New method of integration step correction for orbits with penumbra transitions

The article is devoted to the problem of numerical orbital prediction with penumbral zones. The authors analyzed the existing shadow models used for calculating solar radiation pressure. By carrying out series of numerical experiments the shadow functions along the trajectories of geostationary space objects for various shadow models are obtained. The authors of the article proposed an algorithm allowing the determination of time frames of the penumbral regions for space objects in elliptical orbits. The authors obtained two algebraic equations of no higher than the fourth order defining the boundaries of the penumbral regions. The analysis of the equations is carried out. Based on the algorithm a method for adjusting the step of numerical integration is created. This method automatically takes in account a dramatic change in the strength of solar radiation pressure in the penumbral regions. The established method is tested on the problem of forecasting geostationary orbits. The authors’ method is compared with step adjustment algorithms in Gauss - Everhart integrators of high approximation orders. It is illustrated that the proposed method makes it possible to accelerate the process of numerical integration for the considered class of orbits.