Some characteristics of orbits for a spacecraft around Mercury

Solar sails are a type of propulsion that uses solar radiation pressure to generate acceleration. The fundamental goal for any solar sail design is to provide a large and flat reflective film which requires a minimum of structural support mass. This research takes into account the non-sphericity of the central body, the perturbation of the third body and the solar radiation pressure to analyze the behavior of the orbit of a spacecraft when it has a solar sail around Mercury. We present an approach where we plot maps to analyze frozen orbits with longer lifetimes around Mercury. A set of initial conditions, which may contribute with the scientific missions planned to visit the planet Mercury in the next few years, are presented. Frozen orbits were found, i.e., orbits with smaller variation of the orbital elements. An approach is also presented to analyze the effect of the non-sphericity of Mercury on the motion of the spacecraft. In addition, the J2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$J_{2}$$\end{document} and J3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$J_{3}$$\end{document} zonal terms are also considered, as well as the C22\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_{22 }$$\end{document} sectorial term.