Sun-synchronous solar reflector orbits designed to warm Mars

Although the Martian environment is very cold (averaging about $-60^{\circ }$ 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 solar reflectors to increase the total solar insolation. In this study, Sun-synchronous solar reflectors orbits with inclination equal or less than $90^{\circ }$ with respect to the orbital plane of Mars are considered to intervene with the Mars’ climate system. With different inclinations, a family of Sun-synchronous solar reflectors orbits distributes azimuthally the energy intercepted by the reflector. The two-body problem 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 $90^{\circ }$ , taking into account the effects of solar radiation pressure for a perfectly reflecting space mirror and Mars’ $J_{2}$ oblateness perturbation.