Fast Design Method and System for the Transfer Orbit of the Sun-Earth L5 Libration Point

Abstract

The present invention provides a rapid design method and system for the transfer orbit of the Sun-Earth L5 libration point. Based on the heliocentric two-body orbit analytical model, the number of transfer loops, transfer time, and eccentricity of the transfer orbit are set, and the semi-major axis of the transfer orbit is calculated. According to the semi-major axis, eccentricity of the transfer orbit in step 1 and the orbital parameters of the Earth, the inclination of the transfer orbit is set, and the Earth zero-radius sphere of influence model is used to calculate the magnitude and direction of the hyperbolic excess velocity of the detector. It is set that the detector applies a braking impulse once when arriving at the L5 point, and the magnitude and direction of the impulse are calculated by using the transfer orbit parameters in steps 1-2. Taking the heliocentric two-body transfer orbit parameters calculated by the above steps as the initial value guess, the heliocentric multi-body orbit model is used to calculate the high-precision transfer orbit through iterative optimization. The method in the present invention realizes the trade-off among orbit accuracy, computational amount, and design efficiency, effectively reduces the number of iterations, reduces the computational amount, and ensures the robustness of numerical iteration.

Description

Technical Field

[0001] The present invention relates to the technical field of spacecraft orbit design and optimization, and particularly to a rapid design method and system for a transfer orbit of the Sun-Earth L5 libration point. Background Art

[0002] In recent years, due to its good stability, the L5 point of the Sun-Earth system has brought great application prospects, and related mission designs have become the focus of the aerospace engineering and application fields. The distance between the L5 point of the Sun-Earth system and the Earth is approximately 1 AU, and the nearby space environment is relatively ideal. Placing a detector at this point can obtain the advantage of a long baseline. By cooperating with near-Earth satellites, three-dimensional observations of the Sun can be achieved, and early warnings of the Earth's space environment can be carried out. At the same time, from the perspective of deep space exploration measurement and control, communication satellites can also be placed at the L5 point of the Sun-Earth system to serve deep space exploration. So far, several spacecraft have been launched to the L1 and L2 points of the Sun-Earth system, and the related research results are relatively rich. However, for the L5 point of the Sun-Earth system, there is not only less theoretical research, but also no spacecraft has reached this area in engineering. With the development of deep space exploration technology, the scientific value of the L5 point of the Sun-Earth system has become increasingly prominent, and its corresponding orbit design has become a hot topic.

[0003] Generally speaking, the degree of attention to the research on the transfer orbit of the L5 libration point of the Sun-Earth system is still insufficient, and the related research results are also relatively lacking, which does not match its important scientific value. Therefore, it is necessary to further study the transfer orbit of the L5 libration point of the Sun-Earth system to provide an effective orbit design scheme for its mission design.

[0004] At present, some research has been carried out on the mission design of the libration point of the three-body system. After retrieval, the main ones related to the transfer orbit design are as follows: The paper "Preliminary Design of a Solar Stereo Exploration Mission at the Sun-Earth L4 / L5 Points" (Space Electronic Technology, Vol. 4, 2018: 68-74) proposed a technical concept of deploying a detector at the L4 / L5 points of the Sun-Earth to carry out solar stereo exploration, evaluated the orbit transfer method and cost to reach the L5 point, and put forward the overall scheme concept of the detector. However, this literature focuses on the overall technology of the detector and does not discuss the transfer orbit design method.

[0005] The patent document with the publication number CN105912819A discloses a rapid design method for the Earth-Moon L1 Lagrangian point transfer orbit, belonging to the technical field of spacecraft orbit design and optimization, and includes the following steps: The detector applies the first maneuvering pulse at the ideal orbit insertion point of the target Halo orbit, and recursively calculates backward from the Halo orbit of the L1 Lagrangian point to the perilune position that meets the gravity assist constraint; The detector applies the second maneuvering pulse at the perilune and enters the Earth-Moon transfer orbit segment; The detector applies the third maneuvering pulse to finally achieve capture into the Earth parking orbit. Since the design method adopts the reverse integration strategy, the actual detector trajectory starts from the Earth and finally reaches the Halo orbit of the Earth-Moon L1 Lagrangian point. However, this patent document focuses on the design of the L1 point transfer orbit of the Earth-Moon system.

