Abstract
The stability of collinear and triangular libration points is investigated in the photogravitational elliptic restricted three-body problem, in which two primary bodies emit light energy simultaneously. The conditions of stability of the collinear and triangular libration points are obtained based on a linearized set of equations of perturbed motion for various values of the eccentricity of the Keplerian orbits and the mass ratio of the primary bodies. The maximal numerical value is defined for the eccentricity at which a stable libration point can still exist. It is demonstrated how the parametric resonance causes an instability of collinear and triangular libration points; the evolution of the origination of the instability zones is traced. The minimal eccentricity value is found at which zones of instability of triangular libration points arise.
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Zimovshchikov, A.S., On the Stability of the Triangular Libration Points in the Photogravitational Elliptic Restricted Three-Body Problem with Two Radiating Bodies, Zadachi issledovaniya ustoichivosti i stabilizatsii dvizheniya (Problems of the Investigation of the Stability and Stabilization of the Motion), Moscow: Vychisl. Tsentr Ross. Akad. Nauk, part 1, pp. 68-77.
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Zimovshchikov, A.S., Tkhai, V.N. Instability of Libration Points and Resonance Phenomena in the Photogravitational Elliptic Restricted Three-Body Problem. Solar System Research 38, 155–164 (2004). https://doi.org/10.1023/B:SOLS.0000022826.31475.a7
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DOI: https://doi.org/10.1023/B:SOLS.0000022826.31475.a7
Keywords
- Light Energy
- Parametric Resonance
- Libration Point
- Resonance Phenomenon
- Keplerian Orbit