A method for capturing a planet system resonance orbit based on satellite gravitational assistance

Abstract

The application discloses a kind of planetary system resonance orbit capture methods based on satellite gravity assistance, belong to deep space probe orbit design and optimization technical field, comprising: before probe reaches target planet perihelion, utilize target satellite gravity assistance to reduce hyperbolic overspeed and match orbit inclination, obtain power-assisted capture section;Speed reduction pulse is applied at perihelion to enter large ellipse orbit, and modulation pulse is applied at apocenter to establish repeated encounter condition with target satellite, obtain capture section;Candidate resonance ratio set is constructed and the shortest total transfer time feasible sequence is screened;Optimization model of transfer between twice power assistance is constructed based on single resonance ratio, each power assistance transfer section is solved according to sequence order;Three trajectory splicing obtains complete transfer trajectory.The application is integrated by power-assisted speed reduction and resonance deorbiting, significantly reduces the speed increment demand, reduces propellant consumption.

Description

Technical Field

[0001] This invention relates to the field of deep space probe orbit design and optimization technology, and in particular to a method for capturing planetary system resonance orbits based on satellite gravity assistance. Background Technology

[0002] After reaching their target planet, deep space probes need to perform orbital capture maneuvers to transform their interplanetary transfer hyperbolic orbit into a closed orbit around the target planet. This is a crucial step in deep space exploration missions. The velocity increment required for the capture maneuver directly affects the probe's propellant load and mission feasibility; therefore, reducing the capture velocity increment and improving propulsion efficiency remain core issues in orbital design.

[0003] In existing technologies, planetary capture by probes typically employs a single large-pulse deceleration at the planet's pericenter, directly braking the probe from a hyperbolic orbit into the target orbit. This method relies on the propulsion system to provide the entire velocity increment, resulting in high capture maneuver costs and heavy propellant consumption. For missions exploring distant large planets such as Neptune and Jupiter, the probe's relative velocity upon reaching the target planet is relatively high, making the velocity increment required for a single pulse capture particularly substantial, severely limiting payload capacity.

[0004] To reduce the velocity increment during capture, some existing technologies utilize the target planet's satellite for gravitational assistance after planetary capture, gradually reducing orbital energy by flying over the satellite. However, this sequential "capture first, then assist" strategy has two shortcomings: First, the capture phase design does not consider the orbital geometry constraints of subsequent satellite flyovers, resulting in a mismatch between the highly elliptical orbit after capture and the satellite's assist conditions, requiring additional maneuvers for orbital correction, increasing mission complexity and propellant costs. Second, after initial capture, the planet is in a highly elliptical orbit, and the descent process requires multiple large-amplitude propulsion and braking maneuvers, relying entirely on the propulsion system to change orbital energy, which is inefficient and lacks systematic utilization of satellite resonance assist. Furthermore, existing segmented independent optimization design methods treat the planetary capture phase and the satellite assist phase separately, resulting in a disconnect between capture and assist designs, making it difficult to achieve a natural match of orbital states between the two stages. Summary of the Invention

[0005] The purpose of this invention is to provide a planetary system resonance orbit capture method based on satellite gravity assistance, which aims to solve the problems of high capture maneuver costs, orbit reduction dependence on large pulses, and disconnect between capture and leveraging design in the prior art. By leveraging-assisted capture, establishing repeated encounter conditions through centroid modulation, and multiple satellite orbit reductions guided by resonance ratio sequence, low-energy capture and efficient orbit reduction of planetary systems can be achieved.

