Collision risk analysis method, system and storage medium for low-orbit giant constellations

Abstract

This application discloses a method, system, and storage medium for analyzing collision risks of low-orbit mega-constellations. The method includes at least one of the following: performing short-term and long-term collision risk analyses on the constellation. The short-term collision risk analysis involves calculating the short-term collision probability of satellites in the low-orbit mega-constellation, and the calculation process includes: analyzing the propagation curve of space target orbit prediction errors, initial screening of dangerous space targets, analyzing space target proximity, and calculating the probability of intersection and collision between two space targets. The long-term collision risk analysis involves calculating the average collision probability of the constellation over its lifetime, and the calculation process includes: streamlining the model, calculating space target density, calculating space target attenuation rates, calculating the number of collision-disintegration fragments, and calculating the average collision probability over the constellation's lifetime. This application can analyze the short-term and long-term collision risks of low-orbit mega-constellations to ensure constellation safety.

Description

Technical Field

[0001] The present application relates to a spacecraft risk prediction method and system, belonging to the field of spacecraft measurement and control, and in particular to a low-orbit giant constellation collision risk analysis method, system and storage medium. Background Art

[0002] Currently, low-Earth orbit mega-constellations are gradually entering the deployment phase. With the continued network deployment of Starlink and OneWeb constellations, more and more countries and commercial internet companies are accelerating the construction of their own low-Earth orbit mega-constellations. These constellations will add tens of thousands of satellites and a significant amount of space debris to low-Earth orbit. The surge in the number of space objects increases the probability of spacecraft collisions. Once a collision occurs, the resulting space debris significantly increases the probability of secondary collisions within the constellation, severely impacting not only the safety of the low-Earth orbit mega-constellations themselves but also the space environment. Ensuring constellation safety has become a crucial research topic for constellations.

[0003] Existing technologies primarily focus on the long-term evolution of collision probabilities, with limited statistical analysis of short-term collision probabilities. Furthermore, collision probability calculations currently rely on theoretically randomly generated constellation data, rather than processing measured data. Consequently, their accuracy and relevance are limited. Summary of the Invention

[0004] According to a first aspect of the present application, a method for analyzing collision risks of a low-orbit mega-constellation is provided. The method can perform short-term and long-term collision risk analysis on a low-orbit mega-constellation and provide early warning to ensure constellation safety.

[0005] The method for analyzing the collision risk of a low-orbit mega-constellation includes a short-term collision risk analysis of a low-orbit mega-constellation. The short-term collision risk analysis includes the following steps:

[0006] Analyze the propagation curve of the space target orbit prediction error. This curve is added to the subsequent short-term collision probability calculation and is the basis for the calculation of the space rendezvous target error. The space target includes intact objects and space debris. The orbit prediction error is the difference between the orbit prediction data and the actual orbit data of the space target.

[0007] Preferably, the orbit prediction data of the space target adopts the SGP4 orbit prediction model; screening dangerous space targets;

[0008] A proximity analysis is performed on the dangerous space target to calculate a short-term collision probability of the low-orbit mega-constellation.

[0009] Furthermore, analyzing the space target orbit prediction error propagation curve includes:

[0010] The orbit prediction errors of space targets are calculated respectively, and the error propagation curve is obtained by fitting the curve.

[0011] Preferably, the calculation of the orbit prediction error of the space target comprises the steps of:

[0012] The standard deviation between the actual orbital data of intact objects and space debris within the same orbital altitude range of ±20 km and the orbital prediction data is calculated. The least squares method is used to fit the curve to obtain the fitting curve coefficient of the orbital prediction error over time within the maximum statistical time. The fitting formula is:

[0013]

[0014]

[0015] Where y day is the error statistic, a1, b1 are the coefficients of the linear error curve equation, a2, b2, c2 are the coefficients of the parabolic error curve equation, t day is the evolution time, t end The maximum statistical time.

[0016] Furthermore, the screening of dangerous space targets includes:

[0017] Based on the geometric relationship between the apogee and perigee of the space target and the constellation shell, the space target is screened out of the apogee and perigee of the space target and the constellation shell. Based on the time window, the space target is screened out of the arc segment of the orbit within the constellation shell and the space target latitude is within the range of the constellation shell to obtain dangerous space targets.

