CN110175431A - It a kind ofly is admittedly that down space fragment space density determines method - Google Patents

Abstract

A method for determining the space density of space debris in a ground-fixed system, which relates to the field of aerospace technology, in order to solve the problem that the existing space density algorithms are based on the J2000 inertial coordinate system, and the space density algorithm established under the J2000 inertial coordinate system cannot achieve geosynchronous The problem of describing the space debris environment in the orbital region according to the distribution of geographical longitude includes the following steps: Step 1, the space unit division of the geosynchronous orbit protection area in the earth-fixed coordinate system: Step 2, the space debris orbit position is discrete: Step 3, the orbit discrete point Position calculation: Step 4, identifying the space unit corresponding to the discrete orbital point of each space debris; Step 5, calculating the probability of debris staying in each space unit; Step 6, calculating the space density. The invention can realize the difference analysis of the distribution of space debris at different geographic longitude positions, can more specifically describe the space debris environment in the geosynchronous orbit area, and improve the assessment accuracy of the spacecraft space debris environment in this area.

Description

A Method for Determining the Spatial Density of Space Debris in Geofixed System

technical field

The invention relates to the field of aerospace technology, in particular to a method for determining the space density of space debris under the ground system.

Background technique

Space debris refers to non-functional man-made objects in orbit or re-entering the atmosphere, including their fragments and components. Space density is one of the basic parameters to describe the space-time distribution of space debris, and it is also one of the theoretical basis for the design of spacecraft protection schemes

The geosynchronous orbit satellite's operation period is consistent with the earth's rotation period, so its coverage area on the earth is basically stable, and it can realize continuous work on the same area. Geosynchronous orbit satellites are often used in communications, weather, radio and television, missile early warning, data relay, etc. Different from other orbital regions, the orbital period of spacecraft in the geosynchronous orbital region is basically the same, and most of them are near-circular orbits with orbital inclinations close to 0°. Geographic longitude position is an important orbital parameter for space activities in geosynchronous orbit.

Space debris is the product of space activities, and its distribution is directly affected by space activities. The detection data show that, affected by the law of human spaceflight activities and the orbital perturbation factors of space objects, compared with other orbital regions, the distribution of space debris in the geosynchronous orbital region has significant characteristics: the orbital inclination of most space objects does not exceed 15°, It operates in a near-circular orbit and the orbital period is basically the same (approximately the earth's rotation period). The concentrated distribution of the orbital period of space objects in the geosynchronous orbit region makes the debris environment in this region relatively stable in the earth-fixed coordinate system.

Space debris poses a non-negligible threat to the safe operation of spacecraft in orbit. The space debris environmental engineering model can realize the evaluation of space-time distribution of space debris environment, which is the basis for the design of spacecraft protection scheme. Space density is the output of the space debris environmental engineering model. A reasonable and reliable space density algorithm is the basic premise to ensure the accuracy of the engineering model, and it is also an important basic data source for spacecraft risk assessment and protection design.

Space density is used to describe the space-time distribution of space debris, which is defined as the average number of space debris per unit volume at a certain spatial location. The spatial density distribution of space debris is the basis for evaluating the environment of spacecraft space debris. In the existing research in related fields, the spatial density algorithm in the J2000 inertial coordinate system is relatively mature, and the calculation of the spatial density distribution with orbital height and latitude can be realized. Dong Dan and Zhang Pingping of Harbin Institute of Technology proposed an algorithm for the distribution of space density with orbital height and latitude. The algorithm assumes that the spatial density of space debris is uniformly distributed with longitude. Peng Keke proposed a space density algorithm based on discrete orbital elements, which assumes that the orbital position of space debris is stable and is not affected by perturbation factors. However, the existing algorithms are all based on the J2000 inertial coordinate system, which cannot describe the longitude distribution of space objects in the ground-fixed coordinate system.

