Space debris environment three-dimensional network evolution method

Abstract

The invention discloses a space debris environment three-dimensional network evolution method, and belongs to the field of aerospace. The method comprises the following steps: dividing an LEO orbit into a plurality of space volume elements according to a geocentric distance, right ascension, declination and an area-to-mass ratio, then dividing space objects in each volume element into a plurality of space object groups according to an orbit inclination angle and the area-to-mass ratio, selecting a macroscopic quantity of the density of the object groups as a state variable, and considering multi-source environmental factors such as atmospheric resistance perturbation and the like; and establishing a space debris environment three-dimensional network evolution model by adopting a continuity equation to realize rapid prediction of debris evolution at any position in the space. The method also utilizes the established three-dimensional network evolution model of the space debris environment to predict the low-orbit space debris environment under the sun and geomagnetic activities, and analyzes the influence of the sun and geomagnetic activities on the space debris environment evolution. Satellite launching, space traffic management and space debris treatment can be supported and optimized, and related engineering technical problems are solved.

Description

Technical Field

[0001] The present invention relates to a three-dimensional network evolution method for a space debris environment, in particular to a three-dimensional network evolution method for a space debris environment and a method for analyzing the influence of solar geomagnetic activity on the evolution of the debris environment, and belongs to the field of aerospace. Background Art

[0002] As of February 2024, the number of cataloguable objects in the space environment has reached nearly 28,000, of which spacecraft account for only one-third, and the rest are space debris. The deteriorating space debris environment will greatly increase the collision risk of spacecraft in orbit. Therefore, for the target spacecraft, analyzing the evolution of debris in its operating space and conducting long-term collision risk assessment are prerequisites for the safe implementation of space missions.

[0003] At present, there are two main types of space debris environment evolution models. One is a microscopic model that tracks the motion state of a single debris. The debris events of this type of model are implemented using Monte Carlo technology, which relies on a large amount of computing resources and time. The other type is a macroscopic model with the number and density of debris as variables. The macroscopic model is established using differential equations (groups). The evolution of the number of debris can be obtained by solving the differential equations. Compared with the microscopic model, it has considerable computational efficiency and has become a popular research method that is currently being developed and improved.

[0004] However, the current macro models have certain limitations. Almost all macro models have the problem of simple spatial division (grouping only according to orbital altitude, and even not distinguishing between altitude layers), and cannot predict the state of space objects at any spatial position (latitude and longitude); moreover, the perturbation models of most models are relatively simple, such as not considering the perturbation of the Earth's flattening, and the influence of solar activity and geomagnetic activity. The impact of these environmental factors on the evolution of debris cannot be ignored. The right ascension drift of the ascending node caused by the Earth's flattening perturbation will cause the transfer of space objects between different longitude areas at the same latitude; and extreme weather such as geomagnetic storms will cause a sudden increase in atmospheric resistance and accelerate the decay of the object's orbit. For example, the 40 Starlink satellites launched on February 3, 2022 were affected by geomagnetic storms and re-entered the Earth's atmosphere and were damaged. It can be seen that although the macro model has great advantages in efficiency, the accuracy of spatial division and environmental perturbations still needs to be improved.

[0005] Therefore, it is necessary to study a method that takes into account multiple environmental factors, such as atmospheric resistance, J 2 The macroscopic debris evolution model of perturbations, solar and geomagnetic activities, etc., can improve the problem of insufficient accuracy of traditional macroscopic evolution models while effectively avoiding computational redundancy and achieving efficient prediction of debris evolution. Summary of the invention

[0006] The purpose of the present invention is to solve the problem that the existing space debris environment evolution method has low computational efficiency and low precision, resulting in low efficiency and inaccuracy in collision risk assessment, and thus causing danger to satellites, and to provide a three-dimensional network evolution method for space debris environment. This method divides the LEO orbit into several space volume elements according to the distance from the center of the earth, right ascension, declination and surface mass ratio, and then divides the space objects in each volume element into several space object groups according to the orbital inclination and surface mass ratio. The density of the object group is selected as the macroscopic quantity as the state variable, and multi-source environmental factors such as atmospheric resistance perturbation are considered. The continuity equation is used to establish a three-dimensional network evolution model of the space debris environment, and the rapid prediction of the evolution of debris at any position in space is realized. The present invention also provides an analysis method for the influence of solar and geomagnetic activities on the evolution of space debris environment. The established three-dimensional network evolution model of the space debris environment is used to predict the low-orbit space debris environment under solar and geomagnetic activities, support the optimization of satellite launch, space traffic management and space debris governance, and solve related engineering and technical problems.

[0007] The objectives of the present invention are achieved through the following technical solutions.