[0006] To achieve the above objectives, this invention provides a method for capturing resonant orbits of planetary systems based on satellite gravity assistance, comprising the following steps: S1. After the probe enters the gravitational influence sphere of the target planet, before reaching the pericenter of the target planet, the probe uses the gravitational assistance of the target satellite to reduce the hyperbolic speed of the probe relative to the target planet, and makes the inclination angle deviation between the orbital plane of the probe and the orbital plane of the target satellite no greater than a preset angle threshold, thus obtaining the transfer trajectory of the gravity-assisted capture segment. S2. The probe applies a deceleration pulse at the pericenter of the target planet, is captured by the target planet and enters a highly elliptical orbit, and applies a modulation pulse in the neighborhood of the apocenter of the highly elliptical orbit to adjust the pericenter altitude of the highly elliptical orbit so that it can meet the target satellite again, thus obtaining the capture segment transfer trajectory. S3. Construct a candidate resonance ratio set, where the resonance ratio is the ratio of the orbital period of the probe to the orbital period of the target satellite; generate all finite resonance ratio sequences composed of elements in the candidate resonance ratio set; retain feasible sequences that satisfy the borrowing deflection angle constraint for each borrowing operation, the borrowing deflection angle constraint being determined by the minimum allowable borrowing height of the probe relative to the target satellite; among the feasible sequences that satisfy the constraint, select the resonance ratio sequence with the shortest total transfer time as the periodic sequence; S4. Based on the single resonance ratio in the resonance-lowering segment, construct an optimization model for the transfer between two leverage operations; S5. Discretize the resonance-reducing trajectory segment into several sequentially connected leverage transfer segments, and solve the optimization model constructed in S4 in the order of the periodic sequence to obtain the transfer trajectory of the resonance-reducing trajectory segment. S6. The transfer trajectory of the leveraged capture segment, the transfer trajectory of the capture segment, and the transfer trajectory of the resonance descent segment are spliced ​​together to obtain the complete transfer trajectory.

[0007] Preferably, in S1, the process of the probe using the target satellite to achieve gravity assistance is described by two variables: the leverage radius multiplier and the leverage plane angle B. The optimization objective is to minimize the hyperbolic hypervelocity when the probe reaches the pericenter of the target planet, and to satisfy the safety constraints of the probe's leverage altitude relative to the target satellite, the safety altitude constraint of the pericenter of the target planet, and the constraint of the tilt deviation.

[0008] Preferably, the lever radius of the detector relative to the target satellite is determined by the product of the lever radius multiplier and the radius of the target satellite, and the lever radius is not less than the sum of the radius of the target satellite and the safe altitude.

[0009] Preferably, in S2, the deceleration pulse applied by the detector at the pericenter is a tangential deceleration pulse, and the modulation pulse is applied in the neighborhood of the distal point of the large elliptical orbit.

[0010] Preferably, the capture segment transfer trajectory is obtained by solving the following optimization problem: The second set of optimization variables includes: the apocenter altitude of the probe in its highly elliptical orbit after capture, the total flight time from capture at the pericenter to re-encounter with the target satellite, and the time allocation factor used to determine the timing of mid-course correction maneuvers. The objective function is to minimize the sum of the magnitudes of the near-center deceleration pulse and the far-center modulation pulse; The constraint is that when the detector encounters the target satellite again, the hyperbolic overspeed relative to the target satellite does not exceed a preset upper limit.

[0011] Preferably, in S4, the optimization model is as follows: The leverage radius, leverage plane angle B, and flight time of each transfer segment are used as the third optimization variables; The optimization objective is to minimize the speed increment of the mid-course correction maneuver applied at the moment of mid-course correction maneuver between two leverage operations; The constraints include: the deviation between the total flight time and the transfer time determined by S3 is within the allowable range; the deviation between the orbital period of the probe and the orbital period determined by S3 is within the allowable range; and the leverage radius for each leverage operation is not less than the leverage radius corresponding to the minimum allowable leverage altitude.

[0012] Preferably, the total flight time between two leverage operations is allocated by a time scaling factor as a first transfer time from the leverage moment to the mid-course correction maneuver moment and a second transfer time from the mid-course correction maneuver moment to the next leverage moment.

[0013] Preferably, the numerical range of each resonance ratio in the candidate resonance ratio set is no greater than the preset maximum resonance ratio value.

