Stellarn & Yvaelis
Stellarn Stellarn
Yvaelis Yvaelis
Stellarn Stellarn
Hey Yvaelis, ever thought about how the orbital resonances in multi‑planet systems can be treated as an optimization problem? I keep spotting these patterns in the Kepler data, and I wonder if there’s a way to formalize the stability as a kind of objective function. What do you think?
Yvaelis Yvaelis
Yeah, that’s the right way to slice it. Treat each resonance as a constraint and let the “fitness” be the sum of deviations from the stable‑orbit map. You’ll end up with a cost function that penalises chaotic drift. It’s a neat way to turn messy data into a solvable optimisation problem. If you need the math, just ask—I’ll cut the fluff.
Stellarn Stellarn
Thanks, Yvaelis. That sounds promising—could you send me the equations for the stability map you’re using? I'd love to see how you quantify the deviations.
Yvaelis Yvaelis
Sure. For each adjacent pair of planets I define the resonance offset \[ \Delta_{ij}= \frac{p}{q}\,\frac{n_j}{n_i}-1 \] where \(n_i\) and \(n_j\) are the mean motions and \(p:q\) the target resonance. The stability index is then \[ S=\sum_{(i,j)} w_{ij}\,\Delta_{ij}^2 \] with weights \(w_{ij}\) that encode the desired strength of the resonance (higher for tighter constraints). Minimising \(S\) over the orbital parameters gives the most stable configuration. That’s the core of the objective function I use.
Stellarn Stellarn
Nice, that’s a clean formulation. I’ll set up a quick simulation with a few test cases and see how the minima line up with the observed periods. If the residuals stay low, we might be onto a stable family of exoplanet systems. Thanks for the clean model—will let you know if any quirks pop up.
Yvaelis Yvaelis
Sounds like a solid test. If the residuals spike, maybe the model’s too rigid; tweak the weights and see if the system relaxes. Keep me posted on the quirks.