Some families of periodic oscillations in the restricted problem with small mass-ratios of three bodies

Details Some families of periodic oscillations in the restricted problem with small mass-ratios of three bodies Some families of periodic oscillations in the restricted problem with small mass-ratios of three bodies

Sep 1975

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1975ap%26ss..36..245m&link_type=abstract

Astrophysics and Space Science, vol. 36, Sept. 1975, p. 245-272.

Astronomy and Astrophysics

Astrophysics

6

Circular Orbits, Elliptical Orbits, Lagrangian Equilibrium Points, Orbital Mechanics, Stable Oscillations, Three Body Problem, Astronomical Coordinates, Asymmetry, Collinearity, Equipotentials, Graphs (Charts), Jacobi Integral, Periodic Variations, Tables (Data)

Scientific paper

This paper reports on the numerical determination of families of periodic oscillations in the case u=O.000 95 of the restricted problem. The families emanating out of the collinear Lagrangian points L1, L2, L3 are examined as well as some asymmetric periodic oscillations related to them. An effort is made to complete the global picture of simple-periodic symmetric oscillations in the present case of the problem (the S-J case). This is done by examining the orbits with initial conditions such that the infinitesimal body starts from a position on the cr1-axis (c~o2 =0) with a negative initial velocity (~o2 <0) perpendicular to this axis ~ =0). In a previous article this investigation has been carried out for negative values of ~, where the position of the small primary defines c~ = 0. Now we proceed to consider orbits with ~ >0. The phase portrait of asymmetric periodic orbits is also examined

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