[0014] Preferably, in S5, the resonance-lowering segment is discretized into multiple leverage transfer segments. According to the order of each resonance ratio in the periodic sequence determined in S3, the optimization model constructed in S4 is called sequentially for sequential solution, and the end state of the previous transfer is used as the initial state of the next transfer.

[0015] Preferably, in S6, the end of the transfer trajectory of the leveraged capture segment and the beginning of the transfer trajectory of the capture segment are connected at the pericenter of the target planet, and the end of the transfer trajectory of the capture segment and the beginning of the transfer trajectory of the resonance descent segment are connected at the position where the probe and the target satellite first meet.

[0016] Therefore, the present invention employs the above-mentioned method for capturing planetary system resonance orbits based on satellite gravity assistance, which has the following beneficial effects: (1) Low capture velocity increment requirement: This invention introduces satellite gravity assistance for the first time before the capture of the planetary system pericentrism, and uses the natural gravitational field to pre-deflect the probe’s velocities, which effectively reduces the velocity increment requirement of the planetary capture pulse and reduces propellant consumption.

[0017] (2) Less propellant consumption during orbit descent: After the initial capture of the planet, this invention does not rely on multiple large-amplitude thrust braking to descent the orbit. Instead, it establishes orbital conditions for repeated approaching and leveraging of the satellite by small-amplitude modulation of the apocentric point. Combined with multiple satellite resonance leveraging, the orbital period is gradually reduced, which significantly saves propellant.

[0018] (3) High efficiency of track design: This invention simplifies the evaluation model by using resonance ratio sequence to quickly screen the optimal orbit reduction order, avoiding the exhaustive calculation of complete orbit integration for a large number of candidate sequences required by traditional methods, thus improving the efficiency of track design.

[0019] (4) Seamless connection of each segment of trajectory: The present invention will model the three segments of the assisted capture segment, the capture segment and the resonance descent segment in a unified manner. The end of the assisted capture segment and the beginning of the capture segment are connected at the pericenter of the planet, and the end of the capture segment and the beginning of the resonance descent segment are connected at the first encounter point of the satellite. The orbital state between each segment is naturally continuous and no additional correction maneuver is required.

[0020] (5) Wide range of applications: This invention is applicable to planetary system exploration, satellite orbit exploration and low-energy capture and deorbiting missions in similar "large planet-large mass satellite" systems, and has strong engineering promotion value.

[0021] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0022] Figure 1 This is a flowchart illustrating a method for capturing a planetary system resonant orbit based on satellite gravity assistance according to the present invention. Figure 2 This is a schematic diagram of the transfer trajectory of the Neptune capture segment (including the gravity-assisted capture segment and the capture segment) in an embodiment of the present invention; Figure 3 This is a schematic diagram of the transfer trajectory of the Haiwei-1 resonance orbit reduction segment in an embodiment of the present invention; Figure 4 This is a schematic diagram of the overall transfer trajectory of the probe within the target planetary system (taking Neptune as an example) in an embodiment of the present invention. Detailed Implementation

[0023] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0024] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0025] Example 1 like Figure 1 As shown, this embodiment uses a Neptune system exploration mission as the application scenario, with Neptune as the target planet and Triton as the target moon. The probe has completed interplanetary transfer and entered Neptune's Sphere of Influence (SOI). Figure 1 As shown, this embodiment is implemented step by step according to the process from S1 to S6.

[0026] S1: Design of Transfer Trajectory for Assisted Capture Segment After the probe enters the gravitational influence sphere of the target planet, before reaching the pericenter of the target planet, it uses the gravitational assistance of the target satellite to reduce the hyperbolic speed of the probe relative to the target planet, and ensures that the inclination deviation between the orbital plane of the probe and the orbital plane of the target satellite is no greater than a preset angle threshold, thus obtaining the transfer trajectory of the gravity-assisted capture segment.

[0027] The pericentric point is the point on the orbit around the target planet where the probe is closest to the center of the planet. In this embodiment, the pericentric point height of Neptune is the height of the probe above the surface of Neptune.

