## 1 Introduction  
After entering the scheduled orbital flight phase, spacecraft are in an environment with a high vacuum, cold black, and thermal radiation (solar radiation, planetary reflection, and planetary radiation) for a long period of time [1, 2, 3, 4, 5]. To enable the spacecraft to work normally and reliably in these environments and complete the scheduled tasks, in the development process, the spacecraft must be in a full-vacuum, cold black, and space heat flow environment under vacuum thermal tests following various test specifications or standards to ensure the stable operation of the spacecraft [6, 7, 8]. In the vacuum thermal test of spacecraft, the simulation of external heat flow occupies a crucial position [9]. The external heat flow can be simulated by infrared heating cages, infrared irradiation lamps, solar simulators, etc. [10]. At present, the simulation of external heat flow on spacecraft is mainly based on the absorption heat flow simulation method using an infrared heating cage. The principle is to energize the infrared heating cage so that its strip produces heat and transfers the heat flow to the spacecraft using infrared radiation. Then, the heat flow absorbed by the spacecraft's surface is equal to that absorbed by the surface in space when it is in orbit. The spectral characteristics of the heat flow in space are not considered, but only the two must have the same thermal effect. The key to the simulation of external heat flow through an infrared heated cage for a spacecraft lies in calculating the radiative heat transfer. For the calculation of the radiative heat transfer of the infrared heating cage, the relationship model of the radiative heat transfer between the spacecraft surface, the infrared heating cage, and the heat sink can be established by the theoretical formula of the radiative heat transfer. [PERSON] et al. [11] utilized a combination of testing and calculation to simulate the external heat flow and to determine the power supply to the heating partitions of the individual infrared cages through the establishment of a model of the cabin outer service heat test to carry out the analysis and calculation of the experimental external heat flow. [PERSON] et al. [12] proposed a calculation method for infrared heating cage radiation heat transfer based on the point heat flow, and the experimental heat flow was numerically simulated by establishing an analytical experimental external heat flow model with finite element software. [PERSON] [13] and others modelled the radiative heat transfer between the spacecraft instrument console, the infrared cage, and the heat sink, and they derived the relationship between the instrument console arrival heat flux density and the equivalent absorbed heat flux density on the inner side of the instrument console and the infrared cage strip charging current. [PERSON] et al. [14] used the finite element method to establish the system simulation model of the infrared heating cage-black sheet heat flow meter. By appropriately enlarging the size of the heating cage and adjusting the paste position of the heat flow meter, the statistical variance of the heat flow density on the heat dissipation surface decreased from 102.0 to 27.0. However, the above method is only applicable to a small number of simple infrared heating cages. The angular coefficients between the heated area and its corresponding and nearby infrared heating cages can be accurately obtained by solving the formulae, and the subsequent calculations can obtain the development parameters of the infrared heating cages. For large and complex infrared heating cages, solving the formula requires a large workload and poor accuracy, which affects the test cycle and test results.