## 6 Simulation Analyses
### Pre-Identification of Continuous Tangential Thrust Parameters  
Take, for example, the two observations described in Table 4.  
The two observations were each simulated 100 times, and each simulation exhibited a different random observation error after using the single-arc segment orbit determination method described in Section 3 to obtain the semi-major axes of the two arc segments noted as \(a_{1}\), \(a_{2}\). The results are shown in Figure 8. \begin{table}
\begin{tabular}{c c c} \hline \(t_{10}\) & \(t_{1k}\) & \(\Delta t_{1}\) \\ \hline
2024-01-25 12:05:01 & 2024-01-25 12:12:28 & 00:07:27 \\ \hline \(t_{20}\) & \(t_{2k}\) & \(\Delta t_{2}\) \\ \hline
2024-01-26 11:34:40 & 2024-01-26 11:43:15 & 00:08:25 \\ \hline \(\Delta t\) & \multicolumn{2}{c}{23:29:39} \\ \hline \end{tabular}
\end{table} 
Table 4: Arc time for two observations. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Orbital** & **Eccentricity** & **Inclination/(\({}^{\circ}\))** & **RAAN/(\({}^{\circ}\))** & **Argument of** & **Mean** \\
**Altitude/km** & **Eccentricity** & **Inclination/(\({}^{\circ}\))** & **RAAN/(\({}^{\circ}\))** & **Perigee/(\({}^{\circ}\))** & **Anomaly/(\({}^{\circ}\))** \\ \hline
380 & 0 & 53 & 352.937 & 336.98 & 63.025 \\ \hline \end{tabular}
\end{table} 
Table 2: Initial orbital elements at the ignition point of a Starlink satellite. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Station Name** & **Fac1** & **Fac2** & **Fac3** & **Fac4** & **Fac5** \\ \hline Latitude & 34.5869 N & 46.82 N & 38.83 N & 36.06 N & 18.2 N \\ \hline Longitude & 109.51 E & 130.37 E & 76.92 E & 120.36 E & 109.5 E \\ \hline Station Name & Fac6 & Fac7 & Fac8 & Fac9 & \\ \hline Latitude & 41.515 N & 5.757 N & 31.818 S & 8.181 S & \\ \hline Longitude & 14.362 E & 44.059 E & 22.543 E & 38.062 W & \\ \hline \end{tabular}
\end{table} 
Table 3: Ground radar equipment latitude and longitude data. According to Equation (20), the tangential acceleration is solved inversely by \(a_{1}\) and \(a_{2}\). The results are shown in Figure 9, and the relative error of tangential acceleration is shown in Figure 10. It can be seen that the average relative error of solving the tangential acceleration based on two arc segments separated by 23 h is only 3.2%. The tangential acceleration and its average relative error were calculated from radar observation arcs at different time intervals, and the relationship between the relative error of tangential acceleration and the observation time interval is shown. When the time interval between two observations is greater than 7 h, the relative measurement error of tangential acceleration can reach 5% or less. This is shown in Figure 11. The circles in the figure represent the average relative error values of 100 observations at that moment. Figure 8: Semi-major axis results for two initial orbit determinations. Figure 9: Results of tangential acceleration calculation. Electric propellers usually have multi-mode operation capability, and their performance in terms of thrust, power, and specific impulse can be optimally adjusted according to different mission requirements, with strong mission adaptability. The smaller the tangential acceleration, the slower the rate of change of the semi-major axis and, consequently, the poorer the accuracy of the tangential acceleration inversely solved from the orbit determination of the two radar observations. A longer interval between two radar observations is required to achieve a relative measurement error of 5%. The simulation is set up with continuous tangential accelerations of 1.8 \(\times\) 10\({}^{-4}\) m/s\({}^{2}\), 1.3 \(\times\) 10\({}^{-4}\) m/s\({}^{2}\) and 0.5 \(\times\) 10\({}^{-4}\) m/s\({}^{2}\). The results are shown in Figure 12, Figure 13, and Figure 14, respectively. When the continuous tangential acceleration is 1.8 \(\times\) 10\({}^{-4}\) m/s\({}^{2}\) and the interval between two radar observations is greater than 11 h, a solution error of 5% or less can be achieved.