Transfer orbit design method and system for a circumlunar highly elliptical frozen orbit

Abstract

The application discloses a transfer orbit design method and system of a lunar orbit large ellipse frozen orbit based on eccentricity vector targeting. The transfer orbit lifting type is determined in advance in a transfer stage, the transfer orbit is selected as a lifting orbit, launching and arriving are lifted, the lunar orbit is ensured as a large ellipse frozen orbit with a far point above the south hemisphere of the moon, the eccentricity vector targeting is used to generate a transfer orbit meeting task constraints, the near point amplitude angle is adjusted near the far point after the moon is captured, the lunar orbit large ellipse frozen orbit is efficiently generated, and finally, a pulse is applied at the near point according to task requirements to transfer to a large ellipse frozen orbit with a required period.

Description

Technical Field

[0001] This invention relates to the field of transfer orbit design technology for a highly elliptical frozen orbit around the moon, and more specifically, to a transfer orbit design method for designing a lunar transfer orbit starting from perigee and running to a highly elliptical frozen orbit around the moon. Background Technology

[0002] Communication conditions between Earth and the far side of the Moon and the polar regions are poor, and relying solely on tracking and control stations on Earth is insufficient to meet the complex needs of future lunar exploration. Therefore, a lunar communication, navigation, and remote sensing system is needed to provide relay communication, navigation, and remote sensing services for users on the lunar surface and in lunar orbit. A highly elliptical frozen orbit around the Moon has become the core of current lunar polar exploration and the establishment of lunar research stations. However, there is currently no research on a trajectory scheme that starts from perigee and designs a Moon-Earth transfer orbit to reach a highly elliptical frozen orbit around the Moon. Furthermore, there are currently four types of ascent and descent orbits for Moon-Earth transfer orbit design, requiring analysis and selection of a suitable one. Using the eccentricity vector target method to solve for the Moon-Earth transfer orbit allows for pre-designing the orbit for descent launch and descent arrival. Summary of the Invention

[0003] The technical problem to be solved by this invention is how to efficiently generate large elliptical frozen orbits.

[0004] The present invention solves the above-mentioned technical problems through the following technical means:

[0005] A transfer orbit design method based on eccentricity vector target design for a lunar highly elliptical frozen orbit is used to design a lunar transfer orbit starting from perigee and run to a lunar highly elliptical frozen orbit, including the following steps:

[0006] Step 1: Define the geocentric inertial coordinate system and the lunar orbital coordinate system, set the perigee time, transfer time, perigee radius, geocentric inertial system inclination, lunar perigee radius, lunar orbital coordinate system inclination, and select the ascent and descent orbit types for the Earth departure segment and the Moon arrival segment.

[0007] Step 2: In the geocentric inertial frame, read the ephemeris to obtain the Moon's position and right ascension and declination at the perigee. Calculate the right ascension of the ascending node and the argument of perigee of the Earth-Moon transfer orbit. Calculate the semi-major axis, eccentricity, and true anomaly at the perigee of the Earth-Moon transfer orbit. This determines the orbital parameters of the starting orbit from the geocentric point, obtains the initial value of the eccentricity vector in the geocentric segment, and calculates the position and velocity of the Earth-Moon transfer orbit at the Moon's sphere of influence. Then, transfer the position and velocity to the lunar orbital coordinate system to obtain the initial value of the eccentricity vector in the lunar orbital segment.

[0008] Step 3: Calculate the time, position, and velocity of the Earth-centered starting orbit to the Moon's influence sphere in the Earth-centered inertial frame based on the eccentricity vector of the Earth-centered segment. Calculate the position and velocity of the Moon-centered arrival orbit after a certain time in the lunar orbit coordinate system based on the eccentricity vector of the lunar segment. Then, switch the state to the Earth-centered inertial frame, calculate the position and velocity tolerances, iterate through the eccentricity vectors of the Earth-centered and lunar segments, and use the results from the initial calculations as initial values ​​to solve using a high-precision model to obtain a complete Earth-Moon transfer orbit that satisfies the mission constraints.

[0009] Step 4: Fix the perigee altitude and inclination of the lunar capture orbit, calculate the capture orbit period, and enter the lunar capture orbit;

[0010] Step 5: Fix the lunar periapsis argument, inclination, and lunar periapsis altitude of the target orbit. Adjust the lunar periapsis argument at the apoapsis to obtain a large elliptical frozen orbit around the moon. Finally, apply pulses at the lunar periapsis to transfer the target orbit to the large elliptical frozen orbit with the required period, as needed for the mission.

[0011] Furthermore, in step one, the following is performed:

[0012] Step 1.1: Define the geocentric inertial coordinate system and the lunar orbital plane coordinate system;

[0013] In a geocentric inertial frame of reference, the X-axis represents the direction of the line connecting Earth and the Moon as the probe enters the Moon, the Z-axis represents the direction of the normal to the Moon's orbit, and the Y-axis is determined by the right-hand rule; in the lunar orbit coordinate system, xy The plane is the celestial plane. x The axis is the intersection of the lunar orbit plane and the lunar equatorial plane. z The direction of the white path plane;

[0014] Step 1.2: Calculate the perigee time to determine the type of ascending and descending orbit;

[0015] The perigee time of the Earth-Moon transfer orbit can be calculated using the perigee time and transfer time of the Earth-Moon transfer orbit;

[0016] Based on the launch site location, a descending launch orbit was selected; considering that the target of the probe is the lunar south pole, the lunar orbit is designed as a highly elliptical frozen orbit with the apogee above the lunar southern hemisphere, so a descending arrival orbit was selected; the launch and arrival orbits of the Earth-Moon transfer orbit are descending launch and descending arrival orbits.

[0017] Furthermore, in step two, the following is performed:

[0018] Step 2.1: Define the two-body model;

[0019] The dual-body model uses the lunar sphere of influence as the boundary. When the probe moves within the lunar sphere of influence, only the gravitational pull of the Moon's center is considered. After leaving the sphere of influence, it is only subject to the gravitational pull of the Earth's center. The Earth-Moon transfer orbit is divided into a geocentric segment and a lunar-centric segment, which are calculated separately using the lunar sphere of influence as the boundary.

[0020] Step 2.2: Calculate the initial value of the eccentricity vector of the geocentric segment;

[0021] Eccentricity vector e The calculation formula is

[0022] (1)

[0023] In the formula μ For gravitational parameters, r , v Let the position and velocity vectors of the probe be the vectors at any given moment; by solving for the vectors at any point on the orbit... r and v The eccentricity vector of the orbit can then be obtained, and the state vector can be solved by the orbital parameters;

[0024] By reading the ephemeris to obtain the Moon's position in the geocentric inertial frame at the moment of perigee, the right ascension and declination of the Moon's position can be obtained. Based on the right ascension and declination, the right ascension of the ascending node and the argument of perigee of the transfer orbit can be approximated using a spherical triangle. Other orbital parameters of the Earth-Moon transfer orbit are then solved using the target-shooting method: based on the perigee radius of the Earth-Moon transfer orbit... r pE Transfer time t Trans and the radius of the perigee r pM Assuming the perigee lies on the extension of the lunar position vector, the initial value of the orbital apogee radius is given as...

[0025] (2)

[0026] In the formula r aE The apogee radius;

[0027] The apogee radius of the transfer trajectory is determined by firing at the target; the firing equation is as follows:

[0028] (3)

[0029] (4)

[0030] (5)

[0031] (6)

[0032] (7)

[0033] In the formula, the true nearest point angle f f It can be derived from the angle of the near point. M f Calculations show that r f This represents the orbital radius at the perigee, and the target is... fvec Minimum; find the apogee radius r aE Then, using the above formula, the semi-major axis of the Earth-Moon transfer orbit can be obtained. a E eccentricity e E and the true periapsis at the moment of near-lunar point f f This yields a set of orbital parameters, which are converted into position and velocity vectors, and initial values ​​for the geocentric segment eccentricity vector. e E0 It can be calculated;

[0034] Step 2.3: Calculate the initial value of the eccentricity vector of the lunar segment;

[0035] The state vector at the point of lunar influence is obtained by recursively calculating the orbital parameters. The above calculations were performed in a geocentric inertial frame. This state vector is then transferred to the lunar orbital plane coordinate system to calculate the initial value of the eccentricity vector at the lunar center. e M0 .

[0036] Furthermore, in step three, the following is performed:

[0037] Step 3.1: Based on the eccentricity vector of the geocentric segment, calculate the time and position velocity when the object reaches the lunar influence sphere;

[0038] Calculate the orbital parameters at the pericenter based on the eccentricity vector:

[0039] First, calculate the right ascension and declination of the pericentrism.

[0040] (8)

[0041] (9)

[0042] In the formula e x , e y , e z for e The directional components; the right ascension and argument of the ascending node can be obtained from the right ascension and declination;

[0043] The magnitude of the eccentricity vector is equal to the eccentricity. Substituting the perigee radius and eccentricity of the geocentric segment of the orbit into formulas (3) and (4) yields the semi-major axis.

[0044] After obtaining the orbital parameters of the geocentric segment based on the eccentricity vector of the geocentric segment, the time taken for the orbit to reach the lunar sphere of influence can be calculated. t P and position-velocity vectors;

[0045] Step 3.2: Calculate the position and velocity over a certain period of time by using the eccentricity vector of the lunar segment.

[0046] The lunar orbital parameters for the lunar center segment can be obtained from the eccentricity vector of the lunar center segment, and the orbital parameters can be calculated by working backwards for a certain period of time. t M = t trans - t P The position and velocity vectors at the orbital splicing point are obtained, and the state vector in the lunar orbit coordinate system is converted into the state vector in the geocentric inertial system.

[0047] Step 3.3: Solve the lunar transfer orbit by splicing conic sections using target shooting, and use the target shooting solution as the initial value to solve the problem using a high-precision model.

[0048] The initial value of the geocentric segment eccentricity vector obtained from steps 2.2 and 2.3. e E0 Initial value of the eccentricity vector of the lunar segment e M0 As the initial value for target shooting, the difference between the position and velocity vectors is obtained by calculating steps 3.1 and 3.2. The target shooting iterates the eccentricity vectors of the geocentric segment and the lunar eccentricity vector until the position and velocity tolerances are met. The target shooting solution is used as the initial value to solve the problem using a high-precision model, and finally a complete Earth-Moon transfer orbit that meets the mission constraints is obtained.

