Transfer orbit design method in on-orbit service of synchronous orbit satellite
By optimizing the transfer orbit design using a genetic algorithm based on the HPOP model, the problem of high fuel consumption for geostationary satellites was solved, and a low fuel consumption transfer orbit design was achieved, which is suitable for close-range observation and exploration in geostationary orbit.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- NAT UNIV OF DEFENSE TECH
- Filing Date
- 2026-01-17
- Publication Date
- 2026-04-28
AI Technical Summary
In the current technology, during the on-orbit service of geostationary orbit satellites, it is increasingly difficult to efficiently handle satellite malfunctions or failures. Moreover, the existing transfer orbit design methods consume a lot of fuel, especially for orbital adjustments of target satellites with large inclination angles.
A genetic algorithm based on the HPOP model was used to distinguish between coplanar and non-coplanar transfers, and to design ascending, descending, and co-orbital transfer trajectories. The mathematical model of the transfer trajectories was optimized, and the illumination angle and relative position at the end of the rendezvous were optimized through the genetic algorithm to reduce fuel consumption.
It achieves a low-burnup transfer orbit design, meets the lighting conditions and relative position requirements at the end of the rendezvous, and is suitable for close-range observation and exploration in geostationary orbit.
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Figure CN121935993A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of space technology, and in particular relates to a method for designing transfer orbits in on-orbit services of geostationary satellites. Background Technology
[0002] With the rapid development of aerospace technology, the number of new satellites entering orbit each year is increasing daily. However, satellite malfunctions or failures caused by factors such as the space environment, design flaws, and exceeding service life are becoming increasingly common. Considering the costs of satellite production, development, operation, and management, utilizing in-orbit service satellites (hereinafter referred to as service satellites) for on-orbit maintenance of faulty or failed satellites (hereinafter referred to as target satellites) is of great significance in fault diagnosis and troubleshooting, as well as extending the service life and reusing retired satellites.
[0003] During on-orbit servicing of geostationary satellites, the service satellite typically needs to be maneuvered to the vicinity of the target satellite via a transfer orbit to observe and probe the target satellite, acquiring its characteristic data to provide necessary target satellite information for subsequent close-range on-orbit maintenance operations. Optimizing the service satellite transfer orbit strategy is a key factor and crucial step in improving the efficiency and quality of on-orbit servicing.
[0004] Current service satellite transfer orbit design methods mostly employ approaches, hovering, and fly-around techniques to achieve close-range imaging of the target satellite in order to obtain its characteristic data. This method consumes a significant amount of fuel and affects the on-orbit lifespan of the service satellite. For targets with large inclination angles, the fuel consumption is even more pronounced due to the need for orbital plane adjustments. Summary of the Invention
[0005] To address the challenge of effectively imaging high-orbit target satellites with low fuel consumption, this invention provides a transfer orbit design method for geostationary satellites in on-orbit servicing. This method differentiates between coplanar and non-coplanar transfers based on whether the service satellite and target satellite are located in the same orbital plane, and further distinguishes between ascending, descending, and co-orbiting transfers based on the difference in orbital altitude between the two satellites. The method employs a mathematical optimization model for the transfer orbit obtained from a genetic algorithm based on the HPOP model. This model can be used for close-range observation and detection of target satellites by service satellites in geostationary orbit, ensuring that the relative positions and illumination conditions of the two satellites at the end of the rendezvous meet operational requirements, while also minimizing fuel consumption.
[0006] The objective of this invention is specifically achieved through the following technical solutions:
[0007] This invention discloses a transfer orbit design method for geostationary satellites in on-orbit servicing, the method comprising:
[0008] Step 1: Based on the start time of the operation, the service satellite and the target satellite in their initial state, distinguish between coplanar transfer and non-coplanar transfer based on whether the two satellites are in the same orbital plane. Then, based on the difference in the orbital altitude of the two satellites, distinguish between ascending transfer, descending transfer and co-orbiting transfer. Finally, determine the total transfer time of the service satellite in different initial states by considering the relative position of the two satellites at the end of the rendezvous and the illumination angle of the service satellite's imaging of the target satellite.
[0009] Step 2: Based on the total transfer time and the relative positions of the two satellites at the end of the rendezvous, construct a mathematical model of the transfer orbit to obtain the time the service satellite spends in the initial orbit, transfer orbit, and approach orbit during the transfer process, as well as the velocity increment for completing the Hohmann transfer.
[0010] Step 3: The relative position vector angle between the two stars at the end of the rendezvous is used as the objective function, the total transfer time is used as the constraint, and the time the service star spends in the initial orbit and the approach orbit during the transfer is used as the optimization variable. The range of values for the optimization variable is set, and the initial values of the optimization variable are used as individuals in the initial population of the genetic algorithm. The genetic algorithm of the HPOP model is used to optimize the objective function, and the optimal solution is output to correct the corresponding parameters in the mathematical model of the transfer orbit, thus obtaining the mathematical optimization model of the transfer orbit.
[0011] The beneficial effects of this invention are:
[0012] This paper distinguishes between coplanar and non-coplanar transfers for the initial states of the service satellite and the target satellite. A transfer orbit design method for geostationary satellite in-orbit servicing is proposed, and a mathematical model of the transfer orbit is constructed. The total transfer time required for the service satellite to complete ascending, descending, and same-orbit transfers under coplanar and non-coplanar initial conditions is obtained. The time taken for the service satellite to operate in the initial orbit, transfer orbit, and approach orbit during the transfer process, as well as the velocity increment for completing the Hohmann transfer, are also calculated. This method saves fuel consumption. For coplanar transfers, transfer orbits considering illumination conditions and rendezvous distances are designed. For non-coplanar transfers, transfer orbits considering the rendezvous time with the target satellite at the ascending and descending nodes are designed. To simultaneously ensure the illumination angle and distance between the two stars at the end of the rendezvous and reduce the calculation error caused by the transfer orbit mathematical model, the genetic algorithm of the HPOP model was used to optimize the relative position vector angle between the two stars at the end of the rendezvous and the illumination angle of the service satellite imaging the target star as the objective function. The initial parameters in the transfer orbit mathematical model were corrected, and the illumination angle and relative position of the two stars at the end of the rendezvous were optimized. Finally, the optimized transfer orbit mathematical model was obtained. This invention achieves effective imaging of high-orbit targets with low fuel consumption through the optimized transfer orbit mathematical model. It can be used by geostationary service satellites to conduct close-range observation and detection of target stars, ensuring that the relative position and illumination conditions of the two stars at the end of the rendezvous meet the operational requirements. Attached Figure Description
[0013] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments.
