A method for analyzing the deflection distance of near-Earth asteroids in a multi-spacecraft interception strategy

Abstract

The present invention relates to the field of near-Earth planet defense technology, specifically a near-Earth asteroid deflection distance analysis method for a multi-spacecraft interception strategy, including setting initial conditions and establishing a target variable system during the process of multiple spacecraft continuously impacting a target asteroid, and by introducing a momentum multiplication effect and establishing a recursive model for multiple spacecraft continuous impacts, it is possible to accurately calculate the deflection distance of the target asteroid after a single or multiple impacts, filling the gap in the prior art in the multi-spacecraft interception scenario. This method not only reduces the computational cost, but also optimizes the interception strategy design, provides the optimal direction for each impact, thereby maximizing the deflection effect, significantly improving the flexibility and success rate of planetary defense missions, and providing important technical support for responding to the threat of near-Earth target asteroids.

Description

Technical Field

[0001] The present invention relates to the field of near-Earth planet defense technology, and in particular to a near-Earth asteroid deflection distance analysis method for a multi-spacecraft interception strategy. Background Art

[0002] The deflection distance refers to the change in the closest approach (CA) distance between the target asteroid and the Earth before and after the kinetic energy impact. , also known as the minimum distance between the star and the earth (i.e. the minimum distance between the target asteroid and the earth), its mathematical expression is:

[0003]

[0004] In the formula Refers to the time point when the target asteroid is closest to the Earth, that is, the moment when the asteroid is closest to the Earth. and They refer to the vectors from the Earth's center to the target asteroid at the closest moment before and after the target asteroid is deflected. When deflection is favorable, Calculate the closest time between the star and the earth Generally, a one-dimensional minimum algorithm is used, and its specific expression is:

[0005]

[0006] Where: b and ɑ are the upper and lower bounds of the given time search window. Generally, the length of the ɑb interval should be greater than one orbital period of the target asteroid.

[0007] The existing methods for calculating the deflection distance can be divided into two categories: numerical methods and analytical methods. The numerical method needs to consider the influence of multiple perturbations, such as the gravity of the eight planets, the gravity of the four main target asteroid belts of CVPH, the gravity of the moon, the solar light pressure, the Yarkovsky effect, the relativistic effect, the earth's thermal perturbation, etc. The calculation amount is extremely high and the calculation cost is relatively high. Therefore, the analytical calculation method is often used to calculate the deflection distance of the target asteroid.

[0008] The existing analytical calculation methods for deflection distance include the Izzo model and the Vasile model. The Izzo model is only applicable under relatively harsh conditions, and it has the problem of being unable to judge whether the minimum distance between the satellite and the ground is getting closer or farther, such as Figure 1 As shown in the figure, the target asteroid has a hyperbolic trajectory within the Earth's sphere of influence. The deflection distance calculated by Izzo analysis may be a positive gain or a negative gain. Therefore, the Vasile model is commonly used to analyze and calculate the deflection distance after the spacecraft intercepts it.

[0009] Unfortunately, the Vasile model is only applicable to single-spacecraft interception strategies. In actual planetary defense missions, in order to achieve the ultimate deflection effect, multiple spacecraft may be used to implement kinetic impacts on the target asteroid to deflect its orbit. Moreover, the Vasile model does not take into account the momentum multiplication effect that occurs during hypervelocity collisions, that is, the influence of the momentum transfer coefficient on the final deflection distance.

[0010] In summary, the current analytical calculation method for the deflection distance cannot meet the needs of multiple spacecraft interception in actual planetary defense missions, and cannot give a more accurate deflection distance calculation result in combination with the momentum transfer coefficient.

[0011] The most applicable deflection distance analytical model is the Vasile model, which was originally used to calculate the minimum orbital intersection distance change before and after the target asteroid is deflected. The specific method is based on the Gaussian perturbation equation to solve the change in the six elements of the target asteroid's orbit caused by the instantaneous change of the velocity vector of the target asteroid in the case of impact deflection. ,in , , , , , The impact moment The semi-major axis of the target asteroid's orbit , eccentricity , orbital inclination , right ascension of ascending node , perigee angular distance 、Mean Anomaly The amount of change.