Geosynchronous orbit is one of the key areas for space activities. Different from other orbital regions, the orbital period of space objects in geosynchronous orbit is basically the same, and is relatively close to the rotation period of the earth, which leads to a relatively stable distribution of the space debris environment in this region with respect to geographical longitude. The existing spatial density algorithms are all based on the J2000 inertial coordinate system, which cannot describe the distribution of the space debris environment in the geosynchronous orbit region along with the geographical longitude.

Contents of the invention

The purpose of the present invention is: all existing spatial density algorithms are based on the J2000 inertial coordinate system, and the spatial density algorithm established under the J2000 inertial coordinate system cannot realize the problem that the space debris environment in the geosynchronous orbit area is described according to the geographical longitude distribution .

The present invention adopts the following technical solutions to realize: a method for determining the spatial density of space debris under the ground solid system, comprising the following steps:

Step 1. Space unit division of the geosynchronous orbit protection area in the earth-fixed coordinate system:

In the fixed coordinate system of the earth, according to the orbital height, geographic longitude and latitude, the orbital space range with an orbital height between 35786±200km and a latitude between ±15° is discretized into a series of spatial units;

Step 2. The orbital position of space debris is discretized:

Discretize the orbits of space debris according to the mean anomaly angle according to the number of orbital elements of space debris;

Step 3. Calculation of track discrete point positions:

Calculate the specific orbital altitude, latitude and geographic longitude corresponding to each orbital discrete point respectively;

Step 4, identifying the space unit corresponding to the discrete point of each space debris orbit;

Step 5. Calculate the probability of debris staying in each space unit:

According to the division of discrete orbital positions and space units in step 3 and step 4, count the number of discrete orbital positions corresponding to each spatial unit, and obtain the stay probability by the ratio of the number of discrete orbital positions and the total discrete points;

Step 6. Calculate the spatial density:

The spatial density is obtained by the ratio of the stay probability to the volume of the spatial unit.

Further, the step size of the discretization satisfies k _M =10, where k _M is a discretization coefficient.

Further, the second step discretizes the average anomaly angle M of the space debris based on the stable assumption of the geographic longitude of the fragments, and records the number of discrete parts as N _M , and the average anomaly angle corresponding to the j _Mth discrete point is:

Further, the geocentric distance r _jM , latitude φ _jM and geographic longitude λ _jM corresponding to the j _Mth discrete point are:

in, is the near point angle, is the mean anomaly angle, a is the semi-major axis, e is the eccentricity, i is the orbital inclination, ω is the perigee angular distance, Ω is the right ascension of the ascending node, and λ _Ω is the geographic longitude corresponding to the orbit’s ascending node.

Further, the apex angle mean anomaly It can be obtained by the following formula:

Wherein, ω _e is the earth's rotation angular velocity, μ is the gravitational constant, μ≈398600km ³ /s ² .

Further, the discrete number N _M is determined based on the division step of the space unit.

Further, the steps for determining the number of discrete shares N _M are as follows: denote the step size of the orbital height, latitude and longitude interval in step 1 as Δr, Δφ, Δλ, then N _M = max{N _r , N _φ , N _λ }

in,

In the formula: π is the circumference ratio, a is the semi-major axis, e is the eccentricity, i is the orbital inclination, μ is the gravitational constant, ω _e is the earth's rotation period, k _M is the dispersion coefficient, k _M =10, TIF is Round up function, max is the maximum value function.

Further, the probability of debris staying in a space unit in the step five is determined based on the discrete number N _M of space debris orbits, the principle of space unit orbit division, and the number of space debris orbit discrete points in a space unit.

