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CN114611273B - Calculation method of collision avoidance region for space targets in sun-synchronous orbit - Google Patents

Calculation method of collision avoidance region for space targets in sun-synchronous orbit Download PDF

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CN114611273B
CN114611273B CN202210183709.4A CN202210183709A CN114611273B CN 114611273 B CN114611273 B CN 114611273B CN 202210183709 A CN202210183709 A CN 202210183709A CN 114611273 B CN114611273 B CN 114611273B
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姜宇
李恒年
张辉
呼延宗泊
刘永杰
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China Xian Satellite Control Center
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Abstract

本发明公开的太阳同步轨道空间目标碰撞规避区域计算方法，针对各类太阳同步轨道上的空间目标的区域进行计算，考虑半长轴定轨偏差及大气阻力引起的半长轴衰减率，利用最新的空间目标编目数据，循环迭代进行太阳同步轨道空间目标碰撞预警的区域的计算，最终给出轨道控制的区域。本发明考虑了太阳同步轨道的特殊性引起的轨道摄动，推导了太阳同步轨道空间目标碰撞规避区域，相比于传统的太阳同步轨道空间目标碰撞规避区域计算，可以获得更为精确的结果。

The method for calculating the collision avoidance area of a space target in a sun-synchronous orbit disclosed in the present invention calculates the area of space targets on various sun-synchronous orbits, considers the semi-major axis attenuation rate caused by the semi-major axis orbit determination deviation and the atmospheric drag, and uses the latest space target cataloging data to iteratively calculate the area of collision warning of space targets in the sun-synchronous orbit, and finally gives the area of orbit control. The present invention considers the orbital perturbation caused by the particularity of the sun-synchronous orbit, derives the collision avoidance area of the space target in the sun-synchronous orbit, and can obtain more accurate results compared to the traditional calculation of the collision avoidance area of the space target in the sun-synchronous orbit.

Description

Method for calculating space target collision avoidance area of solar synchronous orbit
Technical Field
The invention belongs to the technical field of aerospace control methods, and particularly relates to a method for calculating a collision avoidance region of a space target of a solar synchronous orbit.
Background
In-orbit space objects including space vehicles and space debris, etc., in order to prevent the space objects from colliding with the space vehicles, thereby causing disastrous results, it is necessary to pre-calculate the regions during the movement of the space objects. The area is a long and narrow shape area along the flying direction of the space object, and other space objects outside the area cannot collide with the space object within a certain time. The traditional solar synchronous orbit space target collision avoidance area calculation only considers the three-dimensional distance of the space target, ignores the collision probability difference between the normal distance of the orbit plane and the distance in the orbit plane, and leads to inaccurate calculation results.
Disclosure of Invention
The invention aims to provide a method for calculating a solar synchronous orbit space target collision avoidance region, which solves the problem of inaccurate calculation results of the existing method.
The technical scheme adopted by the invention is that the method for calculating the collision avoidance area of the space target of the solar synchronous orbit comprises the following steps:
step 1, calculating the semi-long axis orbit determination deviation and the y-direction deviation caused by two amounts of semi-long axis attenuation rate caused by atmospheric resistance to obtain the region length;
step 2, extrapolating a space target track;
Step 3, calculating the long-term change rate of the inclination angle of the space target track caused by the daily and monthly gravitational perturbation;
Step 4, calculating the normal drift of the solar synchronous orbit space target caused by complex perturbation force;
And 5, calculating the normal radius of the area and the amount of deviation of the normal direction of the center of the area from the reference track, and obtaining the shape of the collision avoidance area.
