Normalizaciones de orden alto en el problema de Hill

• Autores: Martín Lara Coira , Juan Félix San Juan Díaz
• Localización: Monografías de la Real Academia de Ciencias Exactas, Físicas, Químicas y Naturales de Zaragoza, ISSN 1132-6360, Nº. 28, 2006 (Ejemplar dedicado a: Actas de las VIII Jornadas de Mecánica Celeste / coord. por Antonio Elipe Sánchez , J. A. Docobo Durántez ), págs. 23-32
• Idioma: español
• Enlaces
  • Texto completo (pdf)
• Resumen

  • Hill's problem describes the most relevant features in the dynamics around planetary satellites. We consider a system of nondimensional variables, and a small parameter that depends only on the nondimensional semimajor axis. Then, the 3-DOF problem is reduced to1-DOF by means of two Lie transforms. Since a symetry between direct and retrograde inclination orbits arises from the second order approach, we are compelled to reach higher orders. We find that, while the third order approximation break that symmetry, only the fourth order normal from reflects the real Keplerian behavior of retrograde orbits inside Hill radius.