[0014] Figure 1 This is a schematic diagram of the solar illumination angle in this invention.
[0015] Figure 2 This is a schematic diagram of the common-plane lifting track transfer in this invention.
[0016] Figure 3 This is a schematic diagram of the common-plane descent transfer in this invention.
[0017] Figure 4 This is a schematic diagram of the coplanar track lowering and transfer method of the present invention.
[0018] Figure 5 This is a schematic diagram of the coplanar track-raising and transfer of the present invention.
[0019] Figure 6 This is a schematic diagram of the non-plane lifting track transfer in this invention. Detailed Implementation
[0020] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.
[0021] This invention provides a method for designing transfer orbits during on-orbit servicing of geostationary satellites, the method comprising:
[0022] Step 1: Based on the start time of the operation, the service satellite and the target satellite in their initial state, distinguish between coplanar transfer and non-coplanar transfer based on whether the two satellites are in the same orbital plane. Then, based on the difference in the orbital altitude of the two satellites, distinguish between ascending transfer, descending transfer and co-orbiting transfer. At the end of the rendezvous, determine the relative position of the two satellites and the illumination angle of the service satellite's imaging of the target satellite. Determine the total transfer time of the service satellite in different initial states during the transfer process.
[0023] Step 2: Based on the total transfer time and the relative positions of the two satellites at the end of the rendezvous, construct a mathematical model of the transfer orbit to obtain the time the service satellite spends in the initial orbit, transfer orbit, and approach orbit during the transfer process, as well as the velocity increment for completing the Hohmann transfer.
[0024] Step 3: The relative position vector angle between the two stars at the end of the rendezvous is used as the objective function, the total transfer time is used as the constraint, and the time the service star spends in the initial orbit and the approach orbit during the transfer is used as the optimization variable. The range of values for the optimization variable is set, and the initial values of the optimization variable are used as individuals in the initial population of the genetic algorithm. The genetic algorithm of the HPOP model is used to optimize the objective function, and the optimal solution is output to correct the corresponding parameters in the mathematical model of the transfer orbit, thus obtaining the mathematical optimization model of the transfer orbit.
[0025] Preferably, the genetic algorithm can be directly implemented using the genetic algorithm toolbox encapsulated in MATLAB software, and the HPOP model is an open-source high-precision orbit prediction model.
[0026] In the coplanar transfer, the two stars are closest at the end of the rendezvous phase and meet the conditions for imaging with direct sunlight. This indicates that: 1) the angle between the position vector of the service star and the position vector of the target star is 0° in the final state, meaning the service star is directly below or above the target star, and the closest distance between the two stars is the difference in their orbital altitudes; 2) the illumination angle of the service star imaging the target star is 0° in the final state. The definition of the solar illumination angle is as follows: Figure 1 As shown: Solar vector projection refers to the projection of the vector pointing from the target star to the sun onto the target star's orbital plane; service star to target star vector projection refers to the projection of the vector pointing from the service star to the target star onto the target star's orbital plane, and the angle between the two vectors is the solar illumination angle.
[0027] Near the end of the rendezvous, when the distance is closest and conditions for imaging with direct sunlight are met, the service satellite is located between the target satellite and the Sun, and the service satellite, target satellite, and Sun are on the same straight line. The service satellite images the target satellite from above its orbit. The end of the rendezvous, which is the total transfer time, corresponds to 12:00 local time at the lower point of the target satellite. The service satellite images the target satellite from below its orbit. The end of the rendezvous, which is the total transfer time, corresponds to 24:00 local time at the lower point of the target satellite.
[0028] Based on this condition, several coplanar transition times that satisfy the condition can be calculated:
[0029] In step one, the method for calculating the total transfer time when the two stars are coplanar in the initial state includes:
[0030] S1: Initially, the two stars are coplanar, with the service star positioned above the target star's orbit. The service star approaches the target star by lowering its orbital altitude. At the end of the rendezvous, the service star images the target star directly above its orbit, with an illumination angle of 0°. At this point, the total transfer time... for:
[0031] ;
[0032] ;
[0033] in, The start time of the task. The time is 12:00 local time under the target star. It is a positive integer. The initial phase difference between the two stars. Let be the angular velocity of the target star in its orbit. The angular velocity of the service star in its initial orbit. The angular velocity of the service satellite as it approaches its orbit;
[0034] S2: Initially, the two stars are coplanar, with the service star positioned below the target star's orbit. The service star approaches the target star by raising its orbital altitude. At the end of the rendezvous, the service star images the target star directly below its orbit, with an illumination angle of 0°. At this point, the total transfer time... for:
[0035] ;
[0036] ;
[0037] in, The start time of the task. 24:00 at the location of the target star. It is a positive integer. The initial phase difference between the two stars. Let be the angular velocity of the target star in its orbit. The angular velocity of the service star in its initial orbit. The angular velocity of the service satellite as it approaches its orbit;
[0038] S3: Initially, the two stars are coplanar, with the service star and target star at the same orbital altitude. The service star approaches the target star by lowering its orbital altitude. At the end of the rendezvous, the service star images the target star directly below its orbit, with an illumination angle of 0°. At this point, the total transfer time... for:
[0039] ;
[0040] ;
[0041] in, The start time of the task. 24:00 at the location of the target star. It is a positive integer. The initial phase difference between the two stars. The angular velocity of the service star in its initial orbit. The angular velocity of the service satellite as it approaches its orbit;
[0042] S4: Initially, the two stars are coplanar, and the service star and the target star are at the same orbital altitude. The service star approaches the target star by raising its orbital altitude. At the end of the rendezvous, the service star images the target star directly above its orbit, with an illumination angle of 0°. At this point, the total transfer time is... for:
[0043] ;
[0044] ;
[0045] in, The start time of the task. The time is 12:00 local time under the target star. It is a positive integer. The initial phase difference between the two stars. The angular velocity of the service star in its initial orbit. The angular velocity of the service satellite as it approaches its orbit.