[0049] Furthermore, in step four, the following is performed:

[0050] Step 4.1: Determine the capture orbit period T ;

[0051] To ensure the stability of the capture orbit, it must be within the lunar sphere of influence, and the capture orbit period must be no more than 6 days.

[0052] After successful capture, in order to ensure that the probe can operate on orbit for a period of time without hitting the moon in the event of a malfunction that prevents subsequent orbit changes, the maximum capture orbit period is 4 days, provided that the probe does not hit the moon for 60 days.

[0053] After entering the capture orbit, the probe will transfer to a highly elliptical frozen orbit, requiring orbit adjustment at the apogee. The longer the capture orbit period, the lower the velocity at the apogee, and the smaller the velocity increment required for orbit adjustment at the apogee. Therefore, the capture orbit period should be as large as possible.

[0054] Lunar braking capture needs to take into account the actual orbit control speed increment deviation, and the capture speed increment needs to leave a certain margin to ensure that it can be captured in a stable orbit;

[0055] After comprehensive consideration, the capture orbit period was chosen to be 3 days;

[0056] Step 4.2: Calculate the lunar capture orbit parameters;

[0057] Capture orbit semi-major axis a c for

[0058] (10)

[0059] The eccentricity can be calculated using formulas (3) and (4). The right ascension of the ascending node is 0 and has no effect. The argument of the near point is obtained based on time.

[0060] The lunar perigee altitude and inclination of the lunar capture orbit are determined by the Earth-Moon transfer orbit.

[0061] Furthermore, in step five, the following is performed:

[0062] Step 5.1: Adjust the near-lunar maneuver to change the lunar phase angle;

[0063] The far-moon maneuver involves adjusting the perihelion angle of the lunar capture orbit while simultaneously adjusting the orbital inclination to the required angle, thereby obtaining a highly elliptical frozen orbit for the target.

[0064] Due to the dynamics of the Earth-Moon space, the perilune argument of the Earth-Moon transfer orbit varies between 120° and 150° when it reaches the lunar perigee, making it impossible to directly reach the 90° perilune argument required for a highly elliptical frozen orbit. Adjusting the perilune argument through mid-course maneuvers during the Earth-Moon transfer would require a significant velocity increment, making it impractical. Therefore, the orbital argument adjustment was chosen after lunar capture.

[0065] The perilune argument is an in-plane orbital parameter. Based on the Gaussian perturbation equation, the orbital changes are performed at different true anomalies under unit perturbation acceleration on the lunar orbit formed after capture. Adjusting the perilune argument near the apogee is the most efficient.

[0066] Step 5.2: Calculate the frozen orbit of the large ellipse;

[0067] Orbital adjustments were made near the apogee to generate a highly elliptical frozen orbit with a period of 12 hours, with the adjustment target being the perigee argument. ω F ,inclination i F and the height of the perilune h pF ;

[0068] In the two-body configuration, a trajectory change is performed at a certain point on the capture trajectory to reach the target trajectory. ω F , i F and h pF Given the given information, the orbital elements of the target orbit can be determined through spatial geometric relationships. The change position and velocity increment under two-body conditions can be calculated analytically. The calculation process is as follows:

[0069] The position and velocity vector of the orbital change point can be obtained; the radius, right ascension, and declination of that position can be calculated to determine whether it is within the range of the target inclination angle, and the right ascension of the ascending node of the target orbit can be obtained. Ω F And true near point angle f F ;according to

[0070] (11)

[0071] (12)

[0072] The eccentricity of the target frozen orbit can be calculated. e F and semi-major axis a F for

[0073] (13)

[0074] (14)

[0075] In the formula r 0 represents the radius of the trajectory change point. At this point, a set of trajectory parameters for the frozen trajectory are obtained, and the velocity vector of the trajectory at the trajectory change point is calculated. By subtracting the velocity vector at the trajectory change point of the captured trajectory, the trajectory change velocity increment can be obtained. By selecting a suitable trajectory change point to minimize the consumption of the trajectory change velocity increment, and optimizing it under a high-precision model, the optimal trajectory change position and trajectory change velocity increment are determined.

[0076] Finally, to obtain a highly elliptical frozen orbit with a given period, a pulse is applied at the lunar perihelion, and the highly elliptical frozen orbit with the target period is obtained by a target-shooting method.

[0077] Corresponding to the above method, the present invention also provides a transfer orbit design system for a lunar highly elliptical frozen orbit based on eccentricity vector target shooting, used to design an Earth-Moon transfer orbit starting from perigee and run to a lunar highly elliptical frozen orbit, including:

[0078] Earth-Moon Transfer Orbit Input Module: Used to define the geocentric inertial coordinate system and the lunar orbital coordinate system, set the perigee time, transfer time, perigee radius, geocentric inertial system inclination, lunar perigee radius, lunar orbital coordinate system inclination, and select the ascent and descent orbit types for the Earth departure segment and the Moon arrival segment.

[0079] The eccentricity vector initial value calculation module is used to read the ephemeris in the geocentric inertial frame to obtain the position, right ascension, and declination of the Moon at the perigee, calculate the right ascension of the ascending node and the argument of perigee of the Earth-Moon transfer orbit, and calculate the semi-major axis, eccentricity, and true anomaly at the perigee of the Earth-Moon transfer orbit, thereby determining the orbital parameters of the Earth-centric starting orbit, obtaining the initial value of the eccentricity vector in the geocentric segment, and calculating the position and velocity of the Earth-Moon transfer orbit when it reaches the Moon's sphere of influence. The position and velocity are then transferred to the lunar orbital plane coordinate system to obtain the initial value of the eccentricity vector in the lunar orbital segment.

[0080] The Earth-Moon transfer orbit calculation module is used to calculate the time, position, and velocity of the Earth-centered starting orbit to the Moon's influence sphere in the Earth-centered inertial frame based on the eccentricity vector of the Earth-centered segment. In the lunar orbit coordinate system, it calculates the position and velocity of the Moon-centered arrival orbit after a certain period of travel based on the eccentricity vector of the Moon-centered segment. The module then switches the state to the Earth-centered inertial frame to calculate the position and velocity tolerances. It iterates through the eccentricity vectors of the Earth-centered and Moon-centered segments, and uses the results of the iteration as initial values ​​to solve the problem using a high-precision model to obtain a complete Earth-Moon transfer orbit that meets the mission constraints.

[0081] Lunar capture orbit calculation module: used to fix the perigee altitude and inclination of the lunar capture orbit, calculate the capture orbit period, and enter the lunar capture orbit;

[0082] The large elliptical frozen orbit calculation module: fixes the lunar periapsis argument, inclination, and lunar periapsis altitude of the target orbit, adjusts the lunar periapsis argument at the apoapsis, and obtains a large elliptical frozen orbit around the moon; finally, according to mission requirements, pulses are applied at the lunar periapsis to transfer to a large elliptical frozen orbit with the required period.

[0083] Furthermore, the following is executed in the Earth-Moon transfer orbit input module:

[0084] Step 1.1: Define the geocentric inertial coordinate system and the lunar orbital plane coordinate system;

[0085] In a geocentric inertial frame of reference, the X-axis represents the direction of the line connecting Earth and the Moon as the probe enters the Moon, the Z-axis represents the direction of the normal to the Moon's orbit, and the Y-axis is determined by the right-hand rule; in the lunar orbit coordinate system, xy The plane is the celestial plane. x The axis is the intersection of the lunar orbit plane and the lunar equatorial plane. z The direction of the white path plane;

[0086] Step 1.2: Calculate the perigee time to determine the type of ascending and descending orbit;

[0087] The perigee time of the Earth-Moon transfer orbit can be calculated using the perigee time and transfer time of the Earth-Moon transfer orbit;

[0088] Based on the launch site location, a descending launch orbit was selected; considering that the target of the probe is the lunar south pole, the lunar orbit is designed as a highly elliptical frozen orbit with the apogee above the lunar southern hemisphere, so a descending arrival orbit was selected; the launch and arrival orbits of the Earth-Moon transfer orbit are descending launch and descending arrival orbits.

[0089] Furthermore, the following is executed in the eccentricity vector initial value calculation module:

[0090] Step 2.1: Define the two-body model;

[0091] The dual-body model uses the lunar sphere of influence as the boundary. When the probe moves within the lunar sphere of influence, only the gravitational pull of the Moon's center is considered. After leaving the sphere of influence, it is only subject to the gravitational pull of the Earth's center. The Earth-Moon transfer orbit is divided into a geocentric segment and a lunar-centric segment, which are calculated separately using the lunar sphere of influence as the boundary.

[0092] Step 2.2: Calculate the initial value of the eccentricity vector of the geocentric segment;

[0093] Eccentricity vector e The calculation formula is

[0094] (1)

[0095] In the formula μ For gravitational parameters, r , v Let the position and velocity vectors of the probe be the vectors at any given moment; by solving for the vectors at any point on the orbit... r and v The eccentricity vector of the orbit can then be obtained, and the state vector can be solved by the orbital parameters;

[0096] By reading the ephemeris to obtain the Moon's position in the geocentric inertial frame at the moment of perigee, the right ascension and declination of the Moon's position can be obtained. Based on the right ascension and declination, the right ascension of the ascending node and the argument of perigee of the transfer orbit can be approximated using a spherical triangle. Other orbital parameters of the Earth-Moon transfer orbit are then solved using the target-shooting method: based on the perigee radius of the Earth-Moon transfer orbit... r pE Transfer time t Trans and the radius of the perigee r pM Assuming the perigee lies on the extension of the lunar position vector, the initial value of the orbital apogee radius is given as...

