| Abstract: | The regularized equations of motion of the planar Hill problem which includes the effect of the oblateness of the larger primary
body, is presented. Using the Levi-Civita coordinate transformation as well as the corresponding time transformation, we obtain
a simple regularized polynomial Hamiltonian of the dynamical system that corresponds to that of two uncoupled harmonic oscillators
perturbed by polynomial terms. The relations between the synodic and regularized variables are also given. The convenient
numerical computations of the regularized equations of motion, allow derivation of a map of the group of families of simple-periodic
orbits, free of collision cases, of both the classical and the Hill problem with oblateness. The horizontal stability of the
families is calculated and we determine series of horizontally critical symmetric periodic orbits of the basic families g and g'.
This revised version was published online in July 2006 with corrections to the Cover Date. |