The present invention is also characterized in that,
The method specifically comprises the steps of taking the centroid of a space target C as an origin to establish a track coordinate system Cxyz, enabling the Cx axis direction to be the same as the centroid direction of the space target, enabling the Cz axis to point to the normal direction of a track surface of the space target, enabling the Cy axis and the Cz axis to form a right-hand orthogonal coordinate system, setting r to represent the distance from the space target to the centroid, a to represent a semi-long axis, e to represent eccentricity, i to represent inclination angle, Ω to represent the right-hand intersection, ω to represent a near-point amplitude angle, f to represent a true near-point angle, M to represent a near-point angle, u=ω+f, λ=ω+M, setting subscripts 'C' and'd' to represent the space target and a region boundary point respectively, enabling δa0＝ad-ac,δi0＝id-ic,δΩ0＝Ωd-Ωc,δu0＝ud-uc,δM0＝Md-Mc to be the maximum value of track deviation, enabling δr 0＝rd-rc,rc＝[rc 0 0]T to be the component of a position vector of the space target relative to the centroid in the space target track coordinate system, enabling r d＝[xd yd zd]T to be the component of the region boundary point relative to be represented in the space target track coordinate system, setting results to be a, e, i, ω to represent the error, and delta to represent a plus or minus the position vector of the region boundary point relative to the centroid in the space target track coordinate system, and delta to be a minus sign of the three-dimensional curve, and delta/d to be a plus or minus sign, and 34M to the result;
the decay rate of the semi-long axis per second is:
The deviation in the y direction due to the two amounts of semilong axis tracking deviation and semilong axis attenuation rate due to atmospheric resistance is calculated according to the following formula:
In the formula (2), T is time, T is track period, δa 0 is semilong axis track deviation, For semi-long axis decay rate, pi is circumference rate, y + is deviation along +y direction, y - is deviation along-y direction, initial orbit extrapolation, y + and y - are two sides of the region; For the length of the region it is, Is the amount by which the center of the region is offset from the reference track.
The step 2 specifically comprises the steps of adopting a pre-estimated correction formula (3) to conduct track extrapolation:
In the formula (3), x j is an independent variable of the j-th step, y j is a function value of the j-th step, f is an integral function, h is a step length, As the predicted value, y n+1 is the correction value.
The long-term change rate of the space target orbit inclination angle caused by the solar-lunar attraction perturbation in the step 3 is obtained by summing the long-term change rate of the space target orbit inclination angle of the solar synchronous orbit under the solar attraction perturbation effect and the long-term change rate of the space target orbit inclination angle caused by the lunar attraction perturbation;
the long-term change rate of the solar synchronous orbit space target orbit inclination angle under the action of solar attraction perturbation is calculated by the formula (4):
in the formula (4), t is time, i s is a yellow road inclination angle, n s is an angular velocity of revolution of the earth around the sun, and beta s is a yellow meridian of solar visual movement;
the long-term change rate of the space target orbit inclination angle caused by the perturbation of the lunar attraction is calculated by the formula (5):
in (5) M m is the lunar mass, m e is the earth mass,I m is the inclination of the moon orbit, Ω m is the ascent and descent of the moon orbit, n m is the angular velocity of the moon moving around the earth, and r em is the earth-moon average distance.
In the step 4, calculating the normal drift of the solar synchronous orbit space target through a formula (6):
in the formula (6), the calculation unit is radian.
Step 5 specifically includes first, as viewed from the normal, the area deviates from the initial reference track by:
the area normal radius is calculated by equation (8):
the amount by which the normal direction of the area center deviates from the reference orbit is calculated by the formula (9):
Let k=2.0 be the region isolation coefficient, D=kd, the region is properly enlarged, the radius of curvature of the region is
The physical quantities required for the collision avoidance region include the amount z of region deviation from the initial reference trajectory, the region normal radius R p, the amount C drift of region center normal direction deviation from the reference trajectory, the region lengthAmount of deviation of the center of the area from the reference track
The method for calculating the solar synchronous orbit space target collision avoidance region has the beneficial effects that the method is used for calculating the regions of the space targets on various solar synchronous orbits, the semi-long axis attenuation rate caused by semi-long axis orbit determination deviation and atmospheric resistance is considered, the latest space target cataloging data is utilized, the calculation of the regions of the solar synchronous orbit space target collision early warning is performed through cyclic iteration, and finally the orbit control region is provided. According to the method, track perturbation caused by the particularity of the solar synchronous track is considered, the solar synchronous track space target collision avoidance area is deduced, and compared with the traditional solar synchronous track space target collision avoidance area calculation, a more accurate result can be obtained.
Drawings
FIG. 1 is a flow chart of a method of calculating a solar synchronous orbit space target collision avoidance region of the present invention;
fig. 2 is a schematic diagram of a solar synchronous orbit space target collision avoidance region obtained by the embodiment of the invention.
Detailed Description
The invention will be described in detail with reference to the accompanying drawings and detailed description.
