Constellation satellite collision analysis method based on space debris environment topology network model

Abstract

The invention discloses a constellation satellite collision analysis method based on a space debris environment topology network model, and relates to the field of aerospace. The method comprises the following steps: carrying out volume element subdivision on a space target to obtain a plurality of space object group nodes; based on the migration direction of the space target group, the connection relation of the multiple space object group nodes is analyzed and processed, a topological structure is constructed, and a topological network is obtained; carrying out modeling processing on the topology network based on the space debris influence factors by adopting a fluid mechanics method to obtain a space debris environment topology network model; analyzing and solving the space debris environment topology network model by adopting an adjacent matrix to obtain an evolution prediction result of the space debris environment; and performing collision analysis on the constellation satellites according to the evolution prediction result by adopting a collision probability algorithm to obtain a collision analysis result. The invention aims to quickly realize fragment evolution so as to carry out collision analysis of constellation satellites.

Description

Technical Field

[0001] The present application relates to the field of aerospace, and in particular to a constellation satellite collision analysis method based on a space debris environment topology network model. Background Art

[0002] In recent years, with the rapid development of human space activities, especially the frequent launches of mega-constellations, the deterioration of the space debris environment has become increasingly serious. This trend is expected to significantly increase the collision risk of spacecraft in orbit, seriously threatening the safety and sustainability of space missions. Therefore, accurately and efficiently predicting the evolution of space debris and conducting reliable risk assessments for spacecraft are of great significance for ensuring the safe execution of human space activities.

[0003] Analysis of the space debris environment can be conducted at both the microscopic and macroscopic levels. Microscopic models focus on the precise behavior of individual targets, but they consume large amounts of computational resources and are inefficient. Macroscopic models, on the other hand, classify space targets by their characteristics and use groups of them as research units to predict environmental evolution. This offers significant computational efficiency advantages over microscopic approaches. However, existing macroscopic methods often treat different types of space targets separately, solving them using (partial) differential equations separately, ignoring the interactions between targets.

[0004] In reality, the space debris environment is an interconnected system, with complex connections and interactions between different targets. On the one hand, dynamic interactions can occur between different types of targets, even leading to changes in their physical states. For example, a collision between two satellites can produce debris, while an active satellite can become a defunct satellite or debris during post-mission disposal. On the other hand, even targets of the same type can experience positional changes under the influence of various space environments, essentially an indirect interaction between targets with different orbital characteristics. For example, space debris experiences orbital decay due to atmospheric drag, while satellites experience orbital precession due to J2 perturbations. These interactions play a key role in shaping the evolution of the overall space environment. Therefore, characterizing the network relationships between space targets and systematically analyzing their interactions are key research priorities.

[0005] Spacecraft risk assessment relies on the evolution of the space debris environment. Traditional collision event prediction methods are based on the propagation of space target orbits and can determine the target, location, and time of a specific collision. However, these methods are computationally expensive and can only randomly assess individual events, making it difficult to effectively assess the collision risk of a spacecraft over the entire operating area and over a continuous period of time. The concept of collision probability was proposed, which was initially used to assess the risk of collision between celestial bodies (such as asteroids and comets). Based on this method, Kessler and Wetherill respectively developed new collision probability algorithms, eliminating the assumptions of zero eccentricity and zero inclination, and improving the applicability of the model. However, all three methods assume that the orbit is not perturbed. In order to more realistically reflect the orbital state, NASA proposed the CUBE algorithm, which divides the space into multiple volume units and uses the target space density to calculate the collision probability within each unit. ESA released the DRAMA software, which calculates the collision frequency and probability through the space target flux provided by the MASTER model. These methods update the number of orbital elements through uniform time sampling, but they still rely on the microscopic debris evolution model, and still have the problems of high computing resource requirements and low efficiency. There is currently no collision probability algorithm suitable for macroscopic models. Summary of the Invention

[0006] The purpose of this application is to provide a constellation satellite collision analysis method based on a space debris environment topology network model, which can quickly realize debris evolution to perform collision analysis of constellation satellites.

[0007] To achieve the above objectives, this application provides the following solutions:

[0008] In a first aspect, the present application provides a constellation satellite collision analysis method based on a space debris environment topology network model, comprising:

[0009] Perform volume element segmentation on the space target to obtain multiple space object group nodes;

[0010] Based on the migration direction of the spatial target group, the connection relationship of the plurality of spatial object group nodes is analyzed and processed, and a topological structure is constructed to obtain a topological network;

[0011] Using a fluid mechanics method to model the topological network based on the influencing factors of space debris, a topological network model of the space debris environment is obtained;

[0012] The adjacency matrix is ​​used to analyze and solve the space debris environment topology network model to obtain the evolution prediction result of the space debris environment;

[0013] A collision probability algorithm is used to perform collision analysis on the constellation satellites according to the evolution prediction result to obtain a collision analysis result.

[0014] According to the specific embodiments provided in this application, this application discloses the following technical effects:

[0015] This application provides a constellation satellite collision analysis method based on a space debris environment topological network model. By using a topological network to characterize the relationship between space targets and combining it with fluid dynamics methods for modeling and processing, a space debris environment topological network model that describes the debris evolution mechanism is obtained. Based on the established space debris environment topological network model, an adjacency matrix is ​​used for analysis and solution to obtain a prediction result of the evolution of the space debris environment, thereby enabling rapid realization of debris evolution. Then, a collision probability algorithm is used to perform collision analysis on the constellation satellites to obtain collision analysis results. Therefore, this application can quickly realize debris evolution to perform collision analysis on constellation satellites. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0017] Figure 1 This is a flow chart of a constellation satellite collision analysis method based on a topological network model of a space debris environment;

[0018] Figure 2 It is a schematic diagram of the position of the space volume element;

[0019] Figure 3 Schematic diagram of the topological structure of each space object group node;

[0020] Figure 4 Schematic diagram of the change in collision probability of constellation satellites;

[0021] Figure 5 Schematic diagram of the average collision probability distribution of constellation satellites;

[0022] Figure 6 Schematic diagram of the deorbit trajectory of the failed satellite;

[0023] Figure 7 This is a schematic diagram of the distribution of space targets within the area where the failed satellite passes;

[0024] Figure 8 Schematic diagram of collision probability with different types of space targets;

[0025] Figure 9 Schematic diagram of collision probability with space targets of different sizes;

[0026] Figure 10 Create a flow chart for the technology. DETAILED DESCRIPTION

[0027] The following will be combined with the drawings in the embodiments of this application to clearly and completely describe the technical solutions in the embodiments of this application. Obviously, the embodiments described are only part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of this application.

