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For a massless test particle and given a planetary system, 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. A sample input data file to calculate the two-body resonances is available for use with the Fortran77 source code.
For a massless test particle and given a planetary system, 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. A sample input data file to calculate the three-body resonances is available for use with the Fortran77 source code.
Given two planets P1 and P2 with arbitrary orbits, planetary3br calculates all possible semimajor axes that a third planet P0 can have in order for the system to be in a three body resonance; these are identified by the combination k0*P0 + k1*P1 + k2*P2. P1 and P2 are assumed to be not in an exact two-body resonance. The program also calculates three "strengths" of the resonance, one for each planet, which are only indicators of the dynamical relevance of the resonance on each planet. Sample input data are available along with the Fortran77 source code.
Spectra calculates the power spectrum of a time series equally spaced or not based on the Spectral Correlation Coefficient (Ferraz-Mello 1981, Astron. Journal 86 (4), 619). It is very efficient for detection of low frequencies.
ORBE performs numerical integration of an arbitrary planetary system composed by a central star and up to 100 planets and minor bodies. ORBE calculates the orbital evolution of a system of bodies by means of the computation of the time evolution of their orbital elements. It is easy to use and is suitable for educational use by undergraduate students in the classroom as a first approach to orbital integrators.
The Opik method gives the mean probability of collision of a small body with a given planet. It is a statistical value valid for an orbit with given (a,e,i) and undefined argument of perihelion. In some cases, the planet can eject the small body from the solar system; in these cases, the program estimates the mean time for the ejection. The Opik method does not take into account other perturbers than the planet considered, so it only provides an idea of the timescales involved.
rsigma calculates the resonant disturbing function, R(sigma), for a massless particle in an arbitrary orbit perturbed by a planet in circular orbit. This function defines the strength of the resonance (its semi-amplitude) and the location of the stable equilibrium points (the minima). It depends on the variable sigma called critical angle and on the particle's orbital elements a, e, i and the argument of the perihelion. R(sigma) is numerically calculated and the code is valid for arbitrary eccentricities and inclinations, including retrograde orbits.