A constellation satellite collision analysis method based on a space debris environment topology network model

Abstract

The application 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: performing volume element dissection on space targets to obtain a plurality of space object group nodes; analyzing and processing the connection relationship of the plurality of space object group nodes based on the migration direction of the space target group, and constructing a topology structure to obtain a topology network; performing modeling processing on the topology network based on space debris influencing 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 adjacency matrix to obtain evolution prediction results of the space debris environment; and performing collision analysis on constellation satellites according to the evolution prediction results by adopting a collision probability algorithm to obtain collision analysis results. The application aims to quickly realize debris evolution to perform collision analysis on constellation satellites.

Description

Technical Field

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

[0002] In recent years, with the rapid development of human space activities, especially the frequent launches of mega-constellations, the problem of deteriorating space debris environments 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 trend of space debris and conducting reliable risk assessments of spacecraft are of great significance for ensuring the safe execution of human space activities.

[0003] The analysis of space debris environments can be conducted at both micro and macro levels. Microscopic models focus on the precise behavior of individual targets, but they are computationally resource-intensive and inefficient. Macroscopic models, on the other hand, predict environmental evolution by classifying space targets according to their characteristics and treating these groups as research units, offering a significant computational efficiency advantage over microscopic methods. However, existing macroscopic methods often treat different types of space targets separately, solving them individually using (partial) differential equations, neglecting the interactions between targets.

[0004] In reality, the space debris environment is an interconnected system with complex relationships and mutual influences among different targets. On the one hand, dynamic interactions may occur between different types of targets, even triggering changes in their physical states. For example, a collision between two satellites can produce debris, while an operational satellite may be rendered inoperable or become 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 representing indirect interactions between targets with different orbital characteristics. For instance, space debris experiences orbital decay due to atmospheric drag, while satellites experience orbital precession due to J2 perturbations. These interactions play a crucial role in shaping the evolutionary trends of the overall space environment. Therefore, characterizing the network relationships between space targets and systematically analyzing their interactions is key to this research.

[0005] Spacecraft risk assessment relies on the evolution of the space debris environment. Traditional collision event prediction methods, based on the propagation of space target orbits, can determine the specific target, location, and time of a collision, but are computationally expensive and can only assess individual events randomly, making it difficult to effectively assess the collision risk of a spacecraft over the entire operational area and continuous time periods. Therefore, The concept of collision probability was proposed, initially used to assess the risk of collisions between celestial bodies (such as asteroids and comets). Building upon existing methods, Kessler and Wethell developed new collision probability algorithms that eliminated the assumptions of zero eccentricity and zero tilt, improving model applicability. However, all three methods assume the orbit is unperturbed. To more realistically reflect orbital states, NASA proposed the CUBE algorithm, which divides space into multiple volumetric units and calculates the collision probability within each unit using the target spatial density. ESA released the DRAMA software, which calculates collision frequency and probability using the spatial target flux provided by the MASTER model. These methods update orbital elements through uniform time sampling, but they still rely on microscopic debris evolution models, resulting in high computational resource requirements and low efficiency. Currently, there is 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 for constellation satellite collision analysis.

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

[0008] Firstly, this application provides a constellation satellite collision analysis method based on a space debris environment topology network model, including:

[0009] The spatial target is divided into volumetric elements to obtain multiple spatial object groups of nodes;

[0010] 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 topology structure is constructed to obtain a topology network.

[0011] The topological network was modeled based on the influencing factors of space debris using fluid dynamics methods, resulting in a topological network model of the space debris environment.

[0012] The adjacency matrix is ​​used to analyze and solve the topological network model of the space debris environment to obtain the evolution prediction results of the space debris environment.

[0013] A collision probability algorithm is used to perform collision analysis on the constellation satellites based on the evolution prediction results, and the collision analysis results are obtained.

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

[0015] This application provides a collision analysis method for constellation satellites based on a space debris environment topology network model. The method characterizes the relationships between space targets through a topology network and combines this with fluid dynamics methods for modeling, resulting in a space debris environment topology network model describing the debris evolution mechanism. Based on the established space debris environment topology network model, adjacency matrix analysis is used to obtain the evolution prediction results of the space debris environment, thus enabling rapid debris evolution analysis. Then, a collision probability algorithm is used to perform collision analysis on the constellation satellites, yielding the collision analysis results. Therefore, this application can rapidly realize debris evolution for collision analysis of constellation satellites. Attached Figure Description

[0016] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0017] Figure 1 A flowchart of a constellation satellite collision analysis method based on a space debris environment topology network model;

[0018] Figure 2 This is a schematic diagram of the spatial volume element location;

[0019] Figure 3 This is a schematic diagram of the topological structure of the nodes of each spatial object group;

[0020] Figure 4 This is a schematic diagram illustrating the changes in the collision probability of constellation satellites.

[0021] Figure 5 A schematic diagram of the average collision probability distribution of satellites in a constellation;

[0022] Figure 6 A schematic diagram of the deorbit trajectory of a failed satellite;

[0023] Figure 7 This is a schematic diagram showing the distribution of space targets within the area traversed by the failed satellite.

[0024] Figure 8 A schematic diagram illustrating the collision probability with different types of space targets;

[0025] Figure 9 A schematic diagram illustrating the probability of collision with spatial targets of different sizes;

[0026] Figure 10 Flowchart for technical conception. Detailed Implementation

[0027] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those of ordinary skill in the art without creative effort 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 risks 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 space dynamics, enabling a structured representation of the relationships between space targets and 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 through comparison with the classic DRAMA software of the European Space Agency (ESA). Finally, based on the above model, the collision risks of constellation satellites in Low Earth Orbit (LEO) are analyzed, covering both the on-orbit operation and deorbit phases. During operation, the risk of internal collisions between constellation satellites and other satellites within the same constellation is far higher than the risk of collisions with other space targets. Furthermore, during satellite deorbiting, the collision risk reaches its peak when a satellite crosses the operating region of Starlink satellites.

