Solar sail dynamics in the Sun–Earth system: effects of SRP in the Earth Hill’s region

Solar sails have been investigated and explored since costs in space missions may be significantly reduced with the exploitation of a renewable energy source. This work investigates the dynamical effects on the phase space dynamics of a Solar Sail in the presence of the gravitational field of the Sun and Earth. For that, the Circular Restricted Three-Body Problem with the inclusion of the solar radiation pressure acceleration prescribes the time evolution of initial conditions settled in the Earth’s Hill region. In general, the dynamical system considered is conservative, in the sense of being area-preserving. However, only in the case of orthogonal incidence of the solar photons in the sail’s flat surface, the dynamics remain Hamiltonian, preserving a first integral of motion CJβ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_{J\beta }$$\end{document}. To provide an overview of the dynamics of this system, Poincaré sections are presented for the Hamiltonian case of the model and with the motion restricted to the plane. Given that, the qualitative behavior of trajectories is followed as a function of the first integral of motion CJβ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_{J\beta }$$\end{document} and the sail lightness number β\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta$$\end{document}, defined as the ratio between the solar radiation pressure acceleration and the gravitational acceleration of the Sun on the sail. Some remarkable dynamical features are reported. Possible applications and practical implications for trajectories design are discussed.