## 4 Pointing Errors Caused by Thermal Gradient
### Pointing Errors When Antenna Is Stationary  
An experiment was conducted to assess the thermal deformation caused by solar radiation when the antenna remained stationary for five consecutive clear and windless days, from 4 February to 8 February 2019. The AZ and EL angles of the antenna were maintained at 66\({}^{\circ}\) and 88\({}^{\circ}\), respectively. Meanwhile, the measurement system continuously recorded data at a sampling rate of 1 Hz. Figure 12 displays satisfactory unfiltered data.  
As depicted in Figure 12, the antenna alidade exhibits a relatively stable behavior during the non-sunlight period from 22:00 to 10:00. However, it experiences significant tilting between 10:00 to 20:00 due to the non-uniform temperature distribution caused by solar radiation. On average, the five-day experimental data showed an increase in AZ direction tilting at approximately 10:00, peaking at 53.4\({}^{\prime\prime}\) around 14:00, and gradually stabilizing after 18:00. From 10:00 to 18:00, an average azimuth error of 35.7\({}^{\prime\prime}\) was observed. In terms of EL direction tilting, it began at 12:00 and peaked at around 44.5\({}^{\prime\prime}\) by about 16:00 before becoming steady around 20:00. The average tilt in EL direction is 24.4\({}^{\prime\prime}\) between 12:00 and 20:00. It is evident that the onset and peak of EL tilting occur approximately two hours later than those of azimuthal error, which can be attributed to the relationship between antenna alidade orientation and apparent solar motion.  
Figure 12: Thermal deformation caused by solar radiation: tilt in AZ and EL direction.  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **EL Direction** & **AZ Direction** \\ \hline First round & \(11.5^{\prime\prime}\) & \(12.0^{\prime\prime}\) \\ Second round & \(10.9^{\prime\prime}\) & \(11.4^{\prime\prime}\) \\ Third round & \(11.7^{\prime\prime}\) & \(12.0^{\prime\prime}\) \\ Average & \(11.3^{\prime\prime}\) & \(11.8^{\prime\prime}\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: The RMS value of the antenna pointing errors in EL direction and AZ direction.  
Taking February 4 th as an example, Figure 13 illustrates the orientation of the antenna alidade and the apparent motion curve of the sun. The antenna remained stationary while facing northeast at a bearing of 66\({}^{\circ}\). After 09:23, the sun initially illuminates the S-E side of the alidade, resulting in a temperature differential between the S-E and N-W sides that induces rotation around the AZ axis. As a result, the AZ tilt value rapidly increases after sunrise and reaches its zenith at noon (around 14:23). As the sun gradually shifts towards the S-E after noon, the temperature on that side increases compared to the N-E, resulting in a peak tilt in the EL direction when directly radiated by sunlight from the S-W side. This phenomenon explains why there is approximately a two-hour delay between EL tilting and AZ tilting. It should be reminded that the noon time at Urumqi Nanshan Observatory is about 14:00 (UTC+8). This is due to the fact that Urumqi Nanshan Observatory is located in the UTC+6 time zone, while measurement data are recorded using Beijing time, which corresponds to UTC+8.