A design method for hovering scheme of geosynchronous orbit satellite

Abstract

The present invention belongs to the field of space on-orbit service technology, and relates to a method for designing a hovering scheme for a geosynchronous orbit satellite. Hovering is the hovering of a mission satellite relative to any one of a plurality of geosynchronous target satellites, and the design method includes: designing the hovering parameters of the mission satellite relative to the target satellite based on the hovering time, the maximum relative hovering distance, the minimum relative hovering distance, and the illumination constraint, and the hovering parameters include the hovering flight starting point, the hovering flight trajectory length, and the maximum relative speed; designing parking orbit parameters, and the parking orbit parameters include orbital altitude, orbital inclination, ascending node right ascension, and fixed point longitude; formulating a hovering flight starting point transfer optimization scheme based on the principle of minimum fuel, and calculating the position vector of the hovering flight starting point of the mission satellite relative to the target satellite. The hovering flight starting point transfer optimization scheme formulated by the present invention is a hovering flight starting point transfer optimization scheme with better overall fuel consumption and faster calculation speed.

Description

Technical Field

[0001] The present invention relates to the field of space on-orbit service technology, and in particular to a method for designing a hovering solution for a geosynchronous orbit satellite. Background Art

[0002] Geosynchronous orbit satellites have unique orbital characteristics, such as wide coverage of the Earth and fixed sub-satellite trajectory, and play an extremely important role in social and economic development such as communication, navigation, and relay. At the same time, geosynchronous orbit satellites are complex in structure and expensive. In order to save mission costs, extend satellite life, and maintain satellite capabilities, it is crucial to conduct research on geosynchronous orbit satellite on-orbit service technology and build an on-orbit service system.

[0003] The final hovering approach phase to the geosynchronous target satellite is the key to the on-orbit service mission. By making full use of the relative static characteristics of the hovering flight phase, the mission satellite can operate stably at the hovering starting point and proceed to the next phase of work after the mission is completed, which enhances the reliability of the on-orbit service mission. In some specific missions, it is necessary to consider the hovering distance and hovering duration constraints of the mission satellite to the target satellite, as well as the front light constraints.

[0004] Therefore, it is necessary to study the design method of geosynchronous orbit satellite hovering scheme considering time, distance and light constraints. Summary of the invention

[0005] The purpose of the present invention is to propose a hovering scheme design method for a geosynchronous orbit satellite, which obtains the maximum hovering speed and the hovering starting point according to the hovering time, the hovering distance and the illumination constraints; designs the orbital altitude, orbital inclination, the right ascension of the ascending node and the fixed point longitude of the mission satellite according to the characteristics of the target orbit; does not consider the deviation between the hovering starting point and the target satellite first, takes the position of the target satellite as the transfer target position, performs the fuel-saving transfer orbit pre-optimization for transferring the mission satellite to the hovering starting point under the time constraint, and implements the transfer orbit optimization considering the maximum relative speed of the hovering according to the relative speed of the mission satellite to the target satellite after the pre-optimization, and finally obtains the hovering starting point and the speed increment size and application time of the transfer to the hovering starting point.

[0006] In order to achieve the above object, the present invention adopts the following technical scheme:

[0007] The present invention provides a method for designing a hovering scheme of a geosynchronous orbit satellite, wherein the hovering is the hovering of a mission satellite relative to any one of a plurality of geosynchronous target satellites, and the design method comprises the following steps:

[0008] The hovering parameters of the mission satellite relative to the target satellite are designed based on the hovering time, maximum relative hovering distance, minimum relative hovering distance and illumination constraints. The hovering parameters include the hovering flight starting point, the hovering flight trajectory length and the maximum relative speed.

[0009] Design parking orbit parameters, including orbit altitude, orbit inclination, ascending node right ascension, and fixed point longitude;

[0010] An optimization plan for hovering flight starting point transfer is formulated based on the principle of minimum fuel.

[0011] As a possible implementation method, the hovering flight starting point is determined as follows:

[0012] Control the mission satellite to reach a preset position near the target satellite. At this time, the flight trajectory of the mission satellite relative to the target satellite is approximately a straight line;

[0013] The starting point of hovering takeoff is determined according to the illumination constraint, that is, in the direction of the target star's illumination, the intersection of the mission satellite's flight trajectory relative to the target star and the straight line passing through the target star and perpendicular to the direction of the sun is the starting point of hovering takeoff.

