Photon thrust from the solar heating of the LAGEOS I satellite appears to explain much of the eccentricity variations seen in the satellite's orbital elements. We invoke a thermal model of LAGEOS I in which the photon thrust from solar heating is directed along the satellite's spin axis and functionally depends only on the cosine of the angle between the Sun's position and the spin axis. We calibrated the amplitude of the force from the 1980--1983 equivalent along-track acceleration derived from the observed orbital perturbations; during this time the spin axis position is assumed to be known and to be that at orbit injection. The photon thrust from this simple thermal model, plus later spin axis positions obtained from Sun glint data (which show LAGEOS I to be processing), give reasonable agreement with the observed along-track acceleration in the time period of 1988--1995. Thus much of the eccentricity variations seem to be due to thermal thrust and do not have a geophysical origin (atmospheric tides) as has been proposed. However, our solar heating model does not appear to explain the highest peaks and deepest troughs seen in the along-track acceleration, indicating the need for a better thermal model and consideration of other forces, such as that due to anisotropic reflection.¿ 1997 American Geophysical Union