[0046] In non-planar transfers, to conserve fuel on the service satellite, on-orbit imaging of tilted non-planar targets primarily relies on coplanar maneuvers to adjust orbital altitude. This ensures that the service satellite is directly above or below the target satellite when the target satellite crosses the equator, allowing for image formation. Therefore, the total non-planar transfer time... Corresponding to the time of the target star's ascending node Or descending intersection time .
[0047] In step one, the method for calculating the total transition time of the two stars in the initial state includes:
[0048] S10: Initially, the two stars are in opposite orbits, with the service star located below the target star's orbit. The service star approaches the target star by raising its orbital altitude. At the end of the rendezvous, the service star images the target star directly below its orbit. During the opposite orbital transfer, to ensure good illumination conditions for the service star to image the target star at the end of the rendezvous, the target star's ascending node is located at a specific time. Between 06:00 and 18:00, the total transfer time is the time it takes for the target satellite to pass the descending intersection. Otherwise, the total transfer time is the time it takes for the target star to pass the ascending node. When the illumination angle is 0°, the total transfer time is... for:
[0049] ;
[0050] ;
[0051] in, When the target star passes through the ascending node, The time it takes for the target star to pass through its ascending node. The time it takes for the target star to pass through the descending node. The start time of the task. It is a positive integer. The initial phase difference between the two stars. Let be the angular velocity of the target star in its orbit. The angular velocity of the service star in its initial orbit. The angular velocity of the service satellite as it approaches its orbit;
[0052] S20: Initially, the two stars are in opposite orbits, with the service star positioned above the target star's orbit. The service star approaches the target star by lowering its orbital altitude. At the end of the rendezvous, the service star images the target star directly above its orbit. During the opposite orbital descent transfer, to ensure good illumination conditions for the service star to image the target star at the final stage of the rendezvous, the target star's ascending node is local time... Between 06:00 and 18:00, the total transfer time is the time it takes for the target satellite to pass through the ascending node. Otherwise, the total transfer time is the time it takes for the target star to pass the descent intersection. When the illumination angle is 0°, the total transfer time is... for:
[0053] ;
[0054] ;
[0055] in, When the target star passes through the ascending node, The time it takes for the target star to pass through its ascending node. The time it takes for the target star to pass through the descending node. The start time of the task. It is a positive integer. The initial phase difference between the two stars. Let be the angular velocity of the target star in its orbit. The angular velocity of the service star in its initial orbit. The angular velocity of the service satellite as it approaches its orbit;
[0056] S30: Initially, the two stars are on opposite sides, with the service star and the target star at the same orbital altitude. The service star approaches the target star by lowering its orbital altitude. At the end of the rendezvous, the service star images the target star directly below its orbit. To ensure good illumination conditions for the service star to image the target star at the end of the rendezvous, the rendezvous point of the target star is local. Between 06:00 and 18:00, the total transfer time is the time it takes for the target satellite to pass the descending intersection. Otherwise, the total transfer time is the time it takes for the target star to pass the ascending node. When the illumination angle is 0°, the total transfer time is... for:
[0057] ;
[0058] ;
[0059] in, When the target star passes through the ascending node, The time it takes for the target star to pass through its ascending node. The time it takes for the target star to pass through the descending node. The start time of the task. It is a positive integer. The initial phase difference between the two stars. The angular velocity of the service star in its initial orbit. The angular velocity of the service satellite as it approaches its orbit;
[0060] S40: Initially, the two stars are on opposite sides, with the service star and the target star at the same orbital altitude. The service star approaches the target star by raising its orbital altitude. At the end of the rendezvous, the service star images the target star directly above its orbit. To ensure good illumination conditions for the service star to image the target star at the end of the rendezvous, the location of the target star's ascending node is determined by local time. Between 06:00 and 18:00, the total transfer time is the time it takes for the target satellite to pass through the ascending node. Otherwise, the total transfer time is the time it takes for the target star to pass the descent intersection. Illumination angle is 0°, total transfer time for:
[0061] ;
[0062] ;
[0063] in, When the target star passes through the ascending node, The time it takes for the target star to pass through its ascending node. The time it takes for the target star to pass through the descending node. The start time of the task. It is a positive integer. The initial phase difference between the two stars. The angular velocity of the service star in its initial orbit. The angular velocity of the service satellite as it approaches its orbit.
[0064] In step two, the total transition time obtained for several conditions is used. Solve for the corresponding total transition time. Below, the service satellite's initial orbital time is The transfer orbit travel time is Approximate orbital travel time is Based on whether the serving satellite and the target satellite are in the same plane, transfer orbits can be divided into coplanar transfers and non-coplanar transfers. Coplanar and non-coplanar transfers are further divided into ascent transfers, descent transfers, and co-orbit transfers, depending on whether the serving satellite and the target satellite are in the same orbit in the initial state.
[0065] (a) Coplanar transfer
[0066] 1. Upgrade transfer:
[0067] An ascending transfer occurs when the service satellite is initially positioned below the target satellite's orbit. After a period of time in its initial orbit, the service satellite undergoes a Hohmann transfer to enter a closer orbit. After orbiting in the closer orbit for a period, it reaches a point directly below the target satellite, at which point the two satellites are closest and conditions are suitable for imaging with direct sunlight. The transfer process is as follows: Figure 2 As shown.
[0068] In the final state of the coplanar transfer, the two stars are closest and meet the conditions for imaging with direct sunlight. This indicates that: firstly, the angle between the position vectors of the service star and the target star is 0° in the final state, meaning the service star is directly below the target star, and the closest distance between the two stars is the difference in their orbital altitudes; secondly, the illumination angle of the service star imaging the target star is 0° in the final state. The definition of the solar illumination angle is as follows: Figure 1 As shown.
[0069] The solar vector projection refers to the projection of the vector pointing from the target star to the sun onto the target star's orbital plane. The service star to target star vector refers to the projection of the vector pointing from the service star to the target star onto the target star's orbital plane. The angle between the two vectors is the solar illumination angle of the service star imaging the target star, or simply the illumination angle.
