We examine spatial variability of attenuation in the Earth's atmosphere as a cause of asymmetrical eclipses and consequent acceleration of LAGEOS, i.e., the solar radiation pressure on LAGEOS due to the Earth's penumbra. Measurements of atmospheric attenuation derived from the satellite-borne Stratospheric Aerosol and Gas Experiment after the eruption of Mount Pinatubo were used to simulate the largest expected aerosol content of the atmosphere. In our experiment one hemisphere was loaded with volcanic aerosols, while the other was not. The difference between attenuation in the two hemispheres sets a maximum reasonable limit to the size of eclipse asymmetry. This condition would accelerate LAGEOS only about 0.2 picometers per second squared (pm s-2 or 10-12 m s-2) and indicates that eclipse asymmetry can only account for about 40--50% of the remaining unmodeled residuals. This is slightly less than the penumbral acceleration found by Vokrouhlicky et al. (1994). ¿ American Geophysical Union 1995.