# Near-Real-Time Global Thermospheric Density Variations Unveiled by Starlink Ephemeris
## 2 Data and Methods
\begin{table}
\begin{tabular}{c c c c} \hline
**Form** & **Line Number** & **Content** \\ \hline \multirow{6}{*}{Header (Line 1–4)} & 1 & created:2024-10-01 10:18:30 UTC & \\  & 2 & ephemeris\_start:2024-10-01 09:33:42 UTC & \\  & 3 & ephemeris\_source:blend & \\  & 4 & UVW & \\ \hline \multirow{6}{*}{First Ephemeris Point (Line 5–8)} & \multirow{6}{*}{6} & 2024275093342.000 & \multirow{6}{*}{4125.4543221036} \\  & 5 & 4741.3443204153 & 2356.2722509008 & & \\  & & 0.1367078084 & 6.6298975741 & \(-\)3.9309088221 \\  & & 7.1787884970e\(-\)07 & \(-\)4.3946653063e\(-\)07 & 8.6816961396e\(-\)07 \\  & 6 & 4.6892685935e\(-\)10 & \(-\)2.8619644577e\(-\)10 & 1.2167821657e\(-\)06 \\  & & 1.2224254104e\(-\)09 & & \\ \cline{1-1}  & & \(-\)1.0345626097e\(-\)09 & 1.7751967007e\(-\)12 & 2.6256571511e\(-\)12 \\ \cline{1-1}  & 7 & \(-\)5.4598689236e\(-\)10 & 4.3500917993e\(-\)10 & \(-\)1.7690294263e\(-\)12 \\ \cline{1-1}  & & \(-\)9.6760401482e\(-\)13 & & \\ \cline{1-1}  & & 5.5649992482e\(-\)13 & 1.3345625691e\(-\)12 & 2.9188509553e\(-\)12 \\ \cline{1-1}  & 8 & 1.6219733961e\(-\)09 & 1.6559550374e\(-\)15 & \(-\)2.8281793013e\(-\)15 \\ \cline{1-1}  & & 5.4168888107e\(-\)12 & & \\ \hline \end{tabular}
\end{table} 
Table 1: Starlink ephemeris data example. \begin{table}
\begin{tabular}{c c c c c} \hline
**Orbital Shells** & **Altitude (km)** & **Inclination (\({}^{\circ}\))** & **Plane Counts** & **Version** \\ \hline Shell 1 & 550 & 53 & 72 & v0.9/v1.0 \\ Shell 2 & 570 & 70 & 36 & v1.5 \\ Shell 3 & 560 & 97.6 & 6 & v1.5 \\ Shell 4 & 540 & 53.2 & 72 & v1.5 \\ Shell 5 & 560 & 43 & 28 & v1.5/v2.0 mini \\ \hline \end{tabular}
\end{table} 
Table 2: Orbital shells of the first generation Starlink. If a satellite is influenced solely by Earth's gravity, its motion around the Earth could be simplified as a two-body problem, and its orbit could be described by constant Keplerian orbital elements. However, in reality, satellites are subject to additional perturbing forces, causing the orbital elements to change gradually. These time-varying orbital elements are referred to as osculating orbital elements. The perturbations in osculating orbital elements can be analytically decomposed into secular, long-period, and short-period variations [1]. Among these, short-period variations are induced by the periodic motion of the satellite  
Figure 1: Distribution of Starlink satellites in Shell 1. (**a**) Geographic distribution of Starlink satellites projected onto longitude and latitude coordinates, with individual Starlink satellites represented as discrete points. (**b**) Orbital distribution of Starlink satellites projected onto the argument of latitude and the right ascension of the ascending node (RAAN) coordinates, where circular markers denote satellite locations and semi-transparent color bands identify specific orbital planes. (**c**) Quantitative distribution of Starlink satellites per orbital plane, presented as a frequency histogram, different color bands identify specific orbital planes. along its orbit. In this study, we employ a \(20\times 20\) Earth gravitational field model to estimate short-period terms [36; 37]. Then, the mean orbital elements can be obtained by filtering short-period variations from osculating elements. Compared with osculating elements, the mean orbital elements (especially the mean semi-major axis, SMA) can accurately reflect orbital motions caused by atmospheric drag and orbital maneuvers. Figure 2a,b display the osculating and mean SMA of STARLINK-1009 from the reference batch, respectively. The osculating SMA in Figure 2a exhibits sinusoidal periodic fluctuations with peak-to-peak amplitudes of up to 15 km, though the changes between peaks are not pronounced. In contrast, the mean SMA in Figure 2b reveals three distinct orbital phases: Natural Decay, Maneuver, and Ambiguity. The Natural Decay phase (blue data points) represents natural orbital decay, characterized by adjacent SMA differences of less than 5 m and a clear downward trend.