[0028] The development of mega-constellations has exacerbated the deterioration of the space debris environment, posing a significant threat to spacecraft safety. This application aims to explore the evolution of the space debris environment and the collision risk of spacecraft. First, a topological network model of the space debris environment is proposed. This model integrates multidisciplinary methods such as topological networks, fluid dynamics, and aerospace dynamics. It can structuredly represent the relationships between space objects and enable rapid prediction of the space debris environment. Subsequently, a collision probability algorithm is constructed based on this topological network model. This algorithm inherits the efficiency of the topological network model and its reliability is verified by comparison with the European Space Agency's classic DRAMA software. Finally, based on this model, the collision risk of constellation satellites in low-Earth orbit (LEO) is analyzed, covering both the on-orbit operation phase and the deorbit phase. During operation, the risk of internal collisions between constellation satellites and other satellites in the same constellation is much higher than the risk of collisions with other space objects. Furthermore, during deorbit, the collision risk peaks when a satellite crosses the operating area of ​​Starlink satellites.

[0029] A topological network is a mathematical tool used to describe the relationships between nodes in complex systems and has been widely used in fields such as physics, communications, and ecology. In a topological network, nodes represent individuals or elements in the system, while edges represent the interactions between nodes. This structured approach allows for a clear depiction of the connections and dynamics within the system, revealing its evolutionary patterns and underlying behavior. Therefore, applying the concept of topological networks to the study of the space debris environment holds great promise. Within this framework, space objects can be divided into groups based on their type, location, and physical characteristics, with each group considered a node in the network. Based on the dynamic characteristics of the objects, multiple environmental influences, and human space activities, a model of the interactions between nodes is constructed, ultimately forming a topological network of the space debris environment. Solving this network model can predict the future evolution of space objects.

[0030] In order to make the above-mentioned purposes, features and advantages of the present application more obvious and easy to understand, the present application is further described in detail below with reference to the accompanying drawings and specific implementation methods.

[0031] In an exemplary embodiment, Figure 1 As shown, a constellation satellite collision analysis method based on a space debris environment topology network model is provided, including:

[0032] Step 100: Perform volume element segmentation on the space target to obtain multiple space object group nodes.

[0033] The space target is divided into volume elements to obtain multiple space object group nodes, including:

[0034] The Euler method is used to divide the space target into volume elements, wherein the LEO orbit is divided along the radial, right ascension and declination directions according to the set division intervals to obtain multiple space volume elements.

[0035] The intervals are divided according to the orbital inclination and the surface-to-mass ratio to obtain multiple divided intervals.

[0036] A plurality of space object group nodes are determined according to a plurality of partition intervals and a plurality of space volume elements.

[0037] Step 200: Based on the migration direction of the spatial target group, the connection relationship of multiple spatial object group nodes is analyzed and processed, and a topological structure is constructed to obtain a topological network.

[0038] The expression corresponding to the topological network is:

[0039]

[0040] Among them, α is the interval number of orbital altitude; β is the interval number of declination; γ is the interval number of right ascension; θ is the interval number of orbital inclination; η is the interval number of surface mass ratio; is the change in payload density within the αth orbital altitude interval, the βth declination interval, the γth right ascension interval, the θth orbital inclination interval, and the ηth surface-to-mass ratio interval; is the change in the rocket body density within the αth orbital altitude interval, the βth declination interval, the γth right ascension interval, the θth orbital inclination interval, and the ηth surface-to-mass ratio interval; is the change in satellite density in the post-mission disposal state within the αth orbital altitude interval, the βth declination interval, the γth right ascension interval, the θth orbital inclination interval, and the ηth surface-to-mass ratio interval; is the change in density of debris in the αth orbital altitude interval, the βth declination interval, the γth right ascension interval, the θth orbital inclination interval, and the ηth surface-to-mass ratio interval; is the spatial density of the payload in the αth orbital altitude interval, the βth declination interval, the γth right ascension interval, the θth orbital inclination interval, and the ηth area-to-mass ratio interval; is the space density of the rocket body in the αth orbital altitude interval, the βth declination interval, the γth right ascension interval, the θth orbital inclination interval, and the ηth surface-to-mass ratio interval; is the spatial density of post-mission disposal satellites in the αth orbital altitude interval, the βth declination interval, the γth right ascension interval, the θth orbital inclination interval, and the ηth surface-to-mass ratio interval; is the spatial density of debris in the αth orbital altitude interval, the βth declination interval, the γth right ascension interval, the θth orbital inclination interval, and the ηth surface-to-mass ratio interval; T λ is the transfer function of the space object under the action of J2 perturbation; is the payload density in the αth orbital altitude interval, the βth declination interval, the γ±1th right ascension interval, the θth orbital inclination interval, and the ηth surface-to-mass ratio interval; The rocket body density is in the αth orbital altitude interval, the βth declination interval, the γ±1th right ascension interval, the θth orbital inclination interval, and the ηth surface-to-mass ratio interval; is the rocket body density in the α+1th orbital altitude interval, the βth declination interval, the γth right ascension interval, the θth orbital inclination interval, and the ηth surface-to-mass ratio interval; dt is the time step; t is the time; T drag is the orbit-descending function of a space object under the influence of atmospheric drag; T PMD is the orbit reduction function of the space object under the action of post-mission disposal; L is the launch volume element U α,β,γ The density function of space objects within; is the new volume element U α,β,γ The density of failed satellites within ; τ is the success rate of post-mission disposal; is the spatial density of post-mission disposal satellites in the αth orbital altitude interval, the βth declination interval, the γ±1th right ascension interval, the θth orbital inclination interval, and the ηth surface-to-mass ratio interval; is the spatial density of post-mission disposal satellites in the α+1th orbital altitude interval, the βth declination interval, the γth right ascension interval, the θth orbital inclination interval, and the ηth surface-to-mass ratio interval; is the spatial density of debris in the αth orbital altitude interval, the βth declination interval, the γ±1th right ascension interval, the θth orbital inclination interval, and the ηth surface-to-mass ratio interval; is the spatial density of debris in the α+1th orbital altitude interval, the βth declination interval, the γth right ascension interval, the θth orbital inclination interval, and the ηth surface-to-mass ratio interval.

[0041] Step 300: Using a fluid mechanics method to model the topological network based on the factors affecting space debris, to obtain a topological network model of the space debris environment.

[0042] Among them, the fluid mechanics method is used to model the topological network based on the factors affecting space debris, and the topological network model of the space debris environment is obtained, which specifically includes:

[0043] Fluid mechanics methods are used to process continuity influencing factors and determine the continuity equation. The continuity influencing factors are the flow variation information of the debris density field in the altitude direction, the distance from the center of the Earth direction, and the right ascension direction. The continuity equation includes the transfer function of the space object under the action of J2 perturbation, the orbit reduction function of the space object under the action of atmospheric drag, and the orbit reduction function of the space object under the action of PMD.