[0008] The invention discloses a method for predicting the average evolution of space debris environment, which discretizes space debris in layers. The LEO orbit is divided into several space volume elements according to the distance from the center of the Earth, right ascension, declination and surface mass ratio, and the space objects in each volume element are divided into several space object groups according to the orbital inclination and surface mass ratio. The density of the object group is selected as the macroscopic quantity as the state variable, which saves computing resources and improves the efficiency of evolution prediction. The continuity factor in the process of debris environment evolution is considered, and the atmospheric perturbation and J are combined to predict the average evolution of space debris environment. 2 The total perturbation motion equation of the spacecraft under perturbation is characterized by the average orbital decay velocity of the space object and the average transfer velocity of the space object in the same latitude but different longitude intervals. 2 The influence of perturbations on the evolution of the debris environment is considered, and expressions for the average orbital decay rate and the average transfer rate are given to improve the accuracy of the space debris evolution prediction model; the discontinuity factors in the evolution of the debris environment are considered, which are mainly reflected in human space activities, and the space launch activities are modeled. Then, the topological network model is used to further characterize and model the space activities. Considering three types of space objects related to space activities, working satellites (S), failed satellites (F), and satellite remains / debris (N), a constellation model is established; the continuity equation in fluid mechanics is used to establish a three-dimensional network evolution model of the space debris environment; based on the changing laws of solar activity and geomagnetic index, the established three-dimensional network evolution model of the space debris environment is used to predict the low-orbit space debris environment under solar and geomagnetic activities, and analyze the influence of solar activity and geomagnetic activity on the evolution of the space debris environment.

[0009] The present invention discloses a three-dimensional network evolution of a space debris environment, comprising the following steps:

[0010] Step 1: Divide the LEO orbit into several space volume elements according to the distance from the center of the Earth, right ascension and declination, and then divide the space objects in each volume element into several space object groups according to the orbital inclination and surface mass ratio. The density of the space object group is a state variable to improve the calculation efficiency of steps 2 to 4.

[0011] First, the LEO orbit is calculated according to the distance from the center of the earth r, right ascension λ and declination Divide into The space volume elements are divided into Δr, Δλ, For the space volume element U i,j,k , the spatial range it contains is determined by formula (1);

[0012]

[0013] Among them, r i is the median value of the ith geocentric distance layer, is the median value of the jth declination layer, λ k is the median value of the kth right ascension layer; the space objects in each volume element are divided into N according to the orbital inclination and surface mass fraction i ×N a interval; therefore The total number of spatial volume elements is Space object group; volume element U i,j,k The space object group within the pth orbital inclination interval and the qth surface mass ratio interval The spatial density as a state variable.

[0014] Step 2: Consider the continuity factor in the process of debris environment evolution, establish the total perturbation motion equation of the spacecraft under the combination of the Earth's flattening perturbation and atmospheric perturbation, use the average orbital decay rate of space objects to characterize the influence of atmospheric drag on the density evolution of the space object group; use the average transfer speed of the space object group in the same latitude and different longitude intervals to characterize J 2 The influence of perturbations on the density evolution of space object groups; and construct an expression for the influence of continuity factors on the density evolution of space object groups, that is, construct expressions for the average orbital decay velocity and the average transfer velocity respectively, so as to improve the accuracy of the three-dimensional network evolution model of the space debris environment in step four.

[0015] Step 2.1: The total perturbation equation of motion of the spacecraft under the Earth's flattening perturbation and atmospheric perturbation is:

[0016]

[0017] Where a is the semi-major axis of the orbit; i is the orbit inclination; Ω is the right ascension of the ascending node; e is the orbit eccentricity; ω is the depression angle of the perigee; f is the true anomaly; M is the mean anomaly of the space object; r is the distance from the center of the earth; n is the average angular velocity of motion; ρ is the atmospheric density; S is the frontal area of ​​the space object; n represents the average angular velocity of motion; m o is the mass of the space object; J 2 is the Earth's oblateness J 2 Item; C d is the atmospheric drag coefficient; R e is the equatorial radius of the earth; t is the time;

[0018] Step 2.2: For The average decay rate of space objects in the group It is expressed as:

[0019]

[0020] For an object running on a circular orbit, the orbital eccentricity e = 0. Substituting it into equation (2), we get:

[0021]

[0022] Where ρ is the atmospheric density; (A / m o ) q represents the median value of the surface mass fraction layer of q; μ is the earth's gravitational constant; thus, we can know that It is a function related to atmospheric density, orbital altitude, and object surface-to-mass ratio. For a certain space object with a known orbital altitude, the atmospheric density ρ can be determined to obtain Taking into account solar and geomagnetic activities, the atmospheric density model is expressed as:

[0023]

[0024] Where T is the 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; thus, the atmospheric density expression is expressed as:

[0025] ρ=6×10 -10 exp(0.012h 2 -31.5h+5145 / T) (6)

[0026] Substituting (6) into (4), we obtain the average orbital decay rate:

[0027]

[0028] Step 2.3: The relationship between the longitude and latitude of a point on the orbit of a space object and the orbital elements is as shown in equation (8);

[0029]

[0030] It can be seen that the longitude drift speed of any point in space is Drift velocity with right ascension of ascending node equal; for The average transfer speed of space objects in the group From equation (9), we get:

[0031]

[0032] Among them, i p represents the median value of the p-th orbital inclination layer; a e is the equatorial radius of the Earth.