The invention provides a method for calculating a solar synchronous orbit space target collision avoidance region, which is shown in fig. 1 and comprises the following steps:
And step 1, calculating the semi-long axis orbit determination deviation and the y-direction deviation caused by two amounts of semi-long axis attenuation rate caused by atmospheric resistance, and obtaining the region length. And (3) establishing a track coordinate system Cxyz by taking the centroid of the space target C as an origin, wherein the Cx axis direction is the same as the direction from the earth center to the centroid of the space target, the Cz axis points to the normal direction of the track surface of the space target, and the Cy axis, the Cz axis and the Cx axis form a right-hand orthogonal coordinate system. Let r denote the distance of the spatial target to the earth center, a denote the semi-major axis, e denote the eccentricity, i denote the inclination angle, Ω denote the ascent intersection point right ascent, ω denote the near-spot argument, f denote the true near-spot argument, M denote the even near-spot argument, u=ω+f, λ=ω+m. Let the subscripts "c" and "d" represent the spatial target and the region boundary point, respectively, with the spatial target being in a near circular orbit. δa0＝ad-ac,δi0＝id-ic,δΩ0＝Ωd-Ωc,δu0＝ud-uc,δM0＝Md-Mc is set to the maximum value of the tracking error. δr 0＝rd-rc,rc＝[rc 00]T is a component representation of the position vector of the spatial target relative to the centroid in the spatial target orbit coordinate system, and r d＝[xd yd zd]T is a component representation of the position vector of the region boundary point relative to the centroid in the spatial target orbit coordinate system. The set track results are expressed by a, e, i, omega, M, and the track errors are expressed by + -delta a, + -delta e, + -delta i, + -delta omega, + -delta M. For a space target of a near-earth orbit, the semi-long axis daily attenuation rate in the orbit determination result is read, da/(dDay), and the sign is negative, and the unit is meter/day.
The attenuation rate per second of the semi-long axis is
The deviation in y direction due to the two amounts of semi-long axis orbit determination deviation and semi-long axis attenuation rate due to atmospheric resistance is calculated according to the following formula
Wherein T is time, T is track period, δa 0 is semimajor axis tracking deviation,The semi-major axis decay rate, pi is the circumference, y + is the deviation along the +y direction, and y - is the deviation along the-y direction. The initial orbit is extrapolated with the extrapolated orbit as a reference. y + and y - are on both sides of the region.For the length of the region it is,Is the amount by which the center of the region is offset from the reference track. Thereby the zone length is obtained.
Step 2, extrapolating the space target track, and extrapolating the track by adopting a pre-estimated correction formula (3):
wherein x j is the argument of the j-th step, y j is the function value of the j-th step, f is the integral function, h is the step size, As the predicted value, y n+1 is the correction value.
The initial orbit is substituted into instantaneous root number extrapolation, and a10×10-order (or 20×20 and other orders) gravitational field model, solar-lunar attraction and solar pressure are considered, and atmospheric resistance is not considered. Extrapolation is performed with the instantaneous root as a reference value. Since the calculated area center deviation already takes into account the atmospheric resistance, the atmospheric resistance is no longer taken into account in the extrapolation.
And step 3, calculating the long-term change rate of the space target orbit inclination angle caused by the daily and monthly gravitational perturbation. The long-term change rate of the target orbit inclination angle of the solar synchronous orbit space under the action of the perturbation of solar attraction caused by resonance influence is calculated according to the following formula
Where t is time, i s is the yellow road inclination angle, n s is the angular velocity of the earth revolving around the sun, and β s is the yellow meridian of the sun's apparent motion. The long-term change rate of the track inclination angle of the constellation space target is irrelevant to the right ascent point and the right descent point of the space target, and is relevant to the position of the descent point of the space target. The (. Beta. s - Ω) is a quantity determined at the point of intersection of the descent and the ascent, and is not directly related to the right ascent, intersection and the right ascent, intersection. If the cross point of a space object in the quasi-sun synchronous orbit constellation is 12:00 when the solar energy is leveled, the value of beta s -omega is 180 DEG after the value is turned to the interval [0,360 ].
The long-term change rate of the space target orbit inclination angle caused by the perturbation of the lunar attraction is calculated according to the following formula
Wherein the method comprises the steps ofM m is the lunar mass, m e is the earth mass,I m is the inclination of the moon orbit, Ω m is the ascent and descent of the moon orbit, n m is the angular velocity of the moon moving around the earth, and r em is the earth-moon average distance.
