## 1 Introduction  
With the development of satellite communication technology, the contradiction between the supply and demand of spectrum resources has become more and more serious, and it has become a scarce strategic resource. In recent years, the terahertz frequency band, which is higher than microwave, has become a research hotspot all over the world. With the rapid development of terahertz communication technology, China, Germany, Japan, France, the United States, and other countries have successfully carried out terahertz communication system tests [1, 2, 3, 4, 5]. The terahertz frequency band is between the relatively mature microwave frequency band and the infrared frequency band. It has special characteristics. It has both the excellent characteristics of microwave and laser, and has the unique advantages of large bandwidth, narrow beam, strong directivity and so on. However, its molecular absorption characteristics in the atmosphere are relatively obvious. Therefore, for satellite communication, its main application scenario is inter-satellite communication. Due to the high frequency of terahertz waves, the beam angle is narrower than that of microwaves, and direct intensity modulation is generally used in satellite communication systems, which leads to an increase in the bit error rate. The performance of inter-satellite terahertz communication systems is easily restricted by many factors such as pointing error. From a macro perspective, the satellite orbit is fixed, and the antenna pointing tracking between satellites can be accurately calculated according to the orbit parameters. However, the actual situation is that satellites are always affected by various perturbations of the space environment, including the additional gravitational force generated by the non-sphericalshape of the Earth and uneven mass, the gravitational force of the sun, the moon and other celestial bodies, atmospheric resistance, solar light pressure, etc. Under the action of the perturbation force, the orbit and attitude of the satellite are constantly changing, which will cause the deviation of the pointing of the terahertz antenna to produce pointing errors, thus affecting the performance of the terahertz communication system. Reference [6] studied the relative motion between a pair of small satellites during formation flying and proposed a model for orbital perturbation caused by gravitational force, the Earth's oblateness, and solar radiation pressure. They prove that the relative motion of satellites is bounded, which provides a theoretical foundation to characterize the beam misalignment using a Gaussian perturbation, etc. Non-conservative forces include solar pressure, atmospheric drag, and Earth's albedo pressure. These perturbation forces cause different perturbation accelerations to satellites at different orbital altitudes, and have different effects on pointing errors. Therefore, to establish a perturbation model for satellites in different orbits, it is necessary to analyze the specific requirements and make a reasonable choice of various perturbation forces. Figure 2 shows the influence of the main perturbation force on the acceleration of low-orbit (LEO, 200-2000 km), medium-orbit (MEO, 2000-20,000 km) and geostationary orbit (GEO, 35,786 km) satellites, reflecting the influence of different perturbation forces on the motion of satellites at different altitudes. In addition to the central gravity of the earth, low-orbit satellites also need to consider high-order aspheric gravity of the Earth, atmospheric drag, sun-moon gravity, tidal perturbation, and solar light pressure. Due to the high orbital height of geostationary orbit satellites, atmospheric resistance will not affect them, and it is mainly necessary to consider the aspheric gravity of the Earth, the gravity of the sun and the moon, and the solar light pressure, etc. Generally speaking, the motion equation of the satellite photographed motion can be expressed as Equation (1).