[0033] Step 3: Consider the discontinuity factors in the evolution of the debris environment and model the space launch activities; then use the topological network model to further characterize and model the space activities to obtain a model of discontinuity factors; this will help improve the accuracy of the three-dimensional network evolution model of the space debris environment in step 4.

[0034] Step 3.1: Consider the discontinuity factor in the evolution of the debris environment and model the space launch activities to obtain the model

[0035] 1) Based on the actual launch data from 2020 to 2023, the upper and lower bounds of the number of payloads and rocket bodies launched each month / year are obtained. The number of future launches is uniformly distributed within this range. The number of future launches per month / year is obtained by random sampling. L ;

[0036] 2) Using a Gaussian mixture model (GMM), we fit the actual launch information of the payload and rocket body from 2020 to 2023, including orbital parameters and dimensions, and obtain Gaussian mixture results of the actual launch information of the payload and rocket body;

[0037] 3) Finally, the Markov Chain Monte Carlo method (MCMC) is used to extract N from the Gaussian mixture results obtained in step 2). L launch samples, and finally obtain a prediction model for future launch activities Indicates that the emission Satellite density;

[0038] Step 3.2: Construct a physical layer topology network model that considers three activities: space launch, satellite post-mission disposal (PMD), and natural orbit reduction; consider three types of space objects related to space activities, namely, working satellites (S), failed satellites (F), and satellite remains / debris (N), and then divide the three objects into nodes according to orbital altitude and face value. Represents three types of objects in The density of the group, the dynamic equations of each node are (10)~(12);

[0039]

[0040]

[0041] Where: for The density of new failed satellites generated in the system; τ is the success rate of PMD; υ PMD is the PMD descending speed; is the natural orbit descent speed; It's J 2 The speed of object transfer under perturbation; therefore, the model of space activity, that is, the discontinuity factor, is:

[0042]

[0043] Step 4: Combined with the expression of the influence of continuity factors on the density evolution of space object groups in step 2 and the model of discontinuity factors in step 3, the continuity equation in fluid mechanics is used to establish a three-dimensional network evolution model of the space debris environment, so that the established space debris evolution prediction model can improve the efficiency of evolution prediction while ensuring the accuracy of evolution prediction.

[0044] The continuity equation (14) in fluid mechanics is used to model the density evolution of space debris;

[0045]

[0046] in, represents the continuity factor acting on the system, represents the discontinuous factor; the continuous factors considered are the atmospheric drag perturbation and J 2 perturbation, and the discontinuous factors are space launch activities and post-satellite mission disposal; therefore, considering the atmospheric drag, J 2 Perturbation, space launch and satellite mission post-processing The group density evolution equation changes from (14) to (15); the left side of the formula is the change in the number of space objects, and the first and second terms on the right side represent the atmospheric drag and J, respectively. 2Group of objects under the influence of perturbation The third term represents the change in the number of objects caused by space activities;

[0047]

[0048] Among them, V i,j,k is the volume element U i,j,k The volume of is the cross-sectional area in the direction of atmospheric resistance, For J 2 The cross-sectional area in the direction of perturbation is expressed as follows; Space objects caused by atmospheric drag The average decay rate of the orbital altitude is For J 2 The average transfer speed of space objects caused by perturbations in the same latitude but different longitude intervals, It is caused by space activities The amount of change in density of objects within the group;

[0049]

[0050] Substitute equations (16) to (18) into (15); then divide both sides of the equation by Δr·Δλ·r 2 ; Let Δr→0, Δλ→0, Formula (15) is simplified to Formula (19), which gives the three-dimensional network evolution model of space debris environment:

[0051]

[0052] Step 5: Based on the three-dimensional network evolution model of the space debris environment in step 4, analyze the sensitivity of the solar activity index F107 and the geomagnetic index Ap to the evolution of the space debris environment, support the optimization of satellite and constellation launches and their post-mission disposal strategies, space traffic management and space debris governance, and solve related engineering and technical problems.

[0053] Beneficial effects:

[0054] 1. The present invention discloses a three-dimensional network evolution method for space debris environment, which discretizes space debris in layers. The LEO orbit is divided into several space volume elements according to the distance from the center of the earth, right ascension, declination and surface mass ratio, and then the space objects in each volume element are divided into several space object groups according to the orbital inclination and surface mass ratio. The density of the object group is selected as the macroscopic quantity as the state variable, and the continuity equation in fluid mechanics is used to model the space debris environment, which can save computing resources and make the evolution model have high computing efficiency.

