ATLAS OF MEAN MOTION RESONANCES

Tabare Gallardo
Departamento Astronomia, Facultad de Ciencias, Universidad de la Republica, Uruguay
www.fisica.edu.uy/~gallardo


Breaking News: planetary resonances

ATLAS FOR THE SOLAR SYSTEM:


ATLAS FOR GENERIC PLANETARY SYSTEMS:

  • TWO BODY RESONANCES:

    a) PARTICLE IN RESONANCE WITH A PLANET

    • NEW version 2020. Valid for arbitrary planetary systems.

    • Old (deprecated) version:
      Bibcode: ascl:1607.003
      Reference: this algorithm is based on "Atlas of the mean motion resonances in the Solar System" (Gallardo 2006, Icarus).
      Given a planetary system the program "atlas2bgeneral" calculates all resonances in a given range of semimajor axes with all the planets taken one by one. Planets are assumed in fixed circular and coplanar orbits and the test particle with arbitrary orbit. The file atlas2bgeneral.zip contains the source code in f77 and a sample input data file "massivebodies.inp" to calculate the two-body resonances. You need to compile with a fortran compiler. The executable and input data file must be in the same directory. If you are a windows user the file atlas2bgeneralwin.zip contains the executable for windows and a sample input data file. The strength is the semiamplitude of the resonant disturbing function in solar masses, au, days.

    b) PLANET IN RESONANCE WITH PLANET (OR BINARY STAR)

    • planetary resonances. NEW CODE 2021. The present code is a model that describes the resonance strength, width, location and stability of fixed points, as well as periods of small-amplitude librations.


  • THREE BODY RESONANCES:

    You may be interested in this tool: Three Body Resonance Locator on line and for Android.

    a) FOR A MASSLESS TEST PARTICLE

    A particle interacts with two massive bodies, only the particle feels the resonance.
    Bibcode: ascl:1607.004
    Reference: this algorithm is based on Atlas of three body mean motion resonances in the Solar System, Gallardo 2014.
    Given a planetary system the program "atlas3bgeneral" calculates all three body resonances in a given range of semimajor axes with all the planets taken by pairs. Planets are assumed in fixed circular and coplanar orbits and the test particle with arbitrary orbit. The file atlas3bgeneral.zip contains the source code in f77 and a sample input data file "massivebodies.inp" to calculate the three-body resonances. You need to compile with a fortran compiler. The executable and input data file must be in the same directory. If you are a windows user the file atlas3bgeneralwin.zip contains the executable for windows and a sample input data file. Unit of strength: we have taken as unity the strength corresponding to the asteroid 490 Veritas (e=0.095, i=9.3, w=194) inside the resonance 2Veritas - 5Jupiter + 2Saturn.

    b) FOR THREE MASSIVE BODIES

    Three massive bodies interacting, the three bodies feel the resonance in a different way.
    Bibcode: ascl:1607.005
    Reference: this algorithm is based on "Planetary and satellite three body mean motion resonances" (Gallardo, Coito and Badano 2016, Icarus). Preprint arxiv.org/abs/1603.06911.
    Given 2 planets P1 and P2 with arbitrary orbits the program "planetary3br" calculates all possible semimajor axes that a third planet P0 can have in order the system to be in a three body resonance, which are identified by the combination k0*P0 + k1*P1 + k2*P2. The program calculates also three "strengths" of the resonance, one for each planet. You should take a look at the reference paper otherwise you probably will be lost. Take care, the "strengths" are only indicators of the dynamical relevance of the resonance on each planet. Important point: it is assumed that P1 and P2 are not in an exact two-body resonance. The file planetary3br.zip contains the source code in f77 and the input data file "p3br.inp". You must compile with a fortran compiler to generate the executable. The executable and input data file must be placed in the same directory. If you are a windows user the file planetary3brwin.zip contains the executable for windows and a sample input data file.

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