[0014] As a possible implementation method, the length of the hovering flight trajectory is recorded as , calculated based on the maximum relative hovering distance, minimum relative hovering distance and lighting constraints :

[0015]

[0016] in, is the maximum relative hovering distance, is the minimum relative hovering distance, It is the angle between the mission satellite’s flight speed and the direction of the sun.

[0017] As a possible implementation, the maximum relative speed is recorded as , the maximum relative speed is calculated based on the hovering time and the length of the hovering flight trajectory :

[0018]

[0019] in, is the hover time.

[0020] As a possible implementation, the geostationary orbit altitude is , the orbital height is recorded as , .

[0021] As a possible implementation method, the orbit inclination and right ascension of the ascending node are solved by optimizing the function Obtained, as follows:

[0022]

[0023]

[0024] in, is the orbital inclination of the mission star, is the right ascension of the ascending node of the mission star; is the total number of geosynchronous target satellites, For the geosynchronous target satellites, For the The orbital inclination of the geosynchronous target satellite, For the The right ascension of the ascending node of the geosynchronous target satellite; is the speed of the geostationary satellite; is the orbital angle between the mission star and any target star, and .

[0025] As a possible implementation, the fixed point longitude is set to be west of the center value of the fixed point longitude of all target satellites, with a deviation less than or equal to 10 degrees.

[0026] As a possible implementation method, an optimization plan for hovering flight starting point transfer is formulated based on the principle of minimum fuel, which specifically includes the following steps:

[0027] S30. Pre-optimization of the transfer orbit of the mission star, specifically including the following sub-steps:

[0028] S300. Determine the constraint condition that the transfer time from the mission star to the hovering flight starting point does not exceed the maximum transfer time ;

[0029] S301. Determine the initial conditions, including the initial time of the mission star orbit transfer , location is , Mission Star Arrive at the starting point of hovering flight at any time , without considering the deviation between the hovering starting point and the target star, That is The target star position at the moment;

[0030] S302. Solve the optimization parameters based on the transfer orbit pre-optimization objective function of the mission satellite , , ,Right now , , where the track change speed increment is and According to the Lambert orbit change method, the initial moment of the mission star orbit transfer , the mission satellite arrives at the starting point of hovering flight Solution;

[0031] S31. According to the optimized , , Sure The relative speed of the mission star relative to the target star at that moment ,judge The relative speed of the mission star relative to the target star at that moment Is it greater than the maximum relative speed of hovering? If yes, execute S32, otherwise execute S33;

[0032] S32. Update the transfer orbit pre-optimization objective function of the mission star to , , and apply the updated function to solve the optimization parameters , , Then return to S31 until The relative speed of the mission star relative to the target star at that moment Less than or equal to the maximum relative speed of hovering Then, execute S33;

[0033] S33. Calculation The direction of the sun relative to the target star at this moment ; Calculate relative speed With the sun direction Angle ;

[0034] S34. Calculate the position vector of the mission star relative to the target star's hovering flight starting point , .

[0035] Compared with the prior art, the beneficial effects of the present invention are:

[0036] 1. The method for designing a hovering scheme for a geosynchronous orbit satellite proposed in the present invention converts the hovering time, hovering distance and illumination constraints into the maximum relative speed constraints. In the process of transferring the mission satellite to the hovering starting point, the specific hovering position, illumination conditions, relative speed and other constraints are not considered first, but the target satellite position is used as the transfer target position, and the fuel-saving transfer orbit pre-optimization of the mission satellite to the hovering starting point under the time constraint is performed. Then, the maximum relative speed of hovering is converted into the joint optimization constraint of orbit transfer and hovering control, and the transfer orbit and hovering trajectory planning are implemented step by step and iterated mutually, forming a design method with the best overall fuel consumption and the fastest calculation speed.

[0037] 2. The method for designing a hovering scheme for a geosynchronous orbit satellite proposed in the present invention sets the fixed-point longitude of the mission satellite to the west of the center value of the fixed-point longitudes of all target satellites, which can balance the fuel consumption of the mission satellite maneuvering to the hovering starting point of all target satellites, and provides a design method with optimal overall fuel consumption.