[0029] Topological networks are a mathematical tool used to describe the relationships between nodes in complex systems, and have been widely applied in physics, communications, ecology, and other fields. In a topological network, nodes represent individuals or elements within the system, while edges represent interactions between nodes. This structured approach allows for a clear characterization of the internal relationships and dynamic changes within the system, revealing its evolutionary patterns and potential behaviors. Therefore, applying the concept of topological networks to the study of space debris environments holds great promise. Within this framework, space targets can be divided into several 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 targets, multiple environmental influences, and human space activities, an interaction model between nodes is constructed, ultimately forming a topological network of the space debris environment. Solving this network model can predict the future evolutionary trends of space targets.

[0030] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0031] In one exemplary embodiment, such as 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 volumetric element subdivision on the spatial target to obtain multiple spatial object group nodes.

[0033] Specifically, the spatial target is subjected to volume element subdivision to obtain multiple spatial object group nodes, including:

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

[0035] The intervals are divided according to the orbital inclination angle and the surface-to-mass ratio, resulting in multiple intervals.

[0036] Multiple spatial object group nodes are determined based on multiple partitioned intervals and multiple spatial volume elements.

[0037] Step 200: Based on the migration direction of the spatial target group, analyze and process the connection relationship of multiple spatial object group nodes, and construct the topology structure to obtain the topology network.

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

[0039]

[0040] Where α is the orbital altitude interval number; β is the declination interval number; γ is the right ascension interval number; θ is the orbital inclination interval number; and η is the surface-to-mass ratio interval number. The change in effective payload density within the α-th orbital altitude interval, the β-th declination interval, the γ-th right ascension interval, the θ-th orbital inclination interval, and the η-th surface-to-mass ratio interval; It represents the change in rocket body density within the α-th orbital altitude interval, the β-th declination interval, the γ-th right ascension interval, the θ-th orbital inclination interval, and the η-th surface-to-mass ratio interval; It represents the change in satellite density in the post-mission handling state within the α-orbit altitude interval, β-declination interval, γ-right ascension interval, θ-orbit inclination interval, and η-surface-mass ratio interval; It represents the change in the density of the fragments within the α-th orbital altitude interval, the β-th declination interval, the γ-th right ascension interval, the θ-th orbital inclination interval, and the η-th surface mass ratio interval; The spatial density of the effective payload within the α-th orbital altitude interval, the β-th declination interval, the γ-th right ascension interval, the θ-th orbital inclination interval, and the η-th surface-to-mass ratio interval; The spatial density of the rocket body within the α-th orbital altitude interval, the β-th declination interval, the γ-th right ascension interval, the θ-th orbital inclination interval, and the η-th surface mass ratio interval; The spatial density of post-mission processing satellites within the α-orbit altitude interval, the β-declination interval, the γ-right ascension interval, the θ-orbit inclination interval, and the η-surface-mass ratio interval; The spatial density of debris within the α-th orbital altitude interval, the β-th declination interval, the γ-th right ascension interval, the θ-th orbital inclination interval, and the η-th surface mass ratio interval; T λ Let J2 be the transfer function of the spatial object under the perturbation of J2. The effective payload density is defined within the α-th orbital altitude interval, the β-th declination interval, the γ±1-th right ascension interval, the θ-th orbital inclination interval, and the η-th surface-to-mass ratio interval. The rocket body density is defined as follows: α-th orbital altitude interval, β-th declination interval, γ±1-th right ascension interval, θ-th orbital inclination interval, and η-th surface mass ratio interval. The rocket body density is defined as follows: α+1 orbital altitude interval, β declination interval, γ right ascension interval, θ orbital inclination interval, and η surface mass ratio interval; dt is the time step; t is time; T drag T is the orbital descent function of a space object under atmospheric drag; PMD Let L be the orbit reduction function of the space object under post-mission disposal; L is the launch volume element U. α,β,γ Density function of objects in space; For the newly generated volume element U α,β,γ The density of failed satellites within the mission; τ is the success rate of post-mission handling. The spatial density of post-mission processing satellites within the α-orbit altitude interval, the β-declination interval, the γ±1 right ascension interval, the θ-orbit inclination interval, and the η-surface-mass ratio interval; The spatial density of post-mission processing satellites within the α+1 orbital altitude interval, the β declination interval, the γ right ascension interval, the θ orbital inclination interval, and the η surface mass ratio interval; The spatial density of fragments within the α-th orbital altitude interval, the β-th declination interval, the γ±1-th right ascension interval, the θ-th orbital inclination interval, and the η-th surface mass ratio interval; The spatial density of fragments within the α+1 orbital altitude interval, the β declination interval, the γ right ascension interval, the θ orbital inclination interval, and the η surface mass ratio interval.

[0041] Step 300: Use fluid dynamics methods to model the topology network based on the influencing factors of space debris, and obtain the topology network model of the space debris environment.

[0042] Among them, fluid dynamics methods are used to model the topological network based on the influencing factors of space debris, resulting in a topological network model of the space debris environment, specifically including:

[0043] The continuity influencing factors were processed using fluid dynamics methods to determine the continuity equation. The continuity influencing factors are the flow variation information of the debris density field in the height direction, the geocentric distance 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 descent function of the space object under the action of atmospheric drag, and the orbit descent function of the space object under the action of PMD.

