## 1 Introduction  
In recent years, with the explosive growth in the amount of information transmitted by spacecraft, space laser communication technology has gained increasingly widespread application due to its high bandwidth, large transmission capacity, and small terminal size [1, 2, 3, 4, 5]. Establishing a globally covered satellite laser communication network is a growing trend. Additionally, relay satellite systems, as key hubs for space information transmission and efficient space-based telemetry and communication facilities, are widely used in tasks such as rendezvous and docking, lunar exploration, and satellite telemetry and control [6, 7, 8, 9]. Both types of tasks require establishing connections between spacecraft, typically through the multidimensional movement of communication terminals and relay antennas on the spacecraft, and sometimes through attitude adjustments of the spacecraft itself to meet various pointing requirements. Therefore, these tasks need to be conducted under multidimensional pointing attitudes. Space external heat flux has a significant impact on the thermal design of spacecraft. To determine the layout of heat dissipation surfaces and the extreme conditions for thermal analysis, it is essential to analyze space external heat flux [10, 11, 12]. Space external heat flux is the sum of all space thermal radiation reaching the spacecraft and is typically divided into three categories: solar heat flux, Earth albedo, and Earth infrared radiation. Among these, solar heat flux is the most variable and has the primary influence on the heat flux reaching relay satellites and high-orbit laser communication payloads [13; 14; 15]. Therefore, studying solar external heat flux is of great significance. A large body of research has been devoted to the analysis of external space heat flux. [PERSON] et al. [16] conducted a thermal analysis on laser communication terminals of geostationary Earth orbit (GEO) satellites. Given that the optical axis of the antenna is predominantly directed toward the Earth's center, they focused on analyzing the solar external heat flux incident on the Earth-facing surface and derived the variation pattern of external heat flux over one orbital period. [PERSON] et al. [17] investigated a satellite in a circular orbit with an altitude of 500 km and an inclination of 30\({}^{\circ}\). Under the three-axis Earth-pointing attitude, they analyzed the external heat flux of the co-orbital inter-satellite laser communication terminal, which provided a basis for the selection of heat-dissipating surfaces. [PERSON] et al. [18] proposed a fast calculation method for solar radiation heat flux. This method simplifies the positional relationships among the satellite, the Sun, and the Earth to reduce computational parameters, thereby enhancing computational efficiency, with a specific focus on calculating the external heat flux under the three-axis stabilized Earth-pointing attitude. [PERSON] et al. [19] established an analytical model for calculating external heat flux in inclined circular orbits and examined the variation characteristics of external heat flux under the three-axis stabilized Earth-pointing attitude. [PERSON] et al. [20] developed a space quadrant and intelligent occlusion calculation method for external heat flux computation of the China Space Station. The core of this method lies in its capability to intelligently determine complex spatial occlusion scenarios, though it does not account for the influence of complex attitudes. [PERSON] et al. [21] employed the Monte Carlo simulation approach to model the solar radiation, Earth-emitted radiation, and Earth albedo radiation received by space targets, with an emphasis on analyzing two commonly adopted attitudes: Earth-pointing and Sun-pointing. [PERSON] et al.