Orbital parameters of the satellite Intercosmos 10 rocket (1973-82B) have been determined at 296 epochs using about 14,000 optical and radar observations during the 1439 d of its life. 1973-1982B was in an orbit inclined at about 74.0° to the Equator and it decayed on 8 October 1977. The orbital elements were found using the RAE orbit refinement program PROP, in the MACPROP version, giving average orbital accuracies in perigee height and inclination of 110 m and 0.002° respectively. The influence of aerodynamic drag on the motion of 1973-82B is considered. A model of the atmosphere is adopted that allows for oblateness and the diurnal variation. The observed values of eccentricity and inclination are modified by the removal of perturbations due to luni-solar attraction, solid Earth and ocean tides, solar radiation pressure, zonal and low-order long-periodic tesseral harmonic perturbations and changes due to precession. The resulting variations due to drag are analysed to give values of density scale height and three values of the zonal rotation rate of the upper atmosphere at heights between 200 and 300 km.