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

[0045]

[0046] Among them, T λ Let J2 be the transfer function of the spatial object under the perturbation of J2. Let be the spatial density of objects within the α-th orbital altitude interval, the β-th declination interval, the γ-th right ascension interval, the θ-th orbital inclination interval, and the η-th surface-to-mass ratio interval; Let be the spatial density of objects within the α-th orbital altitude interval, the β-th declination interval, the γ±1-th right ascension interval, the θ-th orbital inclination interval, and the η-th surface-to-mass ratio interval; f represents the change in density along the height direction corresponding to the right ascension direction. λ Let λ be the component of the density field along the right ascension direction; λ be the right ascension; G be any group of space objects; P be the payload; R be the rocket body; D be debris; S be the post-mission handling satellite; Δλ be the interval along the right ascension direction. σ represents the spatial density of objects within the declination intervals of the α-th orbital altitude interval, the β-th declination interval, the γ+1-th right ascension interval, and the θ-th orbital inclination interval; σ is the declination. For U α,β,γ+1 Area along the right ascension direction; U α,β,γ+1 Let be the volume element formed by the α-th orbital altitude interval, the β-th declination interval, and the γ+1-th 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 angle; and η is the interval number of the surface-to-mass ratio. for Average transfer velocity in the direction of right ascension; Let be the spatial density of objects within the declination ranges of the α-orbit altitude range, the β-declination range, the γ-right ascension range, and the θ-orbit inclination range; U represents the spatial density of objects within the α-th orbital altitude interval, the β-th declination interval, the γ-1-th right ascension interval, the θ-th orbital inclination interval, and the η-th surface-to-mass ratio interval; α,β,γ U is the volume element formed by the α-orbital altitude interval, the β-declination interval, and the γ-right ascension interval; α,β,γ-1 The volume element formed by the α-th orbital altitude interval, the β-th declination interval, and the γ-1-th right ascension interval; For volume element U α,β,γ Area along the right ascension direction; for Average transfer velocity in the direction of right ascension; For U α,β,γ-1 Area along the right ascension direction; for Average transfer velocity in the right ascension direction; V α,β,γ Let be the volume of the volume element.

[0047] The descent function of a space object under atmospheric drag is expressed as follows:

[0048]

[0049] Among them, T drag This is the orbital descent function of a space object under atmospheric drag. Let be the density of the space object within the α-th orbital altitude interval, the β-th declination interval, the γ-th right ascension interval, the θ-th orbital inclination interval, and the η-th surface-to-mass ratio interval; The spatial density of objects within the α+1 orbital altitude interval, the β declination interval, the γ right ascension interval, the θ orbital inclination interval, and the η surface mass ratio interval; f represents the change in density along the orbital height direction. r U is the component of the density field along the orbital altitude; r is the orbital altitude; G is any type of space object; R is the rocket body; D is debris; Δr is the radial interval; U α+1,β,γ The volume element formed by the α+1 orbital altitude interval, the β declination interval, and the γ right ascension interval; For volume element U α+1,β,γ Area along the right ascension direction; for The natural descent rate in the direction of orbital altitude; For volume element U α,β,γ Area along the orbital height; V α,β,γ Let be the volume of the volume element; for The natural descent rate in the direction of orbital altitude.

[0050] The descent function of a space object under PMD is expressed as follows:

[0051]

[0052] Among them, T PMD For the orbit reduction function of a space object under the post-mission handling effect; Let be the spatial density of objects within the α-th orbital altitude interval, the β-th declination interval, the γ-th right ascension interval, the θ-th orbital inclination interval, and the η-th surface-to-mass ratio interval; Let be the spatial density of objects within the α+1 orbital altitude interval, the β declination interval, the γ right ascension interval, the θ orbital inclination interval, and the η surface mass ratio interval; This represents the change in density along the height direction corresponding to the right ascension direction. f represents the change in density along the orbital height direction. r U is the component of the density field along the orbital altitude; r is the orbital altitude; G is any type of space object; R is the rocket body; D is debris; Δr is the radial interval; U α+1,β,γ The volume element formed by the α+1 orbital altitude interval, the β declination interval, and the γ right ascension interval; For volume element U α+1,β,γ Area along the right ascension direction; for PMD descent rate in the orbital altitude direction; Let be the area of ​​the volume element along the direction of the Earth's radius; for The PMD descent rate in the orbital altitude direction; V α,β,γ Let be the volume of the volume element.

[0053] Based on the continuity equation and the described topological network, a continuous topological network model is determined.

[0054] By employing constellation configuration and fitting historical space launch parameters, a discontinuous topology network model is determined based on discontinuous influencing factors, including satellite launch and post-mission handling.

[0055] Based on the continuous and discontinuous topology network models, a topology network model for the space fragmentation environment is determined.

[0056] Step 400: Use the adjacency matrix to analyze and solve the topological network model of the space debris environment to obtain the evolution prediction results of the space debris environment.

[0057] 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 a preset matrix, the topological network model of the space fragmentation environment is converted into a mathematical model in matrix form.

[0059] The mathematical model is solved using an adjacency matrix to obtain the evolution prediction results of the space debris environment.

[0060] The mathematical model is expressed as follows:

[0061]

[0062] The expression for the adjacency matrix is:

[0063]

[0064] in, The function corresponding to the mathematical model; This is the density matrix of a space object as a function of orbital altitude and right ascension, given a fixed declination, orbital inclination, and surface-to-mass ratio. This is the matrix of density variations of a space object as a function of orbital altitude and right ascension, caused by continuous factors, when the declination, orbital inclination, and surface-to-mass ratio are determined. δ represents the density variation matrix of a space object caused by discontinuous factors as a function of orbital altitude and right ascension, given a fixed declination, orbital inclination, and surface-to-mass ratio; δ is the index of the discrete time step. for The value of the discrete time step δ; for The value of the discrete time step δ; for The value of the discrete time step δ; A is the adjacency matrix; A P A is the adjacency matrix of the payload nodes; R A is the adjacency matrix of the rocket body nodes; S For the adjacency matrix of satellite nodes in post-mission processing; A D Let be the adjacency matrix of the fragment nodes.

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

[0066] Collision probability algorithms are used to determine collision probabilities; methods for determining collision probabilities specifically include:

[0067] Determine the spatial volume elements traversed by the target group during its operation, and determine the corresponding spatial density.

