CN110175431B - Space debris space density determination method under earth fixation system - Google Patents

Space debris space density determination method under earth fixation system Download PDF

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CN110175431B
CN110175431B CN201910488123.7A CN201910488123A CN110175431B CN 110175431 B CN110175431 B CN 110175431B CN 201910488123 A CN201910488123 A CN 201910488123A CN 110175431 B CN110175431 B CN 110175431B
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庞宝君
王东方
肖伟科
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Harbin Institute of Technology
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Abstract

A method for determining space debris space density under a geostationary system relates to the technical field of spaceflight, and aims to solve the problems that existing space density algorithms are all based on a J2000 inertial coordinate system, and space density algorithms established under the J2000 inertial coordinate system cannot realize description of space debris environment in a geosynchronous orbit region along with geographical longitude distribution, and the method comprises the following steps: step one, dividing a space unit of a synchronous orbit protection area under an earth fixed connection coordinate system: step two, the track position of the space debris is discrete: step three, calculating the position of the track discrete point: identifying a space unit corresponding to each space debris track discrete point; step five, calculating the fragment staying probability in each space unit: and step six, calculating the space density. The method can realize the difference analysis of the space debris distribution conditions of different geographical longitude positions, can more pertinently describe the space debris environment of the geosynchronous orbit region, and improve the evaluation precision of the space debris environment of the spacecraft in the region.

Description

Space debris space density determination method under earth fixation system
Technical Field
The invention relates to the technical field of spaceflight, in particular to a method for determining space debris space density under a geosolidus system.
Background
Space debris refers to non-functional man-made objects on rails or re-entering the atmosphere, including its debris and components. The space density is one of basic parameters for describing space debris space-time distribution rule and is also one of theoretical bases for designing spacecraft protection schemes
The operation cycle of the geosynchronous orbit satellite is consistent with the rotation cycle of the earth, so that the coverage area of the geosynchronous orbit satellite to the earth is basically stable, and the continuous work of the same area can be realized. Geosynchronous orbit satellites are commonly used in communications, weather, broadcast television, missile early warning, data relays, and the like. Different from other orbit regions, the orbit periods of the spacecraft in the geosynchronous orbit region are basically consistent, and most of the spacecraft are near-circular orbits with the orbit dip angles close to 0 degree. Geo-longitudinal position is an important orbital parameter for geosynchronous orbit space activities.
Space debris is a product of space activity, and the distribution rule of the space debris is directly influenced by the space activity. The detection data show that the distribution rule of space debris in the geosynchronous orbit region has obvious characteristics compared with other orbit regions under the influence of human space activity rule and space object orbit perturbation factors: most space objects have orbital inclination angles not exceeding 15 degrees, run in a near-circular orbit and have basically consistent orbital periods (about the period of the rotation of the earth). The concentrated distribution characteristic of the orbit period of the object in the space of the geosynchronous orbit region enables the fragment environment of the region to be stable under the earth fixed connection coordinate system.
The space debris poses a non-negligible threat to the on-orbit safe operation of the spacecraft. The space debris environment engineering model can realize the evaluation of the space debris environment space-time distribution rule and is the basis of the design of a spacecraft protection scheme. The space density is the output quantity of the space debris environment engineering model, and a reasonable and reliable space density algorithm is the basic premise of ensuring the accuracy of the engineering model and is also an important basic data source for risk assessment and protection design of the spacecraft.
Spatial density is used to describe the spatial-temporal distribution law of spatial patches, which is defined as the average number of spatial patches in a unit volume at a spatial location. The space density distribution of the space debris is the basis for the environmental assessment of the space debris of the spacecraft. In the existing research of related fields, a space density algorithm under a J2000 inertial coordinate system is mature, and calculation of space density along with the height and latitude distribution of a track can be realized. The algorithm of the distribution of space density along with the height and the latitude of the orbit is proposed by the Dongdan of the Harbin industry university, the Zhang Ping et al. The algorithm assumes that the spatial density of the space debris is evenly distributed with longitude. Penaceae proposes a space density algorithm based on discrete track number, and the algorithm assumes that the track position of space debris is stable and is not influenced by perturbation factors. However, the existing algorithms establish a J2000 inertial coordinate system, and cannot describe the longitude distribution condition of the space object in the ground-fixed coordinate system.
