<p>I've been toying around with n-body simulations (using research-grade software) and I've noticed a particular effect in <em>many</em> of my simulations: <strong>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).</strong> 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.</p>
<p>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 &quot;pumping&quot; the semi-major axis of the innermost planet.</p>
<p><strong>Anyone have an idea what is going on? And if so, what parameters in orbital architecture between the planets avoids this mechanism?</strong></p>
<p>Thanks!</p>

CC BY-SA 4.0
2022-03-02T17:35:37.340Z
Does your simulation conserve both, energy and angular momentum? Did you compare the total at the start and at the end of your simulation? Do you loose (or gain) any by numeric accuracy?
planetmaker
CC BY-SA 4.0
2022-03-02T18:13:10.653Z
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: https://en.wikipedia.org/wiki/Kirkwood_gap.  To fix it, set the semi-major axes so you don't have resonant orbital periods.
Connor Garcia
CC BY-SA 4.0
2022-03-02T18:19:57.847Z
@planetmaker The simulator is Posidonius: https://www.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?
n_bandit
CC BY-SA 4.0
2022-03-02T19:56:38.923Z
Another solution would be to make the inner most planet much more massive than the other planets.  Then any exchange of angular momentum between the planets will have greater effect on the outer planets.
Connor Garcia
CC BY-SA 4.0
2022-03-02T21:46:35.237Z
@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.
n_bandit
CC BY-SA 4.0
2022-03-02T21:51:48.277Z
Interesting!  It might be helpful to post the Keplerian orbital elements and star/planet masses for a fast increasing $a$ simulation setup.  Something might jump out for someone in the community or we could test it in an alternative simulator.
Connor Garcia
CC BY-SA 4.0
2022-03-02T21:54:28.273Z
@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?
n_bandit
CC BY-SA 4.0
2022-03-02T21:56:07.700Z
Click the curly bracket icon at the top of your edit screen https://meta.stackexchange.com/questions/22186/how-do-i-format-my-code-blocks
Connor Garcia
CC BY-SA 4.0
2022-03-03T04:32:57.990Z
I think I might know what's going on. It's likely a simulation error, and not an actual orbital mechanism. For a single simulation I just tested, when I switched from an integrator using a set stepping rate (WHFast) to an integrator with automatic stepping adjustment (IAS15) the semi-major axis shift went away—at least up to the ~18 million orbit mark. I haven't tested with a longer sim run (my sim run time went from ~50m to ~6.5hrs). I'm now testing WHFast at a slower step interval (3.125x slower) to see what happens.
n_bandit
CC BY-SA 4.0
2022-03-03T04:34:19.470Z
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.
n_bandit
<orbit><orbital-mechanics><orbital-migration>
In a multi-planet system, what mechanism can cause the innermost planet's semi-major axis to increase?
n_bandit
# In a multi-planet system, what mechanism can cause the innermost planet's semi-major axis to increase?

(Asked by: username_0 on 2022-03-02)

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?**

Thanks!

**Tags:** orbit, orbital-mechanics, orbital-migration

> **Comments:**
> **username_1**: Does your simulation conserve both, energy and angular momentum? Did you compare the total at the start and at the end of your simulation? Do you loose (or gain) any by numeric accuracy?  
> **username_2**: 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: https://en.wikipedia.org/wiki/Kirkwood_gap.  To fix it, set the semi-major axes so you don't have resonant orbital periods.  
> **username_0**: @username_1 The simulator is Posidonius: https://www.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?  
> **username_2**: Another solution would be to make the inner most planet much more massive than the other planets.  Then any exchange of angular momentum between the planets will have greater effect on the outer planets.  
> **username_0**: @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.  
> **username_2**: Interesting!  It might be helpful to post the Keplerian orbital elements and star/planet masses for a fast increasing $a$ simulation setup.  Something might jump out for someone in the community or we could test it in an alternative simulator.  
> **username_0**: @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?  
> **username_2**: Click the curly bracket icon at the top of your edit screen https://meta.stackexchange.com/questions/22186/how-do-i-format-my-code-blocks  
> **username_0**: I think I might know what's going on. It's likely a simulation error, and not an actual orbital mechanism. For a single simulation I just tested, when I switched from an integrator using a set stepping rate (WHFast) to an integrator with automatic stepping adjustment (IAS15) the semi-major axis shift went away—at least up to the ~18 million orbit mark. I haven't tested with a longer sim run (my sim run time went from ~50m to ~6.5hrs). I'm now testing WHFast at a slower step interval (3.125x slower) to see what happens.  
> **username_0**: 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.  

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## 0 answers