Further, the determination steps of the debris residence probability in the space unit are as follows: record the space object orbital period as T, and the space debris residence time corresponding to each discrete point is

Note that the number of discrete orbital points of space debris in the space unit Cell _k is n _k , and the probability of space debris in this space unit is:

Further, the step of determining the space density in the step six is as follows: a certain space debris is in the space unit Cell _k ([r _k ,r _k +Δr],[φ _k ,φ _k +Δφ],[λ _k ,λ _k +Δλ]) is P _k , then the mathematical expectation of the number of fragments in the space unit is: E _k =P _k , if there are multiple space fragments involved in the calculation, record the total number of fragments as N _deb , then the space The mathematical expectation of the total number of fragments in unit Cell _k is:

The volume of the space unit Cell _k is

The space density of debris in the space unit Cell _k is

Among them, Δr, Δφ, Δλ are the orbital height, latitude and longitude interval step, r is the distance from the center of the earth, and Δt _one is the residence time of space debris corresponding to each discrete point.

The present invention adopts above-mentioned technical scheme, has following beneficial effect:

Based on the geosynchronous orbit space activities and the distribution characteristics of the space debris environment, the present invention proposes a method for determining the space density of space debris in the ground-fixed system on the basis of the existing space density algorithm. Compared with the traditional space density algorithm, the present invention proposes A method for determining the spatial density of space debris in geostationary systems can realize the difference analysis of the distribution of space debris at different geographic longitudes, and can describe the space debris environment in the geosynchronous orbit area more specifically, and improve the accuracy of spacecraft in this area. Space Debris Environmental Assessment Accuracy.

Description of drawings

Fig. 1 is a flowchart of the present invention.

Figure 2 is a schematic diagram of the division of orbital space units in the ground-fixed coordinate system.

Fig. 3 is a comparison between the evaluation results in the embodiment and the original algorithm.

Figure 4 shows the real distribution of debris in the corresponding orbital space in the embodiment.

Detailed ways

Specific embodiment one: The present embodiment will be specifically described below in conjunction with FIG. 1. In this embodiment, a method for determining the spatial density of space debris under the ground system includes the following steps:

Step 1. Space unit division of the geosynchronous orbit protection area in the earth-fixed coordinate system:

In the fixed coordinate system of the earth, according to the orbital height, geographic longitude and latitude, the orbital space range with an orbital height between 35786±200km and a latitude between ±15° is discretized into a series of spatial units;

Step 2. The orbital position of space debris is discretized:

Discretize the orbits of space debris according to the mean anomaly angle according to the orbital elements of space debris;

Step 3. Calculation of track discrete point positions:

Calculate the specific orbital altitude, latitude and geographic longitude corresponding to each orbital discrete point respectively;

Step 4, identifying the space unit corresponding to the discrete point of each space debris orbit;

The recognition here means that the location of a certain point is known, and its division is identified, for example, the latitude and longitude of a certain point is known, and the province and city it belongs to are identified.

Step 5. Calculate the probability of debris staying in each space unit:

According to the division of discrete orbital positions and space units in step 3 and step 4, the number of discrete orbital positions corresponding to each spatial unit is counted, and the ratio of discrete orbital position numbers and total discrete points is the corresponding stay probability;

Step 6. Calculate the spatial density:

The ratio of the stay probability to the volume of the space unit is the space density, and thus the distribution of the space density with the orbital height, latitude, and geographic longitude can be obtained. Step 6 is to determine according to the probability of space debris staying and the division of space units.

Example:

In order to make the purpose, technical solutions and advantages of the present disclosure clearer, the present disclosure will be further described in detail below in conjunction with the embodiments and with reference to the accompanying drawings 2 , 3 and 4 .

Step 1: Calculate the spatial density in different geographic longitude ranges in the altitude interval of 35,786±200km and the latitude interval of ±0.5°. In the calculation process, Δr=400km, Δφ=1°, Δλ=3°, and 120 spatial regions are divided in total. as shown in picture 2.

