# Atmospheric Density Inversion Based on Swarm-C Satellite Accelerometer
## 4 Discussion and Conclusions  
Compared with the method proposed by [PERSON] et al. [24], the acceleration correction method used in this research is different. [PERSON] et al. regarded the influence of the temperature factor as approximately linear, and this method has been proven feasible. We treat the temperature factor as linear on its basis and use the non-conservative force acceleration data derived from GPS as the calibration standard. The generalized least squares method finds calibration parameters, including deviation coefficients, scale coefficients, linear temperature factors, and trend term coefficients. After the optimal value of the calibration parameter is obtained, the corrected acceleration can be calculated. The acceleration value obtained is smoother, and the necessity of temperature correction is proved by separately showing the influence of temperature on the acceleration of Swarm-C. In the Swarm-C satellite atmospheric drag coefficient calculation experiment, the main reason for the variation of the atmospheric drag coefficient and cross-sectional area of the Swarm-C satellite products is the different atmospheric temperatures around the day and night regions. Therefore, the atmospheric temperature has a significant effect on the drag coefficient. In addition, different attitudes of the satellite during its orbital flight will result in different angles between the atmospheric molecules incident on the satellite panels and  
Figure 11: Time–latitude distribution of atmospheric density on 1 January 2016. (**a**) Before interpolation; (**b**) after interpolation. the normal vector, affecting the results. As a result of our measured atmospheric density, the peak of the curve is between \(0.6*10^{-12}\) and \(1.6*10^{-12}\). There is a certain difference from the inversion result using only the accelerometer because part of the peak signal is corrected, which reduces the overall digital range. The large-area drag coefficient decreases gradually as the angle of incidence of atmospheric molecules increases. The reason is that the direction of the thermal motion of atmospheric molecules is random, and the direction of motion of atmospheric molecules and the direction of relative motion of the atmosphere are superimposed on each other. When the incident angle of the atmosphere is perpendicular to the satellite panel, due to the thermal motion of atmospheric molecules, the speed is not completely perpendicular to the satellite panel. Atmospheres with different altitudes have different compositions and temperatures, leading to different atmospheric drag coefficients. In the Swarm-C accelerometer atmospheric density inversion experiment, the latitude change of the daily average thermal mass density in the southern winter is greater than that in the northern winter. The distribution of atmospheric density in Antarctica and the Arctic has obvious asymmetry. The different positions of the magnetic poles in the northern and southern hemispheres relative to the geographic poles may cause this. Therefore, auroral heating in the southern hemisphere is more likely to produce longitudinal changes in the daily average mass density than in the northern hemisphere. Another possibility is that the asymmetry seems to be caused by solar radiation during the winter solstice. In addition, Joule heating is proportional to ionospheric electron density and conductivity in the southern hemisphere auroral zone. As a result, the atmospheric density is higher in the southern hemisphere compared to its value in the northern hemisphere during the entire time interval considered. This phenomenon's exact cause is unknown and needs further study. Based on this research, we may continue to carry out research from the following aspects in the future. 1. Since it is impossible to know all the hardware conditions and fault causes of the Swarm-C satellite accelerometer, the accelerometer calibration method used in this paper cannot correct the errors caused by all hardware problems of the accelerometer and cannot accurately judge.