[0012] Based on the proximal motion equation, the equation can be used to calculate the change of the geocentric vector at the minimum orbital intersection distance according to the change of the six orbital numbers, as shown in formula (1):

[0013] ; (1)

[0014] The change in the six orbital elements of the target asteroid , calculate the change of the target asteroid's geocentric vector at the minimum orbital intersection distance ,

[0015] in: , and They refer to the changes in the three directions of the target asteroid's geocentric vector in the geocentric coordinate system when it is at the MOID point; the MOID point represents the current minimum orbital intersection distance; in the equation is the true anomaly angle of the target asteroid orbit MOID point, For the latitude parameters of the target asteroid at this moment, , here is the argument of perigee of the target asteroid, ,in is the orbit eccentricity of the target asteroid.

[0016] Furthermore, the Vasile model converts the true anomaly angle of the MOID point into Replaced by the true anomaly angle when the near-Earth target asteroid is at perigee To estimate the minimum distance change between the satellite and the ground, consider , the instantaneous velocity change caused by the mission spacecraft impacting the target asteroid , calculate the minimum distance change between the satellite and the ground. , , are the velocity changes in the tangential, radial and normal directions along the heliocentric orbit of the target asteroid, respectively.

[0017] Based on the Gaussian perturbation equation, we can further obtain equation (2). The Gaussian perturbation equation can be used to deduce the changes in the six orbital elements caused by the instantaneous velocity change of the target asteroid, where h is the specific angular momentum of the target asteroid orbit, and are the true anomaly angle and latitude parameters of the target asteroid at the time of impact.

[0018] (2)

[0019] Substituting the changes of the six orbital elements into the proximal motion equation, we can obtain equation (3):

[0020] (3)

[0021] Considering the influence of orbital period variation on the long-term evolution of the mean anomaly angle of the target asteroid at the closest moment to the Earth, it is necessary to perturb the mean anomaly angle in equation (2): Correction is made, as shown in formula (4)

[0022] (4)

[0023] Where: Refers to the time between the deflection moment and the closest moment between the star and the earth. Refers to the deflection moment, Refers to the moment when the star is closest to the earth. Refers to the average angular velocity change caused by deflection. According to Kepler's third law, the average angular velocity change can be expressed in the form of the gravitational constant 𝜇 and the orbital semi-major axis 𝑎. Now the corrected Replace in equation (2) and combine equation (2) and equation (3) using the matrix equation system (5):

[0024] (5)

[0025] in: The change in the six orbital elements of the target asteroid caused by the deflection, and are the state transfer matrices of the proximal motion equation and the Gaussian perturbation equation, respectively. Their specific expressions are shown in equations (6) and (7):

[0026] (6)

[0027] (7)

[0028] In summary, the most applicable Vasile model can only analytically give the change of the target asteroid's geocentric vector in three directions under a single pulse condition. , and , and the deflection distance is obtained accordingly. However, in actual missions, considering the actual launch and carrying capacity of spacecraft, a single spacecraft deflection strategy may not be enough to provide the target asteroid with enough velocity change to achieve the expected deflection distance, and a multi-spacecraft interception strategy is likely to be implemented. The existing deflection distance analytical model cannot calculate the analytical solution of the deflection distance of the target asteroid under multiple consecutive impacts. Moreover, the existing analytical model does not take into account the momentum multiplication effect when the mission spacecraft and the target asteroid collide at a high speed, so the calculated deflection distance is difficult to guarantee its accuracy.

[0029] In view of this, the present invention provides a near-Earth asteroid deflection distance analysis method for a multi-spacecraft interception strategy. Summary of the invention

[0030] The purpose of the present invention is to provide a near-Earth asteroid deflection distance analysis method for a multi-spacecraft interception strategy, accurately obtain the deflection distance of the target asteroid under single or multiple impacts, help planetary defense missions to design the number of spacecraft and interception orbits, and obtain the maximum deflection distance that can be achieved under a specific interception strategy.

