Thermospheric Mass Density Observations and Empirical Modeling Using the Tianmu-1 Constellation

Thermospheric mass density is a major source of uncertainty in spacecraft orbit prediction, particularly in low earth orbit. Since 2023, the Tianmu-1 constellation has deployed 12 satellites in sun-synchronous orbits at ~500 km altitude, each equipped with the Orbital Neutral Atmospheric Detectors (OADs) to provide in-situ measurements of thermospheric mass density and composition. In this study, density data from five Tianmu-1 satellites (TM02, TM03, TM07, TM11, and TM15) are used to construct a preliminary empirical thermospheric mass density model. The OAD measurements are firstly compared against the independent GRACE-FO accelerometer-derived density data. The results show that the calibrated Tianmu-1 densities agree well with GRACE-FO observations, with correlation coefficients exceeding XX and mean biases below XX%. The calibrated densities are then analyzed to quantify their responses to solar EUV flux and geomagnetic activity. Finally, an empirical density model is developed using the Empirical Orthogonal Function (EOF) decomposition. The EOF-based model reproduces the major spatial-temporal variability of the thermosphere and achieves a modeling accuracy of XX%, demonstrating the potential of the Tianmu-1 constellation for operational thermospheric mass density specification.