[0028] In this embodiment, when the probe enters Neptune's gravitational influence sphere, its initial hyperbolic speedover relative to Neptune is approximately 8.24 km / s, and it enters the Neptune system from the direction of Triton's orbital plane, with an initial orbital plane inclination deviation of approximately 4° from Triton's orbital plane (less than the preset threshold of 5°). Before reaching Neptune's pericenter, the probe will perform a Triton gravitational assist.

[0029] The process of the probe using the target satellite to achieve gravity assistance is described by two variables: the leverage radius multiplier and the leverage plane angle. The optimization objective is to minimize the hyperbolic hypervelocity when the probe reaches the pericenter of the target planet, while satisfying the safety constraints of the probe's leverage altitude relative to the target satellite, the safety altitude constraint of the probe relative to the pericenter of the target planet, and the inclination deviation constraint.

[0030] The specific mathematical model is as follows: Let the velocity vector of the probe relative to Neptune before the glide be... The velocity vector of the target satellite (Triton) is The hyperbolic hypervelocity vector of the probe relative to the satellite's direction of approach is: ; The magnitude of the hyperbolic overspeed is the same before and after the leverage (only the direction changes): ; Leverage geometry is based on leverage radius multipliers. and the angle of plane B Description. The B-plane is a standard tool in space dynamics for describing the geometry of a hyperbolic flyby. The B-plane is perpendicular to the direction of the probe's asymptotic velocity relative to the celestial body; the angle of the B-plane. The orientation angle of vector B in the B plane is defined. This angle, combined with the leverage radius, can fully describe the spatial geometry of the probe as it flies past the satellite. Actual leverage radius. satisfy: ; in The radius of Triton is taken as 1353 km, and the radius of leverage is not less than the sum of the radius of the target satellite and the safe altitude: (This embodiment) =300km).

[0031] Using the eccentricity of the hyperbolic track and the angle of rotation for: ; ; in The gravitational constant of Triton is 1.428 × 10⁻⁶. 13 m 3 / s 2 ), .

[0032] Define a three-axis unit vector in the B-plane coordinate system. , , .in Along the direction of hyperbolic overspeed. Perpendicular to With satellite velocity vector The plane in which it is located Depend on and The cross product is obtained. Specifically, it is defined as: ; ; ; The hyperbolic overspeed vector after leveraging the force is By rotating within plane B, we obtain: ; The probe's velocity relative to Neptune after leveraging the glide path: ; The probe travels along a Keplerian orbit from the glide path to the pericenter of Neptune. The position vector of the glide path is... The flight time from the leverage point to the pericenter is The state at the pericenter is then obtained through Kepler propagation: ; in Neptune's gravitational constant The position and velocity at the pericenter are given. Kepler propagation refers to obtaining the position and velocity after a given flight time by solving Kepler's equations, given the gravitational constant of the celestial body, its initial position, and velocity.

[0033] Hyperbolic speed increase relative to the planet at pericentrism: ; The optimization model for S1 is: the first optimization variable objective function The constraints include: (Satellite-assisted safe altitude) (Safe altitude of planetary pericenter, in this embodiment) =100km) and tilt deviation ≤5°. Among them, The radius of the pericenter is Let be the magnitude of the velocity at the pericenter. After solving, the hyperbolic overspeed at the pericenter decreases to 8.15 km / s, and the tilt angle deviation decreases to approximately 3.2°, yielding the transfer trajectory for the leveraged capture segment (e.g., Figure 2 As shown, in this embodiment, the process from the probe entering Neptune's gravitational influence sphere, flying towards the pericenter with the gravitational assistance of Triton, to the point before capture at the pericenter, together with the subsequent capture segment, constitutes the Neptune capture segment trajectory.

[0034] S2: Design of the transfer trajectory for the capture segment The probe applies a deceleration pulse at the pericenter of the target planet, is captured by the target planet and enters a highly elliptical orbit, and applies a modulation pulse in the neighborhood of the apocenter of the highly elliptical orbit to adjust the pericenter altitude so that it can re-encounter the target satellite, thus obtaining the capture segment transfer trajectory.