Geosynchronous orbit is one of the key areas of aerospace activity. Unlike other orbital regions, geosynchronous orbital space objects have substantially the same orbital period and are closer to the earth's rotation period, which results in a more stable distribution of the space debris environment of the region to geographic longitude. The existing space density algorithms are established based on a J2000 inertial coordinate system, and the description of the space debris environment of a geosynchronous orbit region along with the distribution of the geographical longitude cannot be realized.
Disclosure of Invention
The purpose of the invention is: the method aims to solve the problem that the existing space density algorithms are all based on a J2000 inertial coordinate system, and the space density algorithm established under the J2000 inertial coordinate system cannot realize description of space debris environment of a geosynchronous orbit region along with geographical longitude distribution.
The invention is realized by adopting the following technical scheme: a method for determining space debris space density under a ground fixation system comprises the following steps:
step one, dividing a space unit of a synchronous orbit protection area under an earth fixed connection coordinate system:
under the earth fixed connection coordinate system, discretizing an orbit space range with the orbit height of 35786 +/-200 km and the latitude of +/-15 degrees into a series of space units according to the orbit height, the geographic longitude and the latitude;
step two, the track position of the space debris is discrete:
discretizing the space debris orbit according to the number of the space debris orbits and the mean-near point angle;
step three, calculating the position of the track discrete point:
respectively calculating the specific track height, latitude and geographic longitude corresponding to each track discrete point;
identifying a space unit corresponding to each space debris track discrete point;
step five, calculating the fragment staying probability in each space unit:
according to the discrete track positions and the space units in the third step and the fourth step, counting the number of the discrete track positions corresponding to each space unit, and obtaining the staying probability according to the ratio of the number of the discrete track positions to the total discrete points;
step six, calculating space density:
the spatial density is obtained by the ratio of the probability of stay to the volume of the spatial unit.
Further, the discrete step size satisfies k M10, wherein kMAre discrete coefficients.
Further, the second step is to disperse the space debris approximate point angle M based on the debris geographical longitude stability hypothesis, and the number of the discrete points is recorded as NMJ thMThe corresponding mean and near point angles of the discrete points are as follows:
Figure BDA0002086071380000021
further, the j (th) isMCenter-to-center distance r corresponding to discrete pointsjMLatitude phijMAnd geographic longitude λjMComprises the following steps:
Figure BDA0002086071380000031
Figure BDA0002086071380000032
Figure BDA0002086071380000033
wherein the content of the first and second substances,
Figure BDA0002086071380000034
in order to be closer to the point angle,
Figure BDA0002086071380000035
is a mean paraxial point angle, a is a semimajor axis, e is an eccentricity, i is an orbital inclination angle, omega is a perigee angular distance, omega is a rising point right ascension, and lambda isΩThe geographic longitude corresponding to the intersection point of the orbit.
Further, the approach point angle
Figure BDA0002086071380000036
Flat near point angle
Figure BDA0002086071380000037
Can be derived by the following formula:
Figure BDA0002086071380000038
Figure BDA0002086071380000039
wherein, ω iseIs the angular velocity of rotation of the earth, mu is the gravitational constant, mu is approximately equal to 398600km3/s2。
Further, the discrete number of parts NMThe step size is determined based on the spatial unit division.
Further, the discrete number of parts NMThe determination steps are as follows: step length of the track height, latitude and longitude intervals in the step one is recorded as delta r, delta phi and delta lambda, and then N is obtainedM＝max{Nr,Nφ,Nλ}
Wherein the content of the first and second substances,
Figure BDA00020860713800000310
Figure BDA00020860713800000311
Figure BDA00020860713800000312
in the formula: pi is the circumference, a is the semimajor axis, e is the eccentricity, i is the inclination of the track, mu is the gravitational constant, omegaeIs the period of rotation of the earth, kMIs a discrete coefficient, kMTIF is an upward rounding function, max is a maximum function, 10.
Further, the probability of the fragment staying in the space unit in the step five is based on the discrete number N of the space fragment orbitsMThe space unit orbit dividing principle and the number of discrete points of the space fragment orbit in the space unit are determined.
