An invariant relation in the elliptic restricted problem of three bodies. I

Abstract

view Abstract Citations (5) References (10) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS An invariant relation in the elliptic restricted problem of three bodies. I. Vrcelj, Z. ; Kiewiet de Jonge, J. H. Abstract An invariant relation generalizing the Jacobi integral to the elliptic restricted three-body problem is derived on the basis of the classical perturbation theory and by making use of energy and angular momentum integrals. But the relation contains a nonintegrable term, becoming integrable only in a few special cases. It is shown that in the case of the Lagrange triangular solutions and the Poincare two-body limit the relation reduces to integrals which appear to be linear combinations of the well-known integrals. In the case of perturbed triangular solutions the relation reduces to an approximate integral valid under certain constraints. In the case of small mass ratio of primaries the relation is reducible to another approximate integral valid for planetary-type motions. In the limit of zero eccentricity of the orbits of primaries the relation yields the Jacobi integral. Publication: The Astronomical Journal Pub Date: May 1978 DOI: 10.1086/112230 Bibcode: 1978AJ.....83..514V Keywords: Celestial Mechanics; Invariance; Perturbation Theory; Three Body Problem; Angular Momentum; Eccentric Orbits; Jacobi Integral; Mass Ratios; Orbit Calculation; Astronomy; Three-Body Problem:Restricted full text sources ADS |