[0035] In this embodiment, the deceleration pulse applied by the detector at the pericenter is a tangential deceleration pulse, and the modulation pulse is applied in the neighborhood of the distal point of the large elliptical orbit.

[0036] The transfer trajectory during the capture segment is obtained by solving the following optimization problem: The second optimization variables include the apocentric altitude of the probe in the highly elliptical orbit after capture, the total flight time from the pericentric capture to the re-encounter with the target satellite, and the time allocation factor used to determine the mid-course correction maneuver time; the objective function is to minimize the sum of the magnitudes of the pericentric deceleration pulse and the apocentric modulation pulse; the constraint condition is that the hyperbolic overspeed relative to the target satellite when the probe re-encounters the target satellite does not exceed a preset upper limit value.

[0037] The specific modeling is as follows: The second optimization variable is ,in Let the radius be the centroid. This refers to the total flight time from the moment of pericentrism capture to the moment of re-encounter with Triton. This is the time allocation factor. According to the laws of orbital dynamics, mid-course correction maneuvers with small velocity increments are located near the centroid. The range of values ​​is ∈[0.4,0.6]. In this embodiment, the specific meaning of "centroid neighborhood" is determined by the time allocation factor. The quantization is implemented in the range of [0.4, 0.6], meaning that the mid-course correction maneuver occurs within the first 40% to 60% of the total flight time from the pericenter to the re-encounter point. This range corresponds to the region near the apocenter in the probe's orbital arc. The transition time from the pericenter to the mid-course correction maneuver is: ; The transfer time from the mid-course correction maneuver to the re-encounter with the target satellite is: ; Proximal point capture pulse Calculated from the difference between the pericentric velocities of the hyperbola and the ellipse. Based on The state before the mid-course correction maneuver is obtained by performing Kepler integration. Then, the Lambert problem is solved based on the position of the mid-course correction maneuver and the position of the target satellite at the next leverage point to obtain the state after the mid-course correction maneuver and the hyperbolic overspeed relative to the target satellite. , To determine the target satellite, the required mid-course correction maneuver size is calculated based on its state before and after the maneuver. The Lambert problem refers to finding the velocity vector of a Kepler transfer orbit connecting two points, given two position vectors and flight time. It is a well-known technique in the field of aerospace dynamics.

[0038] The optimized model is: ; The constraint is the hyperbolic overspeed relative to Triton when the probe reaches its position. (The upper limit in this embodiment is 3.8 km / s).

[0039] This embodiment solves for the following: the velocity increment at the pericenter is 1.53 km / s, entering a highly elliptical orbit with a period of approximately 300 days. A modulation pulse of approximately 0.12 km / s is applied near the apocenter to adjust the pericenter altitude, enabling an encounter with Triton. The hyperbolic overspeed relative to Triton is 3.5 km / s (satisfying the upper limit constraint), thus obtaining the capture segment transfer trajectory. For example... Figure 2 As shown, in this embodiment, the highly elliptical orbit after pericentric capture, the trajectory of the apocentric modulation, and the trajectory of re-encountering Triton, together with the preceding gravitational assist capture segment, constitute the complete Neptune capture segment trajectory.

[0040] S3: Rapid screening of resonance ratio sequences Construct a candidate resonance ratio set, where the resonance ratio is the ratio of the orbital period of the probe to the orbital period of the target satellite; generate all finite resonance ratio sequences composed of elements in the candidate resonance ratio set; retain feasible sequences that satisfy the borrowing deflection angle constraint for each borrowing operation, the borrowing deflection angle constraint being determined by the minimum allowable borrowing height of the probe relative to the target satellite; among the feasible sequences that satisfy the constraint, select the resonance ratio sequence with the shortest total transfer time as the periodic sequence.

[0041] The numerical range of each resonance ratio in the candidate resonance ratio set is no greater than the preset maximum resonance ratio value (15 in this embodiment).

