We analyzed X-band radio tracking observations of the Mars Odyssey spacecraft during its aerobraking phase (October 2001-January 2002). Using the precision orbit determination software GEODYN, we obtained estimates of the spacecraft orbital energy lost during each periapsis pass due to atmospheric drag. We also recovered atmospheric density values at each periapsis, assuming simple exponential atmospheric models. Our measurements are in good agreement with the time series from the Odyssey accelerometer instrument, but they are dependent on the a priori scale height used. Using the accelerometer-derived periapsis densities and the precision orbit determination-derived frictional loss of orbital energy, we calculated new scale heights. Each represents the effective scale height of the atmosphere near periapsis for each aerobraking pass. Our results are consistently approximate to 1.7 +/- 0.7 km greater than the published accelerometer values. The accelerometer measurements have higher spatial and temporal resolution when they are available, but these results provide a data set useful for engineering and navigational purposes, to assess variability in the Martian middle atmosphere.