[0070] When the two stars are nearing their closest approach at the end of their lifespan and are suitable for imaging with direct sunlight, and the service star is located between the target star and the Sun, with the service star, target star, and Sun aligned on a straight line, this corresponds to 12:00 or 24:00 local time at the nadir of the target star. Based on this condition, several coplanar transition times that satisfy the given conditions can be calculated. The service satellite's initial operating time is The transfer segment running time is The running time of the near segment is ,but,
[0071] Initially, the two stars are coplanar, with the service star positioned below the target star's orbit. When the service star approaches the target star by raising its orbital altitude, the mathematical model for the transfer orbit includes:
[0072] ;
[0073] ;
[0074] ;
[0075] ;
[0076] The conditions that are satisfied can be found from the above formula. corresponding ;
[0077] ;
[0078] in, Total transfer time; This is the initial orbital running time; This indicates the transfer orbit travel time, which is half a cycle of the transfer orbit. To approximate the orbital travel time; For the initial semi-major axis of the service star's orbit, H represents the semi-major axis of the target star's orbit, and H represents the approach distance. The gravitational constant of Earth; The initial phase difference between the two stars. The angular velocity of the service star in its initial orbit. To provide the angular velocity of the service star as it approaches its orbit, This represents the angular velocity of the target star in its orbit. For the first velocity increment corresponding to the transition of the service satellite from its initial orbit to a near-orbital orbit, This is the second velocity increment corresponding to the transition of the service satellite from its initial orbit to a near-orbital orbit.
[0079] 2. Descending orbit transfer:
[0080] A descent transfer occurs when the service satellite initially orbits above the target satellite. After a period of time in its initial orbit, the service satellite undergoes a Hohmann transfer to enter a closer orbit. After orbiting in the closer orbit for a period, it reaches directly above the target satellite, at which point the two satellites are closest and conditions are suitable for imaging with direct sunlight. The transfer process is as follows: Figure 3 As shown, we have:
[0081] In step two, the two stars are initially coplanar, with the service star positioned above the target star's orbit. When the service star approaches the target star by lowering its orbital altitude, the mathematical model for the transfer orbit includes:
[0082] ;
[0083] ;
[0084] ;
[0085] ;
[0086] The conditions that are satisfied can be found from the above formula. corresponding .
[0087] ;
[0088] in, Total transfer time; This is the initial orbital running time; This indicates the transfer orbit travel time, which is half a cycle of the transfer orbit. To approximate the orbital travel time; For the initial semi-major axis of the service star's orbit, H represents the semi-major axis of the target star's orbit, and H represents the approach distance. The gravitational constant of Earth; The initial phase difference between the two stars. The angular velocity of the service star in its initial orbit. To provide the angular velocity of the service star as it approaches its orbit, This represents the angular velocity of the target star in its orbit. For the first velocity increment corresponding to the transition of the service satellite from its initial orbit to a near-orbital orbit, This is the second velocity increment corresponding to the transition of the service satellite from its initial orbit to a near-orbital orbit.
[0089] 3. Transfer along the same track:
[0090] Co-orbit transfer means that the target satellite and the service satellite are initially in the same orbit. Based on the phase relationship between the two satellites, their relative positions can be categorized as either phase-leading or phase-lagging. The angle that the service satellite rotates along its orbital direction to reach the target satellite is... ,in:
[0091] ;
[0092] After waiting in its initial orbit for a period of time, the service satellite enters its approach orbit through a Hohmann transfer. After running in the approach orbit for a period of time, it reaches directly above or below the target satellite. At this time, the two satellites are closest and the conditions for imaging with the light from the target satellite are met.
[0093] In theory, regardless of whether the phase is ahead or behind, imaging of the target star with the light can be achieved by raising or lowering the orbital altitude during in-orbit transfer. However, to save time, in-orbit lowering is generally used for phase-lagging and in-orbit raising is used for phase-ahead.
[0094] The same-track lowering transfer process is as follows Figure 4 As shown. The mathematical model for the transfer orbit during the initial coplanar, phase-lag-lagging transfer of the two stars to their same orbit includes:
[0095] ;
[0096] ;
[0097] ;
[0098] ;
[0099] ;
[0100] The conditions that are satisfied can be found from the above formula. corresponding .
[0101] ;
[0102] The same track up-track transfer process is as follows: Figure 5 As shown, when the two stars are initially coplanar and have a leading phase during a co-orbital ascent transfer, the mathematical model for the transfer orbit includes:
[0103] ;
[0104] ;
[0105] ;
[0106] ;
[0107] ;
[0108] The conditions that are satisfied can be found from the above formula. corresponding .
[0109] ;
[0110] in, Total transfer time; This is the initial orbital running time; This indicates the transfer orbit travel time, which is half a cycle of the transfer orbit. To approximate the orbital travel time; For the initial semi-major axis of the service star's orbit, H represents the semi-major axis of the target star's orbit, and H represents the approach distance. The gravitational constant of Earth; The initial phase difference between the two stars. The angular velocity of the service star in its initial orbit. To provide the angular velocity of the service star as it approaches its orbit, This represents the angular velocity of the target star in its orbit. For the first velocity increment corresponding to the transition of the service satellite from its initial orbit to a near-orbital orbit, This is the second velocity increment corresponding to the transition of the service satellite from its initial orbit to a near-orbital orbit.
[0111] (ii) Horizontal transfer
[0112] To conserve fuel for the service satellite, when imaging out-of-orbit targets with large inclinations, the main method is to adjust the orbital altitude so that the service satellite is directly above or below the target satellite when the target satellite passes the equator, thus enabling imaging of the target satellite.
[0113] When the target star is in a geosynchronous orbit, it passes the equator twice a day, with an interval of 12 hours. In the worst case, the local time of the target star's ascending node is 06:00 or 18:00. At this time, whether at the ascending or descending node, and whether imaging the target from directly above or below, there is no illumination condition (the illumination angle is about 90°). In other cases, the orbital altitude can be adjusted to select the one with better illumination conditions between the ascending and descending nodes, so that the target star is directly above or below when it passes the equator, and the target star can be imaged.
[0114] According to the definitions of the three transfer methods in coplanar transfer, non-coplanar transfer also includes ascending transfer, descending transfer, and co-orbit transfer. The calculation methods for the three cases are similar. First, we introduce the non-coplanar ascending transfer, which is that in the initial state, the two stars are non-coplanar, and the service star is located below the target star's orbital altitude. After waiting for a period of time in the initial orbit, the service star enters the approach orbit through a Hohmann transfer. After running in the approach orbit for a period of time, it reaches directly below the target star. At this time, the two stars are closest, and the target star is exactly passing through the equator. The transfer process is as follows: Figure 6 As shown.