[0042] Define the orbital period of the detector Orbital period of Triton The ratio (approximately 5.877 days) is the resonance ratio: ; To simplify the solution, this embodiment uses an integer resonance ratio (i.e., The case where =1 corresponds to the candidate set of periodic resonance ratios. The invention will be illustrated using an example, but the method is not limited to integer resonance ratios; fractional resonance ratios are also possible. >1 corresponds to the candidate set of aperiodic resonance ratios. The same applies to the candidate set construction, sequence generation, leveraging deflection angle constraint screening, and shortest transfer time selection processes of this invention. The orbital period of the detector before its first resonance leveraging is denoted as... The target orbital period is denoted as The candidate set of periodic resonance ratios is defined as follows: ; in, The preset maximum resonance ratio is 15 in this embodiment. This is the orbital period (approximately 301 days) before the first encounter with Triton after capture. The target orbital period is (2:1 resonance, approximately 11.6 days).

[0043] The set of all possible finite resonance ratio sequences is defined as: ; in This represents the number of elements in the candidate resonance ratio set. Each sequence... Represents a possible resonance ratio sequence, each sequence having A resonance ratio, let Then there are a total of The segment leverages the transfer of resources.

[0044] Of these candidate sequences, only those that satisfy the borrowing deflection angle constraint in every borrowing attempt are retained. The borrowing deflection angle constraint is determined by the minimum allowable borrowing altitude of the probe relative to the target satellite (in this embodiment, the minimum safe borrowing altitude is 300 km). The feasible sequence set is defined as follows: ; For each feasible sequence The corresponding transfer time is: ; The resonance ratio sequence with the shortest transfer time selected from the set is the transfer sequence that satisfies the leverage angle constraint.

[0045] In this embodiment, the safe leverage altitude relative to Triton is considered to be 300 km. The orbital period of the probe before it re-encounters Triton after being captured by Neptune is 301 days. The target orbit is an orbit that forms a 2:1 resonance with Triton, with a period of approximately 11.6 days. Following the above-mentioned process of candidate set construction, sequence generation, leverage deflection angle constraint screening, and selection of the shortest transfer time, the resonance ratio sequence with the shortest transfer time is obtained as 9:1 – 4:1 – 3:1 – 2:1.

[0046] S4: Construction of Single Resonance Transfer Optimization Model Based on the single resonance ratio in the resonance-lowering segment, an optimized model for the transfer between two leverage operations is constructed.

[0047] The optimization model is as follows: the leverage radius, leverage plane angle B, and flight time of each transfer segment are the third optimization variables; the optimization objective is to minimize the mid-course correction maneuver speed increment applied at the mid-course correction maneuver time between two leverages; the constraints include: the deviation between the total flight time and the transfer time determined by S3 is within the allowable range, the deviation between the orbital period of the probe and the orbital period determined by S3 is within the allowable range, and the leverage radius of each leverage is not less than the leverage radius corresponding to the minimum allowable leverage altitude.

[0048] The total flight time between two leverage operations is allocated by a time scaling factor as the first transfer time from the leverage moment to the mid-course correction maneuver moment and the second transfer time from the mid-course correction maneuver moment to the next leverage moment.

[0049] For the Segment transition, the third optimization variable is ,in This is the total flight time for this segment. As a time scaling factor, For the first The radius of leverage for segment transfer, To leverage the angle of plane B. With the first The radius of leverage for segment transfer And leveraging the angle of plane B The angle of rotation after leveraging the force is determined for the variable, and then the velocity vector after leveraging the force is determined. Similarly, the first... Total flight time of the segment and time scaling factor Determine the timing of the mid-course correction maneuver, then solve the Lambert problem to obtain the state relative to the target satellite at the next leverage point. Establish an optimization model with the goal of minimizing the mid-course correction maneuver.