[0038] 3. The present invention proposes a solution to the optimization function so that the mission star covers all target stars with the minimum orbital maneuvering cost, that is, the maximum speed increment of the mission star maneuvering to the orbital plane of all target stars is minimized, the calculation speed is fast, and the design effect is better. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] The drawings described herein are used to provide a further understanding of the present invention and constitute a part of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the drawings:

[0040] Figure 1 A flow chart of a method for designing a hovering solution for a geosynchronous orbit satellite provided in an embodiment of the present invention;

[0041] Figure 2 The present invention provides a flowchart of an optimization scheme for hovering flight starting point transfer based on the principle of minimum fuel in an embodiment of the present invention. DETAILED DESCRIPTION

[0042] In order to clearly describe the technical solutions of the embodiments of the present invention, in the embodiments of the present invention, words such as "first" and "second" are used to distinguish the same items or similar items with basically the same functions and effects. For example, the first threshold and the second threshold are only used to distinguish different thresholds, and their order is not limited. Those skilled in the art can understand that words such as "first" and "second" do not limit the quantity and execution order, and words such as "first" and "second" do not necessarily limit them to be different.

[0043] It should be noted that, in the present invention, words such as "exemplary" or "for example" are used to indicate examples, illustrations or descriptions. Any embodiment or design described as "exemplary" or "for example" in the present invention should not be interpreted as being more preferred or more advantageous than other embodiments or designs. Specifically, the use of words such as "exemplary" or "for example" is intended to present related concepts in a specific way.

[0044] In the present invention, "at least one" means one or more, and "plurality" means two or more. "And / or" describes the association relationship of associated objects, indicating that three relationships may exist. For example, A and / or B can mean: A exists alone, A and B exist at the same time, and B exists alone, where A and B can be singular or plural. The character " / " generally indicates that the associated objects before and after are in an "or" relationship. The following at least one item (items) or similar expressions thereof refer to any combination of these items, including any combination of single items (items) or plural items (items). For example, at least one item (items) of a, b or c can mean: a, b, c, the combination of a and b, the combination of a and c, the combination of b and c, or the combination of a, b and c, where a, b, c can be single or multiple.

[0045] The embodiment of the present invention aims to provide a method for designing a hovering scheme for a geosynchronous orbit satellite, which obtains the maximum hovering speed and the hovering starting point according to the hovering time, the hovering distance and the illumination constraints; designs the orbital altitude, orbital inclination, the right ascension of the ascending node and the fixed point longitude of the mission satellite according to the characteristics of the target orbit; without considering the deviation between the hovering starting point and the target satellite, the position of the target satellite is used as the transfer target position, and the fuel-saving transfer orbit pre-optimization of the mission satellite to the hovering starting point under time constraints is performed; according to the relative speed of the mission satellite to the target satellite after the pre-optimization, the transfer orbit optimization considering the maximum relative speed of the hovering in real time is performed, and finally the hovering starting point and the speed increment size and application time of the transfer to the hovering starting point are obtained.

[0046] The embodiment of the present invention provides a method for designing a hovering scheme for a geosynchronous orbit satellite, wherein the hovering is the hovering of a mission satellite relative to any one of a plurality of geosynchronous target satellites. Figure 1 , the design method includes the following steps:

[0047] The hovering parameters of the mission satellite relative to the target satellite are designed based on the hovering time, maximum relative hovering distance, minimum relative hovering distance and illumination constraints. The hovering parameters include the hovering flight starting point, the hovering flight trajectory length and the maximum relative speed.

[0048] As a possible implementation method, the hovering flight starting point is determined as follows:

[0049] Control the mission satellite to reach the preset position near the target satellite. At this time, the flight trajectory of the mission satellite relative to the target satellite is approximately a straight line. Assume that the maximum relative hovering distance between the mission satellite and the target satellite is , the minimum relative hovering distance is , then the flight trajectory length of the hovering process is Assume that the hovering time requirement is , then the maximum relative speed of hovering on the relative flight trajectory is .

[0050] The starting point of hovering takeoff is determined according to the illumination constraint, that is, in the direction of the target star's illumination, the intersection of the mission satellite's flight trajectory relative to the target star and the straight line passing through the target star and perpendicular to the direction of the sun is the starting point of hovering takeoff.

[0051] As an example, after considering the lighting conditions, the flight arcs that meet the distance requirements are not necessarily all in the direction of the light. The angle between the mission satellite's flight speed direction and the sun direction is defined as The intersection point of the straight line perpendicular to the sun direction and the flight trajectory is the hovering starting point that meets the lighting constraints.