Further, the step of determining the fragment staying probability in the space unit comprises the following steps: recording the orbit period of the space object as T, and the residence time of the space debris corresponding to each discrete point as
Figure BDA00020860713800000313
Space recording CellkThe number of discrete points of the inner space debris orbit is nkSpace debris in the spaceThe probability within a cell is:
Figure BDA0002086071380000041
further, the determination step of calculating the space density in the sixth step is as follows: cell in space with certain space debrisk([rk,rk+Δr],[φk,φk+Δφ],[λk,λk+Δλ]) Probability of internal stay is PkThen the mathematical expectation of the number of fragments in a spatial unit is: ek＝PkIf a plurality of space fragments participate in the calculation, the total fragment number is recorded as NdebThen space CellkThe mathematical expectation for the total number of fragments in is:
Figure BDA0002086071380000042
space CellkHas a volume of
Figure BDA0002086071380000043
Space CellkSpace density of inner debris of
Figure BDA0002086071380000044
Wherein, Δ r, Δ φ, Δ λ are track height, latitude and longitude interval step, r is geocentric distance, Δ toneThe space debris dwell time for each discrete point.
By adopting the technical scheme, the invention has the following beneficial effects:
the invention provides a method for determining the space debris space density under an earth fixation system based on the geosynchronous orbit space activity and space debris environment distribution characteristics, and compared with the traditional space density algorithm, the method for determining the space debris space density under the earth fixation system can realize the difference analysis of the space debris distribution conditions of different geographic longitude positions, can more pertinently describe the space debris environment of a geosynchronous orbit region, and improves the evaluation precision of the space debris environment of a spacecraft in the region.
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FIG. 1 is a flow chart of the present invention.
Fig. 2 is a schematic diagram of track space unit division under a ground-fixed coordinate system.
FIG. 3 is a comparison of the evaluation results of the embodiment with the original algorithm.
Fig. 4 shows the real distribution of the debris corresponding to the track space in the embodiment.
Detailed Description
The first embodiment is as follows: the present embodiment is specifically described below with reference to fig. 1, and in the present embodiment, a method for determining a space density of a space debris under a geostationary system includes the following steps:
step one, dividing a space unit of a synchronous orbit protection area under an earth fixed coordinate system:
under the earth fixed connection coordinate system, discretizing an orbit space range with the orbit height of 35786 +/-200 km and the latitude of +/-15 degrees into a series of space units according to the orbit height, the geographic longitude and the latitude;
step two, the track position of the space debris is discrete:
discretizing the orbit according to the number of the space debris orbits and the mean and near point angles;
step three, calculating the position of the track discrete point:
respectively calculating the specific track height, latitude and geographic longitude corresponding to each track discrete point;
identifying a space unit corresponding to each space debris track discrete point;
the meaning of the identification here is that the position of a certain point is known, the partition of the point is identified, for example, the longitude and latitude of a certain point are known, and the city belonging to which province is identified.
Step five, calculating the fragment staying probability in each space unit:
according to the discrete track positions and the space unit division in the third step and the fourth step, the number of discrete track positions corresponding to each space unit is counted, and the ratio of the number of discrete track positions to the total discrete points is the corresponding stay probability;
step six, calculating space density:
the ratio of the stay probability to the volume of the space unit is the space density, and therefore distribution of the space density along with the height, the latitude and the geographical longitude of the orbit is obtained. And step six, determining according to the space fragment staying probability and the space unit division.
Example (b):
in order to make the objects, technical solutions and advantages of the present disclosure more apparent, the present disclosure is further described in detail below with reference to fig. 2, 3 and 4 in conjunction with the embodiments.
The method comprises the following steps: the spatial density was calculated for different geographical longitude ranges within the altitude interval of 35,786 + -200 km, latitude interval of + -0.5 deg.. In the calculation process, the Δ r is 400km, the Δ φ is 1 ° and the Δ λ is 3 °, and 120 spatial regions are divided. As shown in fig. 2.
Step two: the debris trajectory positions are discrete. And according to the number of the space debris tracks, equally dividing the track positions according to the mean-near point angle. The information of the number of the fragment tracks adopted by the embodiment is from inventory fragment data distributed by the 2016 U.S. space monitoring network. Semimajor axis (recorded as a), eccentricity (recorded as e), orbit inclination angle (recorded as a), perigee angular distance (recorded as omega), and ascending intersection point geographic longitude (recorded as lambda)Ω) Discrete number of space debris NMComprises the following steps:
Figure BDA0002086071380000051
where TIF is an upward rounding function (the function value is the smallest integer not smaller than the variable value) and max is the maximum function (the function value is the largest of the variable values).