[0018] The geometric relationship includes: intersecting with the constellation shell, being contained in the constellation shell, and being separated from the constellation shell. Intersecting with the constellation shell and being contained in the constellation shell are considered to be within the constellation shell interval. The space target includes intact objects and space debris.

[0019] Furthermore, the proximity analysis is as follows: calculating the relative distance between each of the dangerous space targets, and determining that a collision may occur when the relative distance is less than a given threshold;

[0020] Preferably, before calculating the relative distances between any two hazardous space objects, the space is segmented using spatial discrete volume elements.

[0021] Preferably, the calculation of the short-term collision probability of the low-orbit giant constellation comprises the steps of:

[0022] Fit the trajectories of two potentially colliding hazardous space targets, calculate the moment when the two hazardous space targets are closest, obtain the motion states of the two hazardous space targets at the intersection point, and calculate their collision probability, which is used as the short-term collision probability of the low-orbit mega-constellation.

[0023] Preferably, the fitting adopts Lagrange interpolation method.

[0024] According to a second aspect of the present application, a method for analyzing collision risk of a low-orbit mega-constellation is provided, comprising a long-term collision risk analysis of a low-orbit mega-constellation. The long-term collision risk analysis is to calculate an average collision probability of the low-orbit mega-constellation over its life cycle, comprising the following steps:

[0025] Establish a model hypothesis for the long-term collision probability of low-orbit mega-constellations;

[0026] Under the above assumptions, the spatial density of the space object within the shell is calculated according to the interval height of the constellation shell;

[0027] Based on the distribution of space debris in the low-orbit region, an attenuation model of space debris in the shell is established, and the amount of space debris inflow and outflow is calculated based on the attenuation model;

[0028] Calculate the amount of space debris generated by the collision based on the equivalent mass of the space target;

[0029] Based on the amount of space debris flowing in and out and the amount of space debris generated by the collision, the spatial density of space debris within the constellation shell is calculated as shown in the following formula:

[0030]

[0031] Where N is the amount of space debris, the subscripts i and j denote the type of debris in the jth shell, v is the decay rate, and t is the number of days. Using the definition of density as ρ = N / V, we can derive the time-dependent evolution of the space environment density over the lifetime of the Starlink constellation, where V is the volume of the shell.

[0032] The long-term collision probability of a LEO mega-constellation is calculated based on the spatial density of the space targets within the shell and the spatial density of the space debris within the constellation shell. Since all satellites in orbit besides the constellation satellites are controllable, collisions are by default avoided. Uncontrollable constellation satellites can be treated as space debris. Therefore, the space targets here primarily include LEO mega-constellation satellites and space debris.

[0033] Preferably, the attenuation model is used to represent the average attenuation rate of the space debris in the shell, as shown in the following formula:

[0034]

[0035] Where μ is the Earth's gravitational constant, ρ is the atmospheric resistance, and C d is the atmospheric drag coefficient, A is the area of the space target, m is the mass of the space target; a is the semi-major axis of the orbit;

[0036] Preferably, the amount of space debris generated by the collision is calculated according to the following formula:

[0037]

[0038] Where, N C is greater than the characteristic length l c The number of space debris, characteristic length l c =(l x +l y +l z ) / 3, l x ,l y ,l z is the projection size of the space debris on the three orthogonal principal axes in the NTW coordinate system, is the equivalent mass of the two space targets.

[0039] According to a third aspect of the present application, a low-orbit mega-constellation collision risk analysis system is provided, comprising a memory, a processor, and a low-orbit mega-constellation collision risk analysis program stored and executable on the memory. When executed by the processor, the low-orbit mega-constellation collision risk analysis program implements some or all of the steps of the above-described low-orbit mega-constellation collision risk analysis method.

[0040] According to a fourth aspect of the present application, a computer-readable storage medium is provided, on which a program for analyzing the collision risk of a low-orbit giant constellation is stored. When the program for analyzing the collision risk of a low-orbit giant constellation is executed by a processor, some or all of the steps of the above-mentioned method for analyzing the collision risk of a low-orbit giant constellation are implemented.

[0041] The beneficial effects of this application include:

[0042] 1) This application provides a collision risk analysis method for low-orbit mega-constellations. This method calculates short-term collision probabilities, resulting in short-term collision risk analysis results and timely early warnings to ensure constellation safety. This short-term collision probability primarily addresses the uncertainty of specific spatial locations. Orbital predictions are used to determine the positions of space debris and constellation satellites. A series of methods are used to eliminate locations where collisions are unlikely, retaining those where collisions are likely. A Laplace transform-based collision probability algorithm is then used to calculate the short-term collision probability between constellation satellites and space debris.