[0115] Unlike coplanar transfers, in a non-coplanar transfer, the target star passes exactly across the equator at the end of the rendezvous between the two stars. Therefore, the total time of a non-coplanar transfer is... Corresponding to the time of the target star's ascending node Or descending intersection time In non-plane ascending orbit transfers, to ensure that the serving satellite has good illumination conditions when imaging the target satellite near the end of its orbit, the local time of the target satellite's ascending node must be considered. Between 06:00 and 18:00, the total transfer time is the time it takes for the target satellite to pass the descending intersection. Otherwise, the total transfer time is the time it takes for the target star to pass the ascending node. The principle for determining the total transfer time in non-plane ascending orbit transfer is as follows:
[0116] ;but,
[0117] In step two, the two stars are initially out of orbit, with the service star located below the target star's orbit. When the service star approaches the target star by raising its orbital altitude, the mathematical model for the transfer orbit includes:
[0118] ;
[0119] ;
[0120] ;
[0121] ;
[0122] ;
[0123] in, Total transfer time; This is the initial orbital running time; This indicates the transfer orbit travel time, which is half a cycle of the transfer orbit. To approximate the orbital travel time; For the initial semi-major axis of the service star's orbit, H represents the semi-major axis of the target star's orbit, and H represents the approach distance. The gravitational constant of Earth; The initial phase difference between the two stars. The angular velocity of the service star in its initial orbit. To provide the angular velocity of the service star as it approaches its orbit, This represents the angular velocity of the target star in its orbit. For the first velocity increment corresponding to the transition of the service satellite from its initial orbit to a near-orbital orbit, This is the second velocity increment corresponding to the transition of the service satellite from its initial orbit to a near-orbital orbit.
[0124] In step two, the two stars are initially on opposite sides, with the service star positioned above the target star's orbit. When the service star approaches the target star by lowering its orbital altitude, the mathematical model for the transfer orbit includes:
[0125] ;
[0126] ;
[0127] ;
[0128] ;
[0129] ;
[0130] ;
[0131] in, Total transfer time; This is the initial orbital running time; This indicates the transfer orbit travel time, which is half a cycle of the transfer orbit. To approximate the orbital travel time; For the initial semi-major axis of the service star's orbit, H represents the semi-major axis of the target star's orbit, and H represents the approach distance. The gravitational constant of Earth; The initial phase difference between the two stars. The angular velocity of the service star in its initial orbit. To provide the angular velocity of the service star as it approaches its orbit, This represents the angular velocity of the target star in its orbit. For the first velocity increment corresponding to the transition of the service satellite from its initial orbit to a near-orbital orbit, This is the second velocity increment corresponding to the transition of the service satellite from its initial orbit to a near-orbital orbit.
[0132] In step two, the co-orbit transfer of two stars on opposite sides is divided into phase lead and phase lag based on the phase difference between the two stars. For same-track transfers with leading phase, an upward transfer method is adopted; for same-track transfers with lagging phase, a downward transfer method is adopted.
[0133] When two stars are initially out of plane and have phase lag during a co-orbital descent transfer, the mathematical model for the transfer orbit includes:
[0134] ;
[0135] ;
[0136] ;
[0137] ;
[0138] ;
[0139] ;
[0140] ;
[0141] When two stars are initially out of plane and have leading phases, the mathematical model for the transfer orbit includes:
[0142] ;
[0143] ;
[0144] ;
[0145] ;
[0146] ;
[0147] ;
[0148] ;
[0149] in, Total transfer time; This is the initial orbital running time; This indicates the transfer orbit travel time, which is half a cycle of the transfer orbit. To approximate the orbital travel time; For the initial semi-major axis of the service star's orbit, H represents the semi-major axis of the target star's orbit, and H represents the approach distance. The gravitational constant of Earth; The initial phase difference between the two stars. The angular velocity of the service star in its initial orbit. To provide the angular velocity of the service star as it approaches its orbit, This represents the angular velocity of the target star in its orbit. For the first velocity increment corresponding to the transition of the service satellite from its initial orbit to a near-orbital orbit, This is the second velocity increment corresponding to the transition of the service satellite from its initial orbit to a near-orbital orbit.
[0150] In step three, let the angle between the position vectors of the two stars at the end of the rendezvous be . The illumination angle of the service satellite imaging the target star at the end of the rendezvous period is: To ensure the two stars are as close as possible and to meet the conditions for imaging with direct sunlight, the objective function is: ;
[0151] The constraint is the total transition time. ;
[0152] The time the service satellite spends in the transfer orbit under different transfer scenarios The specific value can be obtained by using the method in step two.
[0153] The ranges of values for the optimization variables are as follows: ; ;
[0154] in, The angle between the position vectors of the two stars at the end of the rendezvous is ; The illumination angle for imaging the target star by the service satellite at the end of the rendezvous period; Total transfer time; This is the initial orbital running time; For the transfer orbit operation time; To approximate the orbital running time.
[0155] Verification Instance
[0156] To verify the effectiveness of the present invention, simulation time periods and initial orbital parameters of the two satellites were set for both coplanar transfer and non-coplanar transfer cases. Using the established mathematical models of the initial transfer orbit and the transfer orbit, the position vector angle and illumination angle of the two satellites in the rendezvous model before and after correction were obtained.
[0157] (a) Coplanar orbital transfer
[0158] 1. Example Description:
[0159] The initial orbital elements of the service satellite and the target satellite are shown in Table 1.
[0160] Table 1
[0161] Semi-long wheelbase / km Eccentricity Pitch o ]] Periapsis elevation o ]] <![CDATA[Right ascension of the ascending node / o > <![CDATA[True anomaly / o > Target Star 42166.3 0 0 0 0 72.0 Service Star 42066.3 0 0 0 0 67.0
[0162] The orbital epochs for both satellites are 19 Jun 2020 04:00:00.000 UTCG, and the operation start and end times are [19 Jun 2020 04:00:00.000 UTCG] to [25 Jun 2020 04:00:00.000 UTCG]. The approach distance is 30 km, and the simulation step size is 60 s.
[0163] 2. Simulation Analysis:
[0164] The HPOP model is used to calculate the UTC time corresponding to 24:00:00 local time at the target satellite's nadir point during the operation period, while also satisfying the coplanar ascent transfer time. Theoretical constraints apply. Table 2 shows the corresponding transition times within the simulation period.