Step 2: Discrete orbital positions of fragments. According to the number of orbital elements of space debris, its orbital position is equally divided according to the mean anomaly. The debris orbit element information used in this embodiment comes from the cataloged debris data released by the US Space Monitoring Network in 2016. The discrete number of space debris of semi-major axis (denoted as a), eccentricity (denoted as e), orbital inclination (denoted as a), perigee angular distance (denoted as ω), and ascending node geographic longitude (denoted as λ _Ω ) N _M is:

Among them, TIF is the round-up function (the function value is the smallest integer not less than the variable value), and max is the maximum value function (the function value is the maximum value among the variable values).

The discretization principle is the equidistant dispersion based on the mean anomaly angle. Then the j _Mth discrete point corresponds to the mean anomaly angle M _jM :

Step 3: Calculating the discrete orbital position (orbital altitude, latitude, geographic longitude) corresponding to each bisection point respectively. The j _Mth discrete point corresponds to the geocentric distance r _jM , latitude φ _jM and geographic longitude λ _jM as follows:

where the apex angle is mean anomaly It can be obtained by the iterative method as follows:

Step 4, judging the spatial unit corresponding to each discrete orbital position;

Step 5: Calculate the probability of debris staying in each space unit, and calculate the number of discrete orbit positions corresponding to each space unit according to the above-calculated discrete orbit positions and the division of space units. The ratio of the number of discrete orbital positions to the total discrete points is the corresponding dwell probability.

Step 6: Calculating the space density, the ratio of the stay probability to the volume of the space unit is the space density. The distribution of space density with orbital height, latitude, and geographic longitude is thus obtained. Note that the geocentric distance corresponding to the space unit Cell _k is [r _k , r _k +Δr], latitude [φ _k ,φ _k +Δφ], and geographic longitude [λ _k ,λ _k +Δλ]. Its volume V _k is:

where r _k is the lower limit of the orbit height, Δr is the step size of the orbit height interval, φ _k is the lower limit of the latitude, Δφ is the step size of the latitude interval, and λ _k is the lower limit of the geographic longitude interval.

The distribution of the geosynchronous orbit regional cataloged fragments according to the geographic longitude obtained in this embodiment in 2016 is shown by the solid line in Fig. 3 . The dotted line in the figure is the evaluation result under the original algorithm. Figure 4 shows the distribution of the number of cataloged objects with geographical longitude given by the measured data. It can be seen from this that the calculation results provided by this patent are consistent with the real distribution of space objects in this area, and can better describe the space debris environment in the geosynchronous orbit area.

Embodiment 2: This embodiment is a further description of Embodiment 1. The difference between this embodiment and Embodiment 1 is that the discrete step size satisfies k _M =10, where k _M is a discrete coefficient.

Embodiment 3: This embodiment is a further description of Embodiment 1. The difference between this embodiment and Embodiment 1 is that the step 2 discretizes the mean anomaly angle M of space debris based on the stable assumption of the geographic longitude of the fragments. Record the number of discrete copies as N _M , and the mean anomaly angle corresponding to the j _Mth discrete point is:

Embodiment 4: This embodiment is a further description of Embodiment 3. The difference between this embodiment and Embodiment 3 is the geocentric distance r _jM , latitude φ _jM and geographic distance corresponding to the j _Mth discrete point. The longitude λ _jM is:

in, is the near point angle, is the mean anomaly angle, a is the semi-major axis, e is the eccentricity, i is the orbital inclination, ω is the perigee angular distance, Ω is the right ascension of the ascending node, and λ _Ω is the geographic longitude corresponding to the orbit’s ascending node.

Embodiment 5: This embodiment is a further description of Embodiment 4. The difference between this embodiment and Embodiment 4 is that the near point angle mean anomaly It can be obtained by the following formula:

Wherein, ω _e is the earth's rotation angular velocity, μ is the gravitational constant, μ≈398600km ³ /s ² . ω _e = 360° every 23 hours, 56 minutes and 4 seconds.

Embodiment 6: This embodiment is a further description of Embodiment 3. The difference between this embodiment and Embodiment 3 is that the number of discrete shares N _M is determined based on the division step of a space unit.

