Analytic perturbative theories in highly inhomogeneous gravitational fields

► Inhomogeneous gravity potential, polar-nodal vars, arbitrary deg spherical harmonics. ► Averaged 2ord, arbitrary deg Hamiltonian, in closed-form by Lie transformations. ► Method for initial conditions for frozen orbits, setting I, e, g of the desired orbit. ► Apply it to 624-Hektor:spherical harmonics derived assuming constant density.