Atmospheric mass densities in the lower thermosphere below 200 km have not been adequately determined, but they are crucial for re-entry prediction of space objects. In this paper, based on precise orbit data of the re-entry objects SZ-10 MODULE and TIANGONG 1 (COSPAR identifiers 2013-029H and 2011-053A, respectively; NORAD catalog numbers 39193 and 37820, respectively), the semi-major axis decay numerical method and the improved energy balance method are adopted to retrieve thermospheric mass densities below 200 km altitude, and a total of 7044 and 4698 points of valid densities data with one-minute temporal resolution are obtained, respectively. Then the retrieved densities after preprocessing are compared with the NRLMSISE-00 empirical model of the atmosphere. It shows that there is an excellent consistency between these two methods with the Pearson correlation coefficients around 1.00, the retrieved densities of which are also in good agreement with the model with the Pearson correlation coefficients above 0.97 (their systematic biases are about 1.1% and 4.5% with standard deviations of about 14% and 20% for these two objects respectively), but the retrieved densities of the semi-major axis decay numerical method have a smaller systematic bias from the model than the results of the improved energy balance method which is computationally more efficient. In addition, the corresponding retrieved densities and their ratios to the model are further analyzed in terms of latitude and local solar time, and the retrieved densities of these two methods are also in good consistency within about 97%. The maximum mean deviations from the model in both dimensions reach about 12%. It reveals the variations of the thermospheric mass densities below 200 km altitude with latitude and local solar time due to solar activity. Additionally, it also indicates that the NRLMSISE-00 model underestimates the thermospheric densities at high solar activity and overestimates the densities at low solar activity, as compared to the retrieved densities that are regarded as true values.
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