And 4, calculating the normal drift of the solar synchronous orbit space target caused by complex ingestion power. The drift of the normal direction of the space target caused by the orbit determination deviation, the semi-long axis attenuation rate caused by the atmospheric resistance and the tilt perturbation caused by the solar-lunar attraction is calculated according to the following formula:
the calculation unit is radian.
And 5, calculating the amount of deviation of the normal radius of the area and the normal direction of the center of the area from the reference track. The area deviates from the original reference trajectory (extrapolated with two volumes plus J2 terms) as viewed from normal
The area normal radius is calculated as follows
The amount of deviation of the normal direction of the zone center from the reference track is calculated as follows
Output region two sides y + and y -, region centerRegion length |y +-y- |, region radius R p, region center normal offset from C drift, let k=2.0 be the region isolation coefficient,D=kd, the region is properly enlarged, the radius of curvature of the region is
The shape of the collision avoidance region is obtained, and the physical quantities required for the collision avoidance region include an amount z of the region deviating from the initial reference orbit, a region normal radius R p, an amount C drift of the region center normal direction deviating from the reference orbit, and a region lengthThe center of the region is tangentially offset from the reference track by an amountThe method comprises the steps of (1) obtaining the amount of tangential deviation of the area length and the area center from the reference track, and (4) obtaining the amount of tangential deviation of the area center from the initial reference track, the amount of tangential deviation of the area center from the reference track, and the amount of tangential deviation of the area center from the reference track.
Examples
The local time is 30 minutes at the point of the falling intersection of a certain solar synchronous orbit satellite, the semi-long axis of the orbit of the satellite is 7180000m, the orbit inclination angle is 98.6deg, the right-hand warp of the initial time rising intersection is 120deg, the semi-long axis attenuation rate is 10m per day, the maximum deviation of the semi-long axis of the orbit of the satellite is set to be 6m, the maximum deviation of the inclination angle of the orbit is 0.001deg, the white-red intersection angle is 18.3deg, the right-hand warp of the white-channel rising intersection point is-12 deg, and the regional isolation coefficient is 2.0. After 1 day of calculation, the size, shape and center position of the safe area.
According to the calculation steps, the length of the collision avoidance area is 1.6139km, and the length direction of the collision avoidance area is along the satellite running direction. The normal radius 27.8045m of the collision avoidance area, the normal drift of the area is-0.1570 m (facing the satellite running direction, positive to the right and negative to the left). Figure 2 gives a schematic representation of the safe area after 1 day. For visual purposes, the scales of the different coordinate axes in fig. 2 are not uniform. As can be seen from fig. 2, the collision avoidance area is a very elongated one cylinder.

Claims (6)