[0097] (2)

[0098] In the formula r aE The apogee radius;

[0099] The apogee radius of the transfer trajectory is determined by firing at the target; the firing equation is as follows:

[0100] (3)

[0101] (4)

[0102] (5)

[0103] (6)

[0104] (7)

[0105] In the formula, the true nearest point angle f f It can be derived from the angle of the near point. M f Calculations show that r f This represents the orbital radius at the perigee, and the target is... fvec Minimum; find the apogee radius r aE Then, using the above formula, the semi-major axis of the Earth-Moon transfer orbit can be obtained. a E eccentricity e E and the true periapsis at the moment of near-lunar point f f This yields a set of orbital parameters, which are converted into position and velocity vectors, and initial values ​​for the geocentric segment eccentricity vector. e E0 It can be calculated;

[0106] Step 2.3: Calculate the initial value of the eccentricity vector of the lunar segment;

[0107] The state vector at the point of lunar influence is obtained by recursively calculating the orbital parameters. The above calculations were performed in a geocentric inertial frame. This state vector is then transferred to the lunar orbital plane coordinate system to calculate the initial value of the eccentricity vector at the lunar center. e M0 .

[0108] Furthermore, the following is executed in the Earth-Moon transfer orbit calculation module:

[0109] Step 3.1: Based on the eccentricity vector of the geocentric segment, calculate the time and position velocity when the object reaches the lunar influence sphere;

[0110] Calculate the orbital parameters at the pericenter based on the eccentricity vector:

[0111] First, calculate the right ascension and declination of the pericentrism.

[0112] (8)

[0113] (9)

[0114] In the formula e x , e y , e z for e The directional components; the right ascension and argument of the ascending node can be obtained from the right ascension and declination;

[0115] The magnitude of the eccentricity vector is equal to the eccentricity. Substituting the perigee radius and eccentricity of the geocentric segment of the orbit into formulas (3) and (4) yields the semi-major axis.

[0116] After obtaining the orbital parameters of the geocentric segment based on the eccentricity vector of the geocentric segment, the time taken for the orbit to reach the lunar sphere of influence can be calculated. t P and position-velocity vectors;

[0117] Step 3.2: Calculate the position and velocity over a certain period of time by using the eccentricity vector of the lunar segment.

[0118] The lunar orbital parameters for the lunar center segment can be obtained from the eccentricity vector of the lunar center segment, and the orbital parameters can be calculated by working backwards for a certain period of time. t M = t trans - t P The position and velocity vectors at the orbital splicing point are obtained, and the state vector in the lunar orbit coordinate system is converted into the state vector in the geocentric inertial system.

[0119] Step 3.3: Solve the lunar transfer orbit by splicing conic sections using target shooting, and use the target shooting solution as the initial value to solve the problem using a high-precision model.

[0120] The initial value of the geocentric segment eccentricity vector obtained from steps 2.2 and 2.3. e E0 Initial value of the eccentricity vector of the lunar segment e M0 As the initial value for target shooting, the difference between the position and velocity vectors is obtained by calculating steps 3.1 and 3.2. The target shooting iterates the eccentricity vectors of the geocentric segment and the lunar eccentricity vector until the position and velocity tolerances are met. The target shooting solution is used as the initial value to solve the problem using a high-precision model, and finally a complete Earth-Moon transfer orbit that meets the mission constraints is obtained.

[0121] Furthermore, the following is executed in the lunar capture orbit calculation module:

[0122] Step 4.1: Determine the capture orbit period T ;

[0123] To ensure the stability of the capture orbit, it must be within the lunar sphere of influence, and the capture orbit period must be no more than 6 days.

[0124] After successful capture, in order to ensure that the probe can operate on orbit for a period of time without hitting the moon in the event of a malfunction that prevents subsequent orbit changes, the maximum capture orbit period is 4 days, provided that the probe does not hit the moon for 60 days.

[0125] After entering the capture orbit, the probe will transfer to a highly elliptical frozen orbit, requiring orbit adjustment at the apogee. The longer the capture orbit period, the lower the velocity at the apogee, and the smaller the velocity increment required for orbit adjustment at the apogee. Therefore, the capture orbit period should be as large as possible.

[0126] Lunar braking capture needs to take into account the actual orbit control speed increment deviation, and the capture speed increment needs to leave a certain margin to ensure that it can be captured in a stable orbit;

[0127] After comprehensive consideration, the capture orbit period was chosen to be 3 days;

[0128] Step 4.2: Calculate the lunar capture orbit parameters;

[0129] Capture orbit semi-major axis a c for

[0130] (10)

[0131] The eccentricity can be calculated using formulas (3) and (4). The right ascension of the ascending node is 0 and has no effect. The argument of the near point is obtained based on time.

[0132] The lunar perigee altitude and inclination of the lunar capture orbit are determined by the Earth-Moon transfer orbit.

[0133] Furthermore, the following is executed in the large ellipse frozen orbit calculation module:

[0134] Step 5.1: Adjust the near-lunar maneuver to change the lunar phase angle;

[0135] The far-moon maneuver involves adjusting the perihelion angle of the lunar capture orbit while simultaneously adjusting the orbital inclination to the required angle, thereby obtaining a highly elliptical frozen orbit for the target.

[0136] Due to the dynamics of the Earth-Moon space, the perilune argument of the Earth-Moon transfer orbit varies between 120° and 150° when it reaches the lunar perigee, making it impossible to directly reach the 90° perilune argument required for a highly elliptical frozen orbit. Adjusting the perilune argument through mid-course maneuvers during the Earth-Moon transfer would require a significant velocity increment, making it impractical. Therefore, the orbital argument adjustment was chosen after lunar capture.

[0137] The perilune argument is an in-plane orbital parameter. Based on the Gaussian perturbation equation, the orbital changes are performed at different true anomalies under unit perturbation acceleration on the lunar orbit formed after capture. Adjusting the perilune argument near the apogee is the most efficient.

[0138] Step 5.2: Calculate the frozen orbit of the large ellipse;

[0139] Orbital adjustments were made near the apogee to generate a highly elliptical frozen orbit with a period of 12 hours, with the adjustment target being the perigee argument. ω F ,inclination i F and the height of the perilune h pF ;

[0140] In the two-body configuration, a trajectory change is performed at a certain point on the capture trajectory to reach the target trajectory. ω F , i F and h pF Given the given information, the orbital elements of the target orbit can be determined through spatial geometric relationships. The change position and velocity increment under two-body conditions can be calculated analytically. The calculation process is as follows:

[0141] The position and velocity vector of the orbital change point can be obtained; the radius, right ascension, and declination of that position can be calculated to determine whether it is within the range of the target inclination angle, and the right ascension of the ascending node of the target orbit can be obtained. Ω F And true near point anglef F ;according to

[0142] (11)

[0143] (12)

[0144] The eccentricity of the target frozen orbit can be calculated. e F and semi-major axis a F for

[0145] (13)

[0146] (14)

[0147] In the formula r 0 represents the radius of the trajectory change point. At this point, a set of trajectory parameters for the frozen trajectory are obtained, and the velocity vector of the trajectory at the trajectory change point is calculated. By subtracting the velocity vector at the trajectory change point of the captured trajectory, the trajectory change velocity increment can be obtained. By selecting a suitable trajectory change point to minimize the consumption of the trajectory change velocity increment, and optimizing it under a high-precision model, the optimal trajectory change position and trajectory change velocity increment are determined.

[0148] Finally, to obtain a highly elliptical frozen orbit with a given period, a pulse is applied at the lunar perihelion, and the highly elliptical frozen orbit with the target period is obtained by a target-shooting method.

[0149] The advantages of this invention are:

[0150] This invention determines the ascent and descent type of the transfer orbit in advance during the Earth-Moon transfer phase. The Earth-Moon transfer orbit is selected as a descent launch and descent arrival, ensuring that the lunar orbit is a highly elliptical frozen orbit with the apogee above the southern hemisphere of the moon. The invention also uses eccentricity vector targeting to generate an Earth-Moon transfer orbit that meets mission constraints. After lunar capture, the perilune angle is adjusted near the apogee to ensure the efficient generation of the highly elliptical frozen orbit around the moon. Attached Figure Description

[0151] Figure 1 This is a schematic diagram of the transfer trajectory design method for a lunar elliptical frozen orbit based on eccentricity vector target shooting according to the present invention. Detailed Implementation

[0152] 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 in conjunction with the embodiments of the present invention. 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.

[0153] This embodiment discloses a transfer trajectory design method for a lunar elliptical frozen orbit based on eccentricity vector target firing, such as... Figure 1 As shown, the specific implementation steps are as follows:

[0154] Step 1: Define the geocentric inertial coordinate system and the lunar orbital coordinate system, set the perigee time, transfer time, perigee radius, geocentric inertial system inclination, lunar perigee radius, lunar orbital coordinate system inclination, and select the ascent and descent orbit types for the Earth departure segment and the Moon arrival segment.

[0155] Step 1.1: Define the geocentric inertial coordinate system and the lunar orbital plane coordinate system.

[0156] In a geocentric inertial frame of reference, the X-axis is the direction of the line connecting Earth and the Moon as the probe enters the Moon, the Z-axis is the direction of the normal along the Moon's orbit, and the Y-axis is determined by the right-hand rule; in the lunar orbit coordinate system, xy The plane is the celestial plane. x The axis is the intersection of the lunar orbit plane and the lunar equatorial plane. z It is the direction of the white path plane.

[0157] The perigee time of the Earth-Moon transfer orbit is set at 11:00:00 on January 22, 2024, with a transfer time of 112 hours, a perigee altitude of 200 km, a geocentric inertial frame inclination of 21°, a lunar perigee altitude of 200 km, and a lunar orbital plane inclination of 80°.

[0158] Step 1.2: Calculate the perigee time to determine the type of rising and falling rails.

[0159] The perigee time of the Earth-Moon transfer orbit can be calculated as 3:00:00 on January 27, 2024, using the perigee time and transfer time of the Earth-Moon transfer orbit.

[0160] Based on the launch site location, a descending launch orbit was selected. Simultaneously, considering the target is the lunar south pole, the lunar orbit is designed as a highly elliptical frozen orbit with the apogee above the lunar southern hemisphere; therefore, a descending arrival orbit was chosen. The launch and arrival orbits for the Earth-Moon transfer orbit are descending launch and descending arrival orbits, respectively.