[0044] The transfer function of a space object under the action of J2 perturbation is expressed as follows:

[0045]

[0046] Among them, T λ is the transfer function of the space object under the action of J2 perturbation; is the spatial density of space objects in the αth orbital altitude interval, the βth declination interval, the γth right ascension interval, the θth orbital inclination interval, and the ηth surface-to-mass ratio interval; is the spatial density of space objects in the αth orbital altitude interval, the βth declination interval, the γ±1th right ascension interval, the θth orbital inclination interval, and the ηth surface-to-mass ratio interval; is the density change in the height direction corresponding to the right ascension direction; f λ is the component of the density field in the right ascension direction; λ is the right ascension; G is any type of space object group; P is the payload; R is the rocket body; D is the debris; S is the post-mission disposal satellite; Δλ is the division interval in the right ascension direction; is the spatial density of space objects in the declination of the αth orbital altitude interval, the βth declination interval, the γ+1th right ascension interval, and the θth orbital inclination interval; σ is the declination; For U α,β,γ+1 The area in the right ascension direction; U α,β,γ+1 is the volume element formed by the αth orbital altitude interval, the βth declination interval, and the γ+1th right ascension interval; α is the orbital altitude interval number; β is the declination interval number; γ is the right ascension interval number; θ is the interval number of the orbital inclination; η is the interval number of the surface mass ratio; for Average transfer speed in the right ascension direction; is the spatial density of space objects in the αth orbital altitude interval, the βth declination interval, the γth right ascension interval, and the θth orbital inclination interval; is the spatial density of space objects in the αth orbital altitude interval, the βth declination interval, the γ-1th right ascension interval, the θth orbital inclination interval, and the ηth surface-to-mass ratio interval; U α,β,γ is the volume element formed by the αth orbital altitude interval, the βth declination interval, and the γth right ascension interval; U α,β,γ-1 The volume element is formed by the αth orbital altitude interval, the βth declination interval, and the γ-1th right ascension interval; is the volume element U α,β,γ Area in the right ascension direction; for Average transfer speed in the right ascension direction; For U α,β,γ-1 Area in the right ascension direction; for The average transfer speed in the right ascension direction; V α,β,γ is the volume of the volume element.

[0047] The orbit reduction function of a space object under the influence of atmospheric drag is expressed as follows:

[0048]

[0049] Among them, T drag is the orbit-descending function of a space object under the influence of atmospheric drag; is the density of space objects in the αth orbital altitude interval, the βth declination interval, the γth right ascension interval, the θth orbital inclination interval, and the ηth surface-to-mass ratio interval; is the spatial density of space objects in the α+1th orbital altitude interval, the βth declination interval, the γth right ascension interval, the θth orbital inclination interval, and the ηth surface-to-mass ratio interval; is the density change in the height direction corresponding to the track height direction; f r is the component of the density field in the orbital height direction; r is the orbital height; G is any type of space object; R is the rocket body; D is the debris; Δr is the division interval in the radial direction; U α+1,β,γ The volume element is formed by the α+1th orbital altitude interval, the βth declination interval, and the γth right ascension interval; is the volume element U α+1,β,γ Area in the right ascension direction; for The natural descent rate in the orbital altitude direction; is the volume element U α,β,γ The area in the direction of track height; V α,β,γ is the volume of the volume element; for The natural descent rate in the orbital altitude direction.

[0050] The orbit reduction function of a space object under the action of PMD is expressed as follows:

[0051]

[0052] Among them, T PMD is the orbit-demotion function of the space object under the action of post-mission disposal; is the spatial density of space objects in the αth orbital altitude interval, the βth declination interval, the γth right ascension interval, the θth orbital inclination interval, and the ηth surface-to-mass ratio interval; is the spatial density of space objects in the α+1th orbital altitude interval, the βth declination interval, the γth right ascension interval, the θth orbital inclination interval, and the ηth surface-to-mass ratio interval; is the density change in the height direction corresponding to the right ascension direction; is the density change in the height direction corresponding to the track height direction; f r is the component of the density field in the orbital height direction; r is the orbital height; G is any type of space object; R is the rocket body; D is the debris; Δr is the division interval in the radial direction; U α+1,β,γ The volume element is formed by the α+1th orbital altitude interval, the βth declination interval, and the γth right ascension interval; is the volume element U α+1,β,γ Area in the right ascension direction; for PMD deorbit rate in the orbit height direction; is the area of ​​the volume element in the direction of the earth's radius; for PMD orbit reduction rate in the orbit height direction; V α,β,γ is the volume of the volume element.

[0053] A continuous topological network model is determined according to the continuity equation and the topological network.

[0054] By adopting the method of constellation configuration and fitting the parameters of historical space launch activities, a discontinuous topological network model is determined according to the discontinuous influencing factors; the discontinuous influencing factors include: satellite launch and post-mission disposal.

[0055] According to the continuous topological network model and the discontinuous topological network model, the space debris environment topological network model is determined.

[0056] Step 400: Analyze and solve the space debris environment topology network model using the adjacency matrix to obtain the evolution prediction result of the space debris environment.

[0057] Among them, the adjacency matrix is ​​used to analyze and solve the topological network model of the space debris environment, and the evolution prediction results of the space debris environment are obtained, including:

[0058] Based on the preset matrix, the space debris environment topology network model is converted into a mathematical model in matrix form.

[0059] The adjacency matrix is ​​used to solve the mathematical model and obtain the evolution prediction results of the space debris environment.

[0060] The expression of the mathematical model is:

[0061]

[0062] The expression of the adjacency matrix is:

[0063]

[0064] in, is the function corresponding to the mathematical model; is the density matrix of space objects changing with orbital altitude and right ascension when the declination, orbital inclination and surface-to-mass ratio are fixed; is the density variation matrix of the space object caused by the continuity factor as the orbital altitude and right ascension change when the declination, orbital inclination and surface-to-mass ratio are determined; is the density variation matrix of the space object caused by discontinuous factors as the orbital altitude and right ascension change when the declination, orbital inclination and surface-to-mass ratio are determined; δ is the sequence number of the discrete time step; for The value of δ at the discrete time step; for The value of δ at the discrete time step; for The value of δ at the discrete time step; A is the adjacency matrix; A P is the adjacency matrix of payload nodes; A R is the adjacency matrix of the rocket body nodes; A S A is the adjacency matrix of the satellite nodes after the mission; D is the adjacency matrix of the fragment nodes.

[0065] Step 500: Using a collision probability algorithm, perform collision analysis on the constellation satellites according to the evolution prediction result to obtain a collision analysis result.

[0066] The collision probability algorithm is used to determine the collision probability; the method for determining the collision probability specifically includes:

[0067] Determine the spatial volume elements that the spatial target group passes through during operation and determine the corresponding spatial density.

[0068] Using the formula Determine spatial target flux.

[0069] The collision probability is determined based on the spatial target flux, the spatial volume element and the corresponding spatial density.

[0070] Among them, F α,β,γ is the space target flux; N I The number of intervals divided by the orbital inclination; N Ais the number of intervals divided by the area-to-mass ratio; θ is the interval number of the orbital inclination; η is the interval number of the area-to-mass ratio; is the density of the space object; σ is the intersection cross-sectional area of ​​the collision; is the relative collision velocity between the spacecraft and the space target.