1.太阳同步轨道空间目标碰撞规避区域计算方法，其特征在于，包括以下步骤：1. A method for calculating a collision avoidance zone for a space target in a sun-synchronous orbit, comprising the following steps: 步骤1、计算半长轴定轨偏差及大气阻力引起的半长轴衰减率两个量引起的y方向的偏差，获得区域长度；Step 1, calculate the deviation in the y direction caused by the semi-major axis orbit determination deviation and the semi-major axis attenuation rate caused by atmospheric drag, and obtain the region length; 步骤2、空间目标轨道外推；Step 2: Extrapolation of space target orbit; 步骤3、计算日月引力摄动引起的空间目标轨道倾角长期变化率；Step 3, calculate the long-term change rate of the orbital inclination of the space target caused by the gravitational perturbations of the sun and the moon; 步骤4、计算复杂摄动力引起的太阳同步轨道空间目标法向漂移；Step 4, calculating the normal drift of the space target in the sun-synchronous orbit caused by the complex perturbation force; 步骤5、计算区域法向半径和区域中心法向方向偏离基准轨道的量，获得碰撞规避区域的形状。Step 5: Calculate the deviation of the normal radius of the region and the normal direction of the center of the region from the reference track to obtain the shape of the collision avoidance region. 2.如权利要求1所述的太阳同步轨道空间目标碰撞规避区域计算方法，其特征在于，所述步骤1具体包括：以空间目标C的质心为原点建立轨道坐标系Cxyz，Cx轴方向和地心至空间目标质心方向相同，Cz轴指向空间目标轨道面法线方向，Cy轴和Cz轴、Cx轴成右手正交坐标系；设r表示空间目标到地心的距离，a表示半长轴，e表示偏心率，i表示倾角，Ω表示升交点赤经，ω表示近地点幅角，f表示真近点角，M表示平近点角，u＝ω+f，λ＝ω+M；设下标“c”和“d”分别代表空间目标和区域边界点，空间目标处在近圆轨道；令δa0＝ad-ac，δi0＝id-ic，δΩ0＝Ωd-Ωc，δu0＝ud-uc，δM0＝Md-Mc为定轨偏差的最大值；δr0＝rd-rc，rc＝[rc 0 0]T为空间目标相对地心的位置矢量在空间目标轨道坐标系的分量表示，rd＝[xd yd zd]T为区域边界点相对地心的位置矢量在空间目标轨道坐标系的分量表示；设定轨结果用a,e,i,Ω,ω,M表示，定轨误差用±δa,±δe,±δi,±δΩ,±δω,±δM表示；对于近地轨道的空间目标来说，读取定轨结果中半长轴每天衰减率，da/(dDay)，符号为负，单位为米/天；2. The method for calculating the collision avoidance area of a sun-synchronous orbit space target according to claim 1, characterized in that the step 1 specifically comprises: establishing an orbital coordinate system Cxyz with the center of mass of the space target C as the origin, the direction of the Cx axis is the same as the direction from the center of the earth to the center of mass of the space target, the Cz axis points to the normal direction of the orbital plane of the space target, and the Cy axis, Cz axis and Cx axis form a right-handed orthogonal coordinate system; let r represent the distance from the space target to the center of the earth, a represent the semi-major axis, e represent the eccentricity, i represent the inclination, Ω represent the right ascension of the ascending node, ω represent the argument of perigee, f represent the true anomaly, M represent the mean anomaly, u＝ω+f, λ＝ω+M; let the subscripts "c" and "d" represent the space target and the area boundary point respectively, and the space target is in a near-circular orbit; let δa 0 ＝ ad - ac , δi 0 ＝ id - ic , δΩ 0 ＝ Ωd - Ωc , δu 0 ＝ ud - uc , δM 0 = M d -M c is the maximum value of the orbit determination deviation; δr 0 = r d - r c , r c = [r c 0 0] T is the component representation of the position vector of the space target relative to the center of the earth in the space target orbit coordinate system, r d = [x d y d z d ] T is the component representation of the position vector of the regional boundary point relative to the center of the earth in the space target orbit coordinate system; the set orbit result is represented by a, e, i, Ω, ω, M, and the orbit determination error is represented by ±δa, ±δe, ±δi, ±δΩ, ±δω, ±δM; for space targets in low-Earth orbit, read the semi-major axis daily attenuation rate in the orbit determination result, da/(dDay), the sign is negative, and the unit is meter/day; 半长轴每秒衰减率为：The decay rate of the semi-major axis per second is: 半长轴定轨偏差及大气阻力引起的半长轴衰减率两个量引起的y方向的偏差按照下式计算：The deviation in the y direction caused by the semi-major axis orbit determination deviation and the semi-major axis attenuation rate caused by atmospheric drag is calculated according to the following formula: 式(2)中，t为时间，T为轨道周期，δa0为半长轴定轨偏差，为半长轴衰减率，π为圆周率，y+为沿着+y方向的偏差，y-为沿着-y方向的偏；初始轨道外推，以外推的轨道为参考基准；y+和y-为区域两边；为区域长度，为区域中心偏离基准轨道的量。In formula (2), t is time, T is orbit period, δa 0 is the semi-major axis orbit determination error, is the semi-major axis decay rate, π is the circumference, y + is the deviation along the +y direction, y - is the deviation along the -y direction; the initial orbit is extrapolated, and the extrapolated orbit is used as the reference; y + and y - are the two sides of the region; is the region length, is the amount by which the center of the region deviates from the reference orbit. 