[0055] 2. The present invention discloses a three-dimensional network evolution method for space debris environment. It considers the continuity factor in the evolution process of debris environment, combines the total perturbation motion equation of spacecraft under the earth's flattening perturbation and atmospheric perturbation, and uses the average orbital decay speed of space objects and the average transfer speed of space objects in different longitude intervals at the same latitude to characterize the atmospheric drag and J respectively. 2 The influence of perturbations on the evolution of the debris environment is analyzed, and expressions for the average orbital decay rate and the average transfer rate are given; the discontinuity factors in the evolution of the debris environment are considered, which are mainly reflected in human space activities, and the space launch activities are modeled. Then the topological network model is used to further characterize and model the space activities. The topological network model analyzes the relationship between various space objects by analogy by analyzing the topological relationship of the equivalent network. Each node in the network is a group of objects, and the link connection represents the relationship between objects. Considering three types of space objects related to space activities, working satellites (S), failed satellites (F), and satellite remains / fragments (N), a constellation model is established, which can improve the accuracy of the space debris evolution prediction model.

[0056] 3. The present invention discloses a three-dimensional network evolution method for space debris environment, which can be used to predict the solar activity index F 107 and the geomagnetic index A p Analyze the sensitivity of the evolution of the space debris environment to support the optimization of satellite and constellation launches and their post-mission disposal strategies, space traffic management and space debris management, and solve related engineering and technical problems. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 It is a schematic diagram of the position of the space volume element in the present invention;

[0058] Figure 2 This is a schematic diagram of the topological network model of aerospace activities in the present invention;

[0059] Figure 3 A schematic diagram of the generation and disappearance mechanism of space objects of the present invention;

[0060] Figure 4 is the F of 2013-2023 in the embodiment 107 and A p Index change graph;

[0061] Figure 5 In the embodiment F 107 A graph showing the effect of the index on the evolution of space debris density;

[0062] Figure 6 In the embodiment F 107 A graph showing the effect of the index on the evolution of the number of space debris;

[0063] Figure 71 is a diagram showing the effect of a geomagnetic storm on a single object in an embodiment; wherein FIG. (a) is a diagram showing the change of the orbital altitude and atmospheric drag of a single object in an embodiment at different geomagnetic storm levels over time; FIG. (b) is a schematic diagram showing the sudden change of atmospheric drag of a single object in an embodiment at the moment of being subjected to a geomagnetic storm;

[0064] Figure 8 A schematic diagram comparing the effects of geomagnetic storm levels and durations on the debris environment in the embodiment;

[0065] Fig. 9 The present invention is a flow chart of a three-dimensional network evolution method for a space debris environment. DETAILED DESCRIPTION

[0066] In order to better illustrate the purpose, technical solutions and advantages of the present invention, the invention is further described below in conjunction with the accompanying drawings and embodiments.

[0067] As of February 2024, the number of cataloguable objects in the space environment has reached nearly 28,000, of which spacecraft account for only one-third, and the rest are space debris. The deteriorating space debris environment will greatly increase the collision risk of spacecraft in orbit. Therefore, for the target spacecraft, analyzing the evolution of debris in its operating space and conducting long-term collision risk assessment are prerequisites for the safe implementation of space missions.

[0068] At present, space debris environment evolution models are mainly divided into two categories. One is the microscopic model that tracks the motion state of a single debris, such as NASA's LEGEND, ESA's DELTA and other engineering models. The debris events of this type of model are implemented with Monte Carlo technology, which relies on a lot of computing resources and time. The other is a macroscopic model with the number and density of debris as variables. The macroscopic model is established using differential equations (groups), and the evolution of the number of debris can be obtained by solving the differential equations. Compared with the microscopic model, it has considerable computational efficiency and has become a popular research method that is currently being developed and improved.

[0069] However, the current macro models have certain limitations. Almost all macro models have the problem of simple spatial division (grouping only according to orbital altitude, and even not distinguishing between altitude layers), and cannot predict the state of space objects at any spatial position (latitude and longitude); moreover, the perturbation models of most models are relatively simple, such as not considering the perturbation of the Earth's oblateness, and the atmospheric drag model does not consider the influence of solar activity and geomagnetic activity. The impact of these environmental factors on the evolution of debris cannot be ignored. The right ascension drift of the ascending node caused by the Earth's oblateness perturbation will cause the transfer of space objects between different longitude areas at the same latitude; and extreme weather such as geomagnetic storms will cause a sudden increase in atmospheric drag and accelerate the decay of the object's orbit. For example, the 40 Starlink satellites launched on February 3, 2022 were affected by geomagnetic storms and re-entered the Earth's atmosphere and were damaged. Although macro models have great advantages in efficiency, the accuracy of spatial division and environmental perturbations still needs to be improved.

[0070] like Fig. 9 As shown, the present embodiment discloses a three-dimensional network evolution method for a space debris environment, and the specific implementation steps are as follows:

[0071] Step 1: Divide the LEO orbit into several space volume elements according to the distance from the center of the Earth, right ascension and declination, and then divide the space objects in each volume element into several space object groups according to the orbital inclination and surface mass ratio. The density of the space object group is a state variable to improve the calculation efficiency of steps 2 to 4.