[0068] Using formula Determine the target flux in space.

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

[0070] Among them, F α,β,γ N represents the spatial target flux. I The number of intervals divided by the orbital inclination angle; N Aθ represents the number of intervals divided by the surface-to-mass ratio; θ represents the interval number of the orbital inclination angle; η represents the interval number of the surface-to-mass ratio. σ represents the density of the object in space; σ represents the intersection area of ​​the collision. This refers to the relative collision velocity between the spacecraft and the space target.

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

[0072] First, the Eulerian method is used to perform volumetric element subdivision of the space target. The LEO orbit is divided according to geocentric distance (radial), right ascension, and declination. Each spatial volume element is divided into intervals Δr, Δλ, and Δλ along the radial, right ascension, and declination directions. For the spatial volume element U α,β,γ Its positional relationship with spatial objects (taking the payload as an example) is as follows: Figure 2 As shown, the formula corresponding to the spatial range it encompasses is as follows.

[0073]

[0074] Where, r α Let r be the orbital altitude in the α-th orbital altitude range; r is the orbital altitude. λ represents the declination direction; λ represents the right ascension; Δr represents the division interval in the radial direction; Δλ represents the declination direction corresponding to the βth declination interval; Δλ is the division interval along the right ascension direction. The interval is the division along the declination direction; λ γ It is the right ascension of the γth right ascension interval.

[0075] Then, the space object is divided into N according to its orbital inclination angle and surface mass ratio. I ×N A This results in several intervals. Therefore, various spatial objects are categorized according to their spatial location, orbit, and dimensions. A group of spatial objects.

[0076] Select the volume element U α,β,γ Within, and in the θ-th orbital inclination interval and the η-th surface mass ratio interval, the spatial density of the four object groups. and This refers to macroscopic state changes and acts as an independent node in the topological network. Based on the definition of spatial density, taking payload as an example, It can be represented as:

[0077]

[0078] Where, N P Indicates that it is located in the volume element U α,β,γ The total effective load number, with the orbital inclination angle in the θ interval and the surface-to-mass ratio in the η interval; P n Indicates the payload number; and These represent the volume elements U that the effective payload enters and exits. α,β,γ Time; V α,β,γ The volume of a volume element can be expressed by the following formula:

[0079]

[0080] The connections between network nodes are analyzed, and a topology is constructed. Due to the J2 perturbation, all types of space targets will migrate along the right ascension direction; targets without orbital maintenance capabilities will naturally decay radially under the influence of atmospheric drag. The failed satellite is subjected to a post-mission disposal (PMD) by deploying a drag-enhancing membrane structure. If the device deploys successfully, the PMD is considered successful, and the failed satellite will deorbit under the enhanced atmospheric drag; if the device fails to deploy, the PMD is considered a failure, and the failed satellite will disintegrate into debris. Since this application only considers short-term evolution within one year, collisions and explosions are not considered.

[0081] Therefore, the spatial target group within each volume unit mainly migrates along the right ascension and geocentric distance directions. To simplify modeling, the three-dimensional spatial topology network consisting of geocentric distance-right ascension-declination can be simplified into a two-dimensional network of right ascension-geocene distance, and constructed independently within each declination interval, such as... Figure 3 As shown. Furthermore, assuming the orbit is circular, the distance to the Earth's center is equivalent to the orbital height, which facilitates visualization.

[0082]

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

[0084] The continuity factors in the continuity equation, i.e., the continuous influencing factors, are mainly reflected in: That is, the divergence of a multidimensional vector field f, used to measure the "source" (outflow) or "sink" (inflow) property of the vector field near a certain point. Analogous to the space debris environment evolution model (space debris environment topology network model) of this application, due to the volume element U of the space object... i,j,k Based on the high latitude and longitude three-dimensional space, the fragment density field in space is defined. but That is This can be expressed as:

[0085]

[0086] and These represent the changes in density along the altitude, longitude, and latitude directions, respectively. Therefore, It describes the net change in space debris within the region, i.e. how the movement of debris along the longitude, latitude, and altitude directions affects the debris density within the region.

[0087] There are two reasons why the density of a space object changes in the altitude direction: first, atmospheric drag perturbations cause the orbital altitude of a space object without orbital maintenance capabilities to gradually decrease; second, PMD (partial atmospheric drag) causes a failed satellite to gradually descend into a lower orbit. For U... i,j,k The group of spatial objects within a volume element, It can be represented as:

[0088]

[0089] in, The density of a spatial object; Let be the area of ​​the volume element along the direction of the Earth's radius; for The average decay rate of spatial objects within the group.

[0090]

[0091] in, For volume element U α，β，γ Area along the Earth's radius.

[0092] The density variation of space targets along the geocentric distance is primarily caused by two factors: atmospheric drag and mission post-disposal (PMD). Atmospheric drag naturally lowers the orbital altitude of targets lacking orbital maintenance capabilities (such as rocket bodies and debris); while PMD lowers the orbital altitude of defunct satellites. For payloads, their density along the geocentric distance remains constant.

[0093]

[0094]

[0095] in, This is a coefficient representing the increase in the density of a spatial object along the orbital height direction; It is a coefficient representing the decrease in density of a space object along the orbital height direction.

[0096]

[0097] The average natural descent rate:

[0098]

[0099] Average PMD descent rate:

[0100]

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

[0105] From the above derivation, we can obtain 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 represented as:

[0108]

[0109] in, It represents the area of ​​the volume element along the right ascension direction.

[0110]

[0111] The migration of space targets along the right ascension direction is primarily caused by the J2 perturbation. This perturbation leads to a flow of space target density between volumetric units with the same declination but different right ascensions. When the orbital inclination of the target population satisfies the prograde orbit condition, its density distribution will migrate from east to west; conversely, for the retrograde orbit, the density distribution will migrate from west to east.