[0043] 2) This application provides a collision risk analysis method for low-orbit megaconstellations. This method can calculate the long-term collision probability and generate long-term collision risk analysis results, providing early warning for constellation safety. The long-term collision probability is primarily calculated using the hypothetical PIB collision probability calculation formula. Because space debris varies in size and density, space debris is categorized by radius, and the density variation of different types of space debris within the constellation shell is calculated. Density variation is primarily caused by the generation of new space debris by collisions and the natural decay of space debris. Therefore, calculations are performed separately for both collisional disintegration and orbital decay.

[0044] 3) The present application provides a low-orbit giant constellation collision risk analysis system, which has high operating efficiency through customized memory, processor, and a low-orbit giant constellation collision risk analysis program stored and executable on the memory.

[0045] 4) This application provides a computer-readable storage medium specifically for storing a program for low-orbit giant constellation collision risk analysis, with good confidentiality performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 This is a flow chart of a method for analyzing collision risk of a low-orbit giant constellation in one embodiment of the present application;

[0047] Figure 2 This is a schematic diagram of the relationship between the apogee and perigee of a space target and the constellation shell in one embodiment of the present application;

[0048] Figure 3 This is a schematic diagram of the division of spatial volume elements in one embodiment of the present application;

[0049] Figure 4 This is a schematic diagram of the attenuation of a space object within a shell in one embodiment of the present application;

[0050] Figure 5 The error ellipsoid distribution of two spacecraft in the encounter coordinate system in one embodiment of the present application;

[0051] Figure 6 This is a distribution diagram of the eccentricity of space debris in the low-orbit region versus the semi-major axis of the orbit in one embodiment of the present application. DETAILED DESCRIPTION

[0052] The present application is described in detail below with reference to embodiments, but the present application is not limited to these embodiments.

[0053] See also Figure 1 , which shows a flow chart of the low-orbit giant constellation collision risk analysis method of the present application, which includes at least one of the following: short-term collision risk analysis and long-term collision risk analysis.

[0054] In one embodiment, the short-term collision risk analysis involves calculating the collision probability of satellites in a low-orbit mega-constellation over a seven-day period. This calculation process includes four steps: analyzing the propagation curve of space target orbit prediction errors, initially screening for hazardous space targets, analyzing the proximity of space targets, and calculating the probability of a collision between two space targets.

[0055] In one embodiment, long-term collision risk analysis includes calculating the average collision probability of the constellation during its life cycle. The calculation process includes five steps: simplifying the hypothetical calculation model, calculating the density of space targets, calculating the attenuation rate of space targets, calculating the number of collision disintegration fragments, and calculating the average collision probability during the constellation life cycle.

[0056] The coordinate systems and transformation relationships used in this application are defined and explained as follows, including the geocentric inertial coordinate system and the NTW orbital coordinate system.

[0057] 1. Geocentric Inertial Coordinate System

[0058] The geocentric inertial coordinate system is also known as the J2000 coordinate system because its X-axis points to the mean equinox at 12:00 on January 1, 2000. The Z-axis of the coordinate system points to the north celestial pole, the X-axis points to the mean equinox, and the Y-axis forms a right-handed rectangular coordinate system with the Z and X axes.

[0059] 2.NTW orbital coordinate system

[0060] The NTW coordinate system takes the center of mass of the space target as the coordinate origin, the T axis is tangent to the track and consistent with the direction of motion, the N axis is located in the track plane and perpendicular to the direction of motion, and the W axis is consistent with the normal direction of the track surface.

[0061] In the space target error analysis model, the SGP4 model is used to predict the space target's orbit, and the target's TLE data is used as the actual orbit data. Therefore, the orbit prediction error is the difference between the orbit data predicted by the SGP4 model and the TLE data. Table 1 shows the standard deviation statistics of the errors along the three orbital coordinate axes for several typical orbital satellites, and Table 2 shows the standard deviation statistics of the errors along the three orbital coordinate axes for several typical orbital space debris.