3.如权利要求2所述的太阳同步轨道空间目标碰撞规避区域计算方法，其特征在于，所述步骤2具体包括：采用预估校正公式(3)进行轨道外推：3. The method for calculating the collision avoidance zone of a space target in a sun-synchronous orbit according to claim 2, wherein step 2 specifically comprises: using the estimation correction formula (3) to perform orbit extrapolation: 式(3)中，xj为第j步的自变量，yj为第j步的函数取值，f为积分函数，h为步长，为预估值，yn+1为校正值。In formula (3), xj is the independent variable of the jth step, yj is the function value of the jth step, f is the integral function, h is the step length, is the estimated value, and y n+1 is the corrected value. 4.如权利要求3所述的太阳同步轨道空间目标碰撞规避区域计算方法，其特征在于，所述步骤3中日月引力摄动引起的空间目标轨道倾角长期变化率由太阳引力摄动作用下的太阳同步轨道空间目标轨道倾角长期变化率和月球引力摄动引起的空间目标轨道倾角长期变化率求和得到；4. The method for calculating the collision avoidance area of a sun-synchronous orbit space target according to claim 3, wherein the long-term change rate of the orbital inclination of the space target caused by the gravitational perturbation of the sun and the moon in step 3 is obtained by summing the long-term change rate of the orbital inclination of the sun-synchronous orbit space target under the gravitational perturbation of the sun and the long-term change rate of the orbital inclination of the space target caused by the gravitational perturbation of the moon; 太阳引力摄动作用下的太阳同步轨道空间目标轨道倾角长期变化率通过公式(4)计算：The long-term change rate of the orbital inclination of a sun-synchronous orbit space target under the action of solar gravitational perturbation is calculated by formula (4): 式(4)中，t为时间，is为黄道倾角，ns为地球绕太阳公转的角速率，βs为太阳视运动的黄经；In formula (4), t is time, is is the inclination of the ecliptic, ns is the angular velocity of the Earth's revolution around the Sun, and βs is the ecliptic longitude of the Sun's apparent motion; 月球引力摄动引起的空间目标轨道倾角长期变化率通过公式(5)计算：The long-term change rate of the orbital inclination of the space target caused by the lunar gravitational perturbation is calculated by formula (5): 式(5)中mm为月球质量，me为地球质量，im为月球轨道的倾角，Ωm为月球轨道的升交点赤经，nm为月球绕地球运动的角速率，rem为地月平均距离。In formula (5) m m is the mass of the moon, m e is the mass of the earth, im is the inclination of the lunar orbit, Ω m is the right ascension of the ascending node of the lunar orbit, nm is the angular velocity of the moon's motion around the earth, and rem is the average distance between the earth and the moon. 5.如权利要求4所述的太阳同步轨道空间目标碰撞规避区域计算方法，其特征在于，所述步骤4中通过公式(6)计算太阳同步轨道空间目标法向漂移：5. The method for calculating the collision avoidance area of a sun-synchronous orbit space target according to claim 4, wherein in step 4, the normal drift of the sun-synchronous orbit space target is calculated by formula (6): 式(6)中，计算单位为弧度。In formula (6), the calculation unit is radian. 6.如权利要求5所述的太阳同步轨道空间目标碰撞规避区域计算方法，其特征在于，所述步骤5具体包括：首先从法向看，区域偏离初始参考轨道为：6. The method for calculating the collision avoidance area of a sun-synchronous orbit space target according to claim 5, wherein step 5 specifically comprises: first, from the normal direction, the area deviates from the initial reference orbit as follows: 则区域法向半径通过公式(8)计算：Then the area normal radius is calculated by formula (8): 区域中心法向方向偏离基准轨道的量通过公式(9)计算：The deviation of the normal direction of the center of the region from the reference track is calculated by formula (9): 令K＝2.0为区域隔离系数，d＝Kd，区域进行了适当放大，区域曲率半径为 Let K = 2.0 be the regional isolation coefficient, d = Kd, the area is appropriately enlarged, and the radius of curvature of the area is 碰撞规避区域需要的物理量包括：区域偏离初始参考轨道的量z，区域法向半径Rp，区域中心法向方向偏离基准轨道的量Cdrift，区域长度区域中心偏离基准轨道的量 The physical quantities required for the collision avoidance zone include: the amount z of the zone deviating from the initial reference orbit, the normal radius Rp of the zone, the amount Cdrift of the normal direction of the center of the zone deviating from the reference orbit, and the length of the zone. The amount by which the center of the region deviates from the reference track
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