[0072] First, the LEO orbit is calculated according to the distance from the center of the earth r, right ascension λ and declination Divide into The space volume elements are divided into Δr, Δλ, For the space volume element U i,j,k , the spatial range it contains is determined by formula (1);

[0073]

[0074] Among them, r i is the median value of the ith geocentric distance layer, is the median value of the jth declination layer, λ k is the median value of the kth right ascension layer; the space objects in each volume element are divided into N according to the orbital inclination and surface mass fraction i ×N a interval; therefore The total number of spatial volume elements is Space object group; volume element U i,j,k The space object group within the pth orbital inclination interval and the qth surface mass ratio interval The spatial density as a state variable.

[0075] Step 2: Consider the continuity factor in the process of debris environment evolution, establish the total perturbation motion equation of the spacecraft under the combination of the Earth's flattening perturbation and atmospheric perturbation, use the average orbital decay rate of space objects to characterize the influence of atmospheric drag on the density evolution of the space object group; use the average transfer speed of the space object group in the same latitude and different longitude intervals to characterize J 2 The influence of perturbations on the density evolution of space object groups; and construct an expression for the influence of continuity factors on the density evolution of space object groups, that is, construct expressions for the average orbital decay velocity and the average transfer velocity respectively, so as to improve the accuracy of the three-dimensional network evolution model of the space debris environment in step four.

[0076] Step 2.1: The total perturbation equation of motion of the spacecraft under the Earth's flattening perturbation and atmospheric perturbation is:

[0077]

[0078] Where a is the semi-major axis of the orbit; i is the orbit inclination; Ω is the right ascension of the ascending node; e is the orbit eccentricity; ω is the depression angle of the perigee; f is the true anomaly; M is the mean anomaly of the space object; r is the distance from the center of the earth; n is the average angular velocity of motion; ρ is the atmospheric density; S is the frontal area of ​​the space object; n represents the average angular velocity of motion; m o is the mass of the space object; J 2 is the Earth's oblateness J 2 Item; C d is the atmospheric drag coefficient; R e is the equatorial radius of the earth; t is the time;

[0079] Step 2.2: For The average decay rate of space objects in the group It is expressed as:

[0080]

[0081] For an object running on a circular orbit, the orbital eccentricity e = 0. Substituting it into equation (2), we get:

[0082]

[0083] Where ρ is the atmospheric density; (A / m o ) q represents the median value of the surface mass fraction layer of q; μ is the earth's gravitational constant; thus, we can know that It is a function related to atmospheric density, orbital altitude, and object surface-to-mass ratio. For a certain space object with a known orbital altitude, the atmospheric density ρ can be determined to obtain Taking into account solar and geomagnetic activities, the atmospheric density model is expressed as:

[0084]

[0085] Where T is the 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; thus, the atmospheric density expression is expressed as:

[0086] ρ=6×10 -10 exp(0.012h 2 -31.5h+5145 / T) (25)

[0087] Substituting (6) into (4), we obtain the average orbital decay rate:

[0088]

[0089] Step 2.3: The relationship between the longitude and latitude of a point on the orbit of a space object and the orbital elements is as shown in equation (8);

[0090]

[0091] It can be seen that the longitude drift speed of any point in space is Drift velocity with right ascension of ascending node equal; for The average transfer speed of space objects in the group From equation (9), we get:

[0092]

[0093] Among them, i p represents the median value of the p-th orbital inclination layer; a e is the equatorial radius of the Earth.

[0094] Step 3: Consider the discontinuity factors in the evolution of the debris environment and model the space launch activities; then use the topological network model to further characterize and model the space activities; this will help improve the accuracy of the three-dimensional network evolution model of the space debris environment in step 4.

[0095] Step 3.1: Consider the discontinuity factor in the evolution of the debris environment and model the space launch activities to obtain the model

[0096] 4) Based on the actual launch data from 2020 to 2023, the upper and lower bounds of the number of payloads and rocket bodies launched each month / year are obtained. The number of future launches is uniformly distributed within this range. The number of future launches per month / year is obtained by random sampling. L ;

[0097] 5) Using a Gaussian mixture model (GMM), the real launch information of the payload and rocket body from 2020 to 2023 is fitted, including orbital parameters and dimensions, and the Gaussian mixture results of the real launch information of the payload and rocket body are obtained;

[0098] 6) Finally, the Markov Chain Monte Carlo method (MCMC) is used to extract N from the Gaussian mixture results obtained in step 2). L launch samples, and finally obtain a prediction model for future launch activities Indicates that the emission Satellite density;

[0099] Step 3.2: Construct a physical layer topology network model that considers three activities: space launch activities, post-mission disposal of satellites (PMD), and natural orbit reduction; consider three types of space objects related to space activities, namely, working satellites (S), failed satellites (F), and satellite remains / debris (N), and then divide the three objects into nodes according to orbital altitude and face value. Represents three types of objects in The density of the group, the dynamic equations of each node are (10)~(12);