[0006] The patent document with the publication number CN105574261A discloses a design method for the Earth-Moon libration point transfer orbit with lunar gravity assist, belonging to the field of spacecraft orbit design and optimization. Select the position of the orbit insertion point of the target Halo orbit and the desired lunar gravity assist magnitude, and integrate the state variables of the orbit insertion point using Equation (1) until the spacecraft reaches the expected lunar gravity assist position. Use relevant optimization algorithms to correct and adjust the state variables of the orbit insertion point so that the state at the gravity assist position satisfies the constraint conditions of Equation (3), and then determine the magnitude of the maneuver velocity increment required for the spacecraft to enter the Halo orbit. By reasonably selecting parameters such as the lunar gravity assist constraint conditions and the orbit insertion point of the Halo orbit, a low-energy consumption transfer orbit that meets the mission requirements can be effectively designed. However, this patent document focuses on the design of the L2 point transfer orbit of the Earth-Moon system.

[0007] The patent document with the publication number CN104793613A discloses a method for rendezvous control between unstable libration point orbits of a spacecraft in the Sun-Earth system, including: determining the initial orbit, target orbit, and rendezvous process time for the spacecraft to rendezvous in the libration point orbit of the Sun-Earth system, and establishing a rendezvous dynamics model for the controlled spacecraft; Based on the established rendezvous dynamics model for the controlled spacecraft, establish a nonlinear optimal control problem; Use the symplectic numerical method to solve the nonlinear optimal control problem within a finite long time to obtain the co-state variables; Update the control input of the current sub-time interval using the obtained co-state variables, complete the dynamics simulation of one sub-time interval, and obtain the current spacecraft state variables using the navigation method; Progress the sub-time interval, use the current spacecraft terminal state as the initial state of the next sub-time interval, and repeat steps 302 to 400 in sequence until the rendezvous mission between the spacecraft in the unstable libration point orbits is completed. However, this patent document takes the Sun-Earth L1 / L2 points as the research object and focuses on the rendezvous control between orbits. Summary of the Invention

[0008] Aiming at the defects in the prior art, the purpose of the present invention is to provide a rapid design method and system for the transfer orbit of the Earth-Sun L5 libration point.

[0009] A rapid design method and system for the transfer orbit of the Earth-Sun L5 libration point provided by the present invention includes the following steps:

[0010] Step 1: Based on the heliocentric two-body orbit analytical model, set the number of transfer circles, transfer time and eccentricity of the transfer orbit, and calculate the semi-major axis of the transfer orbit;

[0011] Step 2: According to the semi-major axis, eccentricity of the transfer orbit in Step 1 and the orbital parameters of the Earth, set the inclination angle of the transfer orbit, and use the Earth zero-radius influence sphere model to calculate the magnitude and direction of the hyperbolic excess velocity of the detector;

[0012] Step 3: Set that the detector applies a braking pulse when reaching the L5 point, and calculate the magnitude and direction of the pulse using the transfer orbit parameters in Steps 1-2;

[0013] Step 4: Using the heliocentric two-body transfer orbit parameters calculated in Steps 1-3 as the initial value guesses, adopt the heliocentric multi-body orbit model, and calculate the high-precision transfer orbit through iterative optimization.

[0014] Preferably, Step 1 specifically includes the following steps:

[0015] Step 1.1: Set the position of the braking pulse at the perihelion or aphelion of the transfer orbit;

[0016] Step 1.2: Make a guess about the initial value of the semi-major axis of the transfer orbit, adopt the heliocentric two-body orbit model, and use the transfer time to calculate the heliocentric phase angle of the detector when reaching the pulse position;

[0017] Step 1.3: Construct a shooting equation.

