ATLAS OF TWO BODY MEAN MOTION RESONANCES IN THE SOLAR SYSTEM
VERSION 2020

Tabare Gallardo
Departamento Astronomia, Facultad de Ciencias, Uruguay
www.fisica.edu.uy/~gallardo
gallardo(at)fisica.edu.uy


Summary



Plots

Plots in the plane (a,e) showing the domains (widths of the stable librations) of the MMRs for test particles with i=10. Superposition of resonances means chaos. Plot (a,width) for test particles with e=0.15, i=8 (typical of asteroids). Height of the lines represent the width in au. Code colour indicates the planet responsible for the resonance: Mercury=red, Venus=green, Earth=blue, Mars=yellow, Jupiter=black, Saturn=red, Uranus=green, Neptune=blue. Some examples showing the inclination effect. All resonances kp:k with kp <= 10, k <= 10.

Tables

All resonances verifying kp <= 20, k <= 20 with all the planets, calculated for typical (e,i) values of asteroids (e=0.15, i=8)

Programs



Usage

Suppose you are studying the dynamics of a small body and you want to know if it is captured in a resonant motion. You have two possibilities:

Conventions

   resonance kp:k verify kp*np = k*n

   if kp > k is an interior resonance (3:2 the Hildas)
   if kp < k is an exterior resonance (2:3 the plutinos)

   principal critical angle:

   sigma = k*lambda - kp*lambda_planet + (kp-k)*varpi
   lambda = longper + mean anomaly
   varpi = longper = longnod + argper


Limitations

The general description of the MMRs obtained with the codes are quite good. Only one planet is taken into account for each calculation then secular or resonant effects due to other planets can modify the results. The metod assumes that the borders of the resonance are symmetric with respect to the nominal position of the resonance.

Some fundamental references for MMRs with arbitrary inclinations



Some links:



Back to the web of the atlas of resonances