[0165] Table 2
[0166] Total coplanar transfer time / s Corresponding UTCG time 392532 23 Jun 2020 17:02:12 478932 24 Jun 2020 17:02:12
[0167] By establishing the mathematical model of the initial transfer trajectory, the calculation is performed. The corresponding service satellites at the initial orbit, transfer orbit, and approach orbit times, as well as the two velocity increments for completing the orbit transfer, are shown in Table 3. Table 3 shows the maneuver strategies corresponding to different transfer times.
[0168] Table 3
[0169] / s / s / s / m / s / m / s 289571 42986 59975 1.3 1.3 252652 42986 183294 1.3 1.3
[0170] The calculation results , The initial value, as the individual in the first generation of the genetic algorithm, is used to perform genetic algorithm (transfer strategy correction method) based on HPOP model. , After making corrections, for multi-objective optimization problems, a set of optimal solutions will be obtained. Selecting any solution from this set, we compare the changes in the angle between the position vectors and the illumination angle at the end of the rendezvous between the two stars before and after the correction, as shown in Tables 4 and 5. Tables 4 and 5 are... and Corrected the changes at the end of the rendezvous period between the two satellites.
[0171] Table 4
[0172] / s / s Position vector angle Illumination angle Before revision 289571 59975 0.0147 30.4212 Revised 290921 58625 0.0003 23.4405
[0173] Table 5
[0174] / s / s Position vector angle Illumination angle Before revision 252652 183294 0.0358 46.8174 Revised 256020 179926 0.0001 23.4305
[0175] (ii) Transfer of orbits in opposite directions
[0176] 1. Example Description
[0177] In the non-planar orbital transfer example, the target star's orbital inclination was set to 0.2°, while all other parameters remained consistent with those for the coplanar transfer.
[0178] 2. Simulation Analysis
[0179] The HPOP model was used to calculate the UTC time corresponding to the target satellite's passage through the equator during the operation period, while also satisfying the coplanar ascent and transfer time. Theoretical constraints apply. Table 6 shows the corresponding transition times within the simulation period.
[0180] Table 6
[0181] Total coplanar transfer time / s Corresponding UTCG time Local time corresponding to the sub-satellite point 364462 23 Jun 2020 09:14:22 (Descending node) 16:12:07 407624 23 Jun 2020 21:13:44 (Ascending Node) 04:11:34 450791 June 24, 2020 09:13:11 (Descending node) 16:10:56 493932 June 24, 2020 21:12:12 (Ascending Node) 04:10:02
[0182] According to the principle of optimal selection of ascending and descending node points, the lighting conditions at the ascending node are better than those at the descending node, so the location is chosen... , Imaging of the non-planar target is performed continuously, and calculations are performed based on the established mathematical model of the initial transfer trajectory. , The corresponding service satellites are in their initial orbit, transfer orbit, and approach orbit at the corresponding times, as well as the two velocity increments during the orbit transfer. Table 7 shows the maneuvers corresponding to different transfer times.
[0183] Table 7
[0184] / s / s / s / m / s / m / s 301565 42986 19911 1.3 1.3 283122 42986 81516 1.3 1.3 264677 42986 143128 1.3 1.3 246242 42986 204704 1.3 1.3
[0185] The calculation results , The initial value, as the individual in the first generation of the genetic algorithm, is used to perform genetic algorithm (transfer strategy correction method) based on HPOP model. , After correction, for multi-objective optimization problems, a set of optimal solutions will be obtained. A solution set is randomly selected from this set, and the changes in the angle between the position vectors and the illumination angle at the end of the rendezvous between the two stars before and after the correction are compared. Table 8 shows... The changes at the end of the rendezvous period of the two satellites before and after the correction are shown in Table 9. Corrected the changes at the end of the rendezvous period between the two satellites.
[0186] Table 8
[0187] / s / s Position vector angle Illumination angle Before revision 283122 81516 0.0858 68.2462 Revised 286543 78095 0.0857 46.8304
[0188] Table 9
[0189] / s / s Position vector angle Illumination angle Before revision 246242 204704 0.0909 79.8654 Revised 253682 197264 0.0908 34.7188
[0190] The beneficial effects of this invention are:
[0191] To differentiate between coplanar and non-coplanar transfers for the initial states of the service satellite and the target satellite, a transfer orbit design method for geostationary satellite in-orbit servicing is proposed. A mathematical model of the transfer orbit is constructed to obtain the total transfer time required for the service satellite to complete ascending, descending, and co-orbiting transfers under coplanar and non-coplanar initial conditions. The method also calculates the time the service satellite spends in its initial orbit, transfer orbit, and approach orbit during the transfer process, as well as the velocity increment for completing the Hohmann transfer, thus saving fuel consumption. For coplanar transfers, a transfer orbit considering illumination conditions and rendezvous distance is designed; for non-coplanar transfers, a transfer orbit considering the rendezvous with the target satellite at the time of its ascending and descending nodes is designed. Finally, to simultaneously ensure the illumination angle and distance between the two stars at the end of the rendezvous and reduce the calculation error caused by the transfer orbit mathematical model, the genetic algorithm of the HPOP model was used to optimize the relative position vector angle between the two stars at the end of the rendezvous and the illumination angle of the service satellite imaging the target star as the objective function. The initial parameters in the transfer orbit mathematical model were corrected, and the illumination angle and relative position of the two stars at the end of the rendezvous were optimized. Finally, the optimized transfer orbit mathematical model was obtained. This invention achieves effective imaging of high-orbit targets with low fuel consumption through the optimized transfer orbit mathematical model. It can be used by geostationary orbit service satellites to conduct close-range observation and detection of target stars, ensuring that the relative position and illumination conditions of the two stars at the end of the rendezvous meet the operational requirements.
[0192] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.
Claims
1. A method for designing transfer orbits during on-orbit servicing of geostationary satellites, characterized in that, The method includes: Step 1: Based on the start time of the operation, the service satellite and the target satellite in their initial state, distinguish between coplanar transfer and non-coplanar transfer based on whether the two satellites are in the same orbital plane. Then, based on the difference in the orbital altitude of the two satellites, distinguish between ascending transfer, descending transfer and co-orbiting transfer. Finally, determine the total transfer time of the service satellite in different initial states by considering the relative position of the two satellites at the end of the rendezvous and the illumination angle of the service satellite's imaging of the target satellite. Step 2: Based on the total transfer time and the relative positions of the two satellites at the end of the rendezvous, construct a mathematical model of the transfer orbit to obtain the time the service satellite spends in the initial orbit, transfer orbit, and approach orbit during the transfer process, as well as the velocity increment for completing the Hohmann transfer. Step 3: The relative position vector angle between the two stars at the end of the rendezvous is used as the objective function, the total transfer time is used as the constraint, and the time the service star spends in the initial orbit and the approach orbit during the transfer is used as the optimization variable. The range of values for the optimization variable is set, and the initial values of the optimization variable are used as individuals in the initial population of the genetic algorithm. The genetic algorithm of the HPOP model is used to optimize the objective function, and the optimal solution is output to correct the corresponding parameters in the mathematical model of the transfer orbit, thus obtaining the mathematical optimization model of the transfer orbit.
