A method for calculating large-scale space debris flux

Abstract

This invention relates to the fields of aerospace and artificial intelligence, providing an efficient method for large-scale space debris flux calculation, comprising: step S1, acquiring basic information of n space debris to be calculated; step S2, determining the target space debris i as the observed object, and determining its orbital parameters using the two rows of roots of the target space debris i; step S3, constructing a screening hollow spherical shell; step S4, first-stage flux screening calculation; step S5, second-stage precise flux calculation: for all candidate debris, further determining whether the candidate debris orbits cross the target spherical region within the time interval [0,t]; counting the number of such candidate debris within time t, as the final flux value. This invention can reduce the computational overhead of determining the orbital intersection of large-scale debris, effectively improving the real-time performance and applicability of flux calculation.

Description

Technical Field

[0001] This invention relates to the fields of aerospace and artificial intelligence, and in particular to a method for calculating large-scale space debris flux. Background Technology

[0002] With the booming development of global space activities, the number of spacecraft in low Earth orbit (LEO) and medium Earth orbit (MEO) has exploded, leading to an increasingly serious space debris problem. These high-speed fragments, even those as small as centimeters, can cause fatal collision damage to spacecraft in orbit. LEO, especially the low Earth orbit region at altitudes of 400-1500 km, is a core resource for space activities. Its orbital capacity (including frequency, position, and inclination) is limited. Situational awareness can quantify debris density distribution, identify high-risk orbital areas, and provide data support for orbit planning and satellite decommissioning strategies. This can slow down debris accumulation at its source and ensure the long-term availability of orbital resources.

[0003] Space debris flux, as a core indicator characterizing the number of debris passing through a specific area per unit time, is a crucial basis for spacecraft collision risk assessment, protective design, and space environment management. Existing flux calculation methods primarily rely on full orbital propagation (such as debris-by-debris orbital extrapolation based on the SGP4 model), but the computational complexity increases quadratically when the number of debris reaches a certain level. Flux data is a core indicator for measuring orbital "health": excessively high long-term flux in a certain orbital region indicates that the region is approaching the critical state of "Kessler syndrome" (a positive feedback loop where debris collisions generate new debris), necessitating restrictions on new spacecraft entry or the initiation of debris removal missions.

[0004] Therefore, a large-scale space debris flux calculation method can effectively improve flux calculation efficiency compared to the traditional global traversal calculation, thereby enhancing the optimization of space debris environment models and sustainable management of space resources, and providing accurate quantitative basis for satellite on-orbit collision early warning and safe operation of low-Earth orbit constellations.

[0005] Patent application CN114021248A discloses a "method for determining the risk of space debris impact on aerospace vehicles," which involves a method for calculating space debris flux. The method involves "selecting a suitable space debris environment engineering model and calculating the annual cumulative flux of space debris of different sizes on the vehicle's orbit and the cumulative flux of space debris during the vehicle's on-orbit period." The main shortcomings of this method are: first, judging the orbital crossing of large-scale debris requires massive spatiotemporal intersection calculations, making single-region flux calculation inefficient and time-consuming, unable to meet the real-time collision warning requirements of low-Earth orbit constellations; second, the space debris environment model needs to be calibrated based on massive flux data: by comparing the measured flux with the model's calculated flux, the debris size distribution and orbital distribution parameters are corrected to improve the model's prediction accuracy; otherwise, accuracy will decrease. In this situation, traditional calculation methods are designed for single debris and are difficult to adapt to modern dynamic computing scenarios. Summary of the Invention

[0006] This invention addresses the technical challenges of existing technologies that require massive spatiotemporal intersection calculations for determining orbital crossings of large-scale debris, resulting in low efficiency and long computation times for single-region flux calculations. These limitations fail to meet the real-time collision warning requirements of low-Earth orbit constellations and the need for space debris environment models to be calibrated based on massive flux data. The invention provides a large-scale space debris flux calculation method. Through a two-stage approach, it achieves efficiency breakthroughs through layered filtering, synergistic optimization of accuracy and real-time performance, and universal expansion adaptability to various scenarios. This constructs an efficient, accurate, and universal flux quantification model for large-scale debris environments. This method reduces the computational overhead of determining orbital intersections for large-scale debris and effectively improves the real-time performance and applicability of flux calculations.

[0007] This invention provides a method for calculating large-scale space debris flux, comprising the following steps:

[0008] Step S1: Obtain the basic information of the n space fragments that need to be calculated. The basic information includes two rows of root count data for each space fragment.

