Generalized analytical results on n-ejection–collision orbits in the RTBP: analysis of bifurcations
In the planar circular restricted three-body problem and for any value of the mass parameter µ¿(0,1) and n=1 , we prove the existence of four families of n-ejection–collision (n-EC) orbits, that is, orbits where the particle ejects from a primary, reaches n maxima in the (Euclidean) distance with re...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/387476 |
| Acceso en línea: | https://hdl.handle.net/2117/387476 https://dx.doi.org/10.1007/s00332-022-09873-y |
| Access Level: | acceso abierto |
| Palabra clave: | Dynamics RTBP Hill problem Ejection-Collision orbits Bifurcations Dinàmica Classificació AMS::70 Mechanics of particles and systems::70F Dynamics of a system of particles, including celestial mechanics Àrees temàtiques de la UPC::Física::Física de partícules |
| Sumario: | In the planar circular restricted three-body problem and for any value of the mass parameter µ¿(0,1) and n=1 , we prove the existence of four families of n-ejection–collision (n-EC) orbits, that is, orbits where the particle ejects from a primary, reaches n maxima in the (Euclidean) distance with respect to it and finally collides with the primary. Such EC orbits have a value of the Jacobi constant of the form C=3µ+Ln2/3(1-µ)2/3 , where L>0 is big enough but independent of µ and n. In order to prove this optimal result, we consider Levi-Civita’s transformation to regularize the collision with one primary and a perturbative approach using an ad hoc small parameter once a suitable scale in the configuration plane and time has previously been applied. This result improves a previous work where the existence of the n-EC orbits was stated when the mass parameter µ>0 was small enough. Moreover, for decreasing values of C, there appear some bifurcations which are first numerically investigated and afterward explicit expressions for the approximation of the bifurcation values of C are discussed. Finally, a detailed analysis of the existence of n-EC orbits when µ¿1 is also described. In a natural way, Hill’s problem shows up. For this problem, we prove an analytical result on the existence of four families of n-EC orbits, and numerically, we describe them as well as the appearing bifurcations. |
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