[0031] To achieve the above object, the present invention provides the following technical solutions:

[0032] In a first aspect, the present invention provides a near-Earth asteroid deflection distance analysis method for a multi-spacecraft interception strategy, comprising the following steps:

[0033] Step S1: Setting initial conditions: During the process of multiple spacecraft continuously impacting the target asteroid, the heliocentric vector, true anomaly angle and angular momentum of the target asteroid are set as static constants within the impact interval;

[0034] Step S2: Establishing the target variable system: defining the orbital state, velocity change, orbital six element change and state transfer matrix of the target asteroid;

[0035] Step S3: Optimal impact direction model: The change of the six orbital elements of the target asteroid at the time of the first impact and the change of the geocentric vector of the target asteroid at the minimum orbital intersection distance are written into a state transfer matrix in matrix form through the proximal motion equation;

[0036] Step S4: Calculate the optimal speed direction: by analyzing the maximum eigenvalue and eigenvector of the matrix, obtain the speed direction with the maximum deflection distance;

[0037] Step S5: Calculate the maximum deflection distance of each impact: Calculate the maximum deflection distance of each impact under the unit pulse optimal speed change;

[0038] Step S6: Considering the momentum multiplication effect: combining the actual velocity change and the momentum transfer coefficient β, the actual maximum perigee change is calculated;

[0039] Step S7: Establish a recursive equation group: add up the deflection effects of multiple impacts to obtain the total deflection distance under the multi-spacecraft interception strategy, and calculate the minimum distance between the satellite and the ground after deflection.

[0040] As a preferred implementation of the first aspect of the present invention, the target variable system includes the orbital state of the target asteroid when it is not affected by the deflection, the orbital state of the target asteroid after the i-th spacecraft impact, The velocity change caused by the ith impact, the change in the six orbital elements caused by the ith impact, and the state transfer matrix of the Gaussian perturbation equation at the ith impact.

[0041] As a preferred embodiment of the first aspect of the present invention, the proximal motion equation is used to calculate the change in the six elements of the target asteroid orbit at the i-th impact. Changes in the target asteroid's geocentric vector at the minimum orbital intersection distance Connect them together to obtain the state transfer matrix of the proximal motion equation.

[0042] As a preferred implementation of the first aspect of the present invention, the optimal impact direction under each impact is the optimal speed direction at the time of this impact. When the modulus of the corresponding product of the state transfer matrix of the Gaussian perturbation equation and the state transfer matrix of the proximal motion equation at each impact is the largest, this impact causes the deflection distance, i.e., the minimum distance between the satellite and the ground, to change by the largest amount.

[0043] As a preferred implementation of the first aspect of the present invention, when the magnitude of the velocity change brought about by the impact is constant, the deflection caused by the velocity change is the largest, and the direction of the impact should be parallel to the eigenvector of the maximum eigenvalue of the corresponding Gram matrix, so as to obtain the optimal velocity change per unit pulse. Under the condition of the optimal velocity change, the deflection distance brought about by each impact reaches the maximum value.

[0044] As a preferred implementation of the first aspect of the present invention, the actual maximum perigee change can be obtained by considering the actual speed change and the momentum multiplication effect, and the multiple of the actual speed change and the unit optimal speed change is extracted to obtain the momentum transfer coefficient.

[0045] As a preferred implementation mode of the first aspect of the present invention, the analytical solution of a single impact is extended to the scenario of multiple impacts. For the continuous impacts of n spacecraft, when the n spacecraft intercept the target asteroid, a core matrix recursive equation group is established to calculate the total deflection distance.

[0046] As a preferred implementation of the first aspect of the present invention, the following steps are also included:

[0047] The accurate analytical expression of the deflection distance is obtained when the momentum multiplication effect is considered under the multi-spacecraft interception strategy. The optimal impact direction and the corresponding maximum deflection distance at each impact are extracted through the analytical expression, and then the maximum value of the minimum distance between the satellite and the ground after deflection is obtained.