[0052] As a possible implementation method, the length of the hovering flight trajectory is recorded as , calculated based on the maximum relative hovering distance, minimum relative hovering distance and lighting constraints :

[0053]

[0054] in, is the maximum relative hovering distance, is the minimum relative hovering distance, It is the angle between the mission satellite’s flight speed and the direction of the sun.

[0055] From the above formula, we can see that the minimum relative hovering distance is half the chord length, and the maximum relative hovering distance is the entire chord length.

[0056] As a possible implementation, the maximum relative speed is recorded as , the maximum relative speed is calculated based on the hovering time and the length of the hovering flight trajectory :

[0057]

[0058] in, is the hover time.

[0059] Design parking orbit parameters, including orbit altitude, orbit inclination, ascending node right ascension, and fixed point longitude;

[0060] As an example, the orbital altitude can adopt a parking orbit that is lower than the geosynchronous orbit, or a geosynchronous orbit. Since the geosynchronous orbit is far away from the earth, the orbital altitude difference of several hundred kilometers has little effect on the orbital velocity. Therefore, for domestic regional targets, the geosynchronous orbit can be used as the parking orbit, and coverage of certain targets can be achieved by selecting a suitable fixed point longitude.

[0061] As a possible implementation, the geostationary orbit altitude is , the orbital height is recorded as , .

[0062] In this embodiment, the orbital altitude is considered according to the geosynchronous orbit, but the relevant results can also be applied to orbits slightly lower than the geosynchronous orbit.

[0063] The orbital plane normal in inertial space is mainly determined by the orbital inclination and the right ascension of the ascending node. The orbital plane normal of the parking orbit can be designed by grouping according to the orbital inclination and the right ascension of the ascending node. The design goal of the orbital inclination and the right ascension of the ascending node of the mission satellite parking orbit is to make the mission satellite cover all target stars with the minimum orbital plane maneuvering cost, that is, the maximum velocity increment of the mission satellite maneuvering to the orbital plane of all target stars is the smallest.

[0064] As a possible implementation method, the orbit inclination and right ascension of the ascending node are solved by optimizing the function Obtained, as follows:

[0065]

[0066]

[0067] in, is the orbital inclination of the mission star, is the right ascension of the ascending node of the mission star; is the total number of geosynchronous target satellites, For the geosynchronous target satellites, For the The orbital inclination of the geosynchronous target satellite, For the The right ascension of the ascending node of the geosynchronous target satellite; is the speed of the geostationary satellite; is the orbital angle between the mission star and any target star, and The angle of the orbital plane determines the velocity increment required for the satellite to maneuver to the same orbital plane.

[0068] As a possible implementation, the fixed point longitude is set to be west of the center value of the fixed point longitude of all target satellites, with a deviation less than or equal to 10 degrees.

[0069] For example, under the given target position and mission time conditions, the fixed point longitude is the main factor affecting fuel consumption. The design of the fixed point longitude of the mission satellite should be based on the fixed point longitude of the target satellite and the fuel consumption of the mission satellite maneuvering to the hovering starting point of all target satellites; for the two cases where the mission satellite and the target satellite are coplanar or non-planar, under the same geographical longitude difference, the fuel consumed by the mission satellite maneuvering to the east orbit is less than the fuel consumed by maneuvering to the west orbit. In order to balance the fuel consumption of maneuvering to the hovering starting point of all target satellites, the fixed point longitude of the mission satellite is set to the west of the center value of the fixed point longitude of all target satellites, and the deviation is less than or equal to 10 degrees.

[0070] An optimization plan for hovering flight starting point transfer is formulated based on the principle of minimum fuel.

[0071] The hovering mission includes long-range orbit transfer optimization and short-range hovering control. In the long-range orbit transfer calculation, there is no need to consider the specific hovering position, lighting conditions, speed and other constraints. The target star can be directly aimed at for calculation, which reduces the optimization parameters and constraints, reduces the amount of calculation, and makes the optimization algorithm easy to converge. In the short-range hovering control, the characteristic parameter of relative speed is selected, and the coupling of long-range rendezvous and short-range hovering control is transformed into an optimization constraint. The orbit transfer and hovering trajectory planning are implemented step by step and iterated to form an optimization plan for the transfer of the hovering flight starting point with the best overall fuel consumption and the fastest calculation speed.