[0161] Step 2: In the geocentric inertial frame, read the ephemeris to obtain the Moon's position and right ascension and declination at the perigee. Calculate the right ascension of the ascending node and the argument of perigee of the Earth-Moon transfer orbit. Calculate the semi-major axis, eccentricity, and true anomaly at the perigee of the Earth-Moon transfer orbit. This determines the orbital parameters of the starting orbit from the geocentric point, obtains the initial value of the eccentricity vector in the geocentric segment, and calculates the position and velocity of the Earth-Moon transfer orbit at the Moon's sphere of influence. Then, transfer the position and velocity to the lunar orbital plane coordinate system to obtain the initial value of the eccentricity vector in the lunar orbital segment.

[0162] Step 2.1: Define the two-body model.

[0163] The dual-body model uses the lunar sphere of influence as the boundary. When the probe is moving within the lunar sphere of influence, only the gravitational pull of the Moon's center is considered; after leaving the sphere, it is only subject to the gravitational pull of the Earth's center. The Earth-Moon transfer orbit is divided into a geocentric segment and a lunar-centric segment, calculated separately using the lunar sphere of influence as the boundary. The radius of the lunar sphere of influence is 66,200 km.

[0164] Step 2.2: Calculate the initial value of the eccentricity vector of the geocentric segment.

[0165] Eccentricity vector e The calculation formula is

[0166] (29)

[0167] In the formula μ For gravitational parameters, Earth's gravitational parameters μ E =398,600 km 3 / s 2 Lunar gravitational parameters μ M =4903 km 3 / s 2 , r , v Let be the position vector and velocity vector of the detector at any given moment. This is achieved by solving for the position and velocity vectors of any point on the orbit. r and v The eccentricity vector of the orbit can then be obtained, and the state vector can be solved by the orbital parameters.

[0168] Obtain the Moon's position vector in the Earth-centric inertial frame at the moment of perigee by reading the ephemeris. r M =[-315593.517, 217801.740, 126531.079] km, calculate the right ascension of the Moon's location. α M =2.537, declination δ M=0.319, and the ascending node right ascension of the transfer orbit can be approximated using a spherical triangle based on right ascension and declination. Ω E = 1.503° and perigee argument ω E = -2.046°.

[0169] Solving for other orbital parameters of the Earth-Moon transfer orbit using the target shooting method: based on the perigee radius of the Earth-Moon transfer orbit. r pE =6578.137 km, transfer time t Trans =112 h and perigee radius r pM =1938 km, assuming the perigee lies on the extension of the lunar position vector, the initial value of the orbital apogee radius is given as...

[0170] (30)

[0171] In the formula r aE Let be the radius of the apogee, initial value. r aE =405728.762 km.

[0172] The apogee radius of the transfer trajectory is determined by firing at the target; the firing equation is as follows:

[0173] (31)

[0174] (32)

[0175] (33)

[0176] (34)

[0177] (35)

[0178] In the formula, the true nearest point angle f f It can be derived from the angle of the near point. M f Calculations show that r f This represents the orbital radius at the perigee, and the target is... fvec Minimum. Calculate the apogee radius. r aE =411808.126 km. After calculating the apogee radius, the semi-major axis of the Earth-Moon transfer orbit can be obtained using the above formula. a E eccentricitye E and the true periapsis at the moment of near-lunar point f f This yields a set of orbital parameters, which are converted into position and velocity vectors, and initial values ​​for the geocentric segment eccentricity vector. e E0 It can be calculated.

[0179] A set of orbital parameters were calculated. a E ; e E ; i E ; Ω E ; ω E ; f E = [209193.131 km; 0.968; 0.366°; 1.502°; -2.046°; 3.110°]; Calculate the eccentricity vector of the geocentric segment. e E0 =[0.772, -0.497, -0.308].

[0180] Step 2.3: Calculate the initial value of the eccentricity vector of the lunar segment.

[0181] The state vector at the point of influence of the Moon is obtained by recursively calculating the orbital parameters. The above calculations were performed in a geocentric inertial frame. This state vector is then transferred to the lunar orbital plane coordinate system to calculate the initial value of the eccentricity vector at the lunar center. e M0 =[0.165, 1.014, 0.206].

[0182] Step 3: Calculate the time, position, and velocity of the Earth-centered starting orbit to the Moon's influence sphere in the Earth-centered inertial frame based on the eccentricity vector of the Earth-centered segment. Calculate the position and velocity of the Moon-centered arrival orbit after a certain time in the lunar orbit coordinate system based on the eccentricity vector of the lunar segment. Then, switch the state to the Earth-centered inertial frame, calculate the position and velocity tolerances, iterate through the Earth-centered and lunar eccentricity vectors, and use the results from the initial calculations as initial values ​​to solve using a high-precision model to obtain a complete Earth-Moon transfer orbit that meets the mission constraints.

[0183] Step 3.1: Calculate the time and position velocity when the object reaches the lunar influence sphere based on the eccentricity vector of the geocentric segment.

[0184] Calculate the orbital parameters at the pericenter based on the eccentricity vector:

[0185] First, calculate the right ascension and declination of the pericentrism.

[0186] (36)

[0187] (37)

[0188] In the formula e x , e y , e z for e The directional components. The right ascension and declination of the orbit can be used to obtain the right ascension of the ascending node and the argument of the pericenter.

[0189] The magnitude of the eccentricity vector is equal to the eccentricity. Substituting the perigee radius and eccentricity of the geocentric segment of the orbit into formulas (31) and (32) yields the semi-major axis.

[0190] After obtaining the orbital parameters of the geocentric segment based on the eccentricity vector of the geocentric segment, the time taken for the orbit to reach the lunar sphere of influence can be calculated. t P And position and velocity vectors.

[0191] Step 3.2: Calculate the position and velocity over a certain period of time by using the eccentricity vector of the lunar segment.

[0192] The lunar orbital parameters for the lunar center segment can be obtained from the eccentricity vector of the lunar center segment, and the orbital parameters can be calculated by working backwards for a certain period of time. t M = t trans - t P The position and velocity vectors at the orbital splicing point are obtained, and the state vector in the lunar orbit coordinate system is converted into the state vector in the geocentric inertial system.

[0193] Step 3.3: Solve the lunar transfer orbit by splicing conic sections using target shooting, and use the target shooting solution as the initial value to solve the problem using a high-precision model.

[0194] The initial value of the geocentric segment eccentricity vector obtained from steps 2.2 and 2.3. e E0 and e Initial value of the eccentricity vector of the lunar segment M0 As the initial value for target shooting, the difference between the position and velocity vectors is calculated in steps 3.1 and 3.2. The target shooting iterates the eccentricity vectors of the geocentric segment and the lunar eccentricity vector until the position and velocity tolerances are met. The target shooting solution is then used as the initial value to solve the problem using a high-precision model, and finally a complete Earth-Moon transfer orbit that meets the mission constraints is obtained.

[0195] The Earth-Moon transfer orbit was calculated. Among other things, the eccentricity vector of the geocentric segment... eE = [0.793, -0.466, -0.301], Earth-centric orbital parameters [ a E ; e E ; i E ; Ω E ; ω E ; f E [206607.490 km; 0.968; 21°; 91.108°; 240.182°; 0°], the time required to reach the lunar influence sphere. t P =3.864 days; Calculated runtime t M =0.802 day, lunar segment eccentricity vector e M =[0.530, 0.655, 0.937], lunar center orbital parameters[ a M ; e M ; i M ; Ω M ; ω M ; f M = [7445.305 km; 1.260; 80°; 242.292°; 130.991°; 0°]; The conic section splicing point is located at [-238375.034, 189769.076, 90593.843] km, and the speed is [-0.665, 0.259, 0.261] km / s.

[0196] Step 4: Fix the perigee altitude and inclination of the lunar capture orbit, calculate the capture orbit period, and enter the lunar capture orbit.

[0197] Step 4.1: Determine the capture orbit period T .

[0198] To ensure the stability of the capture orbit, it must be within the lunar sphere of influence, with a maximum capture orbit period of 6 days.

[0199] After successful capture, in order to ensure that the probe can operate on orbit for a period of time without colliding with the moon in the event of a malfunction that prevents subsequent orbital maneuvers, the maximum capture orbit period is 4 days, provided that the probe does not collide with the moon for 60 days.

[0200] After entering the capture orbit, the probe will transfer to a highly elliptical frozen orbit, requiring orbit adjustment at the apogee. The longer the capture orbit period, the lower the velocity at the apogee, and the smaller the velocity increment required for orbit adjustment at the apogee. Therefore, the capture orbit period should be as large as possible.

[0201] Lunar braking capture needs to take into account the actual orbital control speed increment deviation, and the capture speed increment needs to leave a certain margin to ensure that it can be captured in a stable orbit.

[0202] After comprehensive consideration, a capture orbit period of 3 days was selected.

[0203] Step 4.2: Calculate the lunar capture orbit parameters.

[0204] Capture orbit semi-major axis a c for

[0205] (38)

[0206] The eccentricity can be calculated using formulas (31) and (32). The right ascension of the ascending node is 0 and has no effect. The argument of the near point is obtained based on time.

[0207] The lunar perigee altitude and inclination of the lunar capture orbit are determined by the Earth-Moon transfer orbit.

[0208] The orbital parameters of the perigee in the lunar orbital coordinate system were calculated. a C ; e C ; i C ; Ω C ; ω C ; f C ] =[20282.344 km; 0.904; 80°; 0°; 130.991°; 0°].

[0209] Step 5: Fix the lunar periapsis argument, inclination, and lunar periapsis altitude of the target orbit. Adjust the lunar periapsis argument at the apoapsis to obtain a highly elliptical frozen orbit around the moon. Finally, apply pulses at the lunar periapsis to transfer the orbit to the required period of the highly elliptical frozen orbit, as needed for the mission.

[0210] Step 5.1: Adjust the near-lunar point angle using far-lunar maneuvers.

[0211] The far-moon maneuver involves adjusting the perihelion angle of the lunar capture orbit while simultaneously adjusting the orbital inclination to the required angle, thereby obtaining a highly elliptical frozen orbit for the target.