[0009] Step S2: Determine the target space debris i whose flux needs to be calculated as the observed object, and determine its orbital parameters using the two rows of roots of the target space debris i.

[0010] Step S3: Construct a hollow spherical shell for screening; the hollow spherical shell for screening is centered on the Earth's center and has an outer radius of R. e +h i +r i The inner radius is R e +h i -r i A hollow sphere, in which h i This is the height of the debris above the ground;

[0011] Step S4: First-stage flux screening calculation: Within a given time interval [0,t], count whether the orbits of all n-1 non-target fragments k (k≠i) cross the hollow spherical shell region; if the orbit of a non-target fragment intersects with the hollow spherical shell, then the non-target fragment is considered a candidate fragment.

[0012] Step S5, Second Stage Precise Flux Calculation: For all candidate fragments, further determine whether the candidate fragment trajectory crosses the target sphere region within the time interval [0,t]; count the number of such candidate fragments within time t, as the final flux value.

[0013] Furthermore, step S2 includes the following steps S21 to S23:

[0014] Step S21: Traverse all n space fragments by obtaining the two rows of roots, and read the orbital parameters θ = (n, e, i, Ω, ω, M) of each space fragment. The orbital parameters include the average motion n and eccentricity e of the fragment.

[0015] Step S22: Select n-1 non-target fragments k (k≠i) other than the space fragment i whose flux needs to be calculated, and read the orbital parameters θ of the non-target fragments. k =(n k ,e k i k ,Ω k ,ω k M k ); and utilize the average motion n of n-1 non-target fragments k The orbital semi-major axis a of the target space debris i is calculated using Kepler's third law. k The calculation formula is as follows:

[0016]

[0017] Where, μ = 3.986004418 × 10 14 m 3 s -2 The standard gravitational constant of Earth;

[0018] Step S23: Using the selected target space fragment i as the center, set the evaluation sphere radius r. i Construct a sphere with radius r as the evaluation sphere radius. i A spherical region, corresponding to a radius R in space. i =R e +h i +r i The maximum sphere is defined as the maximum computational boundary constraint under this setting, where R e Represents the Earth's radius; evaluates the radius r of a sphere.i ∈[1,10]km;

[0019] The evaluation sphere is defined as the target flux calculation region, and mathematically defined as follows:

[0020]

[0021] Where r i (t) represents the spatial position vector of target fragment i in the inertial coordinate system at time t.

[0022] Furthermore, step S3 includes the following steps S31 to S32:

[0023] Step S31: Considering the influence of orbital ellipticity on spatial distribution, and based on the small eccentricity of the near-Earth orbit and the geometric relationship of orbital mechanics, using the semi-major axis a of the selected target space debris i... i and eccentricity e i To calculate the height h of the target debris above the ground i :

[0024]

[0025] Where R e Represented as Earth's radius;

[0026] Step S32: Simultaneously construct a hollow spherical shell with the Earth's center of mass as its center, and calculate the inner radius R of the hollow spherical shell. in =R e +h i -r i The outer radius is R out =R e +h i +r i The hollow spherical shell is mathematically defined as follows:

[0027]

[0028] Furthermore, step S4 includes the following steps S41 to S42:

[0029] Step S41: Calculate the orbital envelope for each non-target fragment k (k≠i):

[0030]

[0031] Step S42: Construct a candidate fragment set C to determine the orbital envelope of each non-target fragment and the size of the inner and outer diameters of the spherical shell. If the following conditions are met:

[0032]

[0033] If the trajectory of the non-target fragment intersects with the hollow spherical shell, the non-target fragment is considered a candidate fragment, and is added to the candidate fragment set C.

[0034] Furthermore, step S5 includes the following steps S51 to S55:

[0035] Step S51: Sample t within the given time interval window [0, t] with a step size Δt. m =m△t; m represents the total number of samples, t m Indicates the maximum time within the time window;

[0036] Step S52: Using the SGP4 propagation model, calculate the time t for target space debris i and non-target debris k respectively. m The three-dimensional position vector at time:

[0037] r i (t m )=(x i (t m ),y i (t m ),z i (t m )) T

[0038] r k (t m )=(x k (t m ),y k (t m ),z k (t m )) T

[0039] Step S53: Calculate the instantaneous distance between target space debris i and non-target debris k:

[0040]

[0041] Step S54: Define a flux counting indicator function:

[0042]