The principle of dispersion is equidistant dispersion according to the mean anomaly angle. Then j (th)MCorresponding mean and near point angle M of discrete pointsjM：
Figure BDA0002086071380000061
Step three: and respectively calculating the discrete track position (track height, latitude and geographic longitude) corresponding to each equally divided point. J (th)MCenter distance r of discrete pointjMLatitude phijMGeographic longitude λjMComprises the following steps:
Figure BDA0002086071380000062
Figure BDA0002086071380000063
Figure BDA0002086071380000064
wherein the angle of approach point is
Figure BDA0002086071380000065
Flat near point angle
Figure BDA0002086071380000066
Can be derived from an iterative method by:
Figure BDA0002086071380000067
Figure BDA0002086071380000068
judging a space unit corresponding to each discrete track position;
and step five, calculating the fragment staying probability in each space unit, and counting the number of discrete track positions corresponding to each space unit according to the discrete track positions calculated above and the division of the space units. The ratio of the number of discrete track positions to the total discrete points is the corresponding dwell probability.
And step six, calculating the space density, wherein the ratio of the stay probability to the space unit volume is the space density. The distribution of the space density with the height, the latitude and the geographic longitude of the orbit is obtained. Space recording CellkCorresponding earth center distance range is [ r ]k,rk+Δr]Latitude [ phi ]k,φk+Δφ]Geographic longitude [ lambda ]k,λk+Δλ]. Volume V thereofkComprises the following steps:
Figure BDA0002086071380000069
in the formula rkIs the lower limit of the track height, and delta r is the step length of the track height interval phikIs the lower limit of latitude, and is the step length of latitude interval, lambdakIs the lower limit of the geographic longitude interval.
The distribution of the 2016 geosynchronous orbit region inventory pieces obtained in this example with geographic longitude is shown by the solid line in fig. 3. The dotted line in the figure is the evaluation result under the original algorithm. Fig. 4 shows the distribution of the number of catalogued objects with geographical longitude given by the measured data. Therefore, the calculation result provided by the method is consistent with the real distribution rule of the object in the area space, and the space debris environment of the geosynchronous orbit area can be better described.
The second embodiment is as follows: this embodiment mode is a further description of the first embodiment mode, and is different from the first embodiment mode in that the step length at the time of dispersion satisfies k M10, wherein kMAre discrete coefficients.
The third concrete implementation mode: this embodiment is a further description of the first embodiment, and the difference between this embodiment and the first embodiment is that in the second step, the space debris mean-near-point angle M is discretized based on the assumption that the geographic longitude of the debris is stable, and the number of discretizations is NMJ thMThe corresponding mean and near point angles of the discrete points are as follows:
Figure BDA0002086071380000071
the fourth concrete implementation mode is as follows: this embodiment mode is a further description of a third embodiment mode, and the difference between this embodiment mode and the third embodiment mode is the jth embodiment modeMCenter-to-center distance r corresponding to discrete pointsjMLatitude phijMAnd geographic longitude λjMComprises the following steps:
Figure BDA0002086071380000072
Figure BDA0002086071380000073
Figure BDA0002086071380000074
wherein the content of the first and second substances,
Figure BDA0002086071380000075
in order to be closer to the point angle,
Figure BDA0002086071380000076
is a mean paraxial point angle, a is a semimajor axis, e is an eccentricity, i is an orbital inclination angle, omega is a perigee angular distance, omega is a rising point right ascension, and lambda isΩThe geographic longitude corresponding to the intersection point of the orbit.
The fifth concrete implementation mode: this embodiment mode is a further description of a fourth embodiment mode, and the difference between this embodiment mode and the fourth embodiment mode is that the approximate point angle is described
Figure BDA0002086071380000077
Flat near point angle
Figure BDA0002086071380000078
Can be derived by the following formula:
Figure BDA0002086071380000079
Figure BDA00020860713800000710
wherein, ω iseIs the angular velocity of rotation of the earth, mu is the gravitational constant, mu is approximately equal to 398600km3/s2。ωe360 ° every 23 hours 56 minutes 4 seconds.
The sixth specific implementation mode is as follows: this embodiment mode is a further description of a third embodiment mode, and the difference between this embodiment mode and the third embodiment mode is the discrete number of parts NMThe step size is determined based on the spatial unit division.