[0212] Due to the dynamics of the Earth-Moon space, the perilune argument of the Earth-Moon transfer orbit varies between 120° and 150° when it reaches the lunar perigee, making it impossible to directly reach the 90° perilune argument required for a highly elliptical frozen orbit. Adjusting the perilune argument through mid-course maneuvers during the Earth-Moon transfer would require a significant velocity increment, making it impractical. Therefore, the orbital argument adjustment was chosen to be performed after lunar capture.

[0213] The perilune argument is an in-plane orbital parameter. Based on the Gaussian perturbation equation, it is analyzed that, in the lunar orbit formed after capture, orbital changes are performed at different true anomalies under unit perturbation acceleration. Adjusting the perilune argument near the apogee is the most efficient.

[0214] Step 5.2: Calculate the frozen orbit of the large ellipse.

[0215] Orbital adjustments were made near the apogee to generate a highly elliptical frozen orbit with a period of 12 hours, with the adjustment target being the perigee argument. ω F = 90°, tilt angle i F =115° and the altitude of the perigee h pF =200 km.

[0216] In the two-body configuration, a trajectory change is performed at a certain point on the capture trajectory to reach the target trajectory. ω F , i F and r pF Given the given information, the orbital parameters of the target orbit can be determined through spatial geometric relationships. The orbital change position and velocity increment under two-body conditions can be calculated analytically. The calculation process is as follows:

[0217] By capturing the position and velocity vector of the trajectory change point, the radius, right ascension, and declination of that position can be calculated to determine if it falls within the range of the target inclination angle. The right ascension of the ascending node of the target orbit can then be obtained. Ω F And true near point angle f F .according to

[0218] (39)

[0219] (40)

[0220] The eccentricity of the target frozen orbit can be calculated. e F and semi-major axis a F for

[0221] (41)

[0222] (42)

[0223] In the formula r 0 represents the radius of the trajectory change point. At this point, a set of trajectory parameters for the frozen trajectory is obtained. The velocity vector of this trajectory at the trajectory change point is calculated. The difference between this velocity vector and the velocity vector at the trajectory change point of the captured trajectory is used to obtain the trajectory change velocity increment. By selecting a suitable trajectory change point to minimize the consumption of the trajectory change velocity increment, and optimizing under a high-precision model, the optimal trajectory change position and trajectory change velocity increment are determined.

[0224] The optimal orbit change position under the high-precision model is calculated to be [14043.402, -4706.367, -26691.134] km, and the orbital elements of the large elliptical frozen orbit around the moon at the orbit change point are […]. a F ; e F ; i F ; Ω F ; ω F ; f F ] = [21715.364 km;0.911;115°;218.648°;90°;164.751°].

[0225] To obtain a highly elliptical frozen orbit with a given period, a pulse is applied at the lunar perihelion, and the highly elliptical frozen orbit with the target period is obtained by a target shooting method.

[0226] The orbital elements of the large elliptical frozen orbit with a 12-hour orbital period were calculated. a F ; e F ; i F ; Ω F ; ω F ; f F ] =[6142.7 km; 0.6845; 115°; 218.648°; 90°; 0°].

[0227] Example 2

[0228] Corresponding to the above method, the present invention also provides a transfer orbit design system for a lunar highly elliptical frozen orbit based on eccentricity vector target shooting, used to design an Earth-Moon transfer orbit starting from perigee and run to a lunar highly elliptical frozen orbit, including:

[0229] Earth-Moon Transfer Orbit Input Module: Used to define the geocentric inertial coordinate system and the lunar orbital coordinate system, set the perigee time, transfer time, perigee radius, geocentric inertial system inclination, lunar perigee radius, lunar orbital coordinate system inclination, and select the ascent and descent orbit types for the Earth departure segment and the Moon arrival segment.

[0230] The eccentricity vector initial value calculation module is used to read the ephemeris in the geocentric inertial frame to obtain the position, right ascension, and declination of the Moon at the perigee, calculate the right ascension of the ascending node and the argument of perigee of the Earth-Moon transfer orbit, and calculate the semi-major axis, eccentricity, and true anomaly at the perigee of the Earth-Moon transfer orbit, thereby determining the orbital parameters of the Earth-centric starting orbit, obtaining the initial value of the eccentricity vector in the geocentric segment, and calculating the position and velocity of the Earth-Moon transfer orbit when it reaches the Moon's sphere of influence. The position and velocity are then transferred to the lunar orbital plane coordinate system to obtain the initial value of the eccentricity vector in the lunar orbital segment.

[0231] The Earth-Moon transfer orbit calculation module is used to calculate the time, position, and velocity of the Earth-centered starting orbit to the Moon's influence sphere in the Earth-centered inertial frame based on the eccentricity vector of the Earth-centered segment. In the lunar orbit coordinate system, it calculates the position and velocity of the Moon-centered arrival orbit after a certain period of travel based on the eccentricity vector of the Moon-centered segment. The module then switches the state to the Earth-centered inertial frame to calculate the position and velocity tolerances. It iterates through the eccentricity vectors of the Earth-centered and Moon-centered segments, and uses the results of the iteration as initial values ​​to solve the problem using a high-precision model to obtain a complete Earth-Moon transfer orbit that meets the mission constraints.

[0232] Lunar capture orbit calculation module: used to fix the perigee altitude and inclination of the lunar capture orbit, calculate the capture orbit period, and enter the lunar capture orbit;

[0233] The large elliptical frozen orbit calculation module: fixes the lunar periapsis argument, inclination, and lunar periapsis altitude of the target orbit, adjusts the lunar periapsis argument at the apoapsis, and obtains a large elliptical frozen orbit around the moon; finally, according to mission requirements, pulses are applied at the lunar periapsis to transfer to a large elliptical frozen orbit with the required period.

[0234] Furthermore, the following is executed in the Earth-Moon transfer orbit input module:

[0235] Step 1.1: Define the geocentric inertial coordinate system and the lunar orbital plane coordinate system;

[0236] In a geocentric inertial frame of reference, the X-axis is the direction of the line connecting Earth and the Moon as the probe enters the Moon, the Z-axis is the direction of the normal along the Moon's orbit, and the Y-axis is determined by the right-hand rule; in the lunar orbit coordinate system, xy The plane is the celestial plane. x The axis is the intersection of the lunar orbit plane and the lunar equatorial plane. z The direction of the white path plane;

[0237] Step 1.2: Calculate the perigee time to determine the type of ascending and descending orbit;

[0238] The perigee time of the Earth-Moon transfer orbit can be calculated using the perigee time and transfer time of the Earth-Moon transfer orbit;

[0239] Based on the launch site location, a descending launch orbit was selected; considering that the target of the probe is the lunar south pole, the lunar orbit is designed as a highly elliptical frozen orbit with the apogee above the lunar southern hemisphere, so a descending arrival orbit was selected; the launch and arrival orbits of the Earth-Moon transfer orbit are descending launch and descending arrival orbits.

[0240] Furthermore, the following is executed in the eccentricity vector initial value calculation module:

[0241] Step 2.1: Define the two-body model;

[0242] The dual-body model uses the lunar sphere of influence as the boundary. When the probe moves within the lunar sphere of influence, only the gravitational pull of the Moon's center is considered. After leaving the sphere of influence, it is only subject to the gravitational pull of the Earth's center. The Earth-Moon transfer orbit is divided into a geocentric segment and a lunar-centric segment, which are calculated separately using the lunar sphere of influence as the boundary.

[0243] Step 2.2: Calculate the initial value of the eccentricity vector of the geocentric segment;

[0244] Eccentricity vector e The calculation formula is

[0245] (1)

[0246] In the formula μ For gravitational parameters, r , v Let the position and velocity vectors of the probe be the vectors at any given moment; by solving for the vectors at any point on the orbit... r and v The eccentricity vector of the orbit can then be obtained, and the state vector can be solved by the orbital parameters;

[0247] By reading the ephemeris to obtain the Moon's position in the geocentric inertial frame at the moment of perigee, the right ascension and declination of the Moon's position can be obtained. Based on the right ascension and declination, the right ascension of the ascending node and the argument of perigee of the transfer orbit can be approximated using a spherical triangle. Other orbital parameters of the Earth-Moon transfer orbit are then solved using the target-shooting method: based on the perigee radius of the Earth-Moon transfer orbit... r pE Transfer time t Trans and the radius of the perigee r pM Assuming the perigee lies on the extension of the lunar position vector, the initial value of the orbital apogee radius is given as...

[0248] (2)

[0249] In the formula r aE The apogee radius;

[0250] The apogee radius of the transfer trajectory is determined by firing at the target; the firing equation is as follows:

[0251] (3)

[0252] (4)

[0253] (5)

[0254] (6)

[0255] (7)

[0256] In the formula, the true nearest point angle f f It can be derived from the angle of the near point. M f Calculations show that r f This represents the orbital radius at the perigee, and the target is... fvec Minimum; find the apogee radius r aE Then, using the above formula, the semi-major axis of the Earth-Moon transfer orbit can be obtained. a E eccentricity e E and the true periapsis at the moment of near-lunar point f f This yields a set of orbital parameters, which are converted into position and velocity vectors, and initial values ​​for the geocentric segment eccentricity vector. e E0 It can be calculated;

[0257] Step 2.3: Calculate the initial value of the eccentricity vector of the lunar segment;

[0258] The state vector at the point of lunar influence is obtained by recursively calculating the orbital parameters. The above calculations were performed in a geocentric inertial frame. This state vector is then transferred to the lunar orbital plane coordinate system to calculate the initial value of the eccentricity vector at the lunar center. e M0 .

[0259] Furthermore, the following is executed in the Earth-Moon transfer orbit calculation module:

[0260] Step 3.1: Based on the eccentricity vector of the geocentric segment, calculate the time and position velocity when the object reaches the lunar influence sphere;

[0261] Calculate the orbital parameters at the pericenter based on the eccentricity vector:

[0262] First, calculate the right ascension and declination of the pericentrism.

[0263] (8)

[0264] (9)

[0265] In the formula e x , e y , e z for e The directional components; the right ascension and argument of the ascending node can be obtained from the right ascension and declination;

[0266] The magnitude of the eccentricity vector is equal to the eccentricity. Substituting the perigee radius and eccentricity of the geocentric segment of the orbit into formulas (3) and (4) yields the semi-major axis.