[0072] As a possible implementation method, an optimization scheme for hovering flight starting point transfer is formulated based on the principle of minimum fuel, see Figure 2 , specifically including the following steps:

[0073] S30. Pre-optimization of the transfer orbit of the mission star, specifically including the following sub-steps:

[0074] S300. Determine the constraint condition that the transfer time from the mission star to the hovering flight starting point does not exceed the maximum transfer time ;

[0075] S301. Determine the initial conditions, including the initial time of the mission star orbit transfer ,Location , Mission Star Arrive at the starting point of hovering flight at any time , without considering the deviation between the hovering starting point and the target star, That is The target star position at the moment;

[0076] S302. Solve the optimization parameters based on the transfer orbit pre-optimization objective function of the mission satellite , , ,Right now , , where the track change speed increment is and According to the Lambert orbit change method, the initial moment of the mission star orbit transfer , the mission satellite arrives at the starting point of hovering flight Solution;

[0077] As an example of pre-optimization of the transfer orbit of a mission star, the initial moment of the mission star orbit transfer , location is , Mission Star Arrive at the hovering starting point at the moment , without considering the deviation between the hovering starting point and the target star, That is The position of the target star at the moment can be solved according to the Lambert orbit change method , The corresponding mission satellite orbit change speed increment and , assuming that the transfer time from the mission star to the hovering starting point does not exceed , , , To optimize the parameters, the transfer trajectory pre-optimization objective is: , .

[0078] S31. According to the optimized , , Sure The relative speed of the mission star relative to the target star at that moment ;judge The relative speed of the mission star relative to the target star at that moment Is it greater than the maximum relative speed of hovering? If yes, execute S32, otherwise execute S33;

[0079] As an example, according to the optimized , , , using orbital dynamics equations or Lagrange coefficient method to determine The relative speed of the mission star relative to the target star at that moment .

[0080] S32. Update the transfer orbit pre-optimization objective function of the mission star to , , and apply the updated function to solve the optimization parameters , , Then return to S31 until The relative speed of the mission star relative to the target star at that moment Less than or equal to the maximum relative speed of hovering Then, execute S33;

[0081] S33. Calculation The direction of the sun relative to the target star at this moment ; Calculate relative speed With the sun direction Angle ;

[0082] S34. Calculate the position vector of the mission star relative to the target star's hovering flight starting point , .

[0083] The present invention converts the hovering time, hovering distance and illumination constraints into the maximum relative speed constraints. In the process of transferring the mission satellite to the hovering starting point, the specific hovering position, illumination conditions, relative speed and other constraints are not considered first, but the target satellite position is used as the transfer target position, and the fuel-saving transfer orbit pre-optimization of the mission satellite to the hovering starting point under the time constraint is performed. Then the maximum relative speed of hovering is converted into the joint optimization constraint of orbit transfer and hovering control, and the transfer orbit and hovering trajectory planning are implemented step by step and iterated mutually, forming a design method with the best overall fuel consumption and the fastest calculation speed.

[0084] Although the present invention is described herein in conjunction with various embodiments, in the process of implementing the claimed invention, those skilled in the art may understand and implement other variations of the disclosed embodiments by viewing the drawings, the disclosure, and the illustrations of the drawings. In the specification, the word "comprising" does not exclude other components or steps, and "one" or "an" does not exclude multiple situations. A single processor or other unit can implement several functions listed in the specification. Certain measures are recorded in different embodiments, but this does not mean that these measures cannot be combined to produce good results.

[0085] Although the present invention has been described in conjunction with specific features and embodiments thereof, it is apparent that various modifications and combinations may be made thereto without departing from the spirit and scope of the present invention. Accordingly, this specification and the accompanying drawings are merely exemplary illustrations of the present invention and are deemed to cover any and all modifications, variations, combinations or equivalents within the scope of the present invention. Obviously, those skilled in the art may make various modifications and variations to the present invention without departing from the spirit and scope of the present invention. Thus, the present invention is intended to include such modifications and variations if they fall within the scope of the present invention and its equivalents.

