbits with periods that are multiples of the innermost one in the geometric sequence 1, 2, 4, 8, 16, 32, then the orbital sizes of each will be the orbital size of the first one times 1, 2^3/2, 4^3/2, 8^3/2, etc. The orbits will certainly not be circular, but I would guess that the orbital eccentricities have to be modest (of the Galilean satellites of Jupiter, the largest eccentricity is 0.0101 for Europa), all the orbits prograde and more or less coplanar. Quote Link to comment Share on other sites More sharing options...
Peregrine Posted June 16, 2009 Report Share Posted June 16, 2009 Re: Help with Orbit Laplace Resonance Calculations of Conjunctions Moons in the same orbit but 180 degrees apart is known not to be stable in the long term; that's a senior-level-undergrad homework problem to show that. Just out of curiosity, does the same hold true for 3 at 120 degrees? Quote Link to comment Share on other sites More sharing options...
novi Posted June 16, 2009 Report Share Posted June 16, 2009 Re: Help with Orbit Laplace Resonance Calculations of Conjunctions Just out of curiosity' date=' does the same hold true for 3 at 120 degrees?[/quote'] IIRC, it also is true there, that such a thing is unstable for objects of similar masses. If the central object is of much greater mass*, the other two will be in Lagrange points and reasonably stable. The points are dynamically unstable, but you can rig it so that an object will stay near a Lagrange point for several thousand orbits, give or take. *I forget how much larger it needs to be beyond several orders of magnitude. Quote Link to comment Share on other sites More sharing options...
Kraven Kor Posted June 23, 2009 Report Share Posted June 23, 2009 Re: Help with Orbit Laplace Resonance Calculations of Conjunctions If you have more determination (and a few more firing neurons) than me, you might be able to get something worked up using Universe Sandbox. The program is capable of a lot, but you have to really know what you are doing and have a lot of time, from what I can tell, to actually create a working system in it - moons, planets, whatever. Then you can rotate the view and adjust time scale to get your charts / pics put together. Quote Link to comment Share on other sites More sharing options...
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