We introduce a new version of Hill's problem that incorporates the effects of radiation of the primary and oblateness of the secondary and study the basic dynamical features of this new model-problem. This formulation is more appropriate for some astronomical applications as an approximation to the corresponding restricted three-body problem. We use iterative methods for deriving approximate expressions of the equilibrium point locations and study their stability properties by using a linear stability analysis. All equilibrium points are unstable. We also employ singular perturbations methods for obtaining approximate expressions of the Lyapunov families emanating from equilibrium points, in both coplanar and spatial case, and numerical techniques for their continuation.

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We consider the photogravitational restricted three-body problem with oblateness and study the Sitnikov motions. The family of straight line oscillations exists only in the case where the primaries are of equal masses as in the classical Sitnikov problem and have the same oblateness coefficients and radiation factors. A perturbation method based on Floquet theory is applied in order to study the stability of the motion and critical orbits are determined numerically at which families of three-dimensional periodic orbits of the same or double period bifurcate. Many of these families are computed.

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