[0071] like Figure 10 The figure below is a technical concept diagram of the design scheme of this application in practical application. This application applies topological networks to model the evolution of the space debris environment. By studying the topological relationships of the topological network, we can analogically study the relationship between four space objects: payload (P), rocket body (R), debris (D), and post-mission disposal satellite (S).

[0072] First, the Euler method is used to divide the space target into volume elements. The LEO orbit is divided into the following parts according to the distance from the center of the earth (radial), right ascension, and declination: The space volume elements are divided into Δr, Δλ, For the space volume element U α,β,γ , its positional relationship with the space object (taking payload as an example) is as follows Figure 2 As shown, the formula corresponding to the spatial range it contains is as follows.

[0073]

[0074] Among them, r α is the orbital height in the αth orbital height interval; r is the orbital height; is the declination direction; λ is the right ascension; Δr is the division interval in the radial direction; is the declination direction corresponding to the βth declination interval; Δλ is the division interval in the right ascension direction; is the division interval in the declination direction; λ γ is the right ascension of the γth right ascension interval.

[0075] Then, the space objects are divided into N groups according to their orbital inclination and surface mass fraction. I ×N A Therefore, various space objects are divided into A spatial object group node.

[0076] Select the volume element U α,β,γ The spatial density of the four object groups in the θth orbital inclination interval and the ηth surface mass ratio interval and is the macro state change quantity and serves as an independent node in the topological network. Based on the definition of spatial density, taking the payload as an example, It can be expressed as:

[0077]

[0078] Among them, N P Indicates that the volume element U α,β,γ , and the total payload quantity with orbital inclination in the θth interval and surface mass ratio in the ηth interval; P n Indicates the number of the payload; and Respectively represent the payload entering and exiting the volume element U α,β,γ Time; V α,β,γ The volume of the volume element can be expressed as follows:

[0079]

[0080] Analyze the connection relationship between network nodes and construct a topological structure. Due to the effect of J2 perturbation, all types of space targets will migrate in the right ascension direction; targets that do not have the ability to maintain orbit will naturally decay in the radial direction under the influence of atmospheric drag. Failed satellites perform post-mission disposal (PMD) by deploying a resistance enhancement device with a membrane structure. If the device is successfully deployed, PMD is considered a success, and the failed satellite will leave orbit under the action of enhanced atmospheric drag; if the device fails to deploy, PMD is considered a failure, and the failed satellite will be converted into debris. Since this application only considers short-term evolution within one year, phenomena such as collisions and explosions are not considered for the time being.

[0081] Therefore, the spatial target group in each volume unit mainly migrates along the right ascension direction and the distance from the center of the earth. To simplify the modeling, the three-dimensional spatial topological network composed of the distance from the center of the earth, right ascension, and declination can be simplified to a two-dimensional network of right ascension and distance from the center of the earth, and constructed independently in each declination interval, such as Figure 3 In addition, under the assumption that the orbit is circular, the distance from the center of the Earth is equivalent to the orbital height, which facilitates visualization.

[0082]

[0083] For the space debris environment topological network model, the continuity equation determined by the fluid mechanics method is used to model the debris influencing factors to obtain the continuous topological network model and discontinuous topological network model of the space debris environment topological network model.

[0084] The continuity factor in the continuity equation, that is, the continuity influencing factor, is mainly reflected in That is, the divergence of the multidimensional vector field f is used to measure the "source" (outflow) or "sink" (inflow) properties of the vector field near a certain point. Analogously to the space debris environment evolution model (space debris environment topological network model) of this application, since the volume element U where the space object is located is i,j,k Divide the three-dimensional space into high latitude and longitude to define the debris density field in the space but That is It can be expressed as:

[0085]

[0086] and Represents the density change in the height direction, longitude direction and latitude direction respectively. It describes the net change in space debris in the region, that is, how the flow of debris in longitude, latitude and altitude directions affects the density of debris in the region.

[0087] There are two reasons why the density of space objects changes in the altitude direction. First, atmospheric drag perturbations will cause the orbital altitude of space objects without orbit-keeping capabilities to gradually decay. Second, PMD will cause ineffective satellites to gradually descend in orbit. i,j,k The group of space objects within the volume element, It can be expressed as:

[0088]

[0089] in, is the density of the space object; is the area of ​​the volume element in the direction of the earth's radius; for The average decay rate of space objects within the group.

[0090]

[0091] in, is the volume element U α，β，γ The area in the direction of the Earth's radius.

[0092] The density of space objects varies with distance from the Earth's center due to two main factors: atmospheric drag and post-mission disposal (PMD). Atmospheric drag naturally lowers the orbital altitude of objects without orbit-maintaining capabilities (such as rocket bodies and debris), while PMD lowers the orbital altitude of defunct satellites. For payloads, their density remains constant with distance from the Earth's center.

[0093]

[0094]

[0095] in, is the coefficient of the increase in the density of space objects in the direction of orbital height; is the coefficient of the reduction in the density of space objects in the direction of orbital altitude.

[0096]

[0097] is the average natural orbit-descent rate:

[0098]

[0099] is the average PMD down-orbit rate:

[0100]

[0101] Where μ is the standard gravitational parameter (A / m) η is the median of the ηth surface mass ratio layer; η1 is the surface mass ratio range of the drag increase device-satellite system after the drag increase device is installed; ρ is the atmospheric density. is the median value of the η1th surface mass fraction layer.

[0102] From the perspective of solar and geomagnetic activity, the atmospheric density model can be expressed as:

[0103]

[0104] Where, T1 is temperature; F 10.7 is the solar radio flux at 10.7 cm; A p is the geomagnetic index; m is the molecular mass, which is defined as a function of the altitude h.

[0105] From the above deduction, we can get that T drag and T PMD The expression is as follows:

[0106]

[0107] For the volume unit U α,β,γ The target group within the space, It can be expressed as:

[0108]

[0109] in, Represents the area of ​​the volume element in the right ascension direction.

[0110]

[0111] The migration of space targets in right ascension is primarily caused by the J2 perturbation. This perturbation causes a shift in the density of space targets between volume cells with the same declination but different right ascensions. When the orbital inclination of a target group satisfies the prograde orbit condition, its density distribution shifts from east to west; conversely, for retrograde orbits, the density distribution shifts from west to east.

[0112]

[0113] in, When the orbit height is r The average transfer speed in the right ascension direction; J2 is the Earth's oblateness coefficient; a e is the equatorial radius of the Earth, i θ is the median of the orbital inclination interval.

[0114] T λ The expression is:

[0115]

[0116] Discontinuity factors, that is, discontinuity influencing factors, are mainly satellite launches and post-mission disposal caused by human space activities.

