These codes in Fortran and Python calculate properties of mean motion resonances of a particle with a planet or a system of planets: semimajor axis, libration centers, periods, width, resonance strength and level curves of the Hamiltonian. Arbitrary orbits for both bodies. Based on Gallardo (2020, CMDA) but extended to eccentric planets. An early version of this model was proposed in Gallardo (2006, Icarus).  It can also be considered as a particular case of the model given by Gallardo, Beauge and Giuppone (2021, A&A).

Note:  the usual notation is kp:k, so resonance 1:2 (aka 1/2) corresponds to an asteroid exterior to the planet's orbit and resonance 2:1 (aka 2/1) represents an asteroid interior to the planet's orbit. For the calculations, as critical angle we take sigma = k*lambda_ast- kp*lambda_pla + (kp-k)*varpi_ast.

Fortran codes (new version v3 calculates atlas in the space (a,e))

Python class semianalyticResonance

Reference: Gallardo (2020, CMDA).

examples