[0267] After obtaining the orbital parameters of the geocentric segment based on the eccentricity vector of the geocentric segment, the time taken for the orbit to reach the lunar sphere of influence can be calculated. t P and position-velocity vectors;

[0268] Step 3.2: Calculate the position and velocity over a certain period of time by using the eccentricity vector of the lunar segment.

[0269] The lunar orbital parameters for the lunar center segment can be obtained from the eccentricity vector of the lunar center segment, and the orbital parameters can be calculated by working backwards for a certain period of time. t M = t trans - t P The position and velocity vectors at the orbital splicing point are obtained, and the state vector in the lunar orbit coordinate system is converted into the state vector in the geocentric inertial system.

[0270] Step 3.3: Solve the lunar transfer orbit by splicing conic sections using target shooting, and use the target shooting solution as the initial value to solve the problem using a high-precision model.

[0271] The initial value of the eccentricity vector obtained from steps 2.2 and 2.3 e E0 Initial value of the eccentricity vector of the lunar segment e M0 As the initial value for target shooting, the difference between the position and velocity vectors is obtained by calculating steps 3.1 and 3.2. The target shooting iterates the eccentricity vectors of the geocentric segment and the lunar eccentricity vector until the position and velocity tolerances are met. The target shooting solution is used as the initial value to solve the problem using a high-precision model, and finally a complete Earth-Moon transfer orbit that meets the mission constraints is obtained.

[0272] Furthermore, the following is executed in the lunar capture orbit calculation module:

[0273] Step 4.1: Determine the capture orbit period T ;

[0274] To ensure the stability of the capture orbit, it must be within the lunar sphere of influence, and the capture orbit period must be no more than 6 days.

[0275] After successful capture, in order to ensure that the probe can operate on orbit for a period of time without hitting the moon in the event of a malfunction that prevents subsequent orbit changes, the maximum capture orbit period is 4 days, provided that the probe does not hit the moon for 60 days.

[0276] After entering the capture orbit, the probe will transfer to a highly elliptical frozen orbit, requiring orbit adjustment at the apogee. The longer the capture orbit period, the lower the velocity at the apogee, and the smaller the velocity increment required for orbit adjustment at the apogee. Therefore, the capture orbit period should be as large as possible.

[0277] Lunar braking capture needs to take into account the actual orbit control speed increment deviation, and the capture speed increment needs to leave a certain margin to ensure that it can be captured in a stable orbit;

[0278] After comprehensive consideration, the capture orbit period was chosen to be 3 days;

[0279] Step 4.2: Calculate the lunar capture orbit parameters;

[0280] Capture orbit semi-major axis a c for

[0281] (10)

[0282] The eccentricity can be calculated using formulas (3) and (4). The right ascension of the ascending node is 0 and has no effect. The argument of the near point is obtained based on time.

[0283] The lunar perigee altitude and inclination of the lunar capture orbit are determined by the Earth-Moon transfer orbit.

[0284] Furthermore, the following is executed in the large ellipse frozen orbit calculation module:

[0285] Step 5.1: Adjust the near-lunar maneuver to change the lunar phase angle;

[0286] The far-moon maneuver involves adjusting the perihelion angle of the lunar capture orbit while simultaneously adjusting the orbital inclination to the required angle, thereby obtaining a highly elliptical frozen orbit for the target.

[0287] Due to the dynamics of the Earth-Moon space, the perilune argument of the Earth-Moon transfer orbit varies between 120° and 150° when it reaches the lunar perigee, making it impossible to directly reach the 90° perilune argument required for a highly elliptical frozen orbit. Adjusting the perilune argument through mid-course maneuvers during the Earth-Moon transfer would require a significant velocity increment, making it impractical. Therefore, the orbital argument adjustment was chosen after lunar capture.

[0288] The perilune argument is an in-plane orbital parameter. Based on the Gaussian perturbation equation, the orbital changes are performed at different true anomalies under unit perturbation acceleration on the lunar orbit formed after capture. Adjusting the perilune argument near the apogee is the most efficient.

[0289] Step 5.2: Calculate the frozen orbit of the large ellipse;

[0290] Orbital adjustments were made near the apogee to generate a highly elliptical frozen orbit with a period of 12 hours, with the adjustment target being the perigee argument. ω F ,inclination i F and the height of the perilune h pF ;

[0291] In the two-body configuration, a trajectory change is performed at a certain point on the capture trajectory to reach the target trajectory. ω F , i F and h pF Given the given information, the orbital elements of the target orbit can be determined through spatial geometric relationships. The change position and velocity increment under two-body conditions can be calculated analytically. The calculation process is as follows:

[0292] The position and velocity vector of the orbital change point can be obtained; the radius, right ascension, and declination of that position can be calculated to determine whether it is within the range of the target inclination angle, and the right ascension of the ascending node of the target orbit can be obtained. Ω F And true near point anglef F ;according to

[0293] (11)

[0294] (12)

[0295] The eccentricity of the target frozen orbit can be calculated. e F and semi-major axis a F for

[0296] (13)

[0297] (14)

[0298] In the formula r 0 represents the radius of the trajectory change point. At this point, a set of trajectory parameters for the frozen trajectory are obtained, and the velocity vector of the trajectory at the trajectory change point is calculated. By subtracting the velocity vector at the trajectory change point of the captured trajectory, the trajectory change velocity increment can be obtained. By selecting a suitable trajectory change point to minimize the consumption of the trajectory change velocity increment, and optimizing it under a high-precision model, the optimal trajectory change position and trajectory change velocity increment are determined.

[0299] Finally, to obtain a highly elliptical frozen orbit with a given period, a pulse is applied at the lunar perihelion, and the highly elliptical frozen orbit with the target period is obtained by a target-shooting method.

[0300] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for designing a transfer orbit for a lunar elliptical frozen orbit based on eccentricity vector target shooting, used to design an Earth-Moon transfer orbit starting from perigee and running to a lunar elliptical frozen orbit, characterized in that, Includes the following steps: Step 1: Define the geocentric inertial coordinate system and the lunar orbital coordinate system, set the perigee time, transfer time, perigee radius, geocentric inertial system inclination, lunar perigee radius, lunar orbital coordinate system inclination, and select the Earth-Moon transfer orbit as a descent launch and descent arrival. Step 2: In the geocentric inertial frame, read the ephemeris to obtain the Moon's position and right ascension and declination at the perigee. Calculate the right ascension of the ascending node and the argument of perigee of the Earth-Moon transfer orbit. Calculate the semi-major axis, eccentricity, and true anomaly at the perigee of the Earth-Moon transfer orbit. This determines the orbital parameters of the starting orbit from the geocentric point, obtains the initial value of the eccentricity vector in the geocentric segment, and calculates the position and velocity of the Earth-Moon transfer orbit at the Moon's sphere of influence. Then, transfer the position and velocity to the lunar orbital coordinate system to obtain the initial value of the eccentricity vector in the lunar orbital segment. Step 3: Calculate the time, position, and velocity of the Earth-centered starting orbit to the Moon's influence sphere in the Earth-centered inertial frame based on the eccentricity vector of the Earth-centered segment. Calculate the position and velocity of the Moon-centered arrival orbit after a certain time in the lunar orbit coordinate system based on the eccentricity vector of the lunar segment. Then, switch the state to the Earth-centered inertial frame, calculate the position and velocity tolerances, iterate through the eccentricity vectors of the Earth-centered and lunar segments, and use the results from the initial calculations as initial values ​​to solve using a high-precision model to obtain a complete Earth-Moon transfer orbit that satisfies the mission constraints. Step 4: Fix the perigee altitude and inclination of the lunar capture orbit, calculate the capture orbit period, and enter the lunar capture orbit; Step 5: Fix the lunar periapsis argument, inclination, and lunar periapsis altitude of the target orbit, and adjust the lunar periapsis argument at the apogee to obtain a large elliptical frozen orbit around the moon; Finally, as required by the mission, a pulse transfer is applied at the perilunar point to the highly elliptical frozen orbit of the required period.

2. The transfer trajectory design method for a lunar elliptical frozen orbit based on eccentricity vector target shooting according to claim 1, characterized in that, Perform the following in step one: Step 1.1: Define the geocentric inertial coordinate system and the lunar orbital plane coordinate system; In a geocentric inertial frame of reference, the X-axis represents the direction of the line connecting Earth and the Moon as the probe enters the Moon, the Z-axis represents the direction of the normal to the Moon's orbit, and the Y-axis is determined by the right-hand rule; in the lunar orbit coordinate system, xy The plane is the celestial plane. x The axis is the intersection of the lunar orbit plane and the lunar equatorial plane. z The direction of the white path plane; Step 1.2: Calculate the perigee time to determine the type of ascending and descending orbit; The perigee time of the Earth-Moon transfer orbit can be calculated using the perigee time and transfer time of the Earth-Moon transfer orbit; Based on the launch site location, a descending launch orbit was selected; considering that the target of the probe is the lunar south pole, the lunar orbit is designed as a highly elliptical frozen orbit with the apogee above the lunar southern hemisphere, so a descending arrival orbit was selected; the launch and arrival orbits of the Earth-Moon transfer orbit are descending launch and descending arrival orbits.