[0100]

[0101] Where: for The density of new failed satellites generated in the system; τ is the success rate of PMD; υ PMD is the PMD descending speed; is the natural orbit descent speed; It's J 2 The speed of object transfer under perturbation; therefore, the model of space activity, that is, the discontinuity factor, is:

[0102]

[0103] Step 4: Combined with the expression of the influence of continuity factors on the density evolution of space object groups in step 2 and the model of discontinuity factors in step 3, the continuity equation in fluid mechanics is used to establish a three-dimensional network evolution model of the space debris environment, so that the established space debris evolution prediction model can improve the efficiency of evolution prediction while ensuring the accuracy of evolution prediction.

[0104] The continuity equation (14) in fluid mechanics is used to model the density evolution of space debris;

[0105]

[0106] in, represents the continuity factor acting on the system, represents the discontinuous factor; the continuous factors considered are the atmospheric drag perturbation and J 2 perturbation, and the discontinuous factors are space launch activities and post-satellite mission disposal; therefore, considering the atmospheric drag, J 2 Perturbation, space launch and satellite mission post-processing The group density evolution equation changes from (14) to (15); the left side of the formula is the change in the number of space objects, and the first and second terms on the right side represent the atmospheric drag and J, respectively. 2 Group of objects under the influence of perturbation The third term represents the change in the number of objects caused by space activities;

[0107]

[0108] Among them, V i,j,k is the volume element U i,j,k The volume of is the cross-sectional area in the direction of atmospheric resistance, For J 2 The cross-sectional area in the direction of perturbation is expressed as follows; Space objects caused by atmospheric drag The average decay rate of the orbital altitude is For J 2 The average transfer speed of space objects caused by perturbations in the same latitude but different longitude intervals, It is caused by space activities The amount of change in density of objects within the group;

[0109]

[0110]

[0111] Substitute equations (16) to (18) into (15); then divide both sides of the equation by Δr·Δλ·r 2 ; Let Δr→0, Δλ→0, Formula (15) is simplified to Formula (19), which gives the three-dimensional network evolution model of space debris environment:

[0112] .

[0113] Step 5: Based on the three-dimensional network evolution model of the space debris environment in step 4, analyze the sensitivity of the solar activity index F107 and the geomagnetic index Ap to the evolution of the space debris environment, support the optimization of satellite and constellation launches and their post-mission disposal strategies, space traffic management and space debris governance, and solve related engineering and technical problems.

[0114] In this embodiment, F 107 and A p They are parameters used to describe the activities of the solar and Earth magnetic fields, respectively. They affect space weather by changing the atmospheric temperature, and thus indirectly affect the evolution of the space debris environment. 107 The index is divided into low activity (F 107 <90), medium activity (90 <F 107 <150), high activity (F 107 >150); geomagnetic activity can be measured according to A p The index is divided into static (0 p <7), unstable state (8 p <15), Active(16 p <29), Small Storm (30 p <49), Big Storm (50 p <99), Extreme Storm (A p >100). F 107 and A p The variation of the index is closely related to the 11-year solar activity cycle. The F 107 With A p Index such as Figure 4 As shown in Figure 1 (data from the National Space Science Center of the Chinese Academy of Sciences). The 11-year solar activity pattern shows that solar activity will reach its peak in 2024, and geomagnetic storms are more frequent during the peak years of solar activity. Therefore, in order to cope with the upcoming extreme weather environment, two simulation scenarios were set up in Case 1 to evaluate the impact of solar activity and geomagnetic storms on debris evolution.

[0115] A. Analysis of the sensitivity of solar activity to debris evolution

[0116] The initial debris environment selects spatially cataloguable objects within the range of [200,1000] km in March 2024, given A p The historical average is 9.57. Select different F 107 Index, a three-dimensional network model is used for numerical simulation, the simulation time is 30 days, and the step length is 1 day. This scenario considers the orbit maintenance of the satellite and assumes that there is no collision or explosion disintegration event in space in a short time.

[0117] ​​​​​ Figure 5 and Figure 6 F 107 As for the impact of the density and number of space objects at different orbital altitudes, it can be seen that the overall reduction of space objects increases with F 107 increases, and F 107 For every 10 increase, the number of objects decreases by 11%. However, the trend of the number of space objects at different orbital altitudes is different. This is because F 107 The change in atmospheric density caused by the increase in F has a more obvious impact on space objects below 600 km. 107 The decay rate of space objects at [400,600] km is faster than that at [600,1000] km. The number of objects at the initial orbital altitude of [200,400] km is relatively small. Space objects above 400 km enter the [200,400] km region under the influence of atmospheric resistance. The inflow of space objects in this region is greater than the outflow, causing the space objects in this region to decay faster with F. 107 Increase and grow.

