## 3 Results
### Non-Conservative Force Modeling Effect of BDS
Because the China Satellite Navigation Office (CSNO) does not disclose the transmit power for BDS-3 satellites [5], the antenna thrust is only applied to BDS-2 MEO in WU. The different solutions for BDS among four ACs in non-conservative force modeling of interest are presented in Table 4.  
For earth radiation pressure and antenna thrust mainly imposing on the radial direction, which is basically consistent with the observation direction of SLR, the effect of these two forces can be reflected in SLR residuals. Figure 7 shows the statistical information, i.e., mean and RMS of SLR residuals of different satellites among the four ACs. For the three IGSO satellites, the RMS of ESA's SLR residuals is notably larger than that of the other ACs (about a factor of 2), which could be attributed to the differences in the geometry parameters and optical coefficients of IGSO satellites. The mean offset of SLR residuals of WU for the BDS-2 MEO (C11) satellite is approximately 5 mm larger than that of CODE and GFZ (ESA's non-conservative force modeling of BDS-2 satellites may have defects in the subsequent comparison), which may be related to the modeling of ERP and AT. Additionally, the RMS of WU for C11 is the smallest among WU, CODE, and GFZ. The mean offset of the SLR residuals of ESA for the BDS-3 CAST (C20 and C21) and SECM (C29 and C30) satellites are the largest, and they both have a positive centimeter-level offset compared with GFZ and WU. When antenna thrust and albedo were modeled, the mean value of SLR residuals had a positive offset with the range of 5 to 10 mm, while the RMS decreased by 1 to 5 mm. \begin{table}
\begin{tabular}{c c c c c} \hline
**Model** & **CODE** & **GFZ** & **WU** & **ESA** \\ \hline SRP & ECOM2 & ECOM & ECOM + PBW(BDS-3) & ECOM + estimated PBW \\ ERP & Not applied & Not applied & Applied in BDS-2 MEO & Applied \\ AT & Not applied & Not applied & Applied in BDS-2 & Not applied \\ \hline \end{tabular}
\end{table} 
Table 4: Parts of non-conservative force modeling strategy among four ACs. To compare the adaptability of SRP modeling, we validated BDS orbits by utilizing SLR observations, and the SLR residuals were then depicted as a function of the sun elevation \(|\beta|\) and the satellite's elongation angle \(\epsilon\) relative to the sun. Comparing the relationship between elongation angle and SLR residual can effectively reflect the effect of SRP modeling. To better analyze the effect of SRP modeling, we generated pictures according to each satellite. Four BDS-2 satellites of WU and ESA are shown in Figure 8 to investigate the relationship between SLR residuals and elongation angle. According to the results, the SLR residual of the BDS-2 IGSO satellite is more dependent on the elongation angle, which indicates that the BDS-2 MEO satellite has a better performance than IGSO satellites. Additionally, the slope with regard to the elongation of the BDS-2 MEO of ESA is higher to that of the BDS-2 IGSO of WU. Combined with the above-mentioned results--that the RMS of the IGSO of ESA is too large--we infer that ESA may have some defects in the SRP modeling of BDS-2 satellites. Figure 9 illustrates the relationship between SLR residuals and the elongation angle for four BDS-3 satellites, highlighting how modeling defects of SRP can be observed through the sun elevation. When the elongation angle is close to 90 degrees, the spread of SLR residuals is smaller for high sun elevations (red dots in Figure 9) than that for low sun elevations (blue dots in Figure 9). This phenomenon occurs because, when the satellite is at a high \(|\beta|\) (the red orbit in Figure 10), the sunlight mainly illuminates the +X surface (the X and the following Z axes are defined in the SCF [37]). When the satellite is at a low \(|\beta|\) (the blue orbit in Figure 10), the +Z and \(-\)Z surfaces are also alternatively illuminated apart from the +X surface, which makes accurately modeling the SRP difficult.