The seventh embodiment: this embodiment mode is a further description of a sixth embodiment mode, and the difference between this embodiment mode and the sixth embodiment mode is the discrete number of parts NMThe determination steps are as follows: step lengths of the track height, the latitude and the longitude interval in the step one are recorded as delta r, delta phi and delta lambda, and N is the discrete standard for ensuring that the difference values of the track height, the latitude and the geographic longitude between any two adjacent discrete points are smaller than the step length of the corresponding space unit intervalM＝max{Nr,Nφ,Nλ}
Wherein the content of the first and second substances,
Figure BDA0002086071380000081
Figure BDA0002086071380000082
Figure BDA0002086071380000083
in the formula: pi is the circumference, a is the semimajor axis, e is the eccentricity, i is the inclination of the track, mu is the gravitational constant, omegaeIs the period of rotation of the earth, kMIs a discrete coefficient, k M10 where TIF is rounded upThe function (the function value is the smallest integer not smaller than the variable value) and max is the maximum function (the function value is the largest value among the variable values).
The specific implementation mode is eight: the present embodiment is a further description of the first embodiment, and the difference between the present embodiment and the first embodiment is that the staying probability of the debris in the space unit in the fifth step is based on the discrete number N of the space debris trajectoryMThe space unit orbit dividing principle (the track height, the latitude and the longitude interval step length is marked as delta r, delta phi and delta lambda) and the discrete point number of the space fragment orbit in the space unit.
The specific implementation method nine: the present embodiment is further described with respect to the eighth embodiment, and the difference between the present embodiment and the eighth embodiment is that the determining step of the fragment staying probability in the space unit is as follows: according to the orbital mechanics, the mean-near point angle of the space debris is uniformly changed along with time. Recording the orbit period of the space object as T, and the residence time of the space debris corresponding to each discrete point under the principle of equal division of the approximate point angle is
Figure BDA0002086071380000084
Space recording CellkThe number of discrete points of the inner space debris orbit is nkAnd the probability that the space debris is in the space unit at any time in the evaluation period is the ratio of the staying time and the orbit period in the space unit:
Figure BDA0002086071380000085
the detailed implementation mode is ten: this embodiment is a further description of the first embodiment, and the difference between this embodiment and the first embodiment is that the determination step of calculating the spatial density in the sixth step is as follows: cell in space with certain space debrisk([rk,rk+Δr],[φk,φk+Δφ],[λk,λk+Δλ]) Probability of stay in PkDue to the presence of spatial debris in the spatial cell at any timeFrom a bernoulli distribution (0-1 distribution), the mathematical expectation for the number of fragments in a spatial unit is: ek＝PkIf a plurality of space fragments participate in the calculation, the total fragment number is recorded as NdebThen space CellkMathematical expectation of total number of fragments in is the summation of mathematical expectations of individual fragment dwells
Figure BDA0002086071380000091
According to the geometric relationship, the space CellkHas a volume of
Figure BDA0002086071380000092
Then the space CellkSpace density of inner debris of
Figure BDA0002086071380000093
Wherein, Δ r, Δ φ, Δ λ are track height, latitude and longitude interval step, r is geocentric distance, Δ toneThe space debris dwell time for each discrete point.
It should be noted that the detailed description is only for explaining and explaining the technical solution of the present invention, and the scope of protection of the claims is not limited thereby. It is intended that all such modifications and variations be included within the scope of the invention as defined in the following claims and the description.