[0117] In this application, launch activities are divided into basic launch activities (excluding constellations) and constellation launch activities. For basic launches, this application uses a Gaussian mixture model (GMM) to fit the parameters of historical space launch activities and uses the Markov Chain Monte Carlo method (MCMC) to perform sampling predictions for future launch activities.

[0118] For constellation launches, this application references the configuration parameters and deployment progress of real low-orbit constellations such as Starlink, Kuiper, and Telesat, and constructs two virtual constellations, A and B. The basic information of the constellations is shown in Table 1.

[0119] Table 1 Basic information of constellations

[0120]

[0121] In addition, based on the above launch model and taking into account the inherent characteristics of ordinary satellites and constellation satellites, the following post-mission disposal strategies are set, as shown in Table 2.

[0122] Table 2 Satellite post-mission disposal strategy

[0123] information describe Deorbit strategy Install drag-enhancing devices such as deorbit sails. Success rate The PMD success rate τ is 90%, and the clearance process considers active collision avoidance.

[0124] In addition, the constellation modeling scheme of the present application adopts the Walker constellation configuration, and the configuration code of the Walker constellation (Walker Delta Pattern constellation) is: N W / P W / F W , i, h1. Where i is the satellite's orbital inclination; h1 is the deployment altitude of the constellation; N W is the total number of satellites in the constellation; P W is the orbital plane number of the constellation; F W Is the phase factor. Suppose a satellite in the constellation is numbered m1, then the right ascension of the ascending node of this satellite is Ω k and the perigee angular distance ω k It can be expressed as:

[0125]

[0126] S W is the number of satellites in each orbit; k is the satellite number; P k is the number of the P uniformly distributed orbits where the satellite numbered k is located; N k For the satellite at its position numbered P k The number in the track.

[0127] The computation of complex networks usually relies on matrix methods. This application uses the adjacency matrix to analyze the topological network of the space debris evolution model. For four types of space targets, assuming that the declination, orbital inclination, and area-mass ratio (AMR) intervals are preset, the distribution of their nodes in terms of distance from the center of the Earth and right ascension is defined as follows:

[0128]

[0129] in, is the density matrix of payload varying with orbital altitude and right ascension when the declination, orbit inclination and surface-to-mass ratio are fixed; is the density matrix of the rocket body as it changes with orbital altitude and right ascension when the declination, orbit inclination, and surface-to-mass ratio are fixed; is the density matrix of the satellite in post-mission disposal as the orbital altitude and right ascension change when the declination, orbit inclination, and surface-to-mass ratio are fixed; P1 is the density matrix of debris changing with orbital altitude and right ascension when the declination, orbital inclination and surface-to-mass ratio are fixed; 1 P1 is the density matrix of the payload in the first orbital altitude interval and the first right ascension interval when the declination, orbit inclination and surface-to-mass ratio are determined; 2 The density matrix of the payload in the first orbital altitude interval and the second right ascension interval when the declination, orbit inclination and area-to-mass ratio are determined; When the declination, orbit inclination and surface mass ratio are determined, the payload is in the first orbital height interval and the Nth orbital height interval. λ Density matrix of right ascension intervals; When the declination, orbit inclination and surface-to-mass ratio are determined, the payload is in the second orbital altitude interval and the Nth λ Density matrix of right ascension intervals; When the declination, orbital inclination and surface mass ratio are determined, the payload is r Density matrices for orbital altitude intervals and first right ascension intervals; When the declination, orbital inclination and surface mass ratio are determined, the payload is r Density matrices for the orbital altitude interval and the second right ascension interval; When the declination, orbital inclination and surface mass ratio are determined, the payload is r Orbital altitude interval and Nth λ Density matrix of right ascension bins.

[0130] When the declination, orbit inclination and surface mass ratio are determined, the rocket body is in the first orbital height interval and the Nth orbital height interval. λ Density matrix of right ascension intervals; When the declination, orbit inclination and surface mass ratio are determined, the rocket body is in the second orbital height interval and the Nth orbital height interval. λ Density matrix of right ascension intervals; When the declination, orbital inclination and surface mass ratio are determined, the rocket body is r Density matrices for orbital altitude intervals and first right ascension intervals; When the declination, orbital inclination and surface mass ratio are determined, the rocket body is r Density matrices for the orbital altitude interval and the second right ascension interval; When the declination, orbital inclination and surface mass ratio are determined, the rocket body is r Orbital altitude interval and Nth λ Density matrix of right ascension bins.

[0131] When the declination, orbit inclination and surface quality ratio are determined, the satellite in post-mission disposal is in the Nth r Orbital altitude interval and Nth λ Density matrix of right ascension intervals; When the declination, orbital inclination and surface mass ratio are determined, the debris is r Orbital altitude interval and Nth λ Density matrix of right ascension bins.

[0132] When the declination, orbit inclination and surface quality ratio are determined, the satellite in post-mission disposal is in the Nth rDensity matrices for orbital altitude intervals and first right ascension intervals; When the declination, orbit inclination and surface quality ratio are determined, the satellite in post-mission disposal is in the Nth r Density matrices for the orbital altitude interval and the second right ascension interval; When the declination, orbital inclination and surface mass ratio are determined, the debris is r Density matrices for orbital altitude intervals and first right ascension intervals; When the declination, orbital inclination and surface mass ratio are determined, the debris is r Density matrices for the orbital altitude interval and the second right ascension interval.

[0133] Then, define the matrix for:

[0134]

[0135] Therefore, the space debris environment evolution (space debris environment topology) network model and the corresponding mathematical model can be expressed as follows:

[0136]

[0137] It can be expressed as:

[0138]

[0139] Where A is the adjacency matrix:

[0140]

[0141] In addition, in the above scenario, the orbital altitude and longitude interval distribution of the newly generated failed satellites are defined as:

[0142]

[0143] in, F1 is the density matrix of the newly generated invalid satellites changing with orbital altitude and right ascension when the declination, orbit inclination and surface mass ratio are determined; 1 F1 is the density matrix of the newly generated invalid satellite in the first orbital altitude interval and the first right ascension interval when the declination, orbit inclination and surface mass ratio are determined; 2 The density matrix of the newly generated invalid satellite in the first orbital altitude interval and the second right ascension interval when the declination, orbit inclination and surface mass ratio are determined; When the declination, orbit inclination and surface quality ratio are determined, the newly generated invalid satellite is in the first orbit height interval and the Nth orbit height interval. λ Density matrix of right ascension intervals; When the declination, orbit inclination and surface quality ratio are determined, the newly generated invalid satellite is in the second orbit height interval and the Nth orbit height interval. λ Density matrix of right ascension intervals; When the declination, orbit inclination and surface quality ratio are determined, the newly generated invalid satellite is r Density matrices for orbital altitude intervals and first right ascension intervals; When the declination, orbit inclination and surface quality ratio are determined, the newly generated invalid satellite is r Density matrices for the orbital altitude interval and the second right ascension interval; When the declination, orbit inclination and surface quality ratio are determined, the newly generated invalid satellite is r Orbital altitude interval and Nth λ Density matrix of right ascension bins. The density matrix of the newly generated invalid satellite in the second orbital altitude interval and the first right ascension interval when the declination, orbit inclination and surface mass ratio are determined; is the density matrix of the newly generated inactive satellite in the second orbital altitude interval and the second right ascension interval when the declination, orbit inclination, and surface-to-mass ratio are determined. T is the transpose.