[0112]

[0113] in, When the orbital height is r The average velocity of transfer along the right ascension direction; J2 is the Earth's oblateness coefficient; a e i is the radius of the Earth's equator. θ It is the median value of the orbital inclination angle range.

[0114] T λ The expression is:

[0115]

[0116] Discontinuous factors, namely discontinuous influencing factors, mainly include satellite launches and post-mission handling caused by human space activities.

[0117] In this application, launch activities are divided into basic launch activities (excluding constellation launch activities) 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 (MCMC) method to sample and predict future launch activities.

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

[0119] Table 1. Basic Information about Zodiac Signs

[0120]

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

[0122] Table 2. Post-Satellite Mission Handling Strategies

[0123] information describe Off-track strategy Install drag-increasing devices such as off-track sails. Success rate The success rate of PMD is 90%, and the clearing process takes into account active collision avoidance.

[0124] Furthermore, the constellation modeling scheme of this 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 constellation's deployment altitude; N W It is the total number of satellites in the constellation; P W It is the orbital plane number of the constellation; F W It is the phase factor. Let m1 be the number of a satellite in the constellation, then the right ascension Ω of the ascending node of this satellite is... k and perigee angular distance ω k It can be represented as:

[0125]

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

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

[0128]

[0129] in, This is the density matrix of the effective payload as a function of orbital altitude and right ascension, given a fixed declination, orbital inclination, and surface-to-mass ratio. This is the density matrix of the rocket body as a function of orbital altitude and right ascension, given a fixed declination, orbital inclination, and surface-to-mass ratio. This is the density matrix of satellites in post-mission processing that varies with orbital altitude and right ascension, given a fixed declination, orbital inclination, and surface-to-mass ratio. P1 represents the density matrix of debris as a function of orbital altitude and right ascension, given a fixed declination, orbital inclination, and surface-to-mass ratio. 1 When declination, orbital inclination, and surface-to-mass ratio are determined, the density matrix of the payload in the first orbital altitude interval and the first right ascension interval; P1 2 When the declination, orbital inclination, and surface-to-mass ratio are determined, the density matrix of the payload in the first orbital altitude interval and the second right ascension interval; When the declination, orbital inclination, and surface-to-mass ratio are determined, the effective payload is in the first orbital altitude range and the Nth orbital altitude range. λ Density matrix of the right ascension interval; When the declination, orbital inclination, and surface-to-mass ratio are determined, the effective payload is in the second orbital altitude range and the Nth orbital altitude range. λ Density matrix of the right ascension interval; When the declination, orbital inclination, and surface-to-mass ratio are determined, the effective load is at the Nth position. r Density matrices for the orbital altitude interval and the first right ascension interval; When the declination, orbital inclination, and surface-to-mass ratio are determined, the effective load is at the Nth position. r Density matrices for the orbital altitude interval and the second right ascension interval; When the declination, orbital inclination, and surface-to-mass ratio are determined, the effective load is at the Nth position. r orbital altitude range and the Nth λ Density matrix of right ascension intervals.

[0130] When the declination, orbital inclination, and surface-to-mass ratio are determined, the rocket body in the first orbital altitude range and the Nth orbital altitude range... λ Density matrix of the right ascension interval; When the declination, orbital inclination, and surface-to-mass ratio are determined, the rocket body is in the second orbital altitude range and the Nth orbital altitude range. λ Density matrix of the right ascension interval; When the declination, orbital inclination, and surface-to-mass ratio are determined, the rocket body on the Nth... r Density matrices for the orbital altitude interval and the first right ascension interval; When the declination, orbital inclination, and surface-to-mass ratio are determined, the rocket body on the Nth... r Density matrices for the orbital altitude interval and the second right ascension interval; When the declination, orbital inclination, and surface-to-mass ratio are determined, the rocket body on the Nth... r orbital altitude range and the Nth λ Density matrix of the right ascension interval.

[0131] When the declination, orbital inclination, and surface-to-mass ratio are determined, the satellite in post-mission processing is in the Nth... r orbital altitude range and Nth λ Density matrix of the right ascension interval; When the declination, orbital inclination, and surface-to-mass ratio are determined, the fragment is on the Nth... r orbital altitude range and the Nth λ Density matrix of right ascension intervals.

[0132] When the declination, orbital inclination, and surface-to-mass ratio are determined, the satellite in post-mission processing is in the Nth... rDensity matrices for the orbital altitude interval and the first right ascension interval; When the declination, orbital inclination, and surface-to-mass ratio are determined, the satellite in post-mission processing 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-to-mass ratio are determined, the fragment is on the Nth... r Density matrices for the orbital altitude interval and the first right ascension interval; When the declination, orbital inclination, and surface-to-mass ratio are determined, the fragment is on the Nth... r Density matrix of orbital altitude interval and second right ascension interval.

[0133] Furthermore, define the matrix for:

[0134]

[0135] Therefore, the mathematical model corresponding to the space debris environment evolution (space debris environment topology) network model can be expressed in the following form:

[0136]

[0137] It can be represented as:

[0138]

[0139] Where A is the adjacency matrix:

[0140]

[0141] Furthermore, under the above scenarios, the orbital altitude and longitude range distribution of the newly generated failed satellites is defined as follows:

[0142]