[0062] Table 1 Statistics of satellite position error standard deviation over time

[0063]

[0064] Table 2 Statistics of the change of space debris position error standard deviation over time

[0065]

[0066] According to the principle of least squares method, the error propagation curve of the space target is fitted as follows:

[0067]

[0068]

[0069] Where y day is the error statistic, a1, b1 are the coefficients of the linear error curve equation, a2, b2, c2 are the coefficients of the parabolic error curve equation, day is the evolution time, t end =7 is the maximum statistical time. Table 3 gives the satellite position error covariance fitting curve coefficients, and Table 4 gives the space debris position error covariance fitting curve coefficients. In Tables 3 and 4, only the coefficients a and b are expressed as linear curves, expressed as y = ax + b; the coefficients containing a, b, and c are expressed as parabolas, expressed as y = ax 2 +bx+c.

[0070] Table 3 Satellite position error covariance fitting curve coefficients

[0071]

[0072] Table 4. Covariance fitting curve coefficients of space debris position error

[0073]

[0074]

[0075] The spatial hazardous target screening method uses a screening method based on far-near locations and a screening method based on time windows.

[0076] Figure 2 This is a schematic diagram of the relationship between the apogee and perigee of the space target in this application and the constellation shell. Figure 3 This is a schematic diagram of the division of space volume elements in this application. After the low-orbit giant constellation is deployed at a certain altitude, the constellation satellites will operate in a certain range near this altitude. This range is called the constellation shell. There are three states between the orbit of a space target and the shell: intersecting, contained in the shell, and separated. Among them, space targets that intersect with or are contained in the shell may collide with the constellation satellite, while space targets that are separated from the shell will not collide with the constellation satellite. Therefore, space targets that may collide with constellation satellites can be preliminarily screened based on the geometric relationship between the apogee and perigee of the space target and the constellation shell.

[0077] Let the constellation shell height be D, the semi-major axis of the constellation satellite nominal orbit be a, and the apogee and perigee of the space target s be Apog s 、Perg sBecause the eccentricity of the LEO giant constellation satellite is approximately 0, the nominal orbit radius of the constellation can be approximately equal to a. The expression filtered by the apogee-perigee and the upper and lower bounds of the constellation shell is:

[0078] Perg s >a+D / 2||Apog s <a-D / 2 (3)

[0079] Low-orbit giant constellation satellites operate within the constellation shell interval. A collision with a satellite is possible only when the space target position is within the constellation shell. Therefore, the arc segment of the target orbit within the constellation shell can be screened through the time window.

[0080] Let the predicted position velocity of space target s at time t be The radius vector of the space target at time t is obtained as:

[0081]

[0082] Since the constellation shell interval is [aD / 2, a+D / 2], the arc segment where the space target and the constellation satellite may collide is:

[0083] aD / 2 <r(t)<a+D / 2 (5)

[0084] In addition, the inclination of the constellation orbit limits the maximum latitude that the constellation shell can reach. When the satellite orbit arc crosses the constellation shell altitude range, the satellite latitude may not be within the constellation shell constraint range, so the satellite latitude needs to be screened. The relationship between satellite position and latitude is:

[0085] δ s =arcsin(sini s sinu s ) (6)

[0086] Where u s is the phase of the space target s, δ s is the latitude of the space target s. When the latitude of the space target s within the window range is greater than the orbital inclination i of the constellation and the orbital inclination offset Δi, it is considered that the space target is unlikely to collide with the constellation satellite and should be eliminated. The screening expression is:

[0087] δ s >i+Δi (7)

[0088] After identifying targets that could collide with constellation satellites, proximity analysis is performed to identify two targets that could collide. In this process, discrete volume elements are used to segment the space, taking into account the large scale of low-orbit mega-constellations, to reduce the computational complexity of pairwise identification of space targets.

[0089] The discrete volume element coordinate system is the J2000 inertial coordinate system. In the inertial coordinate system, the constellation shell is centered on the earth and the spherical coordinates are established along the three directions of the earth's center, longitude and latitude, and are expressed in r min ,λ min 、 As the starting point, follow the interval Divide the constellation shell space into several space volume elements.

[0090] according to Figure 3 It can be obtained that the space volume element C j,k,l The coordinates in three directions are:

[0091]

[0092] Where r min ,λ min 、 are the initial points along the geocentric distance, longitude and latitude directions in the inertial coordinate system, respectively. are the volume element sizes in the directions of geocenter, longitude and latitude respectively, is the space volume element C in the inertial system j,k,l The distance from the center of the earth, the longitude and latitude of the outermost point along the center of the earth close to the x-axis, and J, K, L are the number of divisions of the volume element along the distance from the center of the earth, the longitude and latitude.

