## 1 Introduction
[22] reviewed conventional methods for calculating external heat flux and proposed a methodology to determine external heat flux on arbitrarily oriented spacecraft surfaces based on trajectory data, incorporating the effect of spacecraft rotation about its longitudinal axis on heat flux. However, their computational method is relatively generalized, and the analysis results are limited to one-dimensional rotational attitudes, which are simpler compared to pointing attitudes. [PERSON] et al. [23] put forward a method for calculating external heat flux on convex surfaces applicable to Keplerian orbits and analyzed the external heat flux of spacecraft under conventional orbital attitudes. This method is also restricted to relatively simple attitudes, and further research is required for the calculation of external heat flux under complex attitudes such as inter-satellite pointing. In summary, existing studies on the analysis and calculation of external heat flux have primarily focused on conventional attitudes such as three-axis stabilized Earth-pointing, while there is a paucity of research on external heat flux under complex attitudes like inter-satellite pointing. Spacecraft and payloads usually have to undergo intricate maneuvers to achieve the inter-satellite pointing state. As a result, the geometric relationship between the spacecraft/payload and the Sun under the pointing attitude becomes more complex, leading to more complex variations in external heat flux. This complexity also renders the solution process for external heat flux more formidable. Consequently, to achieve more accurate and effective thermal control design for spacecraft and payloads under various inter-satellite pointing attitudes, it is imperative to conduct research on external heat flux under typical inter-satellite pointing attitudes. Current established methods for calculating external heat flux are suitable for common attitude types, such as three-axis stabilized Earth-pointing attitude, but demonstrate limited applicability for complex attitudes. Building upon conventional algorithms, this study investigates the complex spatial relationships specific to pointing attitudes, with the goal of developing an external heat flux calculation method applicable to complex attitude scenarios. This research will provide a theoretical basis and data support for the corresponding thermal control design. This paper addresses the problem of solving external heat flux for inter-satellite pointing attitudes and conducts research on the external heat flux analysis methods for spacecraft and payloads under inter-satellite pointing attitudes. Based on the proposed method, the solar heat flux reaching the satellite surfaces under two typical relay satellite orbits, namely the Halo orbit and the large elliptical frozen orbit, was calculated, and a thermal analysis of the laser communication payload was performed. The content of each section of this paper is as follows. Section 1 introduces the background and significance of the research. Section 2 describes the method for calculating solar direct heat flux under pointing attitudes. Section 3 calculates the solar heat flux reaching different surfaces of the satellite under Halo and large elliptical frozen orbits. Section 4 establishes a thermal simulation model for the inter-satellite laser communication payload and conducts thermal analysis under typical conditions using the external heat flux analysis method described in Section 2. Section 5 provides the conclusions of the paper.