Generalized Model for Solar Sails

Abstract

E define a new methodology for the analytic description of the force and moment generated by a solar sail of arbitrary shape and surface optical properties. We find that the total force and moment generated by the sail can be completely defined by the computation of a number of constants of the sail, which are only functions of the sail geometry and independent of the incident light. Given these constants, some standard sail properties, and the incident light pressure and direction, the total force and moment acting on the sail can be computed using simple formulas. Specifically, we can characterize the force generated by a solar sail of arbitrary sail geometry under general illumination conditions with 18 numbers. To characterize the moment requires an additional 36 numbers. The advantages of this description are that these constants can be computed off-line and are defined for arbitrarily shaped sails, meaning that only one formalism must be coded to deal with all types of sails. There are a number of limits to this approach. First, this model tacitly assumes that the sail will not change shape as its attitude varies, thus their utility might be somewhat limited or constrained to relatively small angular motions. This limitation will be addressed in the future. Second, it assumes that there is no self-shadowing, that is, that every element of the sail surface will “see” an incident ray. This is a reasonable assumption given the likely mode in which a solar sail will be operated.