Abstract A frozen orbit is beneficial for observation owing to its stationary apsidal line. The traditional gravitational field model of orbits only considers the main zonal harmonic terms J 2 and limited high-order terms, which cannot meet stringent demands all missions. In this study, expanded 15 Hamiltonian canonical form described by Delaunay variables used. coefficients Earth are chosen as...

We propose a methodology to study the bifurcation sequences of frozen orbits when 2nd-order fundamental model satellite problem is augmented with contribution octupolar terms and relativistic corrections. The method based on analysis twice-reduced closed normal forms expressed in suitable combinations invariants Kepler problem, able provide clear geometric view problem.

In this paper, we give a classification of non simply connected seven dimensional Reimannian manifolds of constant positive curvature which admit irreducible cohomogeneity-one actions. We characterize the acting groups and describe the orbits. The first and second homo-topy groups of the orbits have been presented as well.