2. The method for designing transfer orbits for on-orbit servicing of geostationary satellites as described in claim 1, characterized in that, In step one, the method for calculating the total transfer time when the two stars are coplanar in the initial state includes: S1: Initially, the two stars are coplanar, with the service star positioned above the target star's orbit. The service star approaches the target star by lowering its orbital altitude. At the end of the rendezvous, the service star images the target star directly above its orbit, with an illumination angle of 0°. At this point, the total transfer time... for: ； ； in, The start time of the task. The time is 12:00 local time under the target star. It is a positive integer. The initial phase difference between the two stars. Let be the angular velocity of the target star in its orbit. The angular velocity of the service star in its initial orbit. The angular velocity of the service satellite as it approaches its orbit; S2: Initially, the two stars are coplanar, with the service star positioned below the target star's orbit. The service star approaches the target star by raising its orbital altitude. At the end of the rendezvous, the service star images the target star directly below its orbit, with an illumination angle of 0°. At this point, the total transfer time... for: ； ； in, The start time of the task. 24:00 at the location of the target star. It is a positive integer. The initial phase difference between the two stars. Let be the angular velocity of the target star in its orbit. The angular velocity of the service star in its initial orbit. The angular velocity of the service satellite as it approaches its orbit; S3: Initially, the two stars are coplanar, with the service star and target star at the same orbital altitude. The service star approaches the target star by lowering its orbital altitude. At the end of the rendezvous, the service star images the target star directly below its orbit, with an illumination angle of 0°. At this point, the total transfer time... for: ； ； in, The start time of the task. 24:00 at the location of the target star. It is a positive integer. The initial phase difference between the two stars. The angular velocity of the service star in its initial orbit. The angular velocity of the service satellite as it approaches its orbit; S4: Initially, the two stars are coplanar, with the service star and target star at the same orbital altitude. The service star approaches the target star by raising its orbital altitude. At the end of the rendezvous, the service star images the target star directly above its orbit, with an illumination angle of 0°. At this point, the total transfer time... for: ； ； in, The start time of the task. The time is 12:00 local time under the target star. It is a positive integer. The initial phase difference between the two stars. The angular velocity of the service star in its initial orbit. The angular velocity of the service satellite as it approaches its orbit.
3. The method for designing transfer orbits for on-orbit servicing of geostationary satellites as described in claim 2, characterized in that, In step one, the method for calculating the total transition time of the two stars in the initial state includes: S10: Initially, the two stars are out of orbit, with the service star located below the target star's orbit. The service star approaches the target star by raising its orbital altitude. At the end of the rendezvous, the service star images the target star directly below its orbit, with an illumination angle of 0°. At this point, the total transfer time... for: ； ； in, When the target star passes through the ascending node, The time it takes for the target star to pass through its ascending node. The time it takes for the target star to pass through the descending node. The start time of the task. It is a positive integer. The initial phase difference between the two stars. Let be the angular velocity of the target star in its orbit. The angular velocity of the service star in its initial orbit. The angular velocity of the service satellite as it approaches its orbit; S20: Initially, the two stars are out of orbit, with the service star positioned above the target star's orbit. The service star approaches the target star by lowering its orbital altitude. At the end of the rendezvous, the service star images the target star directly above its orbit, with an illumination angle of 0°. At this point, the total transfer time... for: ； ； in, When the target star passes through the ascending node, The time it takes for the target star to pass through its ascending node. The time it takes for the target star to pass through the descending node. The start time of the task. It is a positive integer. The initial phase difference between the two stars. Let be the angular velocity of the target star in its orbit. The angular velocity of the service star in its initial orbit. The angular velocity of the service satellite as it approaches its orbit; S30: Initially, the two stars are out of orbit, and the service star and the target star are at the same orbital altitude. The service star approaches the target star by lowering its orbital altitude. At the end of the rendezvous, the service star images the target star directly below its orbit, and the illumination angle of the service star's image of the target star is 0°. At this point, the total transfer time is... for: ； ； in, When the target star passes through the ascending node, The time it takes for the target star to pass through its ascending node. The time it takes for the target star to pass through the descending node. The start time of the task. It is a positive integer. The initial phase difference between the two stars. The angular velocity of the service star in its initial orbit. The angular velocity of the service satellite as it approaches its orbit; S40: Initially, the two stars are out of orbit, and the service star and the target star are at the same orbital altitude. The service star approaches the target star by raising its orbital altitude. At the end of the rendezvous, the service star images the target star directly above its orbit, and the illumination angle of the service star's image of the target star is 0°. At this point, the total transfer time is... for: ； ； in, When the target star passes through the ascending node, The time it takes for the target star to pass through its ascending node. The time it takes for the target star to pass through the descending node. The start time of the task. It is a positive integer. The initial phase difference between the two stars. The angular velocity of the service star in its initial orbit. The angular velocity of the service satellite as it approaches its orbit.
4. The method for designing transfer orbits for on-orbit servicing of geostationary satellites as described in claim 3, characterized in that, In step two, the two stars are initially coplanar, with the service star located below the target star's orbit. When the service star approaches the target star by raising its orbital altitude, the mathematical model for the transfer orbit includes: ； ； ； ； ； in, Total transfer time; This is the initial orbital running time; This indicates the transfer orbit travel time, which is half a cycle of the transfer orbit. To approximate the orbital travel time; For the initial semi-major axis of the service star's orbit, H represents the semi-major axis of the target star's orbit, and H represents the approach distance. The gravitational constant of Earth; The initial phase difference between the two stars. The angular velocity of the service star in its initial orbit. To provide the angular velocity of the service star as it approaches its orbit, This represents the angular velocity of the target star in its orbit. For the first velocity increment corresponding to the transition of the service satellite from its initial orbit to a near-orbital orbit, This is the second velocity increment corresponding to the transition of the service satellite from its initial orbit to a near-orbital orbit.