Claims (5)

1. A method for determining space debris space density under a ground anchoring system is characterized by comprising the following steps:
step one, dividing a space unit of a synchronous orbit protection area under an earth fixed connection coordinate system:
under the earth fixed connection coordinate system, discretizing an orbit space range with the orbit height of 35786 +/-200 km and the latitude of +/-15 degrees into a series of space units according to the orbit height, the geographic longitude and the latitude;
step two, the track position of the space debris is discrete:
discretizing the space debris orbit according to the number of the space debris orbits and the mean-near point angle;
step three, calculating the position of the track discrete point:
respectively calculating the specific track height, latitude and geographic longitude corresponding to each track discrete point;
identifying a space unit corresponding to each space debris track discrete point;
step five, calculating the fragment staying probability in each space unit:
according to the discrete track positions and the space units in the third step and the fourth step, counting the number of the discrete track positions corresponding to each space unit, and obtaining the staying probability according to the ratio of the number of the discrete track positions to the total discrete points;
step six, calculating space density:
obtaining space density through the ratio of the stay probability to the space unit volume;
the step length in discrete time satisfies kM10, wherein kMIs a discrete coefficient;
and step two, dispersing the space debris approximate point angle M based on the debris geographic longitude stability hypothesis, wherein the dispersion number is recorded as NMJ thMThe corresponding mean and near point angles of the discrete points are as follows:
Figure FDA0003514996500000011
the j (th)MCenter-to-center distance r corresponding to discrete pointsjMLatitude phijMAnd geographic longitude λjMComprises the following steps:
Figure FDA0003514996500000012
Figure FDA0003514996500000013
Figure FDA0003514996500000014
wherein the content of the first and second substances,
Figure FDA0003514996500000015
in order to be closer to the point angle,
Figure FDA0003514996500000016
is a mean paraxial point angle, a is a semimajor axis, e is an eccentricity, i is an orbital inclination angle, omega is a perigee angular distance, omega is a rising point right ascension, and lambda isΩThe geographical longitude corresponding to the point of intersection of the track,
Figure FDA0003514996500000017
is jthMThe latitude corresponding to each discrete point is,
Figure FDA0003514996500000018
latitude, ω, corresponding to the 1 st discrete pointeThe angular velocity of the earth rotation is, mu is a gravitational constant;
the determination step of the fragment staying probability in the space unit comprises the following steps: recording the orbit period of the space object as T, and the residence time of the space debris corresponding to each discrete point as
Figure FDA0003514996500000021
Space recording CellkThe number of discrete points of the inner space debris orbit is nkThe probability of a space debris being in the space cell is:
Figure FDA0003514996500000022
the determination step of calculating the space density in the sixth step is as follows: in space units of certain space debris
Cellk([rk,rk+Δr],[φk,φk+Δφ],[λk,λk+Δλ]) Probability of internal stay is PkThen the mathematical expectation of the number of fragments in a spatial unit is: ek＝PkIf a plurality of space fragments participate in the calculation, the total fragment number is recorded as NdebThen space CellkThe mathematical expectation for the total number of fragments in is:
Figure FDA0003514996500000023
space CellkHas a volume of
Figure FDA0003514996500000024
Space CellkSpace density of inner debris of
Figure FDA0003514996500000025
Wherein, Δ r, Δ φ, Δ λ are track height, latitude and longitude interval step length, NMIs a discrete number of space debris orbits, nkCell for recording spacekNumber of discrete points of inner space debris orbit, rkIs the lower limit of the track height phikAt the lower limit of latitude, λkIs the lower limit of the geographic longitude interval.
2. The method for determining the space density of the space debris under the earth fixation system as recited in claim 1, wherein: the angle of approach point
Figure FDA0003514996500000026
Flat near point angle
Figure FDA0003514996500000027
Can be derived by the following formula:
Figure FDA0003514996500000028
Figure FDA0003514996500000029
wherein, ω iseIs the angular velocity of rotation of the earth, mu is the gravitational constant, mu is approximately equal to 398600km3/s2。
3. The method for determining the space density of the space debris under the earth fixation system as recited in claim 1, wherein: discrete number of parts NMThe step size is determined based on the spatial unit division.
4. The method of claim 3, wherein said discrete number N of said partial space debris isMThe determination steps are as follows: step lengths of the track height, latitude and longitude intervals in the step one are recorded as delta r, delta phi, delta lambda and NM＝max{Nr,Nφ,Nλ}
Wherein the content of the first and second substances,
Figure FDA0003514996500000031
Figure FDA0003514996500000032
Figure FDA0003514996500000033
in the formula: pi is the circumference, a is the semimajor axis, e is the eccentricity, i is the inclination of the track, mu is the gravitational constant, omegaeFor rotation of the earthPeriod k ofMIs a discrete coefficient, kMTIF is an upward rounding function, max is a maximum function, 10.
5. The method according to claim 1, wherein the probability of the stay of the space debris in the space unit in the fifth step is based on the discrete number N of the space debris orbitMThe space unit orbit dividing principle and the number of discrete points of the space fragment orbit in the space unit are determined.
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