[0048] In a second aspect, the present invention provides an electronic device, comprising:

[0049] at least one processor; and,

[0050] A memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor so that the at least one processor can execute the method described in the first aspect.

[0051] In a third aspect, the present invention provides a computer-readable storage medium storing instructions, which, when executed on a computer, causes the computer to execute the method described in the first aspect.

[0052] Compared with the prior art, the present invention has the following beneficial effects:

[0053] By introducing the momentum multiplication effect and establishing a recursive model for continuous impacts of multiple spacecraft, the present invention can accurately calculate the deflection distance after a single or multiple impacts, filling the gap in the existing technology in the multi-spacecraft interception scenario. This method not only reduces the computational cost, but also optimizes the interception strategy design, provides the optimal direction for each impact, thereby maximizing the deflection effect, significantly improving the flexibility and success rate of planetary defense missions, and providing important technical support for responding to the threat of near-Earth target asteroids. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 It is a schematic diagram of the analysis of determining the minimum distance between the satellite and the ground in the background technology of the present invention;

[0055] Figure 2 The present invention is a flow chart of the near-Earth target asteroid deflection distance analysis method applicable to the multi-spacecraft interception strategy. DETAILED DESCRIPTION

[0056] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0057] In the description of the present invention, it should be noted that the terms "vertical", "up", "down", "horizontal", etc. indicate orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the present invention.

[0058] In the description of the present invention, it is also necessary to explain that, unless otherwise clearly specified and limited, the terms "set", "install", "connect", and "connect" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or it can be indirectly connected through an intermediate medium, or it can be the internal communication of two elements. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0059] Example 1

[0060] See also Figure 2 The present invention provides a technical solution: a near-Earth asteroid deflection distance analysis method for a multi-spacecraft interception strategy, comprising the following steps:

[0061] Step S1: Setting initial conditions. During the process of multiple spacecraft continuously impacting the target asteroid, the heliocentric vector, true anomaly angle and angular momentum of the target asteroid are set as static constants within the impact interval.

[0062] Specifically, the impact interval refers to the time interval from the first spacecraft impact to the nth spacecraft impact, which is much shorter than the orbital period of the target asteroid. The changes in the orbital parameters of the target asteroid in a short period of time are ignored, so that the initial conditions of the analytical model of the minimum distance change between the target asteroid and the Earth under the multi-spacecraft strategy can be set well; that is, the heliocentric vector of the target asteroid in the impact interval is True anomaly The angular momentum h is considered as a constant. This simplifies the complexity of the problem and makes the dynamic process of multiple spacecraft continuous impacts approximate to a static or quasi-static problem.

[0063] Step S2: Under the assumption of step S1, the target variable system is established by defining the orbital state, velocity change, orbital six element change and state transfer matrix of the target asteroid;

[0064] Specifically, the target variable system includes the orbital state of the target asteroid when it is not affected by the deflection, the orbital state of the target asteroid after the i-th spacecraft impact, the velocity change caused by the i-th impact, the change of the six orbital elements caused by the i-th impact, and the state transfer matrix of the Gaussian perturbation equation at the i-th impact, providing a clear framework for subsequent mathematical modeling and calculations;

[0065] More specifically, under the setting of step S1, the orbital state of the target asteroid when it is not affected by the deflection is defined as , , the orbital state of the target asteroid after the i-th spacecraft deflects the target asteroid is , , , , is a positive integer, define To obtain The kth element of the array, , is a positive integer, such as , that is, the eccentricity of the second element in the orbital state of the target asteroid after the i-th spacecraft deflects the target asteroid , or the eccentricity of the target asteroid after the i-th spacecraft deflects it .

[0066] The orbital velocity of the target asteroid when it is not deflected by the spacecraft is defined as , the orbital velocity after being deflected by the i-th spacecraft is The velocity change caused by the ith impact on the target asteroid is defined as , ;

[0067] in represents the instantaneous velocity change of the target asteroid after being deflected by the i-th spacecraft; , and They respectively represent the velocity changes of the target asteroid along the tangential, radial and normal directions of the heliocentric orbit of the target asteroid after it is deflected by the i-th spacecraft.

