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On the Orbital Elements of the Two-body Problem with Slowly Decreasing Mass: The Gyldén-Mestchersky Cases

Abad, Alberto ; Calvo, Manuel ; Docobo, José A. ; Elipe, Antonio

The Astronomical journal, 2020-11, Vol.160 (5), p.203 [Periódico revisado por pares]

Madison: The American Astronomical Society

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  • Título:
    On the Orbital Elements of the Two-body Problem with Slowly Decreasing Mass: The Gyldén-Mestchersky Cases
  • Autor: Abad, Alberto ; Calvo, Manuel ; Docobo, José A. ; Elipe, Antonio
  • Assuntos: Astronomy ; ASTROPHYSICS, COSMOLOGY AND ASTRONOMY ; Asymptotic properties ; ASYMPTOTIC SOLUTIONS ; Celestial mechanics ; COSMIC DUST ; Elliptic functions ; EXACT SOLUTIONS ; MASS ; Mathematical analysis ; Orbital elements ; Parameters ; PERIODICITY ; Perturbation ; PERTURBATION THEORY ; Stellar mass loss ; Two body problem
  • É parte de: The Astronomical journal, 2020-11, Vol.160 (5), p.203
  • Notas: AAS26377
    High-Energy Phenomena and Fundamental Physics
  • Descrição: We study the dynamics of two-body problems with gravitational parameters = (t) decreasing with the time. In particular we focus our attention on the behavior of the orbital elements in the first two Gyldén-Mestchersky cases: in the first case (GM-I) , where 0 is the constant initial value of the parameter and a small positive constant. In the second case (GM-II) . In the GM-I problem, using a suitable transformation of the radius vector and the physical time, which reduces the original problem to a pure Kepler problem, we are able to obtain explicit analytical expressions of the orbital elements that hold true for all and therefore derive their asymptotic behavior. Moreover using the alternative scaled time these expressions show clearly their periodic and secular terms. For the GM-II problem a similar transformation to the GM-I problem leads to a perturbed Kepler problem with a radial direction perturbation. Although exact solutions in terms of elliptic functions may be obtained, the use of some integrals leads to analytical expressions of orbital elements that allow us to study their behavior. Finally, some comparisons between the time evolution of elements in both problems are also included.
  • Editor: Madison: The American Astronomical Society
  • Idioma: Inglês
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