RESEARCH IN THE RESTRICTED THREE-BODY PROBLEM.
Final scientific rept. 1 May 66-30 Apr 69,
THESSALONIKI UNIV SALONIKA (GREECE) DEPT OF ASTRONOMY
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Numerical evidence has been given of the existence of a new integral in the Restricted Problem. This integral was expressed in terms of the Delaunay variables in a series form in powers of the mass ratio mu, the eccentricity e and the semi-major axis a. It was shown that Stromgrens family and Henons family of periodic orbits known are linked through the mass ratio mu. Families of figure eight orbits were studied. The same approach was used for other families of periodic orbits. It was again found that certain families are connected. The report has classified the orbits in the restricted 3-body problem which pass through the ineer Lagrangian point L1, according to their first minimum distance from either primary, both for planar and three dimensional orbits. The report has studied the stability of periodic orbits in the restricted three-body problem and similar problems, by studying the variational equations. The report has found several properties of the solutions of the variational equations, and using these properties it has proved that orbits which are linearly stable are also stable to second order terms in the initial displacements. The report has also found the characteristic curves of stable periodic orbits by using the results mentioned above, and also using the third integral. Author
- Celestial Mechanics