[0018] Preferably, in Step 1.3, using the semi-major axis of the transfer orbit in Step 1 as the iterative variable, search and calculate the semi-major axis so that the phase angle deviation between the detector and the L5 point is zero, and converge to obtain the semi-major axis of the transfer orbit.

[0019] Preferably, Step 2 specifically includes the following steps:

[0020] Step 2.1: According to the semi-major axis and eccentricity of the transfer orbit calculated in Step 1, calculate the heliocentric distances of the aphelion and perihelion of the transfer orbit;

[0021] Step 2.2: According to the orbit of the Earth and the parameters of the aphelion and perihelion of the transfer orbit in Step 2.1, calculate the magnitude of the hyperbolic excess velocity of the detector;

[0022] Step 2.3: Determine the magnitude and direction of the hyperbolic excess velocity of the detector.

[0023] Preferably, in the said Step 2.3, according to the eccentricity and semi-major axis of the transfer orbit and the magnitude of the hyperbolic excess velocity of the detector in Step 2.2, calculate the angle between the hyperbolic excess velocity of the detector and the Earth's velocity, and at the same time calculate the other direction angle of the hyperbolic excess velocity according to the set transfer orbit inclination, and finally completely determine the magnitude and direction of the hyperbolic excess velocity of the detector.

[0024] Preferably, Step 3 specifically includes the following steps:

[0025] Step 3.1: After the detector arrives at the L5 point, apply a braking pulse once to make the detector enter the mission orbit;

[0026] Step 3.2: Calculate the magnitude and direction of the pulse.

[0027] Preferably, in the said Step 3.2, according to the mission orbit parameters and transfer orbit parameters, calculate the velocity difference at the pulse position, and then calculate the magnitude and direction of the pulse.

[0028] Preferably, Step 4 specifically includes the following steps:

[0029] Step 4.1: Use the above Steps 1 to 3 to completely determine the two-body parameters of the transfer orbit;

[0030] Step 4.2: Adopt a heliocentric multi-body orbit model to establish a heliocentric multi-body orbit shooting equation;

[0031] Step 4.3: Use the heliocentric two-body transfer orbit parameters in Step 4.1 as the initial value guess, and calculate the high-precision transfer orbit through iterative optimization.

[0032] Preferably, in the said Step 4.2, consider the gravitational effects of the main celestial bodies such as the sun, Jupiter, the Earth, and the moon.

[0033] The present invention also provides a rapid design system for a sun-earth L5 libration point transfer orbit, including the following modules:

[0034] Transfer orbit semi-major axis calculation module: Based on the heliocentric two-body orbit analytical model, set the number of transfer circles, transfer time, and transfer orbit eccentricity, and calculate the transfer orbit semi-major axis;

[0035] Detector hyperbolic excess velocity magnitude and direction calculation module: According to the transfer orbit semi-major axis, eccentricity, and the Earth's orbital parameters, set the transfer orbit inclination, and use the Earth zero-radius influence sphere model to calculate the magnitude and direction of the detector's hyperbolic excess velocity;

[0036] Pulse size and direction calculation module: It is set that the detector applies a braking pulse once when reaching the L5 point, and the size and direction of the pulse are calculated using the transfer orbit parameters.

[0037] High-precision transfer orbit calculation module: Using the calculated heliocentric two-body transfer orbit parameters as the initial value guess, adopting the heliocentric multi-body orbit model, and calculating the high-precision transfer orbit through iterative optimization.·

[0038] Compared with the prior art, the present invention has the following beneficial effects:

[0039] 1. The method in the present invention realizes the trade-off among orbit accuracy, calculation amount, and design efficiency;

[0040] 2. By adopting a simplified analytical orbit model, the present invention can quickly and effectively complete the optimization design of the initial solution of the transfer orbit;

[0041] 3. The present invention effectively reduces the number of iterations, reduces the calculation amount, and ensures the robustness of numerical iteration. Brief Description of the Drawings

[0042] By reading the detailed description of the non-restrictive embodiments with reference to the following drawings, other features, purposes, and advantages of the present invention will become more obvious:

[0043] Figure 1 It is the flowchart of the method of the present invention;

[0044] Figure 2 It is the motion trajectory in the XY plane of the heliocentric rotating coordinate system in the specific embodiment;

[0045] Figure 3 It is the three-dimensional motion trajectory of the heliocentric rotating coordinate system in the specific embodiment. Specific Embodiment

[0046] The present invention will be described in detail below with reference to specific embodiments. The following embodiments will help those skilled in the art to further understand the present invention, but do not limit the present invention in any form. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present invention, several changes and improvements can still be made. These all belong to the protection scope of the present invention.