5. The method for designing a transfer orbit for on-orbit servicing of a geostationary satellite as described in claim 4, characterized in that, In step two, the two stars are initially coplanar, with the service star positioned above the target star's orbit. When the service star approaches the target star by lowering its orbital altitude, the mathematical model for the transfer orbit includes: ； ； ； ； ； in, Total transfer time; This is the initial orbital running time; This indicates the transfer orbit travel time, which is half a cycle of the transfer orbit. To approximate the orbital travel time; For the initial semi-major axis of the service star's orbit, H represents the semi-major axis of the target star's orbit, and H represents the approach distance. The gravitational constant of Earth; The initial phase difference between the two stars. The angular velocity of the service star in its initial orbit. To provide the angular velocity of the service star as it approaches its orbit, This represents the angular velocity of the target star in its orbit. For the first velocity increment corresponding to the transition of the service satellite from its initial orbit to a near-orbital orbit, This is the second velocity increment corresponding to the transition of the service satellite from its initial orbit to a near-orbital orbit.
6. The method for designing a transfer orbit for on-orbit servicing of a geostationary satellite as described in claim 5, characterized in that, In step two, the coplanar orbital transfer of the two stars is divided into phase lead and phase lag based on the phase difference between the two stars. For same-track transfers with leading phase, an upward transfer method is adopted; for same-track transfers with lagging phase, a downward transfer method is adopted. When two stars are initially coplanar and have a phase lag during a co-orbital descent transfer, the mathematical model for the transfer orbit includes: ； ； ； ； ； ； When two stars are initially coplanar and in phase leading, the mathematical model for the transfer orbit includes: ； ； ； ； ； ； in, Total transfer time; This is the initial orbital running time; This indicates the transfer orbit travel time, which is half a cycle of the transfer orbit. To approximate the orbital travel time; For the initial semi-major axis of the service star's orbit, H represents the semi-major axis of the target star's orbit, and H represents the approach distance. The gravitational constant of Earth; The initial phase difference between the two stars. The angular velocity of the service star in its initial orbit. To provide the angular velocity of the service star as it approaches its orbit, This represents the angular velocity of the target star in its orbit. For the first velocity increment corresponding to the transition of the service satellite from its initial orbit to a near-orbital orbit, This is the second velocity increment corresponding to the transition of the service satellite from its initial orbit to a near-orbital orbit.
7. The method for designing transfer orbits for on-orbit servicing of geostationary satellites as described in claim 6, characterized in that, In step two, the two stars are initially out of orbit, with the service star located below the target star's orbit. When the service star approaches the target star by raising its orbital altitude, the mathematical model for the transfer orbit includes: ； ； ； ； ； in, Total transfer time; This is the initial orbital running time; This indicates the transfer orbit travel time, which is half a cycle of the transfer orbit. To approximate the orbital travel time; For the initial semi-major axis of the service star's orbit, H represents the semi-major axis of the target star's orbit, and H represents the approach distance. The gravitational constant of Earth; The initial phase difference between the two stars. The angular velocity of the service star in its initial orbit. To provide the angular velocity of the service star as it approaches its orbit, This represents the angular velocity of the target star in its orbit. For the first velocity increment corresponding to the transition of the service satellite from its initial orbit to a near-orbital orbit, This is the second velocity increment corresponding to the transition of the service satellite from its initial orbit to a near-orbital orbit.
8. The method for designing transfer orbits for on-orbit servicing of geostationary satellites as described in claim 7, characterized in that, In step two, the two stars are initially on opposite sides, with the service star positioned above the target star's orbit. When the service star approaches the target star by lowering its orbital altitude, the mathematical model for the transfer orbit includes: ； ； ； ； ； in, Total transfer time; This is the initial orbital running time; This indicates the transfer orbit travel time, which is half a cycle of the transfer orbit. To approximate the orbital travel time; For the initial semi-major axis of the service star's orbit, H represents the semi-major axis of the target star's orbit, and H represents the approach distance. The gravitational constant of Earth; The initial phase difference between the two stars. The angular velocity of the service star in its initial orbit. To provide the angular velocity of the service star as it approaches its orbit, This represents the angular velocity of the target star in its orbit. For the first velocity increment corresponding to the transition of the service satellite from its initial orbit to a near-orbital orbit, This is the second velocity increment corresponding to the transition of the service satellite from its initial orbit to a near-orbital orbit.
9. The method for designing a transfer orbit for on-orbit servicing of a geostationary satellite as described in claim 8, characterized in that, In step two, the co-orbit transfer of two stars on opposite sides is divided into phase lead and phase lag based on the phase difference between the two stars. For same-track transfers with leading phase, an upward transfer method is adopted; for same-track transfers with lagging phase, a downward transfer method is adopted. When two stars are initially out of plane and have phase lag during a co-orbital descent transfer, the mathematical model for the transfer orbit includes: ； ； ； ； ； ； When two stars are initially out of plane and have leading phases, the mathematical model for the transfer orbit includes: ； ； ； ； ； ； in, Total transfer time; This is the initial orbital running time; This indicates the transfer orbit travel time, which is half a cycle of the transfer orbit. To approximate the orbital travel time; For the initial semi-major axis of the service star's orbit, H represents the semi-major axis of the target star's orbit, and H represents the approach distance. The gravitational constant of Earth; The initial phase difference between the two stars. The angular velocity of the service star in its initial orbit. To provide the angular velocity of the service star as it approaches its orbit, This represents the angular velocity of the target star in its orbit. For the first velocity increment corresponding to the transition of the service satellite from its initial orbit to a near-orbital orbit, This is the second velocity increment corresponding to the transition of the service satellite from its initial orbit to a near-orbital orbit.
10. The method for designing a transfer orbit for on-orbit servicing of a geostationary satellite as described in claim 9, characterized in that, In step three, the objective function is: ; Constraints ; The ranges of values for the optimization variables are as follows: ; ; in, The angle between the position vectors of the two stars at the end of the rendezvous is ; The illumination angle for imaging the target star by the service satellite at the end of the rendezvous period; Total transfer time; This is the initial orbital running time; For the transfer orbit operation time; To approximate the orbital running time.