3. The transfer trajectory design method for a lunar elliptical frozen orbit based on eccentricity vector target shooting according to claim 2, characterized in that, Perform the following in step two: Step 2.1: Define the two-body model; The dual-body model uses the lunar sphere of influence as the boundary. When the probe moves within the lunar sphere of influence, only the gravitational pull of the Moon's center is considered. After leaving the sphere of influence, it is only subject to the gravitational pull of the Earth's center. The Earth-Moon transfer orbit is divided into a geocentric segment and a lunar-centric segment, which are calculated separately using the lunar sphere of influence as the boundary. Step 2.2: Calculate the initial value of the eccentricity vector of the geocentric segment; Eccentricity vector e The calculation formula is (1) In the formula μ For gravitational parameters, r , v Let the position and velocity vectors of the probe be the vectors at any given moment; by solving for the vectors at any point on the orbit... r and v The eccentricity vector of the orbit can then be obtained, and the state vector can be solved by the orbital parameters; By reading the ephemeris to obtain the Moon's position in the geocentric inertial frame at the moment of perigee, the right ascension and declination of the Moon's position can be obtained. Based on the right ascension and declination, the right ascension of the ascending node and the argument of perigee of the transfer orbit can be approximated using a spherical triangle. Other orbital parameters of the Earth-Moon transfer orbit are then solved using the target-shooting method: based on the perigee radius of the Earth-Moon transfer orbit... r pE Transfer time t Trans and the radius of the perigee r pM Assuming the perigee lies on the extension of the lunar position vector, the initial value of the orbital apogee radius is given as... (2) In the formula r aE The apogee radius; The apogee radius of the transfer trajectory is determined by firing at the target; the firing equation is as follows: (3) (4) (5) (6) (7) In the formula, the true nearest point angle f f It can be derived from the angle of the near point. M f Calculations show that r f This represents the orbital radius at the perigee, and the target is... fvec Minimum; find the apogee radius r aE Then, using the above formula, the semi-major axis of the Earth-Moon transfer orbit can be obtained. a E eccentricity e E and the true periapsis at the moment of near-lunar point f f This yields a set of orbital parameters, which are converted into position and velocity vectors, and initial values ​​for the geocentric segment eccentricity vector. e E0 It can be calculated; Step 2.3: Calculate the initial value of the eccentricity vector of the lunar segment; The state vector at the point of lunar influence is obtained by recursively calculating the orbital parameters. The above calculations were performed in a geocentric inertial frame. This state vector is then transferred to the lunar orbital plane coordinate system to calculate the initial value of the eccentricity vector at the lunar center. e M0 .

4. The transfer trajectory design method for a lunar elliptical frozen orbit based on eccentricity vector target shooting according to claim 3, characterized in that, Perform the following in step three: Step 3.1: Based on the eccentricity vector of the geocentric segment, calculate the time and position velocity when the object reaches the lunar influence sphere; Calculate the orbital parameters at the pericenter based on the eccentricity vector: First, calculate the right ascension and declination of the pericentrism. (8) (9) In the formula e x , e y , e z for e The directional components; the right ascension and argument of the ascending node can be obtained from the right ascension and declination; The magnitude of the eccentricity vector is equal to the eccentricity. The semi-major axis is calculated based on the perigee radius and eccentricity of the geocentric segment of the orbit. After obtaining the orbital parameters of the geocentric segment based on the eccentricity vector of the geocentric segment, the time taken for the orbit to reach the lunar sphere of influence can be calculated. t P and position-velocity vectors; Step 3.2: Calculate the position and velocity over a certain period of time by using the eccentricity vector of the lunar segment. The lunar orbital parameters for the lunar center segment can be obtained from the eccentricity vector of the lunar center segment, and the orbital parameters can be calculated by working backwards for a certain period of time. t M = t trans - t P The position and velocity vectors at the orbital splicing point are obtained, and the state vector in the lunar orbit coordinate system is converted into the state vector in the geocentric inertial system. Step 3.3: Solve the lunar transfer orbit by splicing conic sections using target practice, and use the target practice results as initial values ​​to solve the problem using a high-precision model; The initial value of the geocentric segment eccentricity vector obtained from steps 2.2 and 2.

3. e E0 Initial value of the eccentricity vector of the lunar segment e M0 As the initial value for target shooting, the difference between the position and velocity vectors is obtained by calculating steps 3.1 and 3.

2. The target shooting iterates the eccentricity vectors of the geocentric segment and the lunar eccentricity vector until the position and velocity tolerances are met. The target shooting solution is used as the initial value to solve the problem using a high-precision model, and finally a complete Earth-Moon transfer orbit that meets the mission constraints is obtained.

5. The transfer trajectory design method for a lunar elliptical frozen orbit based on eccentricity vector target shooting according to claim 4, characterized in that, Perform the following in step four: Step 4.1: Determine the capture orbit period T ; To ensure the stability of the capture orbit, it must be within the lunar sphere of influence, and the capture orbit period must be no more than 6 days. After successful capture, in order to ensure that the probe can operate on orbit for a period of time without hitting the moon in the event of a malfunction that prevents subsequent orbit changes, the maximum capture orbit period is 4 days, provided that the probe does not hit the moon for 60 days. After entering the capture orbit, the probe will transfer to a highly elliptical frozen orbit, requiring orbit adjustment at the apogee. The longer the capture orbit period, the lower the velocity at the apogee, and the smaller the velocity increment required for orbit adjustment at the apogee. Therefore, the capture orbit period should be as large as possible. Lunar braking capture needs to take into account the actual orbit control speed increment deviation, and the capture speed increment needs to leave a certain margin to ensure that it can be captured in a stable orbit; After comprehensive consideration, the capture orbit period was chosen to be 3 days; Step 4.2: Calculate the lunar capture orbit parameters; Capture orbit semi-major axis a c for (10) The eccentricity is calculated based on the semi-major axis of the capture orbit and the radius of the perigee. The right ascension of the ascending node is 0 and has no effect. The argument of the perigee is obtained based on time. The lunar perigee altitude and inclination of the lunar capture orbit are determined by the Earth-Moon transfer orbit.

6. The transfer trajectory design method for a lunar elliptical frozen orbit based on eccentricity vector target shooting according to claim 5, characterized in that, Perform the following in step five: Step 5.1: Adjust the near-lunar maneuver to change the lunar phase angle; The far-moon maneuver involves adjusting the perihelion angle of the lunar capture orbit while simultaneously adjusting the orbital inclination to the required angle, thereby obtaining a highly elliptical frozen orbit for the target. Due to Earth-Moon space dynamics, the perilpoint argument of the Earth-Moon transfer orbit varies between 120° and 150° when it reaches the perilpoint, making it impossible to directly reach the 90° perilpoint argument required for a highly elliptical frozen orbit. Adjusting the perilpoint argument by performing a mid-course maneuver during the Earth-Moon transfer would require a large velocity increment, which is not feasible. Therefore, the orbital argument adjustment was chosen to be performed after lunar capture. The perilune argument is an in-plane orbital parameter. Based on the Gaussian perturbation equation, the orbital changes are performed at different true anomalies under unit perturbation acceleration on the lunar orbit formed after capture. Adjusting the perilune argument near the apogee is the most efficient. Step 5.2: Calculate the frozen orbit of the large ellipse; Orbital adjustments were made near the apogee to generate a highly elliptical frozen orbit with a period of 12 hours, with the adjustment target being the perigee argument. ω F ,inclination i F and the height of the perilune h pF ; In the two-body configuration, a trajectory change is performed at a certain point on the capture trajectory to reach the target trajectory. ω F , i F and h pF Given the given information, the orbital elements of the target orbit can be determined through spatial geometric relationships. The change position and velocity increment under two-body conditions can be calculated analytically. The calculation process is as follows: The position and velocity vector of the orbital change point can be obtained; the radius, right ascension, and declination of that position can be calculated to determine whether it is within the range of the target inclination angle, and the right ascension of the ascending node of the target orbit can be obtained. Ω F And true near point angle f F ;according to (11) (12) The eccentricity of the target frozen orbit can be calculated. e F and semi-major axis a F for (13) (14) In the formula r 0 represents the radius of the trajectory change point. At this point, a set of trajectory parameters for the frozen trajectory are obtained, and the velocity vector of the trajectory at the trajectory change point is calculated. By subtracting the velocity vector at the trajectory change point of the captured trajectory, the trajectory change velocity increment can be obtained. By selecting a suitable trajectory change point to minimize the consumption of the trajectory change velocity increment, and optimizing it under a high-precision model, the optimal trajectory change position and trajectory change velocity increment are determined. Finally, to obtain a highly elliptical frozen orbit with a given period, a pulse is applied at the lunar perihelion, and the highly elliptical frozen orbit with the target period is obtained by a target-shooting method.

7. A transfer orbit design system for a lunar highly elliptical frozen orbit based on eccentricity vector target shooting, used to design a lunar transfer orbit starting from perigee and run to a lunar highly elliptical frozen orbit, characterized in that, include: Earth-Moon Transfer Orbit Input Module: Used to define the geocentric inertial coordinate system and the lunar orbit coordinate system, set the perigee time, transfer time, perigee radius, geocentric inertial system inclination, lunar perigee radius, lunar orbit coordinate system inclination, and select the Earth-Moon transfer orbit as a descent launch and descent arrival. The eccentricity vector initial value calculation module is used to read the ephemeris in the geocentric inertial frame to obtain the position, right ascension, and declination of the Moon at the perigee, calculate the right ascension of the ascending node and the argument of perigee of the Earth-Moon transfer orbit, and calculate the semi-major axis, eccentricity, and true anomaly at the perigee of the Earth-Moon transfer orbit, thereby determining the orbital parameters of the Earth-centric starting orbit, obtaining the initial value of the eccentricity vector in the geocentric segment, and calculating the position and velocity of the Earth-Moon transfer orbit when it reaches the Moon's sphere of influence. The position and velocity are then transferred to the lunar orbital plane coordinate system to obtain the initial value of the eccentricity vector in the lunar orbital segment. The Earth-Moon transfer orbit calculation module is used to calculate the time, position, and velocity of the Earth-centered starting orbit to the Moon's influence sphere in the Earth-centered inertial frame based on the eccentricity vector of the Earth-centered segment. In the lunar orbit coordinate system, it calculates the position and velocity of the Moon-centered arrival orbit after a certain period of travel based on the eccentricity vector of the Moon-centered segment. The module then switches the state to the Earth-centered inertial frame to calculate the position and velocity tolerances. It iterates through the eccentricity vectors of the Earth-centered and Moon-centered segments, and uses the results of the iteration as initial values ​​to solve the problem using a high-precision model to obtain a complete Earth-Moon transfer orbit that meets the mission constraints. Lunar capture orbit calculation module: used to fix the perigee altitude and inclination of the lunar capture orbit, calculate the capture orbit period, and enter the lunar capture orbit; Large elliptical frozen orbit calculation module: fixes the lunar perihelion argument, inclination, and lunar perihelion height of the target orbit, and adjusts the lunar perihelion argument at the apogee to obtain the large elliptical frozen orbit around the moon; Finally, as required by the mission, a pulse transfer is applied at the perilunar point to the highly elliptical frozen orbit of the required period.