[0043] When the non-target fragment has an instantaneous Euclidean distance of less than r with the target fragment i at a certain moment within the time window. i Then count otherwise

[0044] Step S55: Count the number of candidate fragments of this type within time t, and use it as the final flux value;

[0045] The total flux is:

[0046]

[0047] The flux per unit time and per unit area is:

[0048]

[0049] The time discretization step size Δt satisfies:

[0050]

[0051] Where T min Represented as the minimum orbital period,

[0052] The present invention provides a method for calculating large-scale space debris flux, which has the following beneficial effects:

[0053] 1. This invention employs a two-stage strategy of initial screening with a hollow spherical shell and precise calculation of the target sphere. Utilizing the geometric constraints of the hollow spherical shell, it first filters out fragments where the orbit does not intersect with the target space, compressing the size of the candidate fragment set requiring precise calculation from the full fragment set n to a sparse candidate set m (m << n). This reduces the computational complexity of orbit intersection determination from O(nn) to O(nn). 2 The computational efficiency is reduced to O(mn-m). This mechanism effectively overcomes the computational efficiency bottleneck of traditional full traversal methods in large-scale fragmentation scenarios, providing an algorithmic foundation for real-time throughput computing.

[0054] 2. This invention provides a large-scale space debris flux calculation method that achieves synergistic optimization of accuracy and real-time performance. The hollow spherical shell construction strictly ensures complete coverage of the target space, avoiding misjudgments of the target's interior. The second stage, based on analytical calculations of orbital elements, accurately determines whether debris has crossed the target sphere, ensuring the physical accuracy of the flux calculation. Through two-stage task decoupling, it satisfies the real-time requirements of scenarios such as on-orbit collision warning while avoiding systemic errors introduced by simplified models, thus resolving the inherent contradiction of "mutual exclusion between accuracy and efficiency" in traditional methods.

[0055] 3. The present invention provides a large-scale space debris flux calculation method, which enhances the error robustness of orbit crossing judgment. Space debris i is defined as the center, with a radius of r. i The sphere is used as the flux calculation region. This mechanism improves the robustness of flux calculation under orbital dynamics model errors and reduces the probability of missed detections due to the risk of the orbit being parallel to the plane, which is a problem with traditional methods of selecting a plane for flux calculation.

[0056] 4. This method not only propels the technological leap from "qualitative understanding" to "quantitative control" of space debris threats, but also lays a crucial algorithmic foundation in areas such as spacecraft safety design, on-orbit risk management, and sustainable utilization of space resources. This method provides core support for the engineering application of space debris environmental situational awareness, enhancing the "measurability" and "controllability" of space debris threats, ensuring the safety of space activities and the sustainable utilization of space resources. Attached Figure Description

[0057] Figure 1 This is a flowchart illustrating the implementation of a large-scale space debris flux calculation method provided by the present invention.

[0058] Figure 2 This is a schematic diagram of the constructed hollow spherical shell mentioned in the large-scale space debris flux calculation method provided by this invention. Detailed Implementation

[0059] To make the technical problems solved by the present invention, the technical solutions adopted, and the technical effects achieved clearer, the present invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the present invention and not intended to limit the invention.

[0060] like Figure 1 As shown, the present invention provides a method for calculating large-scale space debris flux, comprising the following steps:

[0061] Step S1: Obtain the basic information of the n space fragments that need to be calculated. The basic information includes the two line elements (TLE) data of each space fragment.

[0062] The TLE data was obtained from the official website of the China Manned Space Engineering Corporation and websites such as CelesTrak. This data compiles a large amount of TLE data from satellites, clearly categorized (e.g., Starlink, GPS, International Space Station), supports searching by satellite number or name, and provides a programming interface. This provides strong data support for this invention.

[0063] Step S2: Determine the target space debris i whose flux needs to be calculated as the observed object, and determine its orbital parameters using the two rows of roots of the target space debris i.

[0064] Define the target space fragment i as the center and the radius as r. i The sphere is used as the flux calculation region. The corresponding space has a radius of R. i =R e +h i +r i The sphere is defined as the maximum computational boundary constraint under this setting, where R eThis represents the Earth's radius.

[0065] Step S2 includes the following steps S21 to S23:

[0066] Step S21: Traverse all n space fragments by obtaining the two rows of roots, and read the orbital parameters θ = (n, e, i, Ω, ω, M) of each space fragment. The orbital parameters include the average motion n and eccentricity e of the fragment.

