I've been toying around with n-body simulations (using research-grade software) and I've noticed a particular effect in many of my simulations: In many arbitrary multi-planet systems I simulate, there is a good chance the innermost planet's semi-major axis will significantly increase over time (~1-10% increase in 'a' after ~10-100 million orbits, and growing). I'm totally puzzled by this. I can't find a rhyme or reason as to why this occurs—I haven't identified any consistent variables in resonance, distance, eccentricity, or any other parameters of the planet.

At first I thought it might be a tidal effect between the star and the innermost planet. But I tested that assumption by removing all the other planets and re-running several of the simulations: no increase in the semi-major axis occurs. This indicates to me some mechanism between the planets themselves is "pumping" the semi-major axis of the innermost planet.

Anyone have an idea what is going on? And if so, what parameters in orbital architecture between the planets avoids this mechanism?


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    $\begingroup$ Check the ratios of orbital periods with the inner planet and each other planet. If an orbital ratio is close to a low integer fraction, you may have effectively put your innermost planet in a Kirkwood gap: en.wikipedia.org/wiki/Kirkwood_gap. To fix it, set the semi-major axes so you don't have resonant orbital periods. $\endgroup$
    – Connor Garcia
    Mar 2, 2022 at 18:13
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    $\begingroup$ @planetmaker The simulator is Posidonius: blancocuaresma.com/s/posidonius/manual/introduction/overview. It conservers angular momentum and energy (with some small degree of error over time of course). I'm not that familiar with how to "read" what the energy and angular momentum graphs mean exactly. Though it looks like, for the ENTIRE system, the "relative energy error" (ΔE/E) tends to be slightly positive (-0.0005 to 0.00125 is fairly typical). The "conservation of angular momentum" (ΔL/L) graph tends to read in the 10e-10 to 10e-8 range for these sims. That help? $\endgroup$
    – n_bandit
    Mar 2, 2022 at 18:19
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    $\begingroup$ @ConnorGarcia This effects doesn't seem to depend on mass ratio. At least not that I've noticed. The inner planet can be much more massive or less than the outer planet, and the effect still sometimes happens in some simulation configurations. $\endgroup$
    – n_bandit
    Mar 2, 2022 at 21:46
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    $\begingroup$ @ConnorGarcia I'm happy to post several example of case files (in python) that Posidonius interprets into a simulation. The Keplerian orbital elements and other info are contained in those and easy to read. It's not possible to attach a file here though, right? How might I share this info? $\endgroup$
    – n_bandit
    Mar 2, 2022 at 21:54
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    $\begingroup$ I suspect the planets are somehow incrementally gaining kinetic energy in the sim that they shouldn't be. But why this would be happening with WHFast and not IAS15 I don't know. $\endgroup$
    – n_bandit
    Mar 3, 2022 at 4:34


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