[0143] in, F1 represents the density matrix of newly generated failed satellites as a function of orbital altitude and right ascension, given a fixed declination, orbital inclination, and surface-to-mass ratio. 1 When declination, orbital inclination, and surface-to-mass ratio are determined, the density matrix of the newly generated failed satellite in the first orbital altitude interval and the first right ascension interval; F1 2 When the declination, orbital inclination, and surface-to-mass ratio are determined, the density matrix of the newly generated failed satellites is given in the first orbital altitude interval and the second right ascension interval; When the declination, orbital inclination, and surface-to-mass ratio are determined, the newly generated failed satellites are in the first orbital altitude range and the Nth orbital altitude range. λ Density matrix of the right ascension interval; When the declination, orbital inclination, and surface-to-mass ratio are determined, the newly generated failed satellites are in the second orbital altitude range and the Nth orbital altitude range. λ Density matrix of the right ascension interval; When the declination, orbital inclination, and surface-to-mass ratio are determined, the newly generated failed satellite is in the Nth position. r Density matrices for the orbital altitude interval and the first right ascension interval; When the declination, orbital inclination, and surface-to-mass ratio are determined, the newly generated failed satellite is in the Nth position. r Density matrices for the orbital altitude interval and the second right ascension interval; When the declination, orbital inclination, and surface-to-mass ratio are determined, the newly generated failed satellite is in the Nth position. r orbital altitude range and the Nth λ Density matrix of the right ascension interval. When the declination, orbital inclination, and surface-to-mass ratio are determined, the density matrix of the newly generated failed satellites in the second orbital altitude interval and the first right ascension interval is obtained. Given that declination, orbital inclination, and surface-to-mass ratio are determined, this represents the density matrix of the newly generated failed satellite in the second orbital altitude interval and the second right ascension interval. T is the transpose.

[0144] but, It can be represented as:

[0145]

[0146] in, Let τ be the density variation matrix of a space object caused by discontinuous factors as a function of orbital altitude and right ascension, given a fixed declination, orbital inclination, and surface-to-mass ratio; τ is the success rate of post-mission handling.

[0147] The above formula can be used to solve the topological network model of the space debris environment, and finally obtain the evolution prediction results of the space debris environment.

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

[0149] Analysis of the specific spacecraft collision probability algorithm construction method:

[0150] Spacecraft collision risk assessment relies on collision probability algorithms. This application proposes a collision probability algorithm. First, the spatial volume elements traversed by the target spacecraft during its operation are determined. Volume element U α,β,γ The space density of the internal spacecraft is Its probability of appearing in this unit can be expressed as Furthermore, when the spacecraft appears in volume unit U α,β,γ When inside, the flux of the space targets it encounters can be expressed as:

[0151]

[0152] in, σ represents the density of space objects, and its predicted value is derived from the established space debris environment evolution model (space debris environment topology network model); σ is the intersection cross-sectional area of ​​collisions. This refers to the relative collision velocity between the spacecraft and the space target.

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

[0154]

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

[0156] Unlike previous algorithms, the algorithm proposed in this application no longer relies on microscopic models, but instead calculates the volume element U through a topological network model of a space fragmentation environment (a macroscopic model). α,β,γ The algorithm uses spatial target density to characterize collision probabilities. Therefore, it inherits the computational efficiency advantages of the topological network model while significantly reducing computational resource consumption.

[0157] Based on the long-term collision probability algorithm for spacecraft constructed above, the collision risk of constellation satellites during on-orbit and deorbit 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 angular distance from the perigee; f is the true anterior angle.

[0161] Figure 4 The graph shows how the average collision probability changes over time, with the average value calculated every half day. As can be seen from the graph, after the constellation deployment is complete, the probability of an internal collision with other satellites within the same constellation is approximately one order of magnitude greater than the probability of an external collision with other space targets. This indicates that its collision risk is primarily dominated by collisions within the constellation.

[0162] also, Figure 5This demonstrates the average probability of internal and external collisions for constellation satellites over a 7-day operational cycle. For satellites in Class A constellations, the risk of internal collisions is approximately 8.4 to 14.4 times that of external collisions; while for Class B constellations, this ratio is even higher, with the risk of internal collisions reaching 144.3 to 210.8 times that of external collisions.

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

[0164] This application employs a method of equipping failed constellation satellites with deorbit sails to accelerate their deorbiting, and assesses the collision risks throughout the entire deorbiting process. The mass of the failed constellation satellite is set at 100 kg, and the effective deorbit sail area is 1104 m². 2 .

[0165] Figure 6 It shows the deorbit trajectory completed by the failed satellite over 7 days. Figure 7 This shows the distribution of space targets within the orbital altitude range traversed by the satellite during its deorbiting process. A total of 22,253 space targets exist within this region, including 18,156 payloads, 769 rocket bodies, and 3,328 debris. These debris are mainly concentrated in a sun-synchronous orbit with an inclination angle close to 97°; payloads are distributed across multiple inclination angles, such as 43°, 53°, and 97°; while the distribution of rocket bodies shows no clear pattern.

[0166] Figure 8 This paper presents the average collision probability between a deorbited, failed satellite and different types of space targets, calculated using a collision probability algorithm. The results show that the collision risk between the satellite and its payload is significantly higher, approximately 10 times that of collisions with debris and 100 times that of collisions with rocket bodies. Furthermore, the collision probability reaches its maximum on day 5.5, at approximately 1.30 × 10⁻⁶. -4 / year / m 2 .

[0167] The size of space targets is a key factor affecting the degree of damage after a spacecraft collision. Therefore, it is necessary to analyze the collision risk between a failed satellite and space targets of different sizes during deorbiting. This application classifies space targets into three categories according to size: small ([0.1, 0.3] meters), medium ([0.3, 1] meters), and large (>1 meter). Figure 9 It shows the average probability of a failed satellite colliding with space targets of different sizes during deorbiting.

[0168] Combination Figure 6 and Figure 9It can be observed that the probability of collision with targets larger than 1 meter increases significantly when the satellite traverses the orbital region of the constellation deployment. The maximum collision risk occurs on day 5.5, at which point the probability of collision with a large target reaches 1.1 × 10⁻⁶. -4 / year / m 2 The peak was primarily attributed to the failed satellite crossing the Starlink constellation orbital region at that moment.