[0067] Step S22: Select n-1 non-target fragments k (k≠i) other than the space fragment i whose flux needs to be calculated, and read the orbital parameters θ of the non-target fragments. k =(n k ,e k i k ,Ω k ,ω k M k ); and utilize the average motion n of n-1 non-target fragments k The orbital semi-major axis a of the target space debris i is calculated using Kepler's third law. k The calculation formula is as follows:

[0068]

[0069] Where, μ = 3.986004418 × 10 14 m 3 s -2 is the Earth's standard gravitational constant.

[0070] Step S23: Using the selected target space fragment i as the center, set the evaluation sphere radius r. i Construct a sphere with radius r as the evaluation sphere radius. i A spherical region, corresponding to a radius R in space. i =R e +h i +r i The maximum sphere is defined as the maximum computational boundary constraint under this setting, where R e Represents the Earth's radius. Evaluate the radius r of a sphere. i ∈[1,10]km.

[0071] The evaluation sphere is defined as the target flux calculation region, and mathematically defined as follows:

[0072]

[0073] Where r i (t) represents the spatial position vector of target fragment i in the inertial coordinate system at time t.

[0074] Step S3, as follows Figure 2 As shown, a hollow spherical shell for screening is constructed, wherein the hollow spherical shell is centered at the Earth's center and has an outer radius of R. e +h i +r i The inner radius is R e +h i -r i A hollow sphere (ringed shell region), in which h i This represents the height of the debris above the ground.

[0075] The spherical shell covers the entire space where the target is located; constructing a hollow spherical shell can reduce the complexity of subsequent orbit crossing calculations.

[0076] Step S3 includes the following steps S31 to S32:

[0077] Step S31: Considering the influence of orbital ellipticity on spatial distribution, and based on the small eccentricity of the near-Earth orbit and the geometric relationship of orbital mechanics, using the semi-major axis a of the selected target space debris i... i and eccentricity e i To calculate the height h of the target debris above the ground i :

[0078]

[0079] Where R e It is expressed as the Earth's radius.

[0080] Step S32: Simultaneously construct a hollow spherical shell with the Earth's center of mass as its center, and calculate the inner radius R of the hollow spherical shell. in =R e +h i -r i The outer radius is R out =R e +h i +r i The hollow spherical shell is mathematically defined as follows:

[0081]

[0082] Step S4: First-stage flux screening calculation: Within a given time interval [0,t], count whether the orbits of all n-1 non-target fragments k (k≠i) cross the hollow spherical shell region; if the orbit of a non-target fragment intersects with the hollow spherical shell, then the non-target fragment is considered a candidate fragment.

[0083] Step S4 includes steps S41 to S42:

[0084] Step S41: Calculate the orbital envelope for each non-target fragment k (k≠i):

[0085]

[0086] Step S42: Construct a candidate fragment set C to determine the orbital envelope of each non-target fragment and the size of the inner and outer diameters of the spherical shell. If the following conditions are met:

[0087]

[0088] If the trajectory of the non-target fragment intersects with the hollow spherical shell, the non-target fragment is considered a candidate fragment, and is added to the candidate fragment set C.

[0089] Step S5, Second Stage Precise Flux Calculation: For all candidate fragments, further determine whether the candidate fragment trajectory crosses the target sphere region within the time interval [0,t] (i.e., whether it actually enters the area centered on the target space fragment i with a radius of r). i (Inside the sphere). Count the number of candidate fragments of this type within time t, and use this as the final flux value.

[0090] Step S5 includes the following steps S51 to S55:

[0091] Step S51: Sample t within the given time interval window [0, t] with a step size Δt. m =m△t. m represents the total number of samples, t... m This indicates the maximum time within the time window.

[0092] Step S52: Using the SGP4 (Simplified General Perturbations 4) propagation model, calculate the propagation time t for target space debris i and non-target debris k respectively. m The three-dimensional position vector at time:

[0093] r i (t m )=(x i (t m ),y i (t m ),z i (t m )) T

[0094] r k (t m )=(x k (t m ),y k (t m ),z k (t m)) T

[0095] Step S53: Calculate the instantaneous distance between target space debris i and non-target debris k:

[0096]

[0097] Step S54: Define a flux counting indicator function:

[0098]

[0099] When the non-target fragment has an instantaneous Euclidean distance of less than r with the target fragment i at a certain moment within the time window. i Then count otherwise

[0100] Step S55: Count the number of candidate fragments of this type within time t, and use it as the final flux value.