[0118] B. Analysis of the sensitivity of geomagnetic activity to debris evolution

[0119] In this case, given F 107 is 150 (high solar activity), A p 8 (unstable state), and four different levels of geomagnetic storms (A p =22(active), A p =40(small storm), A p =75(Big Storm), A p =110 (extreme storm)) on a single space object and space debris environment. In the single space debris scenario, the initial orbital altitude of the space object is 350km and the surface-to-mass ratio is 0.1m 2 / kg, and the geomagnetic index was changed on the 0.5th day of operation to simulate the geomagnetic storm. In the space debris environment evolution scenario, the effects of different geomagnetic storm levels and durations on the space debris environment were analyzed. The initial debris environment selection, simulation parameter settings, and basic assumptions were the same as those in scenario A.

[0120] Figure 7 It shows the impact of geomagnetic storms of different levels on a single space object. It can be seen that geomagnetic storms will cause a sudden increase in the atmospheric resistance experienced by the object, causing it to leave orbit prematurely. Figure 8 The results show the reduction in the number of space objects caused by different geomagnetic storm levels and durations. The reduction in the number of space objects gradually increases with the increase in the geomagnetic index and duration. A geomagnetic storm lasting 7 days will reduce the number of space debris from a few to more than ten. Figure 8The data given will be smaller than the actual situation. On the one hand, this case takes into account the satellite's orbit maintenance. If the satellite's orbit maintenance capability is not sufficient to resist the sudden increase in atmospheric drag, it will become space debris and deorbit under the influence of atmospheric drag. On the other hand, geomagnetic storms will interfere with satellite navigation and communications, increasing the risk of satellite failure.

[0121] In summary, the above are only preferred embodiments of the present invention and are not intended to limit the protection scope of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A three-dimensional network evolution method for space debris environment, characterized by: The following steps are included: Step 1: Divide the LEO orbit into several space volume elements according to the distance from the center of the Earth, right ascension and declination, and then divide the space objects in each volume element into several space object groups according to the orbital inclination and surface mass fraction. The density of the space object group is the state variable; Step 2: Consider the continuity factor in the evolution of the debris environment, establish the total perturbation motion equation of the spacecraft under the combination of the Earth's oblateness perturbation and the atmospheric perturbation, use the average orbital decay rate of space objects to characterize the influence of atmospheric drag on the density evolution of the space object group; use the average transfer rate of the space object group in the same latitude and different longitude intervals to characterize the influence of the J2 perturbation on the density evolution of the space object group; and construct an expression for the influence of the continuity factor on the density evolution of the space object group, that is, construct expressions for the average orbital decay rate and the average transfer rate respectively, so as to improve the accuracy of the three-dimensional network evolution model of the space debris environment in step 4; Step 3: Considering the discontinuity factors in the evolution of the debris environment, model the space launch activities; then use the topological network model to further characterize and model the space activities to obtain a model of discontinuity factors; this is convenient for improving the accuracy of the three-dimensional network evolution model of the space debris environment in step 4; Step 4: Combined with the expression of the influence of continuity factors on the density evolution of space object groups in step 2 and the model of discontinuity factors in step 3, the continuity equation in fluid mechanics is used to establish a three-dimensional network evolution model of the space debris environment, so that the established space debris evolution prediction model can improve the efficiency of evolution prediction while ensuring the accuracy of evolution prediction.

2. A space debris environment three-dimensional network evolution method as claimed in claim 1, characterized in that: It also includes step 5: Based on the three-dimensional network evolution model of the space debris environment in step 4, analyze the solar activity index F 107 and the geomagnetic index A p Sensitivity to the evolution of the space debris environment supports the optimization of satellite and constellation launch and post-mission disposal strategies, space traffic management and space debris management, and solves related engineering and technical problems.

3. A method for three-dimensional network evolution of space debris environment as claimed in claim 1 or 2, characterized in that: The implementation method of step one is: Discretize the space debris in layers; divide the LEO orbit into several space volume elements according to the distance from the center of the Earth, right ascension, declination and surface-to-mass ratio, and then divide the space objects in each volume element into several space object groups according to the orbital inclination and surface-to-mass ratio, and select the density of the object group as a macroscopic quantity as the state variable to improve the calculation efficiency of steps 2 to 4; The LEO orbit is calculated according to the distance from the center of the Earth r, right ascension λ and declination Divide into The space volume elements are divided into Δr, Δλ, For the space volume element U i,j,k , the spatial range it contains is determined by formula (1); Among them, r i is the median value of the ith geocentric distance layer, is the median value of the jth declination layer, λ k is the median value of the kth right ascension layer; the space objects in each volume element are divided into N according to the orbital inclination and surface mass fraction i ×N a interval; therefore The total number of spatial volume elements is Space object group; volume element U i,j,k The space object group within the pth orbital inclination interval and the qth surface mass ratio interval The spatial density as a state variable.

