User:Exoplanetaryscience/OrbitalResonanceStrength

As I had described in a discussion with JDAWiseman, unlike currently described as of February 16th, 2015, orbital resonances are more complicated than simply subtracting the resonances from each other. As JDAWiseman said, it puts a 1:2 resonance, one of the strongest, on par with a 101:100 resonance, or perhaps even something like 3982:3983 resonance. In response, I came up with a few ways to fix that. For the details for each method, see the above link to the discussion.

Method 1

 * s=1/((n1*n2)+(n1-n2))

In this case, s is the strength of the resonance, which equals the multiplicative inverse of the larger resonance times the smaller resonance, plus the larger resonance minus the smaller resonance. In this case, most resonances with a value of 0.1 or higher are strong, while resonances with a value less than 0.01 are considered extremely weak, with values less than 0.005 most likely a coincidence.

Method 2

 * S=1/((n1*n2)+(n1-n2))*d


 * d=1-((p-r)/p)

Although mostly the same, after finding the answer to the previous equation, you multiply it by d, which is found by subtracting the period (p) by the orbital period of a body in the resonance (r) (found by multiplying the orbital period of the primary by the resonance numerator divided by the denominator) and then dividing the value by p. This one helps for bodies not in true resonances, taking into a account the difference from the true resonance compared to their orbit.

Hope this helped to whoever may read this. exoplanetaryscience (talk) 01:09, 17 February 2015 (UTC)