## 2 Previous Studies
### Radio Telescopes  
Around the world, a large number of radio telescopes have been built in order to explore the cosmic environment [64], and great progress has been made in astronomy with the help of radio telescopes in recent decades [65, 66]. The radio radiation from outer space is gathered through the reflection of the main reflector and the subreflector, and the gathered radiation is received through a feed. To ensure the quality of the reflection process, the reflectors are designed in the form of specific shapes, such as paraboloid and spherical surfaces. However, the reflectors will produce deformation under a combination of the effects of temperature, gravity and wind load, leading to differences between their practical and designed shape that may directly affect the working performance of the telescope [67, 68]. Therefore, studying the temperature fields and temperature deformations of radio telescopes is important for the thermal design and control. Fixed radio telescopes are usually designed with the incorporation of super-large-aperture reflectors, such as the Five-hundred-meter Aperture Spherical Telescope (FAST) [69] and the Arecibo Radio Telescope [70]. The influence of temperature deformation on the structure of telescopes with high precision and large apertures is significant, and is usually regarded as an important research component for structural design. On karst depression of Guizhou, the Five-hundred-meter Aperture Spherical Telescope (FAST) was built with a cable-net structure as a supporting system [71]. In the structural design stage, the temperature field of the FAST was simulated on the basis of reasonable assumptions [15]. Due to the shadow effect of the surrounding mountain block [72], the simulated temperature field was significantly non-uniform during the daytime. In particular, during a typical summer day (15 July), the structural temperature difference was more than 10 \({}^{\circ}\)C through most of the daytime. In order to further study the temperature deformation of the FAST, the simulation results of temperature fields were used as the thermal load [73]. Based on the calculation results, the root mean square of the fitting error for the reflector geometry caused by temperature deformation can reach up to a maximum value of 2.5 mm all year around, which is 50% of the allowable overall error for ensuring surface precision, and the fitting error of the reflector local position caused by non-uniform temperature variation is much larger. Through further analysis of fitting errors and the working state of radio telescopes, it is recommended that radio observations be made at sunrise, when the temperature field of the FAST is relatively uniform [74]. Movable radio telescopes are a common design form at present, and can ensure real-time tracking through the rotation of the reflector [75]. Since the 1980s, [PERSON] has studied the thermal behavior of the IRAM-30 m Telescope, and proposed systematic numerical methods for calculating the temperature fields and effects of movable telescope structures [76; 77; 78]. The construction materials of movable radio telescopes mainly include steel and aluminum, which have good thermal conductivity and large specific heat capacity, so the effects of solar radiation and wind on the temperature fields of telescopes should be considered, and the adverse effects of temperature deformation on reflector surface precision and pointing accuracy must be effectively controlled in order to guarantee good observational performance [79]. [PERSON] studied the temperature field and solar cooker effect of the Shanghai 65 m Radio Telescope under different working conditions through model experiments and numerical simulations for several years [80; 81].