[0144] but, It can be expressed as:

[0145]

[0146] in, is the density variation matrix of space objects caused by discontinuity factors as the orbital altitude and right ascension change when the declination, orbital inclination, and surface-to-mass ratio are determined; τ is the success rate of post-mission disposal.

[0147] Through the above formula, the topological network model of the space debris environment can be solved, and finally the evolution prediction results of the space debris environment can be obtained.

[0148] Based on the space debris environment prediction results obtained above, the spacecraft collision risk is obtained by analyzing the method of constructing a long-term collision probability algorithm.

[0149] Specific analysis process of the spacecraft collision probability algorithm construction method:

[0150] Spacecraft collision risk assessment relies on a collision probability algorithm. This application proposes a collision probability algorithm. First, determine the spatial volume unit that the target spacecraft passes through during its operation. The volume element U α,β,γ The space density of the inner spacecraft is The probability of it appearing in this unit can be expressed as Furthermore, when the spacecraft appears in the volume unit U α,β,γ When the space target is within , the flux of the space target it encounters can be expressed as:

[0151]

[0152] in, is the density of space objects, and its predicted value comes from the established space debris environment evolution model (space debris environment topological network model); σ is the collision cross-sectional area, is the relative collision velocity between the spacecraft and the space target.

[0153] Therefore, the spacecraft is in the volume element U α,β,γ The collision probability at each moment It can be expressed as:

[0154]

[0155] By summing the collision probabilities in each volume unit within the spacecraft's operating space, the overall collision probability of the spacecraft can be obtained.

[0156] Different from the previous algorithms, the algorithm proposed in this application no longer relies on the microscopic model, but calculates the volume element U through the space debris environment topological network model (a macroscopic model) α,β,γ The spatial target density within is used to characterize the collision probability. Therefore, the algorithm inherits the advantages of the topological network model in computational efficiency and significantly reduces the consumption of computing resources.

[0157] According to the above-constructed long-term spacecraft collision probability algorithm, the collision risk of the constellation satellites during the on-orbit and off-orbit processes is calculated.

[0158] First, consider a satellite in the A1 constellation. The formula for its initial orbital elements is as follows:

[0159] [aei Ω ω k f]0=[7001km 0 52° 0° 0° 0°].

[0160] Where a is the orbital altitude; e is the eccentricity; i is the orbital inclination; Ω is the right ascension of the ascending node; ω k is the perigee angular distance; f is the true anomaly.

[0161] Figure 4 The figure shows the temporal evolution of the satellite's average collision probability, averaged every half day. The figure shows that after constellation deployment, the satellite's internal collision probability with other satellites in the constellation is approximately one order of magnitude higher than its external collision probability with other space targets, indicating that its collision risk is primarily influenced by intra-constellation collisions.

[0162] also, Figure 5The data shows the average internal and external collision probabilities for satellites in a constellation over a seven-day operational cycle. For satellites in Category A constellations, the internal collision risk is approximately 8.4 to 14.4 times greater than the external collision risk. For Category B constellations, the ratio is even higher, ranging from 144.3 to 210.8 times greater than the external risk.

[0163] These results demonstrate that the deployment of large-scale constellations not only poses a potential threat to existing space targets in orbit but also poses significant security challenges within the constellation itself. Compared to collision threats from the external environment, the risk of collisions between satellites within a constellation is even more pronounced.

[0164] This application adopts the method of configuring a deorbiting sail for a failed constellation satellite to accelerate its deorbiting, and evaluates the collision risk of the constellation satellite during the entire deorbiting process. The mass of the failed constellation satellite is assumed to be 100kg, and the effective deorbiting sail area is 1104m 2 .

[0165] Figure 6 The image shows the deorbit trajectory of the failed satellite over a period of 7 days. Figure 7 The image shows the distribution of space objects within the orbital altitude range that satellites pass through during deorbit. A total of 22,253 space objects are located within this region, including 18,156 payloads, 769 rocket bodies, and 3,328 debris. These debris are primarily concentrated in sun-synchronous orbits with inclinations close to 97°; payloads are distributed at inclinations of 43°, 53°, and 97°; while the distribution of rocket bodies shows no apparent pattern.

[0166] Figure 8 The average collision probability between a deorbited satellite and different types of space targets, calculated using a collision probability algorithm, is presented. The results show that the collision risk between the satellite and the payload is significantly higher, approximately 10 times that of a collision with debris and 100 times that of a collision with the rocket body. Furthermore, the collision probability reaches its maximum value on day 5.5, at approximately 1.30×10 -4 / year / m 2 .

[0167] The size of space objects is a key factor affecting the extent of damage to spacecraft after a collision. Therefore, it is necessary to analyze the collision risk between a failed satellite and space objects of different sizes during deorbit. This application categorizes space objects into three size categories: small (0.1 to 0.3 meters), medium (0.3 to 1 meter), and large (>1 meter). Figure 9 The average collision probability of a failed satellite with space targets of different sizes during its deorbit process is shown.

[0168] Combine Figure 6 and Figure 9It can be found that when the satellite passes through the orbital area where the constellation is deployed, the probability of collision with objects larger than 1 meter increases significantly. The maximum collision risk occurs on the 5.5th day, when the probability of collision with large objects reaches 1.1×10 -4 / year / m 2 This spike is primarily attributed to the failed satellite crossing the Starlink constellation's orbital region at that moment.

[0169] This application establishes a multidisciplinary topological network model of the space debris environment. This model depicts the relationships between space objects through a complex network structure, combining fluid mechanics and aerospace dynamics to describe their evolutionary mechanisms. Compared to microscopic models, this model maintains acceptable error while taking only 1.8% of the computational time, significantly improving computational efficiency.

[0170] This application proposes a collision probability algorithm. Based on a topological network model of the space debris environment, this algorithm inherits the efficiency advantages of macroscopic models. Its predictions are highly consistent with those calculated by ESA's DRAMA software, validating the algorithm's reliability.

[0171] This application constructs a constellation model based on actual constellation planning. Combining the proposed model with an algorithm, we analyze the collision risk of satellites operating within the constellation. The results show that the collision risk between satellites within a constellation can be several times, or even hundreds of times, higher than the risk of collisions with targets in outer space.

[0172] This application simulates the deorbiting process of a defunct satellite equipped with a deorbit sail and analyzes its collision probability. The results show that the risk of a defunct satellite colliding with its payload is highest during the deorbiting process, and the collision probability reaches its maximum when the satellite crosses the Starlink constellation's operating area.

