ABSTRACT
The diurnal Yarkovsky effect, a perturbing force on meter--sized orbiting bodies caused by anisotropic heating and emission of thermal radiation from small spinning solar system bodies, is computed for spheroidal--shaped bodies with an arbitrary flattening. The solution is derived in analytical form for a body which rotates around its axis of symmetry. A numerical solution is presented for the more general case of a precessing body, where the symmetry axis tumbles around a fixed angular momentum vector. In both cases, the obtained Yarkovsky force is compared with the corresponding thermal force acting on a spherical body of the same mass. Differences of up to a factor of $3$ are found, depending on the geometric parameters of the body and its rotational state. However, the agreement between the derived force values in the two cases is much better when an average over all possible orientations of the spin axis and the solar position is considered. This result suggests that the simplified formulation of the diurnal Yarkovsky force based on a spherical geometry can be used, without introducing major mistakes, for long--term integrations of the orbits of small asteroidal fragments in the Solar System.