[0068] The change in the six orbital elements of the target asteroid caused by the ith impact is defined as , ,

[0069] The state transfer matrix of the Gaussian perturbation equation at the i-th impact is defined as .

[0070] Step S3: Establish an optimal impact direction model based on the target variable system, and write the change of the six elements of the target asteroid orbit at the i-th impact and the change of the target asteroid geocentric vector at the minimum orbit intersection distance into a state transfer matrix in matrix form by using the proximal motion equation;

[0071] Specifically, the complex orbital dynamics problem is converted into a mathematical problem in matrix form. Through the proximal motion equation and the state transfer matrix, the changes in the six orbital elements are linked to the changes in the geocentric vector of the target asteroid, providing a mathematical basis for the subsequent optimization of the impact direction. The key to this step is to use matrix equations to simplify the complexity of the problem while retaining its essential characteristics.

[0072] More specifically, the proximal motion equations are used to convert the changes in the six elements of the target asteroid's orbit at the time of the i-th impact into Changes in the target asteroid's geocentric vector at the minimum orbital intersection distance In this connection, the state transfer matrix of the proximal motion equation is , as shown in formula (8);

[0073] (8)

[0074] in: represents the state transfer matrix, express The transposed matrix of Indicates the minimum distance between the star and the earth; represents the semi-major axis of the target asteroid's orbit; , is the orbital eccentricity of the target asteroid; represents the gravitational constant; represents the cosine of the target asteroid's orbital inclination; represents the sine of the target asteroid's orbital inclination; It indicates the true anomaly angle of the target asteroid when the distance between the star and the earth is the minimum; Indicates the latitude parameter of the target asteroid when the distance between the star and the earth is the minimum;

[0075] Step S4: Calculate the optimal speed direction to maximize the deflection effect. By analyzing the maximum eigenvalue and eigenvector of the matrix, obtain the speed direction with the maximum deflection distance;

[0076] Specifically, in order to maximize the deflection distance (the minimum change in the distance between the satellite and the ground), the modulus of the state transfer matrix must be maximized. When the velocity change is constant, the optimal direction should be parallel to the eigenvector corresponding to the maximum eigenvalue of the state transfer matrix, and mathematical tools should be used to optimize the impact direction, thereby improving the deflection efficiency.

[0077] More specifically, the optimal impact direction for each impact is the optimal velocity direction at the i-th impact, and the state transfer matrix of the Gaussian perturbation equation at the i-th impact is As shown in formula (9); subsequently, formula (9) is abbreviated as ;

[0078] (9)

[0079] in: Represents the true anomaly in the impact interval.

[0080] In summary, we can get the matrix equation for the ith impact, as shown in equation (10):

[0081] (10)

[0082] From the form of formula (10), we can know that If we want the i-th impact to cause the deflection distance, that is, the minimum distance change between the satellite and the ground, Maximum required The modulus of is the largest, that is:

[0083] (11)

[0084] in: Indicates the moment when the star is closest to the earth; represents the deflection moment when the i-th spacecraft hits the target asteroid;

[0085] Step S5: Calculate the maximum deflection distance of each impact under the unit pulse optimal speed change.

[0086] Specifically, the maximum deflection distance that can be achieved by each impact is solved through the relationship between the eigenvalue and the eigenvector. At a certain time, in order to Maximum, then need The direction and matrix The maximum eigenvalue of The eigenvector of Under this condition, the optimal speed change per unit pulse can be obtained: Under this condition, the maximum deflection distance that each impact can bring is:

[0087] (12)

[0088] in: yes The transposed matrix of yes The Gram matrix of .

[0089] Step S6: Consider the momentum multiplication effect, combining the actual speed change and momentum transfer coefficient , calculate the actual maximum perigee change:

[0090] Specifically, the theoretical calculation results are corrected by combining the actual physical process. , considering the momentum multiplication effect in hypervelocity collision, making the calculation results closer to the actual situation. This idea emphasizes the combination of theory and practice to improve the accuracy and practicality of the model. Considering the actual velocity change The actual maximum perigee change can be obtained by combining the momentum multiplication effect as shown in equation (13), where is the multiple of the actual speed change and the unit optimal speed change, is the momentum transfer coefficient.