[0173] The research results of this application can provide a theoretical basis for spacecraft safe orbit planning and space debris mitigation.

[0174] This application constructs a topological network model of the space debris environment that integrates multidisciplinary approaches. This model uses a topological network to structure relationships between space objects and characterizes their evolutionary mechanisms by combining fluid mechanics and aerospace dynamics. The method's computational time is only 1.8% of that of a microscopic model, and the error is kept within acceptable limits, demonstrating its reliability and efficiency.

[0175] Furthermore, this application proposes a new collision probability algorithm. Unlike previous algorithms based on microscopic models, this method is based on a topological network model, offering the efficiency advantages of macroscopic modeling. The results were compared with ESA's classic DRAMA software, verifying its reliability.

[0176] This application constructs a constellation activity model based on real-world mega-constellation planning. Using the aforementioned approach, the collision risk faced by constellation satellites during in-orbit operation and decommissioning is analyzed.

[0177] The technical features of the above embodiments can be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0178] This application uses specific examples to illustrate the principles and implementation methods of this application. The description of the above examples is only intended to help understand the method and core concept of this application. At the same time, for those skilled in the art, based on the concept of this application, there may be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting this application.

Claims

1. A constellation satellite collision analysis method based on a space debris environment topology network model, characterized in that: include: Perform volume element segmentation on the space target to obtain multiple space object group nodes; Based on the migration direction of the spatial target group, the connection relationship of the plurality of spatial object group nodes is analyzed and processed, and a topological structure is constructed to obtain a topological network; Using a fluid mechanics method to model the topological network based on the influencing factors of space debris, a topological network model of the space debris environment is obtained; The adjacency matrix is ​​used to analyze and solve the space debris environment topology network model to obtain the evolution prediction result of the space debris environment; A collision probability algorithm is used to perform collision analysis on the constellation satellites according to the evolution prediction result to obtain a collision analysis result.

2. The constellation satellite collision analysis method based on the space debris environment topology network model according to claim 1 is characterized in that: Perform volume element segmentation on the space target to obtain multiple space object group nodes, including: The Euler method is used to divide the space target into volume elements, wherein the LEO orbit is divided into multiple space volume elements according to the set division intervals along the radial, right ascension and declination directions respectively; The interval is divided according to the orbital inclination and the surface-to-mass ratio to obtain multiple divided intervals; A plurality of the space object group nodes are determined according to the plurality of divided intervals and the plurality of the space volume elements.

3. The constellation satellite collision analysis method based on the space debris environment topology network model according to claim 1 is characterized in that: The expression corresponding to the topological network is: Among them, α is the interval number of orbital altitude; β is the interval number of declination; γ is the interval number of right ascension; θ is the interval number of orbital inclination; η is the interval number of surface mass ratio; is the change in payload density within the αth orbital altitude interval, the βth declination interval, the γth right ascension interval, the θth orbital inclination interval, and the ηth surface-to-mass ratio interval; is the change in the rocket body density within the αth orbital altitude interval, the βth declination interval, the γth right ascension interval, the θth orbital inclination interval, and the ηth surface-to-mass ratio interval; is the change in satellite density in the post-mission disposal state within the αth orbital altitude interval, the βth declination interval, the γth right ascension interval, the θth orbital inclination interval, and the ηth surface-to-mass ratio interval; is the change in density of debris in the αth orbital altitude interval, the βth declination interval, the γth right ascension interval, the θth orbital inclination interval, and the ηth surface-to-mass ratio interval; is the spatial density of the payload in the αth orbital altitude interval, the βth declination interval, the γth right ascension interval, the θth orbital inclination interval, and the ηth area-to-mass ratio interval; is the space density of the rocket body in the αth orbital altitude interval, the βth declination interval, the γth right ascension interval, the θth orbital inclination interval, and the ηth surface-to-mass ratio interval; is the spatial density of post-mission disposal satellites in the αth orbital altitude interval, the βth declination interval, the γth right ascension interval, the θth orbital inclination interval, and the ηth surface-to-mass ratio interval; is the spatial density of debris in the αth orbital altitude interval, the βth declination interval, the γth right ascension interval, the θth orbital inclination interval, and the ηth surface-to-mass ratio interval; T λ is the transfer function of the space object under the action of J2 perturbation; is the payload density in the αth orbital altitude interval, the βth declination interval, the γ±1th right ascension interval, the θth orbital inclination interval, and the ηth surface-to-mass ratio interval; The rocket body density is in the αth orbital altitude interval, the βth declination interval, the γ±1th right ascension interval, the θth orbital inclination interval, and the ηth surface-to-mass ratio interval; is the rocket body density in the α+1th orbital altitude interval, the βth declination interval, the γth right ascension interval, the θth orbital inclination interval, and the ηth surface-to-mass ratio interval; dt is the time step; t is the time; T drag is the orbit-descending function of a space object under the influence of atmospheric drag; T PMD is the orbit reduction function of the space object under the action of post-mission disposal; L is the launch volume element U α,β,γ The density function of space objects within; is the new volume element U α,β,γ The density of failed satellites within ; τ is the success rate of post-mission disposal; is the spatial density of post-mission disposal satellites in the αth orbital altitude interval, the βth declination interval, the γ±1th right ascension interval, the θth orbital inclination interval, and the ηth surface-to-mass ratio interval; is the spatial density of post-mission disposal satellites in the α+1th orbital altitude interval, the βth declination interval, the γth right ascension interval, the θth orbital inclination interval, and the ηth surface-to-mass ratio interval; is the spatial density of debris in the αth orbital altitude interval, the βth declination interval, the γ±1th right ascension interval, the θth orbital inclination interval, and the ηth surface-to-mass ratio interval; is the spatial density of debris in the α+1th orbital altitude interval, the βth declination interval, the γth right ascension interval, the θth orbital inclination interval, and the ηth surface-to-mass ratio interval.

4. The constellation satellite collision analysis method based on the space debris environment topology network model according to claim 1 is characterized in that: The topological network is modeled based on the influencing factors of space debris using a fluid mechanics method to obtain a topological network model of the space debris environment, specifically including: Fluid mechanics methods are used to process continuity influencing factors and determine the continuity equation. The continuity influencing factors are flow variation information of the debris density field in the altitude, distance from the center of the Earth, and right ascension directions. The continuity equation includes the transfer function of the space object under the influence of J2 perturbation, the orbit reduction function of the space object under the influence of atmospheric drag, and the orbit reduction function of the space object under the influence of PMD. Determining a continuous topological network model according to the continuity equation and the topological network; By adopting constellation configuration and fitting historical space launch activity parameters, a discontinuous topological network model is determined based on discontinuous influencing factors, wherein the discontinuous influencing factors include: satellite launch and post-mission disposal; A space debris environment topology network model is determined according to the continuous topology network model and the discontinuous topology network model.

