# Impact of Satellite Attitude on Altimetry Calibration with Microwave Transponders
## 4 Results
### Jason-3 Attitude Effects on Transponder Results  
The attitude effects of the Jason-3 spacecraft on range and datation biases were derived using the methodology of Section 3.3. The time series of \(\delta B\) and \(\delta T\) effects for each D018 and A109 cycle with a successful calibration from CDN1 and GVD1 sites are presented in Figure 9. It is evident from the results that the attitude effect on range bias spans from \begin{table}
\begin{tabular}{c c c c} \hline  & **Roll** & **Pitch** & **Yaw** \\ \hline CDN1/GVD1 D018 & 117, 39, 32, 27, 23.5, 21 & 117, 39, 32, 27, 23.5, 21 & 117, 88, 58, 47, 39, 32, 27, 23.5, 21 \\ \hline GVD1 A109 & 117, 39, 32, 27, 23.5, 21 & 117, 70, 51, 39, 32, 27, 23.5, 21 & 117, 58, 39, 32, 27, 23.5, 21 \\ \hline \end{tabular}
\end{table} 
Table 2: Main periods (in days) of Jason-3 attitude angles obtained by spectral analysis with a Hann window. Figure 8: Jason-3 roll, pitch and yaw amplitude spectrum at CDN1 and GVD1 calibration sites. The framed area on the bottom left is zoomed and presented on the upper right part of the figures. approximately \(-2\) mm to \(+1\) mm, whereas the effect on datation varies between \(\pm 110\)\(\upmu\)s. The two effects show an inversely proportional behavior, i.e., as \(\delta B\) increases, \(\delta T\) decreases. It is also apparent from Figure 9 that there are upper and lower limits for the attitude effects on \(\delta T\) generated by attitude variations. The outer limits of attitude effects stem from the CoG-APC baseline length, which is constant (assuming temporal variations are negligible) and restricted by the physical dimensions of the satellite. In order to identify additional patterns in the behavior of \(\delta B\) and \(\delta T\), we provide scatter plots of the generated attitude effects as a function of roll, pitch and yaw angles (Figure 10). From the right diagrams of Figure 10, it is evident that attitude effects become large when the yaw angle is either \(\theta_{y}=0^{\circ}\) or \(\theta_{y}=\pm 180^{\circ}\). The APC precedes the CoG with respect to the transponder location on the ground (Table 1) when the satellite flies with \(\theta_{y}=0^{\circ}\). In this case, the effect on range bias becomes minimum (\(\delta B=-1.7\) mm), and datation grows to a maximum value (\(\delta T=110\)\(\upmu\)s). The opposite behavior arises when the satellite flies with \(\theta_{y}=180^{\circ}\) with CoG preceding the APC (Table 1). In this flying orientation, the effect on range bias becomes the maximum (\(\delta B=0.7\) mm), and datation comes to a minimum (\(\delta T=-110\)\(\upmu\)s). When the satellite is aligned at a right angle with respect to flight direction, where the yaw angle is \(\theta_{y}=\pm 90^{\circ}\), the impact on datation is negligible, i.e., \(\delta T=0\). Datation seems to be affected primarily from the yaw angle. The effect of yaw attitude on \(\delta T\) can be approximated using the relation:  
\[\delta T\simeq\frac{\mathbf{V}_{\mathrm{SAT}}^{x}\cos\theta_{y}}{|\mathbf{u} |}=\frac{|\mathrm{CoG};\mathrm{B}_{0}|\cos\theta_{y}}{|\mathbf{u}|}, \tag{20}\]  
where the \(\mathbf{V}_{\mathrm{SAT}}^{x}\) is the projection component of the CoG-APC baseline vector on the \(x_{B}\)-axis in the SAT system which starts from the CoG and terminates at \(\mathrm{B}_{0}\) as presented in Figure 5a. The \(|\mathbf{u}|\) represents the magnitude of the satellite's velocity in the EFRS. In practice, Equation (20) describes the time it takes for Jason-3 to cover the distance between APC and CoG projected onto the flight direction. The values of \(\delta T\) are evaluated for the complete range of yaw angles using Equation (20). The results are shown in Figure 10. It is evident that the modeled yaw effect of Equation (20) (shown with red dots on Figure 10) is in good agreement with the actual result of the analytical solution (blue dots) for datation.