[0091] (13)

[0092] Step S7: By establishing a recursive equation group, the deflection effects of multiple impacts are accumulated to obtain the total deflection distance under the multi-spacecraft interception strategy;

[0093] Specifically, the analytical solution of a single impact is extended to the scenario of multiple impacts. For the continuous impacts of n spacecraft, the core matrix recursive equations for calculating the deflection distance when n spacecraft intercept the target asteroid are obtained are as follows:

[0094] (14)

[0095] In summary, a core matrix recursive equation group is established to calculate the total deflection distance, which is an analytical calculation method for the deflection distance (the minimum distance change between the satellite and the ground) under the multi-spacecraft deflection strategy, simplifying the calculation process.

[0096] Example 2

[0097] This embodiment provides a near-Earth asteroid deflection distance analysis method for a multi-spacecraft interception strategy based on Embodiment 1, and further includes the following steps:

[0098] The accurate analytical formula of the deflection distance under the multi-spacecraft interception strategy considering the momentum multiplication effect is obtained. Through this analytical formula, the minimum distance between the satellite and the ground after deflection can be further given. The analytical expression of:

[0099]

[0100] When faced with specific problems, it is possible to calculate the deflection distance after multiple impacts with the target asteroid, understand the optimal impact direction and the corresponding maximum deflection distance for each impact, and analytically calculate the maximum value of the minimum distance between the star and the earth after the deflection, to assist in the design of interception orbits for planetary defense missions. This fills the gap in the analytical calculation method for deflection distances under a multi-spacecraft strategy, provides support for the design of interception orbits for planetary defense missions, and transforms theoretical calculation results into guidance for practical applications, thus realizing the practical application of technology.

[0101] Example 3

[0102] The parts not described in this embodiment are as in Embodiment 1. This embodiment shows an electronic device, including:

[0103] at least one processor; and,

[0104] A memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor so that the at least one processor can execute the near-Earth asteroid deflection distance analysis method for a multi-spacecraft interception strategy described in the first aspect.

[0105] The electronic device may have relatively large differences due to different configurations or performances, and may include one or more processors (Central Processing Units, CPU) and one or more memories, wherein the memory stores at least one computer program, and the at least one computer program is loaded and executed by the processor to implement a near-Earth asteroid deflection distance analysis method for a multi-spacecraft interception strategy provided in the above-mentioned method embodiments.

[0106] The electronic device may also include other components for realizing the functions of the device, for example, the electronic device may also have components such as a wired or wireless network interface and an input / output interface for input and output. The embodiments of the present application will not be described in detail here.

[0107] Example 4

[0108] The parts not described in this embodiment are as in Embodiment 1. This embodiment also provides a computer-readable storage medium storing instructions. When the instructions are executed on a computer, the computer executes the near-Earth asteroid deflection distance analysis method of a multi-spacecraft interception strategy.

[0109] Those skilled in the art will appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed in the present invention can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of the present invention.

[0110] Those skilled in the art can clearly understand that, for the convenience and brevity of description, the specific working processes of the systems, devices and units described above can refer to the corresponding processes in the aforementioned method embodiments and will not be repeated here.