[0169] This application establishes a multidisciplinary integrated topological network model for space debris environments. This model characterizes the relationships between space targets through a complex network structure and combines fluid dynamics and aerospace dynamics to describe their evolution mechanism. Compared to microscopic models, this model maintains an acceptable error range while requiring only 1.8% of the computation time, significantly improving computational efficiency.

[0170] This application proposes a collision probability algorithm. Based on the established space debris environment topology network model, this algorithm inherits the efficiency advantages of the macroscopic model. Its prediction results are highly consistent with the calculation results of ESA's DRAMA software, verifying the reliability of the algorithm.

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

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

[0173] The findings 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 space debris environments that integrates multidisciplinary methods. This model utilizes a topological network to structurally represent the relationships between space targets and combines fluid dynamics and aerospace dynamics to characterize their evolution mechanism. The computation time of this method is only 1.8% of that of the microscopic model, and the error is controlled within an acceptable range, verifying its reliability and efficiency.

[0175] Furthermore, this application proposes a novel collision probability algorithm. Unlike previous algorithms based on microscopic models, this method is based on a topological network model, possessing the efficiency advantage 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 methods described above, it analyzes the collision risks faced by constellation satellites during their on-orbit operation and decommissioning.

[0177] The technical features of the above embodiments can be combined in any way. For the sake of brevity, 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 descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of this application. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this application. In summary, the content of this specification should not be construed as a limitation of this application.

Claims

1. A constellation satellite collision analysis method based on a space debris environment topology network model, characterized in that, include: The spatial target is divided into volumetric elements to obtain multiple spatial object groups of nodes; 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 topology structure is constructed to obtain a topology network. The topological network was modeled based on the influencing factors of space debris using fluid dynamics methods, resulting in a topological network model of the space debris environment. The adjacency matrix is ​​used to analyze and solve the topological network model of the space debris environment to obtain the evolution prediction results of the space debris environment. A collision probability algorithm is used to perform collision analysis on the constellation satellites based on the evolution prediction results, and the collision analysis results are obtained. The expression corresponding to the topology network is: ； in, This refers to the orbital altitude range number; The declination interval number; The right ascension interval number; The interval number of the orbital inclination angle; The interval number of the surface-to-weight ratio; For the first Track height range, first Declination interval, the Right ascension interval, the Track inclination interval, the first The change in effective load density within the surface-to-mass ratio range; For the first Track height range, first Declination interval, the Right ascension interval, the Track inclination interval, the first The change in rocket body density within the surface-to-mass ratio range; For the first Track height range, first Declination interval, the Right ascension interval, the Track inclination interval, the first The change in satellite density in the post-mission handling state within the surface-to-mass ratio range; For the first Track height range, first Declination interval, the Right ascension interval, the Track inclination range, first The change in the density of fragments within the surface-to-weight ratio range; For the first Track height range, first Declination interval, the Right ascension interval, the Track inclination interval, the first Spatial density of effective load within the surface-to-mass ratio range; For the first Track height range, first Declination interval, the Right ascension interval, the Track inclination interval, the first The spatial density of the rocket body within the surface-to-mass ratio range; For the first Track height range, first Declination interval, the Right ascension interval, the Track inclination range, first Spatial density of post-mission processing satellites within the surface-to-mass ratio range; For the first Track height range, first Declination interval, the Right ascension interval, the Track inclination range, first Spatial density of fragments within the surface-to-mass ratio range; Let J2 be the transfer function of the spatial object under the perturbation of J2. For the first Track height range, first Declination interval, the Right ascension interval, the Track inclination range, first Effective load density within the surface-to-mass ratio range; For the first Track height range, first Declination interval, the Right ascension interval, the Track inclination range, first Rocket body density within the surface-to-mass ratio range; For the first Track height range, first Declination interval, the Right ascension interval, the Track inclination range, first Rocket body density within the surface-to-mass ratio range; For time step; For time; This is the orbital descent function of a space object under atmospheric drag. For the orbit reduction function of a space object under the post-mission handling effect; For launch in volume element Density function of objects in space; For newly generated volume elements The density of failed satellites within the area; To improve the success rate of post-task handling; For the first Track height range, first Declination interval, the Right ascension interval, the Track inclination range, first Spatial density of post-mission processing satellites within the surface-to-mass ratio range; For the first Track height range, first Declination interval, the Right ascension interval, the Track inclination range, first Spatial density of post-mission processing satellites within the surface-to-mass ratio range; For the first Track height range, first Declination interval, the Right ascension interval, the Track inclination range, first Spatial density of fragments within the surface-to-mass ratio range; For the first Track height range, first Declination interval, the Right ascension interval, the Track inclination range, first Spatial density of fragments within the surface-to-mass ratio range; The topological network is modeled using fluid dynamics methods based on the influencing factors of space debris, resulting in a topological network model of the space debris environment, specifically including: The continuity influencing factors were processed using fluid dynamics methods to determine the continuity equation; the continuity influencing factors are the flow variation information of the debris density field in the height direction, the geocentric distance 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 descent function of the space object under the action of atmospheric drag, and the orbit descent function of the space object under the action of PMD. Based on the continuity equation and the topology network, determine the continuous topology network model; By employing constellation configuration and fitting historical space launch parameters, a discontinuous topology network model is determined based on discontinuous influencing factors, including satellite launch and post-mission handling. Based on the continuous topology network model and the discontinuous topology network model, a topology network model for the space fragmentation environment is determined.

2. The constellation satellite collision analysis method based on a space debris environment topology network model according to claim 1, characterized in that, The spatial target is partitioned using volumetric elements to obtain multiple spatial object groups of nodes, specifically including: The Eulerian method is used to divide the space target into volumetric elements. The LEO orbit is divided into multiple space volumetric elements according to the set intervals along the radial, right ascension and declination directions. The orbital inclination angle and surface-to-mass ratio are used to divide the space into multiple intervals. Multiple spatial object group nodes are determined based on multiple defined intervals and multiple spatial volume elements.

