The geometry of the roche coordinates and zero-velocity curves in the photogravitational three-body problem

The aim of the paper is to study the geometry of the Roche curvilinear coordinates (, , ) in the photogravitational circular restricted three-body problem, with varying radiation pressure, and special attention is given to the geometry of zero-velocity curves specified by the coordinate. The radiation pressure exerted by the primary bodies on the infinitesimal third body is considered the same (q ₁ =q ₂), and the primaries are taken to have equal masses (m ₁ =m ₂). The full range of values of the common radiation factor is explored, from the valueq ₁ =q ₂ = 1 (the gravitational three-body problem) down toq ₁ =q ₂ 0. It is found that radiation has a strong influence on the geometry of the Roche coordinates and the zero-velocity curves.