4. A space debris environment three-dimensional network evolution method as claimed in claim 3, characterized in that: The implementation method of step 2 is: Step 2.1: The total perturbation equation of motion of the spacecraft under the Earth's flattening perturbation and atmospheric perturbation is: Where a is the semi-major axis of the orbit; i is the orbit inclination; Ω is the right ascension of the ascending node; e is the orbit eccentricity; ω is the depression angle of the perigee; f is the true anomaly; M is the mean anomaly of the space object's orbit; r is the distance from the center of the earth; n is the average angular velocity of motion; ρ is the atmospheric density; S is the windward area of ​​the space object; n represents the average angular velocity; m o is the mass of the space object; J2 is the earth's flattening J2 term; C d is the atmospheric drag coefficient; R e is the equatorial radius of the earth; t is the time; Step 2.2: For The average decay rate of space objects in the group It is expressed as: For an object running on a circular orbit, the orbital eccentricity e = 0. Substituting it into equation (2), we get: Where ρ is the atmospheric density; (A / m o ) q represents the median value of the surface mass ratio stratification q; μ is the Earth's gravitational constant; It is a function related to atmospheric density, orbital altitude, and object surface-to-mass ratio. For a certain space object with a known orbital altitude, the atmospheric density ρ can be determined to obtain Taking into account solar and geomagnetic activities, the atmospheric density model is expressed as: Where T is the 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; the atmospheric density expression is expressed as: ρ=6×10 -10 exp(0.012h 2 -31.5h+5145 / T) (6) Substituting (6) into (4), we obtain the average orbital decay rate: Step 2.3: The relationship between the longitude and latitude of a point on the orbit of a space object and the orbital elements is as shown in equation (8); Longitude drift velocity of any point in space Drift velocity with right ascension of ascending node equal; for The average transfer speed of space objects in the group From equation (9), we get: Among them, i p represents the median value of the p-th orbital inclination layer; a e is the equatorial radius of the Earth.

5. A three-dimensional network evolution method for space debris environment as claimed in claim 4, characterized in that: The implementation method of step three is: Step 3.1: Consider the discontinuity factor in the evolution of the debris environment and model the space launch activities to obtain the model 1) Based on the past N y The actual launch data of the year is used to obtain the upper and lower bounds of the number of payloads and rocket bodies launched each month / year. The number of future launches follows a uniform distribution within this range. The number of future launches N per month / year is obtained through random sampling. L ; 2) Use Gaussian mixture model GMM to fit the past N y The actual launch information of payloads and rocket bodies in 2018, The launch information includes orbital parameters and dimensions, and obtains a Gaussian mixture result of the actual launch information of the payload and the rocket body; 3) Using the Markov chain Monte Carlo method MCMC, extract N from the Gaussian mixture result obtained in step 2) L launch samples, and finally obtain a prediction model for future launch activities Indicates that the emission Satellite density; Step 3.2: Construct a physical layer topology network model that considers three activities: space launch activities, post-mission disposal of satellites (PMD), and natural orbit reduction; consider three types of space objects related to space activities, namely, working satellites (S), failed satellites (F), and satellite remains / debris (N), and then divide the three objects into nodes according to orbital altitude and face value. Represents three types of objects in The density of the group, the dynamic equations of each node are (10)~(12); Where: for The density of new failed satellites generated in the system; τ is the success rate of PMD; υ PMD is the PMD descending speed; is the natural orbit descent speed; is the object transfer speed under the action of J2 perturbation; the space activity is expressed by the differential equation shown in formula (13):

6. A three-dimensional network evolution method for space debris environment as claimed in claim 5, characterized in that: In step four, The continuity equation (14) in fluid mechanics is used to model the density evolution of space debris; in, represents the continuity factor acting on the system, represents discontinuous factors; the continuous factors considered are atmospheric drag perturbation and J2 perturbation, and the discontinuous factors are space launch activities and post-satellite mission disposal; considering atmospheric drag, J2 perturbation, space launch and post-satellite mission disposal The group density evolution equation changes from (14) to (15); the left side of formula (15) is the change in the number of space objects, and the first and second terms on the right side represent the group density of objects under the influence of atmospheric drag and J2 perturbation, respectively. The third term represents the change in the number of objects caused by space activities; Among them, V i,j,k is the volume element U i,j,k The volume of is the cross-sectional area in the direction of atmospheric resistance, is the cross-sectional area in the direction of J2 perturbation, and its expression is as follows; Space objects caused by atmospheric drag The average decay rate of the orbital altitude is is the average transfer speed of space objects in the same latitude but different longitude intervals caused by J2 perturbation, It is caused by space activities The amount of change in density of objects within the group; Substitute equations (16) to (18) into (15); divide both sides of the equation by Δr·Δλ·r 2 ; Let Δr→0, Δλ→0, Formula (15) is simplified to Formula (19), which gives the three-dimensional network evolution model of space debris environment:

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