Shape control of slack space reflectors using modulated solar pressure

The static deflection profile of a large spin-stabilized space reflector because of solar radiation pressure acting on its surface is investigated. Such a spacecraft consists of a thin reflective circular film, which is deployed from a supporting hoop structure in an untensioned, slack manner. This paper investigates the use of a variable reflectivity distribution across the surface to control the solar pressure force and hence the deflected shape. In this first analysis, the film material is modelled as one-dimensional slack radial strings with no resistance to bending or transverse shear, which enables a semi-analytic derivation of the nominal deflection profile. An inverse method is then used to find the reflectivity distribution that generates a specific, for example, parabolic deflection shape of the strings. Applying these results to a parabolic reflector, short focal distances can be obtained when large slack lengths of the film are employed. The development of such optically controlled reflector films enables future key mission applications such as solar power collection, radio-frequency antennae and optical telescopes.