Is this planetary system stable?
The host star has a mass of 0.90 M$_\odot$ I'll refer to this star as Helios. I'll refer to the planets as Helios One, Helios Two, etc.
Helios One is 0.55 M$_{\oplus}$ and orbits at 0.75 AU. It's eccentricity is 0.012.
Helios Two is 0.94 M$_{\oplus}$ and orbits at 1.08 AU. Its eccentricity is 0.015
Helios Three is 0.32 M$_{\oplus}$ and orbits at 1.55 AU. It's eccentricity is 0.023
Helios Four is 0.42 times the mass of Jupiter and orbits at 6.02 AU. Its eccentricity is 0.044.
Helios Five is 0.17 M$_{\oplus}$ and orbits at 10 AU. Its eccentricity is 0.060.
Does this system seem realistic? And, of course, the main question is, is it stable?
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1 answer
This is an exceedingly tricky question. Determining the stability of this system is akin to determining the stability of the Solar System, a difficult - and currently unfinished, as far as I know - task. Planetary systems with more than a couple planets are chaotic, meaning that on timescales of ~107 years, they become chaotic and impossible to predict to any degree of accuracy.
If there were simply two planets, I could look for any orbital resonances that would destabilize the system, something that I've written about before. In the cases where $[n:1](2)$ resonances dominate - that is, when the satellites (here, planets) fall into a certain range of masses - then determining stability is (relatively) easy. Here, it isn't.
We can't determine analytically here whether or not the system is stable. I can give you a rough prediction, though, which is that it is stable. Why?
- The planets have relatively low masses (all but one less than the mass of Earth).
- The planets are pretty well spaced apart.
My one concern is that the third and first planets are nearly in a 3:1 resonance, which has the potential to cause instability. But this might not happen. In fact, there's a chance it could stabilize the system even more.
Is the system realistic? I would argue yes. You have three terrestrial planets within about 1.5 AU, which is nothing special. You then have a small gas giant at about 6 AU, a bit further out than Jupiter. Again, this is fine.
What concerns me is that planet way out at 10 AU. It's the least massive of them all - although not by too much - but may still be a terrestrial planet. You have to explain how it came to be way out there. If it formed there, then you need a good explanation; it seems oddly far out. If it was moved back there, you need to explain what caused it to go there. I see one body capable of severely disrupting an orbit, namely, the gas giant. Interactions with the protoplanetary disk and/or the other terrestrial planets could also have had an effect, but those are less likely.
Overall, I'd say you're fine.
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