[0047] As Figure 1 shown, a fast design method and system for the heliocentric L5 libration point transfer orbit provided by the present invention includes the following steps:

[0048] Step 1: Based on the heliocentric two-body orbit analytical model, set the number of transfer circles, transfer time, and eccentricity of the transfer orbit, and calculate the semi-major axis of the transfer orbit. Step 1 specifically includes the following steps:

[0049] Step 1.1: Set the braking pulse position at the perihelion or aphelion of the transfer orbit;

[0050] Step 1.2: Make a guess at the initial value of the semi-major axis of the transfer orbit. Using the heliocentric two-body orbit model, calculate the heliocentric phase angle of the detector when it reaches the pulse position using the transfer time;

[0051] Step 1.3: Construct a shooting equation. In Step 1.3, use the semi-major axis of the transfer orbit in Step 1 as the iteration variable, search and calculate the semi-major axis such that the phase angle deviation between the detector and the L5 point is zero, and converge to obtain the semi-major axis of the transfer orbit.

[0052] Step 2: According to the semi-major axis, eccentricity of the transfer orbit in Step 1 and the orbital parameters of the Earth, set the inclination of the transfer orbit. Using the Earth zero-radius influence sphere model, calculate the magnitude and direction of the hyperbolic excess velocity of the detector. Step 2 specifically includes the following steps:

[0053] Step 2.1: According to the semi-major axis and eccentricity of the transfer orbit calculated in Step 1, calculate the heliocentric distances at the aphelion and perihelion of the transfer orbit;

[0054] Step 2.2: According to the orbit of the Earth and the parameters of the aphelion and perihelion of the transfer orbit in Step 2.1, calculate the magnitude of the hyperbolic excess velocity of the detector;

[0055] Step 2.3: Determine the magnitude and direction of the hyperbolic excess velocity of the detector. In Step 2.3, according to the eccentricity, semi-major axis of the transfer orbit and the magnitude of the hyperbolic excess velocity of the detector in Step 2.2, calculate the angle between the hyperbolic excess velocity of the detector and the Earth's velocity. At the same time, calculate the other direction angle of the hyperbolic excess velocity according to the set inclination of the transfer orbit, and finally completely determine the magnitude and direction of the hyperbolic excess velocity of the detector.

[0056] Step 3: Set the detector to apply a braking pulse when it reaches the L5 point, and calculate the magnitude and direction of this pulse using the transfer orbit parameters in Steps 1 - 2. Step 3 specifically includes the following steps:

[0057] Step 3.1: After the detector reaches the L5 point, apply a braking pulse to make the detector enter the mission orbit;

[0058] Step 3.2: Calculate the magnitude and direction of the pulse. In Step 3.2, according to the mission orbit parameters and transfer orbit parameters, calculate the velocity difference at the pulse position, and then calculate the magnitude and direction of the pulse.

[0059] Step 4: Using the heliocentric two-body transfer orbit parameters calculated in Steps 1 - 3 as the initial value guess, adopt the heliocentric multi-body orbit model, and calculate the high-precision transfer orbit through iterative optimization. Step 4 specifically includes the following steps:

[0060] Step 4.1: Use the above Steps 1 to 3 to completely determine the two-body parameters of the transfer orbit.

[0061] Step 4.2: Adopt a heliocentric multi-body orbit model to establish a heliocentric multi-body orbit shooting equation.