Embodiment 7: This embodiment is a further description of Embodiment 6. The difference between this embodiment and Embodiment 6 is that the steps for determining the number of discrete shares N _M are as follows: orbital height, latitude and The longitude interval steps are denoted as Δr, Δφ, and Δλ. In order to ensure that the difference in orbital height, latitude, and geographic longitude between any two adjacent discrete points is smaller than the discrete criterion of the corresponding space unit interval step, N _M =max{ N _r , N _φ , N _λ }

in,

In the formula: π is the circumference ratio, a is the semi-major axis, e is the eccentricity, i is the orbital inclination, μ is the gravitational constant, ω _e is the earth's rotation period, k _M is the discrete coefficient, k _M =10, where TIF It is the rounding up function (the function value is the smallest integer not less than the variable value), and max is the maximum value function (the function value is the maximum value among the variable values).

Embodiment 8: This embodiment is a further description of Embodiment 1. The difference between this embodiment and Embodiment 1 is that the probability of debris staying in a space unit in the step 5 is based on the discrete number of space debris orbits N _M 1. Space unit orbit division principle (orbital height, latitude and longitude interval steps are denoted as Δr, Δφ, Δλ) and the number of space debris orbit discrete points within a space unit.

Embodiment 9: This embodiment is a further description of Embodiment 8. The difference between this embodiment and Embodiment 8 is that the steps for determining the probability of debris staying in the space unit are as follows: From orbital mechanics, the average space debris The anomaly varies uniformly with time. Note that the orbital period of a space object is T, then under the principle of equally dividing the mean anomaly angle, the residence time of space debris corresponding to each discrete point is

Note that the number of discrete orbital points of space debris in the space unit Cell _k is n _k , and at any time during the evaluation period, the probability of space debris in this space unit is the ratio of the residence time in the space unit to the orbital period:

Embodiment 10: This embodiment is a further description of Embodiment 1. The difference between this embodiment and Embodiment 1 is that the determination steps for calculating the spatial density in the step 6 are as follows: a certain space debris is in the space unit Cell _k ([r _k ,r _k +Δr],[φ _k ,φ _k +Δφ],[λ _k ,λ _k +Δλ]) has a probability of staying in P _k , because whether space debris appears in a space unit at any time Obey the Bernoulli distribution (0-1 distribution), the mathematical expectation of the number of fragments in the space unit is: E _k =P _k , if there are multiple space fragments involved in the calculation, record the total number of fragments as N _deb , then the space The mathematical expectation of the total number of fragments in unit Cell _k is the accumulation of the mathematical expectation of a single fragment

It can be known from the geometric relationship that the volume of the space unit Cell _k is

Then the fragment space density in the space unit Cell _k is

Among them, Δr, Δφ, Δλ are the orbital height, latitude and longitude interval step, r is the distance from the center of the earth, and Δt _one is the residence time of space debris corresponding to each discrete point.

It should be noted that the specific implementation is only an explanation and description of the technical solution of the present invention, and cannot limit the protection scope of rights. All changes made according to the claims and description of the present invention are only partial changes, and should still fall within the protection scope of the present invention.

Claims (10)

