Quasiintegrals of the photogravitational eccentric restricted three-body problem with Poynting–Robertson drag

A restricted three-body problem for a dust particle, in presence of a spherical cometary nucleus in an eccentric (elliptic, parabolic or hyperbolic) orbit about the Sun, is considered. The force of radiation pressure and the Poynting– Robertson effect are taken into account. The differential equations of the particle’s non-inertial spatial motion are investigated both analytically and numerically. With the help of a complex representation, a new single equation of the motion is obtained. Conversion of the equations of motion system into a single equation allows the derivation of simple expressions similar to the integral of energy and integrals of areas. The derived expressions are named quasiintegrals. Relative values of terms of the energy quasiintegral for a smallest, largest, and a mean comet are calculated. We have found that in a number of cases the quasiintegrals are related to the regular integrals of motion, and discuss how the quasiintegrals may be applied to find some significant constraints on the motion of a body of infinitesimal mass.