[0093] Space volume element C j,k,l The center of is expressed as:

[0094]

[0095] Where r j ,λ k 、 is the geocentric distance, longitude and latitude of the center point of the volume element, are the volume element sizes in the directions of geocenter, longitude and latitude respectively, is the space volume element C in the inertial system j,k,l The distance from the center of the earth, the longitude and latitude of the outermost point along the center of the earth close to the x-axis, and J, K, L are the number of divisions of the volume element along the distance from the center of the earth, the longitude and latitude.

[0096] In actual calculations, the range of ±20km from the nominal orbital altitude of a low-orbit megaconstellation is defined as a constellation shell. This shell is then divided into individual volume elements based on the size of the volume element. Due to the large size of this space, it is assumed that targets within each volume element can only collide with targets within that volume element, and that targets between volume elements cannot collide. Therefore, there is no need to determine the relative distances of all targets for collision; only the distances of targets within a volume element need to be determined for collision potential. This significantly reduces the computational effort required to determine relative distances between targets.

[0097] For space targets within the same volume element, the relative distance is determined using a pairwise calculation method. When the relative distance between two satellites within the same volume element is less than the distance required by the "3σ" rule, it can be considered that a collision may occur between the two targets, and a collision probability calculation is required. The "3σ" rule judgment method is:

[0098]

[0099] Where r2 and r1 are the position vectors of the two space targets in the inertial system, is the joint error distance in the inertial coordinate system, and R is the joint radius of the two space targets.

[0100] Then, the Lagrange interpolation method is used to fit the trajectories of the two targets that may collide, and the moment when the two targets are closest is analyzed, which is the most likely place for the targets to collide. Since the fitting curve is a quartic polynomial and the interpolation points are known, it can be assumed that the Lagrange interpolation fitting curve equation is The equations for the linear curve are:

[0101]

[0102] In the formula, a0, a1, a2, a3, a4 are the coefficients of the fitting curve. According to the above formula, the trajectory of the space target can be obtained The same method can be used to obtain the fitting equation expression of the space target velocity.

[0103]

[0104] When the relative distance reaches the minimum value, it is the closest moment τ C ,have:

[0105]

[0106] Where, is the relative position vector. According to the above formula, we can get the time when the two targets are closest to each other. C Always bring in The motion state of the two collision targets in space at the intersection point can be obtained.

[0107] Define the plane perpendicular to the relative velocity vector of the two targets as the meeting plane A. On plane A, take spacecraft O1 (main target) as the coordinate origin, x e Axis pointing to spacecraft O2 (from target), z e The y axis points to the direction of the relative velocity between the two targets. e Axis and x e Axis, z e The axes form a right-hand coordinate system and establish an encounter coordinate system.

[0108] The position error covariance matrix can be given by the fitted position error standard deviation propagation curve. According to different types of space targets, the position error standard deviation curves along the three directions of the NTW coordinate system are brought into the covariance matrix, and the error covariance of the two space targets in the encounter coordinate system changes with time as follows:

[0109]

[0110] In the above formula, C1 and C2 are the errors of the space rendezvous target in the orbital coordinate system, is the error of the space rendezvous target in the encounter coordinate system. The error ellipsoid distribution of the two spacecraft in the encounter coordinate system is as follows: Figure 5 As shown. NTW→ECTR is the transformation matrix from the NTW coordinate system to the encounter coordinate system, and the mean value of the position vector in the encounter coordinate system is:

[0111]

[0112] In the above formula, are the mean values of the position vectors of the two intersecting space targets in the encounter coordinate system, M ECI→ECTR is the transformation matrix from the ECI coordinate system to the encounter coordinate system, is the relative position vector of the space rendezvous target at the closest moment, and the error covariance matrix of the joint error ellipsoid is:

[0113]

[0114] In the above formula, μ c is the mean value of the position vector distribution of the center of the joint error ellipsoid in the encounter coordinate system, C c is the variance of the position vector distribution of the center of the joint error ellipsoid. Therefore, we can get the position vector x in the encounter coordinate system. e The three-dimensional Gaussian distribution probability density function of the joint error ellipsoid at is:

[0115]

[0116] According to the motion state of the two targets at the moment of closest approach, the short-term collision probability of low-orbit giant constellations can be obtained using the space target collision probability calculation method based on Laplace transform.