[0111] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A near-Earth asteroid deflection distance analysis method for a multi-spacecraft interception strategy, characterized by: The following steps are involved: Step S1: Setting initial conditions: During the process of multiple spacecraft continuously impacting the target asteroid, the heliocentric vector, true anomaly angle and angular momentum of the target asteroid are set as static constants within the impact interval; Step S2: Establishing the target variable system: defining the orbital state, velocity change, orbital six element change and state transfer matrix of the target asteroid; Step S3: Optimal impact direction model: The change of the six orbital elements of the target asteroid at the time of the first impact and the change of the geocentric vector of the target asteroid at the minimum orbital intersection distance are written into a state transfer matrix in matrix form through the proximal motion equation; Step S4: Calculate the optimal speed direction: by analyzing the maximum eigenvalue and eigenvector of the matrix, obtain the speed direction with the maximum deflection distance; Step S5: Calculate the maximum deflection distance of each impact: Calculate the maximum deflection distance of each impact under the unit pulse optimal speed change; Step S6: Considering the momentum multiplication effect: combining the actual velocity change and the momentum transfer coefficient β, the actual maximum perigee change is calculated; Step S7: Establish a recursive equation group: add up the deflection effects of multiple impacts to obtain the total deflection distance under the multi-spacecraft interception strategy, and calculate the minimum distance between the satellite and the ground after deflection.

2. The near-Earth asteroid deflection distance analysis method of a multi-spacecraft interception strategy according to claim 1, characterized in that: The target variable system includes the orbital state of the target asteroid when it is not affected by the deflection, the orbital state of the target asteroid after the i-th spacecraft impact, the velocity change caused by the i-th impact, the change of the six orbital elements caused by the i-th impact and the state transfer matrix of the Gaussian perturbation equation at the i-th impact.

3. The near-Earth asteroid deflection distance analysis method of a multi-spacecraft interception strategy according to claim 2, characterized in that: The proximal motion equation is used to link the changes in the six orbital elements of the target asteroid during impact with the changes in the geocentric vector of the target asteroid at the minimum orbital intersection distance to obtain the state transfer matrix of the proximal motion equation.

4. The near-Earth asteroid deflection distance analysis method of a multi-spacecraft interception strategy according to claim 3, characterized in that: The optimal impact direction under each impact is the optimal velocity direction at the time of this impact. When the modulus of the corresponding product of the state transfer matrix of the Gaussian perturbation equation at each impact and the state transfer matrix of the proximal motion equation is the largest, this impact causes the deflection distance, that is, the minimum distance between the satellite and the earth, to change by the largest amount.

5. The near-Earth asteroid deflection distance analysis method of a multi-spacecraft interception strategy according to claim 4, characterized in that: When the magnitude of the velocity change caused by the impact is constant, the direction of the maximum deflection impact caused by the velocity change should be parallel to the eigenvector of the maximum eigenvalue of the corresponding Gram matrix, and the optimal velocity change per unit pulse is obtained. Under the condition of the optimal velocity change, the deflection distance brought by each impact reaches the maximum value.

6. The near-Earth asteroid deflection distance analysis method of a multi-spacecraft interception strategy according to claim 5, characterized in that: Considering the actual speed change and momentum multiplication effect, the actual maximum perigee change can be obtained, and the multiple of the actual speed change and the unit optimal speed change can be extracted to obtain the momentum transfer coefficient.

7. The near-Earth asteroid deflection distance analysis method of a multi-spacecraft interception strategy according to claim 6, characterized in that: The analytical solution of a single impact is extended to the scenario of multiple impacts. For the continuous impacts of n spacecraft, when the n spacecraft intercept the target asteroid, a core matrix recursive equation group is established to calculate the total deflection distance.

8. The near-Earth asteroid deflection distance analysis method of a multi-spacecraft interception strategy according to claim 7, characterized in that: The following steps are also included: The accurate analytical expression of the deflection distance is obtained when the momentum multiplication effect is considered under the multi-spacecraft interception strategy. The optimal impact direction and the corresponding maximum deflection distance at each impact are extracted through the analytical expression, and then the maximum value of the minimum distance between the satellite and the ground after deflection is obtained.

9. An electronic device, characterized in that: include: at least one processor; as well as, A memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor so that the at least one processor can execute a near-Earth asteroid deflection distance resolution method for a multi-spacecraft interception strategy as described in any one of claims 1-8.

10. A computer-readable storage medium storing instructions, which, when executed on a computer, enable the computer to execute the near-Earth asteroid deflection distance analysis method for a multi-spacecraft interception strategy as described in any one of claims 1 to 8.

Images