VERSION 2020

Departamento Astronomia, Facultad de Ciencias, Uruguay

www.fisica.edu.uy/~gallardo

gallardo(at)fisica.edu.uy

- The present plots, tables and programs give the locations in au, strengths, widths (of stable librations) in au, libration periods in years and libration centers in degrees of the MMRs kp:k (kp*np = k*n) between a massless particle and the planets.
- No restrictions in eccentricity nor in inclination: you can calculate MMRs of polar, retrograde and sungrazer objects, for example.
- Widths, libration periods and centers are not universal and depend on the orbital elements (mainly e,i,w) of the asteroid/comet/centaur/TNO (or test particle).
- MMRs are calculated considering fixed orbits for both particle and planet.
- Mean semimajor axes and mean eccentricities were considered for the planets which were assumed with i=0 and varpi_p=0 (varpi is the longitude of the perihelion).
- Calculations are based on the article by Gallardo 2020, (arXiv) for planets in circular orbits and generalized to planets in eccentric orbits.
- EXOPLANETARY SYSTEMS: the codes are general, valid for our system and also for extrasolar systems, just put the right data in the input file plasys.inp

- Region from 0 to 2 au for i=10 degrees (our peaceful neighbourhood).
- Region from 2 to 4 au for i=10 degrees (asteroids).
- Region from 4 to 7 au for i=10 degrees (Trojans!).
- Region from 6 to 13 au for i=10 degrees (the hell...).
- Region from 13 to 21 au for i=10 degrees (Uranus' Trojans, the diversity region).
- Region from 19 to 50 au for i=10 degrees (Neptune's Trojans, Plutinos, twotinos).
- Region from 50 to 225 au for i=10 degrees (1:n and 2:n with Neptune).

- Global atlas from 0 to 230 au calculated for e=0.15, i=8. All resonances kp:k with kp <= 20, k <= 20.

- From 4 to 11 au for direct orbits with i=10.
- From 4 to 11 au for polar orbits with i=90.
- From 4 to 11 au for retrograde orbits with i=170.

- Resonalyzerv2. To compute the resonant disturbing function R(sigma) and to calculate the location in semimajor axis, its strength SR, maximum stable width in au, stable equilibrium points and corresponding libration periods in years. The code takes into account the eccentricity of the planet if you want (that is why the code is v2). IMPORTANT: in the input file plasys.inp you must state the data of the central star and planetary system.
- Superatlasv3. Calculates an atlas of resonances in some interval of (a,e) considering planetary eccentricities. IMPORTANT: in the input file plasys.inp you must state the data of the central star and planetary system.

- Look at the table for the strongest resonances near the semimayor
axis of the body's orbit.
Then, using your numerical integration, compute the corresponding critical angles

sigma = k*lambda - kp*lambda_planet + (kp-k)*varpi

(varpi=argument of the perihelion + longitude of the node) and follow the time evolution. - Or run the program Superatlasv3 and compute the strength according to the (e,i,w,ln) where ln is in fact the difference long of the node asteroid - long of the perihelion planet, (OK, you can put arbitrary value for ln) This is the best choice. Then compute the time evolution of the critical angle(s).

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

- Some fundamental references for MMRs.
- 2 body and 3 body resonances in the Solar System, T. Gallardo.