[0050] The optimization objective is: ; The constraints are: ; in The ideal transfer time is determined for S3. This is the actual orbital period of the probe. The probe orbit period determined for S3. This is the allowable deviation in transfer time (0.1 days in this embodiment). This is the allowable deviation of the orbital period (0.02 days in this embodiment). It is the minimum allowable radius for leveraging (in this embodiment, it is the radius of Haiwei-1 plus 300 km).

[0051] S5: Sequential solution for resonant orbit reduction segment The resonant orbit reduction segment is discretized into several sequentially connected leverage transfer segments (i.e., GTG, Gravity Turn to Gravity Turn, representing the transfer segment from one leverage to the next leverage). The optimization model constructed in S4 is used to solve the problem in the order of the periodic sequence to obtain the transfer trajectory of the resonant orbit reduction segment.

[0052] Specifically, the resonance-lowering segment is discretized into multiple leverage transfer segments. According to the order of the resonance ratios in the periodic sequence determined by S3, the optimization model constructed in S4 is called sequentially for solution. The end state of the previous transfer is used as the initial state of the next transfer.

[0053] This embodiment solves for each resonance orbit sequentially according to the sequence 9→4→3→2. Each segment yields the corresponding leverage parameters and mid-course correction maneuvers, with a total mid-course correction maneuver of approximately 0.08 km / s, resulting in the resonance orbit reduction segment transfer trajectory (e.g., ...). Figure 3 (As shown).

[0054] S6: Track splicing The transfer trajectory of the assisted capture segment, the capture segment transfer trajectory, and the resonance-induced orbit reduction segment transfer trajectory are spliced ​​together to obtain the complete transfer trajectory.

[0055] The splicing method is as follows: the end of the transfer trajectory of the leveraged capture segment connects with the beginning of the transfer trajectory of the capture segment at the pericenter of the target planet, and the end of the transfer trajectory of the capture segment connects with the beginning of the transfer trajectory of the resonance descent segment at the location where the probe and the target satellite first meet. Each segment is naturally continuous in position and velocity vectors, requiring no additional correction maneuvers.

[0056] Finally, the various track segments are spliced ​​together to obtain the complete capture and transfer trajectory (e.g., Figure 4 (As shown).

[0057] Therefore, this invention employs the aforementioned satellite gravity-assisted planetary system resonance orbit capture method. By introducing a satellite gravity-assisted pre-deflection of the approach velocity before planetary pericentrism capture, the capture velocity increment is effectively reduced. By establishing repeatable encounter conditions through small-amplitude modulation at the apocentrism, the traditional method of multiple large-amplitude braking is avoided. Through rapid screening and sequential optimization of the resonance ratio sequence, a complete transfer trajectory without additional correction maneuvers is achieved, with a total mid-course correction maneuver of approximately 0.08 km / s, significantly reducing propellant consumption. This method is suitable for low-energy capture and orbit reduction missions in planetary system exploration.

[0058] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for capturing resonant orbits of planetary systems based on satellite gravity assistance, characterized in that, Includes the following steps: S1. After the probe enters the gravitational influence sphere of the target planet, before reaching the pericenter of the target planet, the probe uses the gravitational assistance of the target satellite to reduce the hyperbolic speed of the probe relative to the target planet, and makes the inclination angle deviation between the orbital plane of the probe and the orbital plane of the target satellite no greater than a preset angle threshold, thus obtaining the transfer trajectory of the gravity-assisted capture segment. S2. The probe applies a deceleration pulse at the pericenter of the target planet, is captured by the target planet and enters a highly elliptical orbit, and applies a modulation pulse in the neighborhood of the apocenter of the highly elliptical orbit to adjust the pericenter altitude of the highly elliptical orbit so that it can meet the target satellite again, thus obtaining the capture segment transfer trajectory. S3. Construct a candidate resonance ratio set, where the resonance ratio is the ratio of the orbital period of the probe to the orbital period of the target satellite; generate all finite resonance ratio sequences composed of elements in the candidate resonance ratio set; retain feasible sequences that satisfy the borrowing deflection angle constraint for each borrowing operation, the borrowing deflection angle constraint being determined by the minimum allowable borrowing height of the probe relative to the target satellite; among the feasible sequences that satisfy the constraint, select the resonance ratio sequence with the shortest total transfer time as the periodic sequence; S4. Based on the single resonance ratio in the resonance-lowering segment, construct an optimization model for the transfer between two leverage operations; S5. Discretize the resonance-reducing trajectory segment into several sequentially connected leverage transfer segments, and solve the optimization model constructed in S4 in the order of the periodic sequence to obtain the transfer trajectory of the resonance-reducing trajectory segment. S6. The transfer trajectory of the leveraged capture segment, the transfer trajectory of the capture segment, and the transfer trajectory of the resonance descent segment are spliced ​​together to obtain the complete transfer trajectory.