8. The transfer trajectory design system for a lunar elliptical frozen orbit based on eccentricity vector target shooting according to claim 7, characterized in that, Execute in the Earth-Moon transfer orbit input module: Step 1.1: Define the geocentric inertial coordinate system and the lunar orbital plane coordinate system; In a geocentric inertial frame of reference, the X-axis is the direction of the line connecting Earth and the Moon as the probe enters the Moon, the Z-axis is the direction of the normal along the Moon's orbit, and the Y-axis is determined by the right-hand rule; in the lunar orbit coordinate system, xy The plane is the celestial plane. x The axis is the intersection of the lunar orbit plane and the lunar equatorial plane. z The direction of the white path plane; Step 1.2: Calculate the perigee time to determine the type of ascending and descending orbit; The perigee time of the Earth-Moon transfer orbit can be calculated using the perigee time and transfer time of the Earth-Moon transfer orbit; Based on the launch site location, a descending launch orbit was selected; considering that the target of the probe is the lunar south pole, the lunar orbit is designed as a highly elliptical frozen orbit with the apogee above the lunar southern hemisphere, so a descending arrival orbit was selected; the launch and arrival orbits of the Earth-Moon transfer orbit are descending launch and descending arrival orbits.

9. The transfer trajectory design system for a lunar elliptical frozen orbit based on eccentricity vector target shooting according to claim 8, characterized in that, Execute the following in the eccentricity vector initial value calculation module: Step 2.1: Define the two-body model; The dual-body model uses the lunar sphere of influence as the boundary. When the probe moves within the lunar sphere of influence, only the gravitational pull of the Moon's center is considered. After leaving the sphere of influence, it is only subject to the gravitational pull of the Earth's center. The Earth-Moon transfer orbit is divided into a geocentric segment and a lunar-centric segment, which are calculated separately using the lunar sphere of influence as the boundary. Step 2.2: Calculate the initial value of the eccentricity vector of the geocentric segment; Eccentricity vector e The calculation formula is (1) In the formula μ For gravitational parameters, r , v Let the position and velocity vectors of the probe be the vectors at any given moment; by solving for the vectors at any point on the orbit... r and v The eccentricity vector of the orbit can then be obtained, and the state vector can be solved by the orbital parameters; By reading the ephemeris to obtain the Moon's position in the geocentric inertial frame at the moment of perigee, the right ascension and declination of the Moon's position can be obtained. Based on the right ascension and declination, the right ascension of the ascending node and the argument of perigee of the transfer orbit can be approximated using a spherical triangle. Other orbital parameters of the Earth-Moon transfer orbit are then solved using the target-shooting method: based on the perigee radius of the Earth-Moon transfer orbit... r pE Transfer time t Trans and the radius of the perigee r pM Assuming the perigee lies on the extension of the lunar position vector, the initial value of the orbital apogee radius is given as... (2) In the formula r aE The apogee radius; The apogee radius of the transfer trajectory is determined by firing at the target; the firing equation is as follows: (3) (4) (5) (6) (7) In the formula, the true nearest point angle f f It can be derived from the angle of the near point. M f Calculations show that r f This represents the orbital radius at the perigee, and the target is... fvec Minimum; find the apogee radius r aE Then, using the above formula, the semi-major axis of the Earth-Moon transfer orbit can be obtained. a E eccentricity e E and the true periapsis at the moment of near-lunar point f f This yields a set of orbital parameters, which are converted into position and velocity vectors, and initial values ​​for the geocentric segment eccentricity vector. e E0 It can be calculated; Step 2.3: Calculate the initial value of the eccentricity vector of the lunar segment; The state vector at the point of lunar influence is obtained by recursively calculating the orbital parameters. The above calculations were performed in a geocentric inertial frame. This state vector is then transferred to the lunar orbital plane coordinate system to calculate the initial value of the eccentricity vector at the lunar center. e M0 .

10. The transfer trajectory design system for a lunar elliptical frozen orbit based on eccentricity vector target shooting according to claim 9, characterized in that, Execute in the Earth-Moon transfer orbit calculation module: Step 3.1: Based on the eccentricity vector of the geocentric segment, calculate the time and position velocity when the object reaches the lunar influence sphere; Calculate the orbital parameters at the pericenter based on the eccentricity vector: First, calculate the right ascension and declination of the pericentrism. (8) (9) In the formula e x , e y , e z for e The directional components; the right ascension and argument of the ascending node can be obtained from the right ascension and declination; The magnitude of the eccentricity vector is equal to the eccentricity. The semi-major axis is calculated based on the perigee radius and eccentricity of the geocentric segment of the orbit. After obtaining the orbital parameters of the geocentric segment based on the eccentricity vector of the geocentric segment, the time taken for the orbit to reach the lunar sphere of influence can be calculated. t P and position-velocity vectors; Step 3.2: Calculate the position and velocity over a certain period of time by using the eccentricity vector of the lunar segment. The lunar orbital parameters for the lunar center segment can be obtained from the eccentricity vector of the lunar center segment, and the orbital parameters can be calculated by working backwards for a certain period of time. t M = t trans - t P The position and velocity vectors at the orbital splicing point are obtained, and the state vector in the lunar orbit coordinate system is converted into the state vector in the geocentric inertial system. Step 3.3: Solve the lunar transfer orbit by splicing conic sections using target practice, and use the target practice results as initial values ​​to solve the problem using a high-precision model; The initial value of the geocentric segment eccentricity vector obtained from steps 2.2 and 2.

3. e E0 Initial value of the eccentricity vector of the lunar segment e M0 As the initial value for target shooting, the difference between the position and velocity vectors is obtained by calculating steps 3.1 and 3.

2. The target shooting iterates the eccentricity vectors of the geocentric segment and the lunar eccentricity vector until the position and velocity tolerances are met. The target shooting solution is used as the initial value to solve the problem using a high-precision model, and finally a complete Earth-Moon transfer orbit that meets the mission constraints is obtained.

11. The transfer trajectory design system for a lunar elliptical frozen orbit based on eccentricity vector target shooting according to claim 10, characterized in that, Executed in the lunar capture orbit calculation module: Step 4.1: Determine the capture orbit period T ; To ensure the stability of the capture orbit, it must be within the lunar sphere of influence, and the capture orbit period must be no more than 6 days. After successful capture, in order to ensure that the probe can operate on orbit for a period of time without hitting the moon in the event of a malfunction that prevents subsequent orbit changes, the maximum capture orbit period is 4 days, provided that the probe does not hit the moon for 60 days. After entering the capture orbit, the probe will transfer to a highly elliptical frozen orbit, requiring orbit adjustment at the apogee. The longer the capture orbit period, the lower the velocity at the apogee, and the smaller the velocity increment required for orbit adjustment at the apogee. Therefore, the capture orbit period should be as large as possible. Lunar braking capture needs to take into account the actual orbit control speed increment deviation, and the capture speed increment needs to leave a certain margin to ensure that it can be captured in a stable orbit; After comprehensive consideration, the capture orbit period was chosen to be 3 days; Step 4.2: Calculate the lunar capture orbit parameters; Capture orbit semi-major axis a c for (10) The eccentricity is calculated based on the semi-major axis of the capture orbit and the radius of the perigee. The right ascension of the ascending node is 0 and has no effect. The argument of the perigee is obtained based on time. The lunar perigee altitude and inclination of the lunar capture orbit are determined by the Earth-Moon transfer orbit.

12. The transfer trajectory design system for a lunar elliptical frozen orbit based on eccentricity vector target shooting according to claim 11, characterized in that, Execute the following in the large ellipse frozen orbit calculation module: Step 5.1: Adjust the near-lunar maneuver to change the lunar phase angle; The far-moon maneuver involves adjusting the perihelion angle of the lunar capture orbit while simultaneously adjusting the orbital inclination to the required angle, thereby obtaining a highly elliptical frozen orbit for the target. Due to Earth-Moon space dynamics, the perilpoint argument of the Earth-Moon transfer orbit varies between 120° and 150° when it reaches the perilpoint, making it impossible to directly reach the 90° perilpoint argument required for a highly elliptical frozen orbit. Adjusting the perilpoint argument by performing a mid-course maneuver during the Earth-Moon transfer would require a large velocity increment, which is not feasible. Therefore, the orbital argument adjustment was chosen to be performed after lunar capture. The perilune argument is an in-plane orbital parameter. Based on the Gaussian perturbation equation, the orbital changes are performed at different true anomalies under unit perturbation acceleration on the lunar orbit formed after capture. Adjusting the perilune argument near the apogee is the most efficient. Step 5.2: Calculate the frozen orbit of the large ellipse; Orbital adjustments were made near the apogee to generate a highly elliptical frozen orbit with a period of 12 hours, with the adjustment target being the perigee argument. ω F ,inclination i F and the height of the perilune h pF ; In the two-body configuration, a trajectory change is performed at a certain point on the capture trajectory to reach the target trajectory. ω F , i F and h pF Given the given information, the orbital elements of the target orbit can be determined through spatial geometric relationships. The change position and velocity increment under two-body conditions can be calculated analytically. The calculation process is as follows: The position and velocity vector of the orbital change point can be obtained; the radius, right ascension, and declination of that position can be calculated to determine whether it is within the range of the target inclination angle, and the right ascension of the ascending node of the target orbit can be obtained. Ω F And true near point angle f F ;according to (11) (12) The eccentricity of the target frozen orbit can be calculated. e F and semi-major axis a F for (13) (14) In the formula r 0 represents the radius of the trajectory change point. At this point, a set of trajectory parameters for the frozen trajectory are obtained, and the velocity vector of the trajectory at the trajectory change point is calculated. By subtracting the velocity vector at the trajectory change point of the captured trajectory, the trajectory change velocity increment can be obtained. By selecting a suitable trajectory change point to minimize the consumption of the trajectory change velocity increment, and optimizing it under a high-precision model, the optimal trajectory change position and trajectory change velocity increment are determined. Finally, to obtain a highly elliptical frozen orbit with a given period, a pulse is applied at the lunar perihelion, and the highly elliptical frozen orbit with the target period is obtained by a target-shooting method.

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