Optimal Steering Law of Refractive Sail

The interaction between electromagnetic waves and matter is the working principle of a photon-propelled spacecraft, which extracts momentum from the solar radiation to obtain a propulsive acceleration. An example is offered by solar sails, which use a thin membrane to reflect the impinging photons. The solar radiation momentum may actually be transferred to matter by means of various optical phenomena, such as absorption, emission, or refraction. This paper deals with the novel concept of a refractive sail, through which the Sun's light is refracted by crossing a film made of polymeric micro-prisms. The main feature of a refractive sail is to give a large transverse component of thrust even when the sail nominal plane is orthogonal to the Sun-spacecraft line. Starting from the recent literature results, this paper proposes a semi-analytical thrust model that estimates the characteristics of the propulsive acceleration vector as a function of the sail attitude angles. Such a mathematical model is then used to analyze a simplified Earth-Mars and Earth-Venus interplanetary transfer within an optimal framework.