# Solar Radiation Pressure Models for BeiDou-3 I2-S Satellite: Comparison and Augmentation
## 2 Characteristics and SRP Models for BeiDou-3 I2-S Satellite
### Box-Wing Model
\begin{array}{ll}a_{D}=&-a_{C}^{\alpha\delta}(|\cos\varepsilon|+\sin \varepsilon+\frac{2}{3})-a_{S}^{\alpha\delta}(|\cos\varepsilon|-\sin \varepsilon-\frac{4}{3}\sin^{2}\varepsilon+\frac{2}{3})\\ &-a_{A}^{\alpha\delta}(\cos\varepsilon+\frac{2}{3}|\cos\varepsilon|\cos \varepsilon)-2a_{C}^{\rho}(|\cos\varepsilon|\cos^{2}\varepsilon+\sin^{3} \varepsilon)\\ &-2a_{C}^{\rho}(|\cos\varepsilon|\cos^{2}\varepsilon-\sin^{3}\varepsilon)-2a_ {A}^{\rho}\cos^{3}\varepsilon\\ a_{B}=&-\frac{4}{3}a_{S}^{\alpha\delta}(\cos\varepsilon\sin\varepsilon)- \frac{2}{3}a_{A}^{\alpha\delta}(|\cos\varepsilon|\sin\varepsilon)\\ &-2a_{C}^{\rho}((|\cos\varepsilon|-\sin\varepsilon)\cos\varepsilon\sin \varepsilon)-2a_{S}^{\rho}((|\cos\varepsilon|+\sin\varepsilon)\cos\varepsilon \sin\varepsilon)\\ &-2a_{A}^{\rho}\cos^{2}\varepsilon\sin\varepsilon\end{array}  \tag{10}\]  
where \(a_{C}^{\alpha\delta}\), \(a_{S}^{\alpha\delta}\) and \(a_{A}^{\alpha\delta}\) indicate the effect of a cubic (C), stretched (S), and asymmetric (\(A\)) contributions of satellite body shape related to absorption plus diffuse reflection (superscript \(\alpha\delta\)), while model parameters \(a_{C}^{\rho}\), \(a_{S}^{\rho}\) and \(a_{A}^{\rho}\) are related to the specular reflection (\(\rho\)) part for the corresponding body shape contributions, and the above parameters can be obtained by,  
\[\begin{array}{ll}a_{i}^{\alpha\delta}=\frac{A_{1}}{M}\frac{S_{0}}{c}(\alpha _{i}+\delta_{i})&a_{i}^{\rho}=\frac{A_{1}}{M}\frac{S_{0}}{c}\rho_{i}\\ a_{i}^{\alpha\delta}=\frac{1}{2}(a_{i+2}^{\alpha\delta}+a_{-z}^{\alpha\delta}) &a_{i}^{\rho}=\frac{1}{2}(a_{+z}^{\rho}+a_{-z}^{\rho})\\ a_{C}^{\alpha\delta}=\frac{1}{2}(a_{i+2}^{\alpha\delta}+a_{+x}^{\alpha\delta}) &aGNSS Monitoring and Assessment system (iGMAS) network. Three solutions, named ECOM1, ECOM2, and ABW were determined according to the SRP models used. The SLR and orbit boundary discontinuities (OBD) have been used for evaluating the orbit quality. SLR residuals exceeding an absolute value of 60 cm were excluded. As 72 h POD arc used, the OBD are obtained as the three-dimensional (3D) orbit difference at midnight epoch between two 3-day arc shifted by 72 h. In addition, the OBDs were treated as outliers and removed once the 3D values of the orbit differences were larger than 200 cm. Figure 1 shows the one-way SLR residuals in the function of the \(\varepsilon\) angle for the three solutions. In expectation, similar as that shown in [3], the SLR residuals of ECOM1 solution show pronounced \(\varepsilon\)-angle-dependent variation with bias up to \(-16.9\) cm. Once the ECOM2 has been used, the bias has been reduced to \(-8.9\) cm with slightly degraded standard derivations from 16.9 to 19.0 cm. However, most importantly, the \(\varepsilon\)-angle-dependent error has been reduced. It is worth noticing that the \(\varepsilon\) angle is actually a function of both \(\beta\) and \(\mu\), as expressed in Equation (12). We therefore decomposed the SLR residuals into the two arguments respectively as shown in Figure 2, and found that a marked v-shaped SLR variation with symmetry to the zero degree of \(\mu\) angle can be identified for the ECOM1 solution, while it did not exist in ECOM2 solution, while the dependence with to \(\beta\) angle is not clear as the \(\mu\) angle. This might be attributed to smaller value of ratio of area-to-mass and less extended body shape used by BeiDou-3 I2-S satellite. For ABW solution, which shows the best SLR validation, the bias of SLR residuals was further reduced to \(-2.2\) cm, and possibly generated by the unmodeled earth radiation pressure and antenna thrust. In addition, there are almost no significant \(\varepsilon\)-angle-dependent variations in SLR residuals. This further demonstrates that ABW has the ability to capture the SRP perturbation quite well.