[0117] The present application provides a method for calculating the long-term collision probability of a low-orbit giant constellation, including: model assumptions; a method for calculating the density of space objects; a space debris attenuation model; and a space target collision and disintegration model.

[0118] In order to simplify the calculation process and reduce the complexity of the calculation, the following assumptions are made for the model:

[0119] All spatial objects are treated as spheres;

[0120] The objects in the initial low-Earth orbit environment are divided into two groups for estimation. One group is “intact objects” with a size larger than 10 cm, such as satellites in orbit, abandoned intact payloads, etc. The radius of these objects is uniformly assumed to be r I =1.9m, mass is M I = 1000kg; the other group is space debris with a size less than 10 cm, and the radius of these debris is uniformly assumed to be r D =10cm, mass is M D =1.2kg;

[0121] The average collision probability calculation model for low-orbit giant constellations within the shell uses the "PIB" model. Based on the density of space objects within the shell, the probability of a constellation collision is:

[0122] CR O-D =π(r O +r D ) 2 V Rrl ρ O ρ D V (13)

[0123] Where, CR O-D is the average collision probability of different targets, r O is the outer envelope radius of the satellite, ρ O is the satellite space density, V Rel is the speed of the satellite relative to the space target, V is the volume of the shell, r D is the size of space debris, ρ D is the density of space debris; the probability CR of the same space object in the shell 0-0 The calculation formula is:

[0124]

[0125] Assuming that the mass and cross-sectional area of the low-orbit giant constellation satellite are M0 and A0 respectively, the mass of the new debris generated by the collision of the constellation satellite on orbit is M CFand cross-sectional area A CF Satisfy the relational expression:

[0126]

[0127] The collision disintegration model meets the NASA collision disintegration model;

[0128] The collision only produces two types of threatening space debris with a radius of 10 cm and a characteristic length that just meets the collision disintegration energy, as well as small debris that does not pose a threat to the satellite's disintegration;

[0129] The collision of space debris with a radius r≤10cm does not produce new collision-threatening debris;

[0130] The debris from the collision is evenly distributed within the shell;

[0131] The average relative speed of collisions between objects in low Earth orbit is 10 km / s;

[0132] Targets other than constellation satellites in the shell are considered uncontrolled, while controlled satellites will not experience collision and disintegration events;

[0133] Each year, the constellation's satellites experience a 2% failure rate due to events such as collisions with tiny debris or equipment failures.

[0134] Under the assumptions, we first need to convert the existence time of the space object in the constellation shell into density. i m ,r i M ] The spatial density within the interval is obtained by averaging the height interval to obtain the spatial target density solution formula in four cases:

[0135] When r p ≠r a ,and When , the spatial density calculation formula is:

[0136]

[0137] When r p ≠r a , And r i M >r a When r i M =r a , the spatial density calculation formula is:

[0138]

[0139] When r p ≠ra , And r i m <r p When r i m =r p , the spatial density calculation formula is:

[0140]

[0141] When [r p ,r a ]∈[r i m ,r i M ], let r i M =r a , r i m =r p ,get:

[0142] If e=0,a∈[r i m ,r i M ] (19)

[0144] In other cases, s(r i m ,r i M )=0. In the formula, r is the distance from the center of the earth, a is the semi-major axis of the orbit, e is the eccentricity of the orbit, r a and r p are the distances from the center of the Earth to the apogee and perigee of the orbit, r i m ,r i M are the geocentric distances to the lower and upper bounds of the constellation shell, respectively.

[0145] After converting space targets into space object densities, it's necessary to study how these densities change over time. Within constellation shells, there are two main reasons for density variations. First, they are caused by the constant inflow and outflow of space objects from the previous shell due to atmospheric drag. Second, they are caused by new debris generated by various events.

[0146] By downloading cataloged targets from the Spacetrack website, we found that there are 19,839 cataloged targets with orbital altitudes below 2,000 km. By counting the eccentricities of these cataloged targets, we can see that the eccentricity of the vast majority of low-orbit targets is less than 0.05. Therefore, it can be approximately assumed that the orbits of space debris in the low-orbit region are circular.