2. The method according to claim 1, characterized in that, In S1, the process of the probe using the target satellite to achieve gravity assistance is described by two variables: the leverage radius multiplier and the leverage plane angle B. The optimization objective is to minimize the hyperbolic hypervelocity when the probe reaches the pericenter of the target planet, while satisfying the safety constraints of the probe's leverage altitude relative to the target satellite, the safety altitude constraint of the pericenter of the target planet, and the tilt deviation constraint.

3. The method according to claim 2, characterized in that, The lever radius of the probe relative to the target satellite is determined by the product of the lever radius multiplier and the radius of the target satellite, and the lever radius is not less than the sum of the radius of the target satellite and the safe altitude.

4. The method according to claim 1, characterized in that, In S2, the deceleration pulse applied by the detector at the pericenter is a tangential deceleration pulse, and the modulation pulse is applied in the neighborhood of the distal point of the highly elliptical orbit.

5. The method according to claim 1, characterized in that, The capture segment transfer trajectory is obtained by solving the following optimization problem: The second set of optimization variables includes: the apocenter altitude of the probe in its highly elliptical orbit after capture, the total flight time from capture at the pericenter to re-encounter with the target satellite, and the time allocation factor used to determine the timing of mid-course correction maneuvers. The objective function is to minimize the sum of the magnitudes of the near-center deceleration pulse and the far-center modulation pulse; The constraint is that when the detector encounters the target satellite again, the hyperbolic overspeed relative to the target satellite does not exceed a preset upper limit.

6. The method according to claim 1, characterized in that, In S4, the optimization model is specifically as follows: The leverage radius, leverage plane angle B, and flight time of each transfer segment are used as the third optimization variables; The optimization objective is to minimize the speed increment of the mid-course correction maneuver applied at the moment of mid-course correction maneuver between two leverage operations; The constraints include: the deviation between the total flight time and the transfer time determined by S3 is within the allowable range; the deviation between the orbital period of the probe and the orbital period determined by S3 is within the allowable range; and the leverage radius for each leverage operation is not less than the leverage radius corresponding to the minimum allowable leverage altitude.

7. The method according to claim 6, characterized in that, The total flight time between two leverage operations is allocated by a time scaling factor as the first transfer time from the leverage moment to the mid-course correction maneuver moment and the second transfer time from the mid-course correction maneuver moment to the next leverage moment.

8. The method according to claim 1, characterized in that, The numerical range of each resonance ratio in the candidate resonance ratio set is no greater than the preset maximum resonance ratio value.

9. The method according to claim 1, characterized in that, In S5, the resonance-lowering segment is discretized into multiple leverage transfer segments. According to the order of resonance ratios in the periodic sequence determined in S3, the optimization model constructed in S4 is called sequentially for sequential solution. The end state of the previous transfer is used as the initial state of the next transfer.

10. The method according to claim 1, characterized in that, In S6, the end of the transfer trajectory of the boost-assisted capture segment and the beginning of the transfer trajectory of the capture segment meet at the pericenter of the target planet, and the end of the transfer trajectory of the capture segment and the beginning of the transfer trajectory of the resonance descent segment meet at the position where the probe and the target satellite first meet.

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