The ultraviolet photometer of the University of Iowa spin scan auroral imaging instrumentation on board the Dynamics Explorer 1 satellite has returned numerous images of the geocorona from altitudes of 570 km to 23,300 km. The geocoronal observations from 1981 through 1985 are compared to a spherically symmetric isothermal Chamberlain model of the exospheric density distribution. Model parameters are varied to obtain an acceptable fit. The radiative transfer equation is solved numerically. Stellar intensities are monitored for an independent calibration of the DE 1 instrument in flight. The solar Ly &agr; flux is estimated through concurrent measurements made by the Solar Mesosphere Explorer satellite, supplemented by published values of ground-observable solar indices. Extraterretrial background intensities are adopted from earlier OGO 5 high-altitude measurements. The optimum fit for 1981 imaging data utilizes a Chamberlain model of temperature T=1050 K and exobase density nc=44,000 atoms cm-3. The exobase is taken as rc=1.08 RE (500 km altitude), and a critical radius for satellite atoms of rcs=3.0 rc is adopted. This model continues to compare well with the DE 1 measurements over the entire 4-year period studied, even though the exobase conditions are expected to have changed appreciably during this interval of declining solar activity. It is concluded that the apparently constant hydrogen density and scale height observed by DE 1 are not directly indicative of the exobase conditions through the classical Chamberlain model but rather show the effects of charge exchange with thermal ions in the plasmasphere. A readily observable departure from spherical symmetry is the geotail, an enhancement in the atomic hydrogen column densities in the antisunward direction.