The satellites LAGEOS-I and LAGEOS-II are essential for the scientific study of various (geo)physical phenomena, such as geocenter motion and absolute scale. The high quality of such science products strongly depends on the absolute quality of the SLR observations and that of the orbit description. Therefore all accelerations experienced by the spacecraft need to be modeled as accurately as possible, the thermal radiation forces being one of them. Traditionally, this is done by estimating so-called empirical accelerations. However, the rotational dynamics of LAGEOS-I in particular no longer allows such a simple approach: a full modeling of the spin behavior, the temperature distribution over the spacecraft surface and the resulting net force prove necessary to achieve the best results. As a first step, a new model, Lageos Spin Axis Model (LOSSAM) has been developed. It is unique in its combination of analytical theory and empirical observations. Its mathematics is taken after previous investigators, although flaws have been corrected. LOSSAM describes the full spin behavior of LOSSAM based on the following phenomena: (1) the geomagnetic field, (2) the Earth's gravity field, (3) the satellite center of pressure offset, and (4) the effective difference in reflectivity between the satellite hemispheres. Its accuracy has been demonstrated by an improvement of about a 50% in the RMS residual of the Yarkovsky-Schach effect signal (as shown by Lucchesi et al. <2004>). Such a high-quality model for rotational behavior is indispensable for a proper force modeling, and hence also for the quality of typical LAGEOS science products.