[0101] The total flux is:

[0102]

[0103] The flux per unit time and per unit area is:

[0104]

[0105] The time discretization step size Δt satisfies:

[0106]

[0107] Where T min Represented as the minimum orbital period,

[0108] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications to the technical solutions described in the foregoing embodiments, or equivalent substitutions for some or all of the technical features, do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for calculating large-scale space debris flux, characterized in that, Includes the following processes: Step S1: Obtain the data to be calculated. N Basic information of each space fragment, including two rows of root count data for each space fragment; Step S2: Identify the target space fragments whose flux needs to be calculated. i As the observed object, utilizing target space debris i Two rows of roots determine its orbital parameters; Step S2 includes the following steps S21 to S23: Step S21: Traverse all the rows of roots obtained from the two rows. N Each space fragment has its orbital parameters read. The orbital parameters include the average motion of the debris therein. n With eccentricity e ; Step S22: Select the space fragments whose flux needs to be calculated. i The rest N -1 non-target fragment k Read the orbital parameters of non-target debris ; and utilize N –Average motion of 1 non-target fragment And Kepler's third law to calculate the target space debris i semi-major axis of the track The calculation formula is as follows: ； in, The standard gravitational constant of Earth; Step S23: Select the target space debris for calculation i Centered on the sphere, set the radius of the evaluation sphere. Construct a sphere with radius equal to the radius of the sphere being evaluated. A spherical region, corresponding to a radius of in space. The maximum sphere is defined as the maximum computational boundary constraint under this setting, where Represents the Earth's radius; assesses the radius of a sphere. ; The evaluation sphere is defined as the target flux calculation region, and mathematically defined as follows: ； in Indicates target fragments i At any moment t Spatial position vector in an inertial coordinate system; Step S3: Construct a hollow spherical shell for screening; the hollow spherical shell for screening is centered on the Earth's center and has an outer radius of... Inner radius is A hollow sphere, in which This is the height of the debris above the ground; Step S3 includes the following steps S31 to S32: Step S31: Considering the influence of orbital ellipticity on spatial distribution, and based on the small eccentricity of the near-Earth orbit and the geometric relationship of orbital mechanics, utilize the selected target space debris. i semi-major axis of the track and eccentricity To calculate the height of the target debris above the ground ; ； in Represented as Earth's radius; Step S32: Simultaneously construct a hollow spherical shell with the Earth's center of mass as its center, and calculate the inner radius of the hollow spherical shell as... The outer radius is The hollow spherical shell is mathematically defined as follows: ； Step S4, First-stage flux initial screening calculation: within a given time interval Inside, statistics of all N -1 non-target fragment k Whether the orbit of a non-target fragment crosses the hollow spherical shell region; if the orbit of a non-target fragment intersects with the hollow spherical shell, then the non-target fragment is considered a candidate fragment; Step S5, Second Stage Precise Flux Calculation: For all candidate debris, further determine whether the candidate debris trajectories are within the time interval. The interior traverses the target sphere region, the target sphere being a target space fragment. i Centered on, with radius A sphere; statistics in time t The number of candidate fragments of this type is used as the final flux value.

2. The method for calculating large-scale space debris flux according to claim 1, characterized in that, Step S4 includes the following steps S41 to S42: Step S41: For each non-target fragment k Calculate the orbital envelope: ； Step S42: Construct a candidate fragment set C This is used to determine the orbital envelope of each non-target debris and the size of the inner and outer diameters of the constructed spherical shell. If the following conditions are met: ； If the trajectory of the non-target fragment intersects with the hollow spherical shell, then the non-target fragment is considered a candidate fragment and is added to the candidate fragment set. C .

3. The method for calculating large-scale space debris flux according to claim 2, characterized in that, Step S5 includes the following steps S51 to S55: Step S51: Within a given time interval window Inner step length Sampling ; m Indicates the total number of samples. t m Indicates the maximum time within the time window; Step S52: Calculate the target space debris using the SGP4 propagation model. i Non-target fragments k In time The three-dimensional position vector at time: ； Step S53: Calculate target space debris i Non-target fragments k Instantaneous distance: ； Step S54: Define a flux counting indicator function: ； When the non-target fragment exists within a time window at a moment that coincides with the target fragment... i The instantaneous Euclidean distance is less than Then count ,otherwise ; Step S55: Statistics on time t The number of candidate fragments of this type is used as the final flux value; The total flux is: ； The flux per unit time per unit area is: ； Time discretization Step size satisfies: ； in Represented as the minimum orbital period, .

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