Astrophys Space Sci ( 2019) 364:147 https://doi.org/10.1007/s10509-019-3633-x ORIGINAL ARTICLE Sun-synchronous solar reﬂector orbits designed to warm Mars F.J.T. Salazar 1 · O.C. Winter 1 Received: 20 February 2019 / Accepted: 20 August 2019 © Springer Nature B.V. 2019 Abstract Although the Martian environment is very cold (averaging about −60 ◦ C), highly oxidizing and desiccated, several studies have proposed human colonization of Mars. To carry out this ambitious goal, terraforming schemes have been designed to warm Mars and implant Earth-like life. Mars climate engineering includes the use of orbiting so- lar reﬂectors to increase the total solar insolation. In this study, Sun-synchronous solar reﬂectors orbits with inclina- tion equal or less than 90 ◦ with respect to the orbital plane of Mars are considered to intervene with the Mars’ cli- mate system. With different inclinations, a family of Sun- synchronous solar reﬂectors orbits distributes azimuthally the energy intercepted by the reﬂector. The two-body prob- lem is considered, and the Gauss’s form of the variational equations is used to ﬁnd the conditions to achieve a Sun- synchronous frozen orbit with inclination equal or less than 90 ◦ , taking into account the effects of solar radiation pressure for a perfectly reﬂecting space mirror and Mars’ J 2 oblateness perturbation. Keywords Terraforming scheme · Mars climate engineering · Sun synchronous orbits · Solar reﬂectors · J 2 oblateness perturbation 1 Introduction A few decades ago, the renowned astronomer Carl Sagan proposed to transform hostile planetary surfaces and atmo- spheres like Venus and Mars into anaerobic environment B F.J.T. Salazar e7940@hotmail.com 1 Grupo de Dinâmica Orbital e Planetologia, São Paulo State University (UNESP), Guaratinguetá, SP, Brazil suitable for humans (Sagan 1961, 1973). This hypothetical process, called terraforming scheme, modiﬁes the environ- ment of any planet deliberately until obtaining a similar en- vironment to the Earth, allowing habitation by most, if not all, terrestrial life forms (McKay 1982; Fogg 1995). Since space exploration business is really limited by the terres- trial resources, a terraforming scheme to ﬁnd new branches of civilization remote from the Earth (space-based civiliza- tions) seems to be a good option for more resources in space that could enable expansion of human society and space business (McKay 1982; Johnson and Holbrow 1977; Oberg 1981; Haynes and McKay 1992). Due to Mars’ similarities to Earth, the establishment of habitable, self-sufﬁcient colonies on Mars is the focus of much scientiﬁc study about possible human coloniza- tion (Sagan 1973; McKay 1982; Avemer and MacEiroy 1976; Lovelock and Allaby 1984; Haynes and McKay 1992; Zubrin 1995; Zubrin and McKay 1997; Fogg 1998). A gen- eral scenario for colonization of Mars would include an Earth-like environment, i.e. the mean global surface tem- perature must be increased. Large-scale planetary schemes proposed to intervene in the Earth’s climate system (geo- engineering) (Keith 2000; McInnes 2010a) are currently ex- plored as a large-scale venture to warm Mars (McInnes 2010b). These schemes basically to increase the amount of solar radiation on the surface of a planet using orbiting so- lar reﬂectors (Canady and Allen 1982; Ehricke 1979; Glaser 1968; Maunter and Parks 1990; Badescu et al. 2006). For example, McInnes (2002) showed that the required reﬂector area to increase the total insolation of Mars by 30%, as part of a large-scale terraforming effort, is of the order 10 13 m 2 (and mass of the order 10 10 kg). This size implies that a large space mirror would be replaced by a large number of smaller reﬂectors distributed about the orbit (Early 1989; Angel 2006; Pearson et al. 2006). Similarly, Salazar et al.