Computer Science – Numerical Analysis
Scientific paper
Oct 1981
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1981icar...48....1d&link_type=abstract
Icarus, vol. 48, Oct. 1981, p. 1-22.
Computer Science
Numerical Analysis
79
Eccentric Orbits, Orbit Calculation, Particle Trajectories, Planetary Orbits, Saturn Satellites, Three Body Problem, Circular Orbits, Coordinates, Elliptical Orbits, Jacobi Integral, Numerical Analysis, Orbital Elements, Planets, Celestial Mechanics, Dynamics, Orbits, Three-Body Problem, Numerical Methods, Analysis, Trajectories, Particles, Calculations, Theoretical Studies, Diagrams, Satellites, Eccentricity
Scientific paper
The fundamental properties of the horseshoe and tadpole orbit solutions to the three-body problem where the mass of the third body is considered negligible are examined and generalized to include the case where the third body has sufficient mass to affect the motion of the satellite with which it is in resonance, as in the case of the coorbital satellites of Saturn. Particle trajectories in the solutions to the restricted three-body problem are found to be closely related to the shape of the associated zero-velocity curves. Particles close to the satellite orbit are shown to move in near-periodic orbits with orbital changes produced in one satellite encountered effectively cancelled by the next. An approximate expression is derived for the minimum angular separation between the satellite and the particle, and dependences of particle lifetimes and the relative widths of horseshoe and tadpole regions on the mass ratio are found. These relations are applied to the coorbital satellites of Saturn, 1980S1 and 1980S3, which are shown to be librating in horseshoe orbits, and it is noted that the satellite masses may thereby be determined. Consideration is also given to the horseshoe and tadpole orbital dynamics of the coorbital satellites of Dione and Tethys.
Dermott Stanley F.
Murray Carl D.
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