## 2 The Impact of Satellite Bus Thermal Deformation on the Laser Communication Load Acquisition Time
For the satellite bus, the micro-vibration level of the whole satellite needs to be controlled within the control ability of the piezoelectric fast-pointing mirror to ensure that the satellite laser communication will not cause a code error or communication link break [22]. However, this is a fine operation after the completion of coarse tracking, which will not influence the acquisition time of the laser communication load. Because the signal optical band of 1550 nm is far away from the beacon optical band of 808 nm, the large array detector commonly used in the capture and tracking system is not sensitive to signal light, and the signal light is not convenient to be used as a beacon light. An independent optical laser beacon is configured at both ends. Table 1 displays a few laser communication load metrics. There are two common configurations for transmission rate when the communication distance is less than 5000 km and less than 3000 km for the satellite, which is now in the experimental stage. Figure 3: Laser communication load system composition: (**a**) appearance; (**b**) system composition. Figure 2: Schematic diagram of the laser link in the same orbit and the different orbit. The scanning mode, resident duration, unclear area size, and other aspects affect the laser communication load acquisition time. Common beacon light scanning techniques include rosette scanning, Lisaru scanning, compound scanning, spiral scanning, rectangular spiral scanning, and others. Each scanning mode has its advantages in terms of difficulty of realization, scanning time, scanning probability, and so on [23]. The paper by [PERSON] [24] suggests a method for figuring out the capture time and determines the connection between the capture time and the uncertain region. Rectangular scanning provides clear advantages in terms of effective coverage and is reasonably straightforward to implement in terms of algorithm, software, and hardware, but the scanning time is quite long. The longest scanning time is estimated using this scanning technique. The capture time of a rectangular scan was calculated by Formula (1). \[T_{acq}\approx\frac{1}{(1-k)^{2}}.\left(\frac{\theta_{U}}{\theta_{BC}}\right)^ {2}.T_{d} \tag{1}\]  
where \(k\) is the overlap coefficient. Considering that the beacon light pointing error will cause the uncertain region to miss scanning in the scanning process, the beam scanning step should take into account the overlapping of adjacent scanning areas to reduce the probability of missing scanning. It is necessary to consider the satellite attitude stability, the stepping error of the pointing mirror, and the optic axis jitter caused by satellite vibration on the pointing mirror to determine the overlap coefficient. The overlap coefficient is set to \(k=60\%\). \(T_{d}\) is the residence time. The resident time is set to \(T_{d}=0.2s\). \(\theta_{BC}\) is the beacon light emission angle. The beacon light with a divergent angle \(\theta_{BC}=0.313\) mrad is used for scanning. \(\theta_{U}\) is the uncertain region after calibration. According to Formula (1), if the acquisition time of the satellite laser communication payload is less than 30 s, \(\theta_{U}\) should be less than 1.53 mrad. To eliminate unrecoverable errors caused by factors such as vibration during satellite transportation and launch, gravity release after orbit, etc., star calibration, inter-satellite calibration, and satellite landmark calibration will be adopted. The error eliminated in the calibration process can be considered a fixed system error, and the influence on the acquisition time can be ignored. On-orbit calibration cannot completely eliminate all undetected system faults. For example, orbit prediction error, attitude measurement error, satellite dynamic deformation error introduced by the satellite bus, open-loop control error of the pointing mirror, coarse tracking residual error, and laser solution accuracy error introduced by the laser communication load itself. These errors are independent and irrelevant.