Evolution of families of collision periodic orbits in the plane restricted three-body problem with mass ratio MU near 1

Details Evolution of families of collision periodic orbits in the plane restricted three-body problem with mass ratio MU near 1 Evolution of families of collision periodic orbits in the plane restricted three-body problem with mass ratio MU near 1

Dec 1984

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1984a%26a...141..162p&link_type=abstract

Astronomy and Astrophysics (ISSN 0004-6361), vol. 141, no. 1, Dec. 1984, p. 162-170.

Astronomy and Astrophysics

Astrophysics

2

Celestial Mechanics, Collision Parameters, Mass Ratios, Periodic Functions, Solar Orbits, Three Body Problem, Jacobi Integral, Jupiter (Planet), Kepler Laws, Orbital Mechanics, Secular Variations

Scientific paper

The evolution of symmetric collision periodic orbits with mass ratio mu near one in the plane circular restricted three-body problem is described. The orbits are direct relative to the rotating system and surround both primaries. An infinite number of mu-C curves of collision periodic orbits are found. Each point of a mu-C curve represents an orbit with m maxima r besides the collision point. The number m increases by one from a mu-C curve to the next one below it. So, as the number of mu-C curves tends to infinity, the number of loops m also tends to infinity. The mu-C curves reach a maximum mu and then turn to the left. The corresponding collision orbits develop two new small loops on both sides of the collision point. The collision periodic orbits with m = 2-10 in the sun-Jupiter case are given, and their interconnections with other known families of collision periodic orbits are found.

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