Surface shape control of integrated paraboloid space reflector consisting of sub-reflectors exploiting modulated solar pressure

Reflectors are very critical space elements and can be used not only as solar collectors/reflectors, telecommunication radio antennas and telescopes but also for dual-usage such as solar sails and solar concentrators to probe and sublimate materials from asteroids when actively controlling the surface shape. In this paper, the surface shape of a slack reflector with negligible elastic deformations will be controlled to be a paraboloid by actively modulating the solar radiation pressure (SRP) force using reflectivity control devices (RCDs) across the reflector. Nonlinear static equilibrium equations for an arbitrary infinitesimal within the reflector along the radial, circumferential and transverse directions are established considering the external modulated SRP force and internal tensions respectively. The coupled radial stress differential governing equation and reflectivity algebraic equation are obtained for the paraboloid reflector by the help of the formulation of an inverse problem based on equilibrium equations previously established. Some analytical and numerical analysis for reflectors with ideal and non-perfect SRP force models are performed respectively. The conclusions concerning about how to control the reflector’s surface shape successfully using allowed reflectivity, resulting in reasonable stress range, moreover, how to get the feasible solutions influenced by the reflector’s size parameters, are all based on the presented analytical and numerical analysis.