[0062] Step 4.3: Use the heliocentric two-body transfer orbit parameters in Step 4.1 as the initial value guess, and calculate a high-precision transfer orbit through iterative optimization. In Step 4.2, consider the gravitational effects of the main celestial bodies such as the sun, Jupiter, the earth, and the moon.

[0063] The present invention also provides a rapid design system for a sun-earth L5 libration point transfer orbit, including the following modules:

[0064] Semi-major axis calculation module of the transfer orbit: Based on the heliocentric two-body orbit analytical model, set the number of transfer circles, transfer time, and eccentricity of the transfer orbit, and calculate the semi-major axis of the transfer orbit.

[0065] Hyperbolic excess velocity magnitude and direction calculation module of the detector: According to the semi-major axis, eccentricity of the transfer orbit, and the orbital parameters of the earth, set the inclination of the transfer orbit, and use the earth zero-radius influence sphere model to calculate the hyperbolic excess velocity magnitude and direction of the detector.

[0066] Pulse magnitude and direction calculation module: Set that the detector applies a braking pulse when arriving at the L5 point, and calculate the magnitude and direction of the pulse using the transfer orbit parameters.

[0067] High-precision transfer orbit calculation module: Use the calculated heliocentric two-body transfer orbit parameters as the initial value guess, adopt the heliocentric multi-body orbit model, and calculate a high-precision transfer orbit through iterative optimization.

[0068] The following is a numerical simulation verification of a rapid design method for a sun-earth L5 libration point transfer orbit: The simulation calculation results are as shown in the Figure 2 and Figure 3 , which respectively give the XY plane and three-dimensional motion trajectories in the sun-earth rotating coordinate system.

[0069] From the perspective of orbit design, the present invention focuses on the establishment of relevant orbit models and algorithm design. The present invention uses an analytical orbit model for preliminary design, obtains the optimal transfer orbit under the conditions of meeting constraints such as transfer time and number of transfer circles, then uses this initial solution as the initial value guess for the high-precision solution, constructs a shooting equation in the sense of a multi-body orbit model, and finally obtains a high-precision optimal transfer orbit through numerical iteration, which can provide a rapid and high-precision design method for the design of a sun-earth L5 libration point transfer orbit.

[0070] The method in the present invention realizes the trade-off among orbital accuracy, computational amount and design efficiency. By adopting a simplified analytical orbit model, the optimal design of the initial solution of the transfer orbit can be completed quickly and effectively. Then, taking this solution as the initial value guess of the high-precision multi-body model can effectively reduce the number of iterations, reduce the computational amount, and ensure the robustness of the numerical iteration.

[0071] The specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the above specific embodiments, and those skilled in the art can make various changes or modifications within the scope of the claims, which does not affect the essence of the present invention. Without conflict, the embodiments of the present application and the features in the embodiments can be combined with each other arbitrarily.

Claims

1. A rapid design method for the transfer orbit of the Sun-Earth L5 libration point, characterized in that, it includes the following steps: Step 1: Based on the heliocentric two-body orbit analytical model, set the number of transfer circles, transfer time and eccentricity of the transfer orbit, and calculate the semi-major axis of the transfer orbit; Step 2: According to the semi-major axis, eccentricity of the transfer orbit in Step 1 and the orbital parameters of the Earth, set the inclination of the transfer orbit, and use the Earth zero-radius influence sphere model to calculate the magnitude and direction of the hyperbolic excess velocity of the detector; Step 3: Set that the detector applies a braking pulse when reaching the L5 point, and calculate the magnitude and direction of this pulse using the transfer orbit parameters in Steps 1-2; Step 4: Take the heliocentric two-body transfer orbit parameters calculated in Steps 1-3 as the initial value guess, and use the heliocentric multi-body orbit model to calculate the high-precision transfer orbit through iterative optimization.

2. The rapid design method for the transfer orbit of the Sun-Earth L5 libration point according to claim 1, characterized in that, the specific steps of Step 1 are as follows: Step 1.1: Set the braking pulse position at the perihelion or aphelion of the transfer orbit; Step 1.2: Make a guess on the initial value of the semi-major axis of the transfer orbit, use the heliocentric two-body orbit model, and calculate the heliocentric phase angle of the detector when reaching the pulse position using the transfer time; Step 1.3: Construct a shooting equation.

