Resumen de Normalizaciones de orden alto en el problema de Hill
Martín Lara Coira 
, Juan Félix San Juan Díaz
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.