1. A method for determining the spatial density of space debris in a ground-solid system, characterized in that it comprises the following steps: Step 1. Space unit division of the geosynchronous orbit protection area in the earth-fixed coordinate system: In the fixed coordinate system of the earth, according to the orbital height, geographic longitude and latitude, the orbital space range with an orbital height between 35786±200km and a latitude between ±15° is discretized into a series of spatial units; Step 2. The orbital position of space debris is discretized: Discretize the orbits of space debris according to the mean anomaly angle according to the number of orbital elements of space debris; Step 3. Calculation of track discrete point positions: Calculate the specific orbital altitude, latitude and geographic longitude corresponding to each orbital discrete point respectively; Step 4, identifying the space unit corresponding to the discrete point of each space debris orbit; Step 5. Calculate the probability of debris staying in each space unit: According to the division of discrete orbital positions and space units in step 3 and step 4, count the number of discrete orbital positions corresponding to each spatial unit, and obtain the stay probability by the ratio of the number of discrete orbital positions and the total discrete points; Step 6. Calculate the spatial density: The spatial density is obtained by the ratio of the stay probability to the volume of the spatial unit. 2 . The method for determining the spatial density of space debris in subterranean solid systems according to claim 1 , characterized in that: the discrete time step size satisfies k _M =10, wherein k _M is a discrete coefficient. 3 . 3. A method for determining the spatial density of space debris under a ground-fixed system according to claim 1, characterized in that: said step 2 discretizes the mean anomaly M of space debris based on the stable assumption of the geographic longitude of the debris, and records the discrete fraction The number is N _M , and the mean anomaly angle corresponding to the j _Mth discrete point is: 4. The method for determining the spatial density of space debris in a ground-solid system according to claim 3, characterized in that: the geocentric distance r _jM , latitude φ _jM and geographic longitude λ _jM corresponding to the j _Mth discrete point for: in, is the near point angle, is the mean anomaly angle, a is the semi-major axis, e is the eccentricity, i is the orbital inclination, ω is the perigee angular distance, Ω is the right ascension of the ascending node, and λ _Ω is the geographic longitude corresponding to the orbit’s ascending node. 5. A method for determining the spatial density of space debris in ground-solid systems according to claim 4, characterized in that: said anomaly angle mean anomaly It can be obtained by the following formula: Wherein, ω _e is the earth's rotation angular velocity, μ is the gravitational constant, μ≈398600km ³ /s ² . 6. A method for determining the space density of subterranean space debris according to claim 3, characterized in that: the discrete number N _M is determined based on the space unit division step. 7. The method for determining the spatial density of space debris under a kind of ground-fixed system according to claim 6, wherein the determination steps of the discrete number N _M are as follows: the step size of the orbital height, latitude and longitude interval in step one Denoted as Δr, Δφ, Δλ, N _M ＝max{N _r , N _φ , N _λ } in, In the formula: π is the circumference ratio, a is the semi-major axis, e is the eccentricity, i is the orbital inclination, μ is the gravitational constant, ω _e is the earth's rotation period, k _M is the dispersion coefficient, k _M =10, TIF is Round up function, max is the maximum value function. 8. The method for determining the spatial density of space debris in a ground-solid system according to claim 1, wherein the probability of debris staying in a space unit in the step 5 is based on the discrete number N _M of space debris orbits, the space unit orbit The principle of division and the number of discrete orbital points of space debris within a space unit are determined. 9. The method for determining the spatial density of space debris in a ground-solid system according to claim 8, wherein the determination steps of the probability of debris staying in the space unit are as follows: note that the orbital period of the space object is T, and each discrete point The corresponding residence time of space debris is Note that the number of discrete orbital points of space debris in the space unit Cell _k is n _k , and the probability of space debris in this space unit is: 10. The method for determining the spatial density of space debris in a ground-solid system according to claim 1, wherein the determination step of calculating the spatial density in said step 6 is as follows: a certain space debris in a space unit The probability of staying in Cell _k ([r _k ,r _k +Δr],[φ _k ,φ _k +Δφ],[λ _k ,λ _k +Δλ]) is P _k , then the mathematical expectation of the number of fragments in the space unit It is: E _k =P _k , if there are multiple space debris involved in the calculation, the total number of debris is recorded as N _deb , then the mathematical expectation of the total number of debris in the space unit Cell _k is: The volume of the space unit Cell _k is The space density of debris in the space unit Cell _k is Among them, Δr, Δφ, Δλ are the orbital height, latitude and longitude interval step, r is the distance from the center of the earth, and Δt _one is the residence time of space debris corresponding to each discrete point.