3. The constellation satellite collision analysis method based on a space debris environment topology network model according to claim 1, characterized in that, The transfer function of a spatial object under the perturbation of J2 is expressed as follows: ； in, Let J2 be the transfer function of the spatial object under the perturbation of J2. For the first Track height range, first Declination interval, the Right ascension interval, the Track inclination range, first The spatial density of objects within the surface-to-mass ratio range; For the first Track height range, first Declination interval, the Right ascension interval, the Track inclination range, first The spatial density of objects within the surface-to-mass ratio range; This represents the change in density along the height direction corresponding to the right ascension direction. For the density field component along the right ascension direction; Right ascension; For any type of spatial object group; For payload; For the rocket body; As fragments; For post-mission handling of satellites; The dividing intervals along the right ascension direction; For the first Track height range, first Declination interval, the Right ascension interval, the Spatial density of objects within the declination range of orbital inclination; Declination; for Area along the right ascension direction; For the first Track height range, first Declination interval, the The volume element formed by the right ascension interval; This refers to the orbital altitude range number; The declination interval number; The right ascension interval number; The interval number of the orbital inclination angle; The interval number of the surface-to-weight ratio; for Average transfer velocity in the direction of right ascension; For the first Track height range, first Declination interval, the Right ascension interval, the Spatial density of objects within the declination range of orbital inclination; For the first Track height range, first Declination interval, the Right ascension interval, the Track inclination range, first The spatial density of objects within the surface-to-mass ratio range; For the first Track height range, first Declination interval, the The volume element formed by the right ascension interval; For the first Track height range, first Declination interval, the The volume element formed by the right ascension interval; volume element Area along the right ascension direction; for Average transfer velocity in the direction of right ascension; for Area along the right ascension direction; for Average transfer velocity in the direction of right ascension; Let be the volume of the volume element.

4. The constellation satellite collision analysis method based on a space debris environment topology network model according to claim 1, characterized in that, The descent function of a space object under atmospheric drag is expressed as follows: ； in, This is the orbital descent function of a space object under atmospheric drag. For the first Track height range, first Declination interval, the Right ascension interval, the Track inclination range, first The density of objects in space within the surface-to-mass ratio range; For the first Track height range, first Declination interval, the Right ascension interval, the Track inclination range, first The spatial density of objects within the surface-to-mass ratio range; This represents the change in density along the height direction corresponding to the orbital height. This represents the component of the density field along the orbital height direction; r The orbital height; Any type of spatial object; For the rocket body; As fragments; The interval is the division in the radial direction; For the first Track height range, first Declination interval, the The volume element formed by the right ascension interval; volume element Area along the right ascension direction; for The natural descent rate in the direction of orbital altitude; volume element Area along the orbital height; Let be the volume of the volume element; for The natural rate of descent in the direction of orbital altitude.

5. The constellation satellite collision analysis method based on a space debris environment topology network model according to claim 1, characterized in that, The descent function of a space object under the influence of PMD is expressed as follows: ； in, For the orbit reduction function of a space object under the post-mission handling effect; For the first Track height range, first Declination interval, the Right ascension interval, the Track inclination range, first The spatial density of objects within the surface-to-mass ratio range; For the first Track height range, first Declination interval, the Right ascension interval, the Track inclination range, first The spatial density of objects within the surface-to-mass ratio range; This represents the change in density along the height direction corresponding to the right ascension direction. This represents the change in density along the height direction corresponding to the orbital height. This represents the component of the density field along the orbital height direction; r The orbital height; Any type of spatial object; For the rocket body; As fragments; The interval is the division in the radial direction; For the first Track height range, first Declination interval, the The volume element formed by the right ascension interval; volume element Area along the right ascension direction; for PMD descent rate in the orbital altitude direction; Let be the area of ​​the volume element along the direction of the Earth's radius; for PMD descent rate in the orbital altitude direction; Let be the volume of the volume element.

6. The constellation satellite collision analysis method based on a space debris environment topology network model according to claim 1, characterized in that, 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: Based on a preset matrix, the spatial fragmentation environment topology network model is converted into a mathematical model in matrix form; The mathematical model is solved using an adjacency matrix to obtain the evolution prediction results of the space debris environment; The mathematical model is expressed as follows: ； ； The expression for the adjacency matrix is: ； in, The function corresponding to the mathematical model; This is the density matrix of a space object as a function of orbital altitude and right ascension, given a fixed declination, orbital inclination, and surface-to-mass ratio. This is the matrix of density variations of a space object as a function of orbital altitude and right ascension, caused by continuous factors, when the declination, orbital inclination, and surface-to-mass ratio are determined. This is the matrix of density variations of a space object as a function of orbital altitude and right ascension, caused by discontinuous factors, when the declination, orbital inclination, and surface-to-mass ratio are determined. The index of the discrete time step; for at discrete time step The value; for at discrete time step The value; for at discrete time step The value; It is an adjacency matrix; This is the adjacency matrix of the payload nodes; This is the adjacency matrix of the rocket body nodes; This is the adjacency matrix for post-mission processing of satellite nodes; Let be the adjacency matrix of the fragment nodes.

7. The constellation satellite collision analysis method based on a space debris environment topology network model according to claim 1, 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 traversed by the target group during its operation, and determine the corresponding spatial density; Using formula Determine the target flux in space; Based on the spatial target flux, the spatial volume element, and the corresponding spatial density, the collision probability is determined. in, For spatial target flux; The number of intervals to divide the track inclination angle; The number of intervals divided by the surface-to-weight ratio; The interval number of the orbital inclination angle; The interval number of the surface-to-weight ratio; The density of a spatial object; The intersection area of ​​the collision; This refers to the relative collision velocity between the spacecraft and the space target.

Images