# Atmospheric Density Inversion Based on Swarm-C Satellite Accelerometer
## 1 Introduction  
Research on thermospheric density has significant meaning for different applications and satellite orbits. Its application scope includes satellite re-entry prediction, maneuver planning and space object orbit maintenance, and propellant fuel carrying capacity estimation. The drag resistance of the atmosphere is the essential component of the non-conservative forces of low-orbit satellites. Therefore, the measurement accuracy of atmospheric density largely determines the satellite's non-conservative force [1]. However, it is challenging to measure and forecast atmospheric density. The empirical atmospheric model's prediction accuracy is affected by the Earth's magnetic field change, solar activity cycle, and Earth's rotation [2, 3, 4]. As a result, the empirical atmospheric density model's prediction accuracy is limited. Satellite manipulation and orbit determination require high-precision information on thermosphere atmospheric density [1, 5, 6]. Hence, studying the complex characteristics of the thermosphere and satellite dynamics modeling is challenging. It is of great significance to study the density of the thermosphere. Under the influence of the complex interaction between the Earth's system and the Sun, the thermosphere atmospheric density has a wide range of spatiotemporal variations [7, 8]. However, the observed data on thermosphere atmospheric density have been very scarce, so the modeling uncertainty of thermosphere atmospheric density is very high [9]. There are three main methods for detecting the thermosphere's density. The first is to use atmospheric density detectors [10]. The mechanism is based on aerodynamics by detecting the temperature inside the sensor and the pressure of the vessel wall. This method is traditional and needs more time. It cannot reflect the atmospheric density around the spacecraft's orbit in time and has low accuracy. The second method is to use orbit data inversion. It is a primary method for thermospheric density measuring. Many known semi-empirical atmospheric models are built upon this method [4; 11; 12; 13]. The method's basic principle is that the atmospheric resistance causes all LEO (low Earth orbit) space objects to spiral downward and eventually re-enter the densest atmosphere. Since the atmospheric density decreases exponentially as the height increases, the elliptical orbit object is subjected to the most potent resistance at its perigee. The resistance causes the kinetic energy to be converted into heat orbital size, reducing the space object's ellipticity [14]. When the space object approaches the end of its life, its orbit becomes almost circular. The density and resistance along the orbit rapidly increase. The long axis decays rapidly, and the decay rate can reach 30 km daily. The satellite deviates from the predetermined orbit under atmospheric drag, so the relationship between the change of the orbital parameters and the atmospheric density can reverse the atmospheric density. The third method uses an onboard accelerometer [15; 16; 17]. The accuracy of the onboard accelerometer is very high, and the gravity satellites CHAMP, GRACE, and Swarm satellites are all equipped with this kind of load. Since the 1960s, satellites from the United States, Italy, and France have carried on-board accelerometers for the study of thermospheric airtight modeling. Beginning in 1968, miniature electrostatic uniaxial accelerometers (MESA) were applied to eight satellites in orbit. Italy launched the spherical San Marco satellite in 1968, carrying an accelerometer. France launched the CASTOR satellite carrying the CACTUS accelerometer in 1975. ONERA developed the CACTUS accelerometer. The satellite was mainly used to test the operation of the CACTUS accelerometer. As an improvement of MESA, the satellite electrostatic three-axis accelerometer (SETA) was used in multiple space missions of the U.S. military for testing in the first half of the 1980s. Some scholars and institutions have used satellite accelerometer data to detect atmospheric density.