[0147] Therefore, the average decay rate of space debris in the shell can be obtained as:

[0148]

[0149] Where μ is the Earth's gravitational constant, ρ is the atmospheric resistance, and C d is the atmospheric drag coefficient, A is the target area, and m is the target mass.

[0150] For large elliptical orbit space debris, due to its high orbital altitude, the debris decays slowly. It is believed that the slight changes in its apogee and perigee during the life of the constellation will not cause changes in the density of space objects within the constellation shell. Therefore, the decay of this part of space debris is not considered.

[0151] Regarding space debris generated by collisions, the probability of collisions between different types of space objects was calculated by counting the number of close encounters between space objects. Based on the close encounters of space objects published on the Spacetrack website, 1,086 events were selected for statistical analysis, examining the distribution of different types of collisions. The overall probability of collisions between catalogued debris was 79.19%, the probability of collisions between catalogued debris and intact objects was 19.98%, and the probability of collisions between intact objects was 0.74%.

[0152] Different collisions produce different effects. Generally speaking, when the energy generated by the center-of-mass collision is greater than 40 kJ / kg, the relationship between the characteristic length and the amount of space debris produced is:

[0153]

[0154] Where, N C is greater than the characteristic length l c The number of space debris, characteristic length l c =(l x +l y +l z ) / 3, l x ,l y ,l z is the projected size of the space debris on the three orthogonal principal axes, is the equivalent mass of the two targets.

[0155] The density of space debris in the constellation shell is a combination of the number of debris generated by collisions and the number of space debris flowing into and out of the constellation shell. The number of debris generated by collisions is calculated based on the collision disintegration model, and the number of space debris flowing in and out is calculated based on the attenuation model. Finally, the density of space debris in the constellation shell is calculated. Figure 4 As shown in Figure 2, the relationship between the amount of space debris caused by space debris entering and leaving the shell and the change in time is:

[0156]

[0157] Where N is the number of debris, the subscripts i and j denote the type of debris in the jth shell of the i-th layer, v is the decay rate, and t is the number of days. Using the definition of density as ρ = N / V, we can derive the temporal evolution of the space environment density over the lifetime of the Starlink constellation, where V is the shell volume.

[0158] Then, the density of constellation satellites in the shell is calculated according to the space object density formula (19), and the “PIB” model in hypothesis (3) is used to finally obtain the relationship between the long-term collision probability of the low-orbit giant constellation and time. Figure 6 A distribution diagram of the eccentricity of space debris in the low-orbit region versus the semi-major axis of the orbit in an embodiment of the present application is given. According to the distribution of the eccentricity of space debris, it can be obtained that the orbit of the space debris is approximately a circular orbit, and the orbit eccentricity can be assumed to be 0.

[0159] In one embodiment, the present application provides a low-orbit giant constellation collision risk analysis system, including a memory, a processor, and a low-orbit giant constellation collision risk analysis program stored and executable on the memory. When the low-orbit giant constellation collision risk analysis program is executed by the processor, it implements some or all of the steps of the above-mentioned low-orbit giant constellation collision risk analysis method.

[0160] In one embodiment, the present application further provides a computer-readable storage medium storing a program for analyzing the collision risk of a low-orbit giant constellation. When the program for analyzing the collision risk of a low-orbit giant constellation is executed by a processor, it implements some or all of the steps of the above-mentioned method for analyzing the collision risk of a low-orbit giant constellation.

[0161] The above descriptions are merely a few embodiments of the present application and do not constitute any form of limitation to the present application. Although the present application discloses the preferred embodiments as above, they are not intended to limit the present application. Any technical personnel familiar with the present profession, without departing from the scope of the technical solution of the present application, using the technical content disclosed above to make slight changes or modifications are equivalent to equivalent implementation cases and fall within the scope of the technical solution.

