## 5 Conclusions  
The composition and content of the atmosphere undergo significant alterations within the altitude range of Low Earth Orbit satellite operation as a consequence of the influence of various factors, including seasonal variations, solar activity, and geomagnetic indices. This results in the formation of the most active region of atmospheric drag. As the primary uptake force, it alters the operational velocity and attitude of the satellite. Atmospheric density inversion based on LEO satellites facilitates the adjustment of operational orbit altitude and velocity according to changes in atmospheric density, thereby prolonging  
Figure 5: (**a**) On 28 April 2024, the atmospheric density inversion results were compared with the NRLMISISE00 model. Orange represents the Nrlmisise00 simulated density, green represents the semi-long axis attenuation method for atmospheric density inversion, and blue represents the accelerometer inversion. (**b**) We take the hourly average of atmospheric density on 28 April 2024. Blue represents the accelerometer average, green is the hourly average corresponding to the semi-long axis attenuation method, and orange is the hourly average density of the Nrlmisise00 model. Figure 6: We linearly fit the semi-long axis attenuation and velocity meter inversion results in Figure 5b with the empirical model, where (**a**) represents the fitting results of the accelerometer and nrlmisise00, and (**b**) represents the fitting effect of the semi-long axis attenuation and nrlmisise00. operational cycles. Furthermore, the extensive observation data provided by LEO satellites can be fully utilized for atmospheric density modeling, which provides a reliable data source for weather numerical simulation and assimilation prediction. This article presents an in-depth and objective comparative and critical analysis of the diverse methodologies utilized for the acquisition of atmospheric density data, the types of data required, and an evaluation of their respective advantages and disadvantages. The use of satellite-borne atmospheric density sounders allows for the coverage of a vast area of the Earth's surface and the detection of phenomena at high altitudes. However, the costs associated with their launch and maintenance are considerable, and there may be delays in the processing and transmission of data, which limits the capability for real-time monitoring. The semi-axis decay method, which is based on dynamics, introduces an error associated with numerical integration and increases the computational volume when orbits are extrapolated. The energy decay method, which is based on the energy conservation theorem, greatly reduces the complexity of the calculation because it does not require the extrapolation of the orbit. There is an error in the energy form of some regenerative forces, which is particularly significant for orbits at higher altitudes. The acceleration calculated by the first two methods does not represent the actual instantaneous atmospheric drag acceleration; rather, it can be regarded as the average acceleration over the specified time interval. The accelerometer is capable of measuring the instantaneous acceleration with greater accuracy. The second part compares the precision orbit data and accelerometer data provided by the SWARM-A satellite. The semi-long axis attenuation method and accelerometer method were used for inversion experiments, and the inversion results were compared with the empirical model Nrlmisise00. The correlation coefficient between the semi-long axis attenuation method and Nrlmisise00 reached 0.9158, and the correlation coefficient between the accelerometer method and Nrlmisise00 reached 0.9204. The accuracy of accelerometer inversion is slightly higher than that of semi-long axis attenuation, which also confirms the feasibility of using orbit data for atmospheric density inversion and provides support for atmospheric modeling of LEO satellites without high-precision accelerometers.