Calculation of light pressure force and torque acting on a spacecraft with a solar sail

We compare two way of calculation of light pressure force and torque acting on a composite solar sail. The first way is based on analytical formulas, which were derived without taking into account shading some parts of the sail by its other parts. The second way uses a detail geometric model of the sail which allows taking proper account of such shading. We assume photons interact with the sail in two ways. Some of them have a specular reflection, the others are absorbed. We ascertain the range of spacecraft attitudes with respect to solar rays in which the analytical formulas are sufficiently exact.