3. The rapid design method for the transfer orbit of the Sun-Earth L5 libration point according to claim 2, characterized in that, in Step 1.3, taking the semi-major axis of the transfer orbit in Step 1 as the iterative variable, search and calculate the semi-major axis so that the phase angle deviation between the detector and the L5 point is zero, and converge to obtain the semi-major axis of the transfer orbit.

4. The rapid design method for the transfer orbit of the Sun-Earth L5 libration point according to claim 1, characterized in that, the specific steps of Step 2 are as follows: Step 2.1: According to the semi-major axis and eccentricity of the transfer orbit calculated in Step 1, calculate the heliocentric distances of the aphelion and perihelion of the transfer orbit; Step 2.2: According to the orbit of the Earth and the parameters of the aphelion and perihelion of the transfer orbit in Step 2.1, calculate the magnitude of the hyperbolic excess velocity of the detector; Step 2.3: Determine the magnitude and direction of the hyperbolic excess velocity of the detector.

5. The rapid design method for the transfer orbit of the Sun-Earth L5 libration point according to claim 4, characterized in that, in Step 2.3, according to the eccentricity, semi-major axis of the transfer orbit and the magnitude of the hyperbolic excess velocity of the detector in Step 2.2, calculate the angle between the hyperbolic excess velocity of the detector and the Earth's velocity, and at the same time calculate the other direction angle of the hyperbolic excess velocity according to the set inclination of the transfer orbit, and finally completely determine the magnitude and direction of the hyperbolic excess velocity of the detector.

6. The rapid design method for the transfer orbit of the Sun-Earth L5 libration point according to claim 1, characterized in that, the specific steps of Step 3 are as follows: Step 3.1: After the detector reaches the L5 point, apply a braking pulse to make the detector enter the mission orbit; Step 3.2: Calculate the magnitude and direction of the pulse.

7. The rapid design method for the transfer orbit of the Sun-Earth L5 libration point according to claim 6, characterized in that, In step 3.2, according to the mission orbit parameters and the transfer orbit parameters, calculate the velocity difference at the pulse position, and then calculate the magnitude and direction of the pulse.

8. The rapid design method for the Sun-Earth L5 libration point transfer orbit according to claim 1, wherein, step 4 specifically includes the following steps: Step 4.1: Use the above steps 1 to 3 to completely determine the two-body parameters of the transfer orbit; Step 4.2: Adopt a heliocentric multi-body orbit model to establish a heliocentric multi-body orbit shooting equation; Step 4.3: Use the heliocentric two-body transfer orbit parameters in step 4.1 as the initial value guess, and calculate the high-precision transfer orbit through iterative optimization.

9. The rapid design method for the Sun-Earth L5 libration point transfer orbit according to claim 8, wherein, in step 4.2, consider the gravitational effects of the Sun, Jupiter, the Earth, and the Moon.

10. A rapid design system for the Sun-Earth L5 libration point transfer orbit, wherein, it includes the following modules: Transfer orbit semi-major axis calculation module: Based on the heliocentric two-body orbit analytical model, set the number of transfer orbits, transfer time, and transfer orbit eccentricity, and calculate the transfer orbit semi-major axis; Detector hyperbolic excess velocity magnitude and direction calculation module: According to the transfer orbit semi-major axis, eccentricity, and the Earth's orbit parameters, set the transfer orbit inclination angle, and use the Earth zero-radius influence sphere model to calculate the detector's hyperbolic excess velocity magnitude and direction; Pulse magnitude and direction calculation module: Set that the detector applies a braking pulse when arriving at the L5 point, and calculate the magnitude and direction of this pulse using the transfer orbit parameters; High-precision transfer orbit calculation module: Use the calculated heliocentric two-body transfer orbit parameters as the initial value guess, adopt the heliocentric multi-body orbit model, and calculate the high-precision transfer orbit through iterative optimization.

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