We present measurements of the density of the Martian atmosphere at ∼400 km altitude. Our analysis used radio tracking data to perform precise orbit determination on the Mars Odyssey spacecraft between March 2002 and November 2005. Recent improvements in a priori physical models make it possible to isolate the contribution of the atmospheric drag from the various forces acting on the spacecraft. For each spacecraft trajectory segment (arc) we adjusted an atmospheric drag coefficient (C_D), which scales the a priori model density. From the drag coefficient we obtained a time series of the measured density. These measurements at the Mars Odyssey orbiting altitude are close to noise level, and the various tests we conducted show the robustness of the measurements. We obtained a better agreement with the atmospheric model used during the second Martian year, when solar activity is lower. Using various simple exponential atmosphere models, we estimated the scale height near the spacecraft periapsis and found values between 25 and 50 km, in the lower range of expected values, and used exospheric temperature estimates to assess the role of EUV heating of the upper atmosphere. We did not observe one-to-one correlation between solar activity and exospheric density, but we detected a solar rotation periodicity in our measurements.