Claims

1. A method for designing a hovering scheme for a geosynchronous orbit satellite, wherein the hovering is the hovering of a mission satellite relative to any one of a plurality of geosynchronous target satellites; characterized in that: The steps include: Designing hovering parameters of the mission star relative to the target star based on the hovering time, the maximum relative hovering distance, the minimum relative hovering distance and the illumination constraints, wherein the hovering parameters include the hovering flight starting point, the hovering flight trajectory length and the maximum relative speed; Design parking orbit parameters, including orbit altitude, orbit inclination, ascending node right ascension, and fixed point longitude; Based on the principle of minimum fuel, an optimization plan for hovering flight starting point transfer is formulated, which includes the following steps: S30. Pre-optimization of the transfer orbit of the mission star, specifically including the following sub-steps: S300. Determine the constraint condition that the transfer time from the mission star to the hovering flight starting point does not exceed the maximum transfer time ; S301. Determine the initial conditions, including the initial time of the mission star orbit transfer ,Location , Mission Star Arrive at the starting point of hovering flight at any time , without considering the deviation between the hovering starting point and the target star, That is The target star position at the moment; S302. Solve the optimization parameters based on the transfer orbit pre-optimization objective function of the mission satellite , , ,Right now , , where the track change speed increment is and According to the Lambert orbit change method, the initial moment of the mission star orbit transfer , the mission satellite arrives at the starting point of hovering flight Solution; S31. According to the optimized , , Sure The relative speed of the mission star relative to the target star at that moment ,judge The relative speed of the mission star relative to the target star at that moment Is it greater than the maximum relative speed of hovering? If yes, execute S32, otherwise execute S33; S32. Update the transfer orbit pre-optimization objective function of the mission star to , , and apply the updated function to solve the optimization parameters , , Then return to S31 until The relative speed of the mission star relative to the target star at that moment Less than or equal to the maximum relative speed of hovering Then, execute S33; S33. Calculation The direction of the sun relative to the target star at this moment ; Calculate relative speed With the sun direction Angle ; S34. Calculate the position vector of the mission star relative to the target star's hovering flight starting point , .

2. The method for designing a hovering scheme for a geosynchronous orbit satellite according to claim 1, characterized in that: The hovering flight starting point is determined as follows: Control the mission satellite to reach a preset position near the target satellite. At this time, the flight trajectory of the mission satellite relative to the target satellite is approximately a straight line; The starting point of hovering takeoff is determined according to the illumination constraint, that is, in the direction of the target star's illumination, the intersection of the mission satellite's flight trajectory relative to the target star and the straight line passing through the target star and perpendicular to the direction of the sun is the starting point of hovering takeoff.

3. The method for designing a hovering scheme for a geosynchronous orbit satellite according to claim 1, characterized in that: The length of the hovering flight trajectory is recorded as , calculated based on the maximum relative hovering distance, minimum relative hovering distance and lighting constraints : in, is the maximum relative hovering distance, is the minimum relative hovering distance, It is the angle between the mission satellite’s flight speed and the direction of the sun.

4. The method for designing a hovering scheme for a geosynchronous orbit satellite according to claim 3, characterized in that: The maximum relative speed is recorded as , the maximum relative speed is calculated based on the hovering time and the length of the hovering flight trajectory : in, is the hover time.

5. The method for designing a hovering scheme for a geosynchronous orbit satellite according to claim 1, characterized in that: The altitude of the geostationary orbit is , the orbital height is recorded as , .

6. The method for designing a hovering scheme for a geosynchronous orbit satellite according to claim 1, characterized in that: The orbital inclination and right ascension of the ascending node are determined based on the principle of minimizing the maximum velocity increment from the mission satellite to the orbital plane of all target satellites.

7. The method for designing a hovering scheme for a geosynchronous orbit satellite according to claim 6, characterized in that: The orbit inclination and right ascension of the ascending node are obtained by solving the optimization function Obtained, as follows: in, is the orbital inclination of the mission star, is the right ascension of the ascending node of the mission star; is the total number of geosynchronous target satellites, For the geosynchronous target satellites, For the The orbital inclination of the geosynchronous target satellite, For the The right ascension of the ascending node of the geosynchronous target satellite; is the speed of the geostationary satellite; is the orbital angle between the mission star and any target star, and .

8. The method for designing a hovering scheme for a geosynchronous orbit satellite according to claim 1, characterized in that: The fixed point longitude is set to be west of the center value of the fixed point longitude of all target stars, with a deviation less than or equal to 10 degrees.

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