5. The constellation satellite collision analysis method based on the space debris environment topology network model according to claim 4 is characterized in that: The transfer function of a space object under the action of J2 perturbation is expressed as follows: Among them, T λ is the transfer function of the space object under the action of J2 perturbation; is the spatial density of space objects in the αth orbital altitude interval, the βth declination interval, the γth right ascension interval, the θth orbital inclination interval, and the ηth surface-to-mass ratio interval; is the spatial density of space objects in the αth orbital altitude interval, the βth declination interval, the γ±1th right ascension interval, the θth orbital inclination interval, and the ηth surface-to-mass ratio interval; is the density change in the height direction corresponding to the right ascension direction; f λ is the component of the density field in the right ascension direction; λ is the right ascension; G is any type of space object group; P is the payload; R is the rocket body; D is the debris; S is the post-mission disposal satellite; Δλ is the division interval in the right ascension direction; is the spatial density of space objects in the declination of the αth orbital altitude interval, the βth declination interval, the γ+1th right ascension interval, and the θth orbital inclination interval; σ is the declination; For U α,β,γ+1 The area in the right ascension direction; U α,β,γ+1 is the volume element formed by the αth orbital altitude interval, the βth declination interval, and the γ+1th right ascension interval; α is the orbital altitude interval number; β is the declination interval number; γ is the right ascension interval number; θ is the interval number of the orbital inclination; η is the interval number of the surface mass ratio; for Average transfer speed in the right ascension direction; is the spatial density of space objects in the αth orbital altitude interval, the βth declination interval, the γth right ascension interval, and the θth orbital inclination interval; is the spatial density of space objects in the αth orbital altitude interval, the βth declination interval, the γ-1th right ascension interval, the θth orbital inclination interval, and the ηth surface-to-mass ratio interval; U α,β,γ is the volume element formed by the αth orbital altitude interval, the βth declination interval, and the γth right ascension interval; U α,β,γ-1 The volume element is formed by the αth orbital altitude interval, the βth declination interval, and the γ-1th right ascension interval; is the volume element U α,β,γ Area in the right ascension direction; for Average transfer speed in the right ascension direction; For U α,β,γ-1 Area in the right ascension direction; for The average transfer speed in the right ascension direction; V α,β,γ is the volume of the volume element.

6. The constellation satellite collision analysis method based on the space debris environment topology network model according to claim 4 is characterized in that: The orbit reduction function of a space object under the influence of atmospheric drag is expressed as follows: Among them, T drag is the orbit-descending function of a space object under the influence of atmospheric drag; is the density of space objects in the αth orbital altitude interval, the βth declination interval, the γth right ascension interval, the θth orbital inclination interval, and the ηth surface-to-mass ratio interval; is the spatial density of space objects in the α+1th orbital altitude interval, the βth declination interval, the γth right ascension interval, the θth orbital inclination interval, and the ηth surface-to-mass ratio interval; is the density change in the height direction corresponding to the track height direction; f r is the component of the density field in the orbital height direction; r is the orbital height; G is any type of space object; R is the rocket body; D is the debris; Δr is the division interval in the radial direction; U α+1,β,γ The volume element is formed by the α+1th orbital altitude interval, the βth declination interval, and the γth right ascension interval; is the volume element U α+1,β,γ Area in the right ascension direction; for The natural descent rate in the orbital altitude direction; is the volume element U α,β,γ The area in the direction of track height; V α,β,γ is the volume of the volume element; for The natural descent rate in the orbital altitude direction.

7. The constellation satellite collision analysis method based on the space debris environment topology network model according to claim 4 is characterized in that: The orbit reduction function of a space object under the action of PMD is expressed as follows: Among them, T PMD is the orbit-demotion function of the space object under the action of post-mission disposal; is the spatial density of space objects in the αth orbital altitude interval, the βth declination interval, the γth right ascension interval, the θth orbital inclination interval, and the ηth surface-to-mass ratio interval; is the spatial density of space objects in the α+1th orbital altitude interval, the βth declination interval, the γth right ascension interval, the θth orbital inclination interval, and the ηth surface-to-mass ratio interval; is the density change in the height direction corresponding to the right ascension direction; is the density change in the height direction corresponding to the track height direction; f r is the component of the density field in the orbital height direction; r is the orbital height; G is any type of space object; R is the rocket body; D is the debris; Δr is the division interval in the radial direction; U α+1,β,γ The volume element is formed by the α+1th orbital altitude interval, the βth declination interval, and the γth right ascension interval; is the volume element U α+1,β,γ Area in the right ascension direction; for PMD deorbit rate in the orbit height direction; is the area of ​​the volume element in the direction of the earth's radius; for PMD orbit reduction rate in the orbit height direction; V α,β,γ is the volume of the volume element.

8. The constellation satellite collision analysis method based on the space debris environment topology network model according to claim 1 is characterized in that: The adjacency matrix is ​​used to analyze and solve the space debris environment topology network model to obtain the evolution prediction results of the space debris environment, including: Based on a preset matrix, the space debris environment topology network model is converted into a mathematical model in a matrix form; The mathematical model is solved using an adjacency matrix to obtain a prediction result of the evolution of the space debris environment; The mathematical model is expressed as follows: The expression of the adjacency matrix is: in, is the function corresponding to the mathematical model; is the density matrix of space objects changing with orbital altitude and right ascension when the declination, orbital inclination and surface-to-mass ratio are fixed; is the density variation matrix of the space object caused by the continuity factor as the orbital altitude and right ascension change when the declination, orbital inclination and surface-to-mass ratio are determined; is the density variation matrix of the space object caused by discontinuous factors as the orbital altitude and right ascension change when the declination, orbital inclination and surface-to-mass ratio are determined; δ is the sequence number of the discrete time step; for The value of δ at the discrete time step; for The value of δ at the discrete time step; for The value of δ at the discrete time step; A is the adjacency matrix; A P is the adjacency matrix of payload nodes; A R is the adjacency matrix of the rocket body nodes; A S A is the adjacency matrix of the satellite nodes after the mission; D is the adjacency matrix of the fragment nodes.

9. The constellation satellite collision analysis method based on the space debris environment topology network model according to claim 1 is characterized in that: The collision probability algorithm is used to determine the collision probability; the method for determining the collision probability specifically includes: Determine the spatial volume elements that the spatial target group passes through during operation and determine the corresponding spatial density; Using the formula Determine space target flux; determining a collision probability based on the spatial target flux, the spatial volume element, and the corresponding spatial density; Among them, F α,β,γ is the space target flux; N I The number of intervals divided by the orbital inclination; N A is the number of intervals divided by the area-to-mass ratio; θ is the interval number of the orbital inclination; η is the interval number of the area-to-mass ratio; is the density of the space object; σ is the intersection cross-sectional area of ​​the collision; is the relative collision velocity between the spacecraft and the space target.

Images