Claims

1. A method for analyzing collision risk of a low-orbit giant constellation, characterized in that: The method includes a short-term collision risk analysis of a low-orbit mega-constellation, the short-term collision risk analysis comprising the steps of: (1) analyzing a propagation curve of an orbit prediction error of a space target; the space target includes an intact object and space debris; the orbit prediction error is the difference between the orbit prediction data and the actual orbit data of the space target; (2) Screening of dangerous space targets; (3) performing a proximity analysis on the hazardous space target and calculating the short-term collision probability of the low-orbit megaconstellation; The analysis of the space target orbit prediction error propagation curve includes: The orbit prediction errors of the space targets are calculated respectively, and the error propagation curves are obtained by fitting the curves. The calculation of the orbit prediction errors of the space targets includes the following steps: The standard deviation between the actual orbital data of intact objects and space debris within the same orbital altitude range of ±20 km and the orbital prediction data is calculated. The least squares method is used to fit the curve to obtain the fitting curve coefficient of the orbital prediction error over time within the maximum statistical time. The fitting formula is: Where y day is the error statistic, a1, b1 are the coefficients of the linear error curve equation, a2, b2, c2 are the coefficients of the parabolic error curve equation, t day is the evolution time, t end The maximum statistical time.

2. The method for analyzing the collision risk of a low-orbit giant constellation according to claim 1, characterized in that: The screening of hazardous space targets includes: Based on the geometric relationship between the apogee and perigee of the space target and the constellation shell, the space target is screened out of the apogee and perigee of the space target and the constellation shell. Based on the time window, the space target is screened out of the arc segment of the orbit within the constellation shell and the space target latitude is within the range of the constellation shell to obtain dangerous space targets. The geometric relationship includes: intersecting with the constellation shell, being contained in the constellation shell, and being separated from the constellation shell; and the space target includes a complete object and space debris.

3. The method for analyzing the collision risk of a low-orbit giant constellation according to claim 1, wherein: The proximity analysis is as follows: calculating the relative distance between each pair of the dangerous space targets, and determining that a collision may occur when the relative distance is less than a given threshold; Before calculating the relative distances between any two hazardous space objects, the space is divided using spatial discrete volume elements.

4. The method for analyzing the collision risk of a low-orbit giant constellation according to claim 3, wherein: The calculation of the short-term collision probability of the low-orbit mega-constellation comprises the following steps: Fit the trajectories of two potentially colliding hazardous space targets, calculate the moment when the two hazardous space targets are closest, obtain the motion states of the two hazardous space targets at the intersection point, and calculate their collision probability, which is used as the short-term collision probability of the low-orbit mega-constellation. The fitting adopts Lagrange interpolation method.

5. A method for analyzing collision risk of a low-orbit giant constellation, characterized in that: The method includes a long-term collision risk analysis of a low-orbit mega-constellation. The long-term collision risk analysis is to calculate an average collision probability of the low-orbit mega-constellation over its life cycle, including the steps of: Establish a model hypothesis for the long-term collision probability of low-orbit mega-constellations; Under the above assumptions, the spatial density of the space object within the shell is calculated according to the interval height of the constellation shell; Based on the distribution of space debris in the low-orbit region, an attenuation model of space debris in the shell is established, and the amount of space debris inflow and outflow is calculated based on the attenuation model; Calculate the amount of space debris generated by the collision based on the equivalent mass of the space target; Calculating the spatial density of the space debris within the constellation shell based on the amount of space debris inflow and outflow and the amount of space debris generated by the collision; The long-term collision probability of the low-orbit giant constellation is calculated based on the spatial density of the space target in the shell and the spatial density of the space debris in the constellation shell. The attenuation model is used to represent the average attenuation rate of the space debris in the shell, as shown in the following formula: Where μ is the Earth's gravitational constant, ρ is the atmospheric resistance, and C d is the atmospheric drag coefficient, A is the area of the space target, m is the mass of the space target, and a is the semi-major axis of the orbit; The amount of space debris generated by the collision is calculated according to the following formula: Where, N C is greater than the characteristic length l c The number of space debris, characteristic length l c =(l x +l y +l z ) / 3, l x ,l y ,l z is the projected size of the space debris on the three orthogonal principal axes, is the equivalent mass of the two space targets.

6. A low-orbit giant constellation collision risk analysis system, characterized in that: The system includes a memory, a processor, and a low-orbit giant constellation collision risk analysis program stored and executable on the memory. When the low-orbit giant constellation collision risk analysis program is executed by the processor, the steps of the low-orbit giant constellation collision risk analysis method according to any one of claims 1 to 5 are implemented.

7. A computer-readable storage medium, characterized in that A computer-readable storage medium stores a program for analyzing the collision risk of a low-orbit giant constellation. When the program for analyzing the collision risk of a low-orbit giant constellation is executed by a processor, the steps of the method for analyzing the collision risk of a low-orbit giant constellation according to any one of claims 1 to 5 are implemented.

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