A space station companion satellite orbit design method for space debris threat warning

Abstract

The present invention discloses a method for designing a companion satellite orbit for space station aimed at early warning of space debris threats, and belongs to the technical field of aerospace. The present invention provides a method for designing a companion satellite orbit for space station aimed at early warning of space debris threats, which writes the CW equation into a parameterized form by combining the parametric equation of the space ellipse, and then uses the geometric meaning of the parameters in combination with the azimuth and distance constraints to give the orbit design result. The design method proposed in the present invention makes full use of the geometric characteristics and mathematical geometry methods of the CW equation, and has the advantages of being intuitive, having obvious physical meaning, and being easy to calculate; at the same time, the present invention supplements the design method of the flyby orbit for early warning of space debris impact in the existing field, and provides ideas, references and technical support for subsequent references in engineering fields.

Description

Technical Field

[0001] The present invention relates to the technical field of aerospace, and specifically to a space station companion satellite orbit design method for space debris threat warning. Background Art

[0002] With the rapid development of human aerospace activities, the amount of space debris is rapidly increasing. According to observations by the U.S. Space Surveillance Network as of July 2011, the number of pieces of space debris with a diameter of 10 cm or greater has reached over 19,000. 80% of the total debris is located in low-Earth orbit (orbital altitude of less than 2,000 kilometers), where the Chinese and International Space Stations operate. Such a large amount of space debris inevitably poses a significant collision threat to space stations. Therefore, measures must be taken to prevent collisions. Currently, the most effective method is to provide early warning using ground-based observation equipment, such as the U.S. Space Surveillance Network and the German Tracking and Imaging Radar System. However, these observation methods are all ground-based, and they lack the required accuracy for smaller pieces of space debris. To address this issue, some researchers have proposed deploying a fleet of satellites equipped with large-aperture telescopes and high-energy lasers near a space station to observe space debris and use lasers to alter its orbit.

[0003] A crucial issue for the aforementioned scheme is the orbital design of the satellite formation. Existing research has designed each satellite's orbit from an absolute perspective, with the goal of large-scale monitoring and clearance. However, in practical applications, significant impact threats often arise in certain locations. To achieve more targeted observation and early warning missions, orbits designed to target specific impact threats require designing orbits. Summary of the Invention

[0004] The purpose of the present invention is to overcome the shortcomings of the above-mentioned prior art and provide a space station companion satellite orbit design method for space debris threat warning.

[0005] In order to achieve the above object, the present invention adopts the following technical solutions:

[0006] A space station companion satellite orbit design method for space debris threat warning includes the following steps:

[0007] S1. Obtaining the azimuth coordinates of space debris with a collision risk, and determining a corresponding expected detection distance based on the azimuth coordinates;

[0008] S2. Establish a parameterized expression of relative orbit based on the CW equation;

[0009] S3. Calculating undetermined parameters in a parameterized expression of a relative flyby orbit according to the azimuth coordinates of the space debris with a collision risk and the corresponding constraints of an expected detection distance;

[0010] S4. Determine a set of relative initial states of the relative flyby orbit based on the calculated undetermined parameters;

[0011] A satellite is launched into the orbit.

[0012] Furthermore, S2 is specifically:

[0013] S2.1. Analyze the geometric characteristics of periodic solutions of CW equations;

[0014] S2.2. Establish the parametric equation of the spatial ellipse;

[0015] S2.3. Establish a parametric expression for the relative flyby orbit based on the parametric equation of the space ellipse.

[0016] Furthermore, S2 includes the following steps:

[0017] S2.1. Based on the geometric characteristics of the periodic solution of the CW equation, the relative flyby orbit is considered to be a set Φ consisting of the intersection of the plane P passing through the origin and the elliptical cylinder C. Thus, any relative motion orbit around the space platform can be calculated using three independent variables (α x ,α y ,a) to uniquely determine, where α x and α y They represent the angles between the normal vector of plane P and the positive directions of the x-axis and y-axis, respectively, and their values ​​range from [-90°, 90°]; a is the major semi-axis of the base ellipse of the elliptical cylinder C;

[0018] S2.2. The orbit around the space station is described by the parametric equation of the space ellipse. The parametric equation of the space ellipse is:

[0019]

[0020] In the formula, (C x ,C y ,C z ) represents the coordinates of the center of the space ellipse, a=(a1, a2, a3) represents the space vector located in the space ellipse surface, b=(b1, b2, b3) represents the space vector located in the space ellipse surface and perpendicular to a;

[0021] Combining formula (1), the periodic solution of the CW equation can be rewritten as follows:

[0022]

[0023] S2.3. By comparing equations (1) and (2), the parameterized expression of the relative flyby orbit is obtained as follows:

[0024]

[0025] in:

[0026]

[0027] Furthermore, the bottom surface of the elliptical cylinder C is an ellipse with a ratio of the major semi-axis a to the minor semi-axis b of 2:1.

[0028] Furthermore, S2.3 also includes:

[0029] The triplet variable (α x ,α y ,a) Expressed by a and b:

[0030]

[0031] Furthermore, S3 is specifically:

[0032] S3.1. Obtain the collision threat azimuth coordinates and expected detection range;

[0033] S3.2. Determine the first undetermined parameter a based on the impact threat azimuth coordinates and the desired detection range;

[0034] S3.3. Calculate the normal vector n relative to the orbital plane based on a;

[0035] S3.4. Determine the second undetermined parameter b based on n.

[0036] Furthermore, the S3 implementation steps are as follows:

[0037] S3.1. Obtain the azimuth vector Treaten of the impact direction of the space debris relative to the origin of the LVLH coordinate system of the space platform and the expected detection distance d;

[0038] S3.2. Calculate vector a in the parameterized relative motion equation based on the orientation vector Treaten and the desired detection distance d, where a = (||Threaten||2-d)·(Threaten / ||Threaten||2);

[0039] S3.3. Use the properties of the vector product to calculate the normal vector n of the orbital plane, n = a × i or n = a × j;

[0040] S3.4. Calculate the unit vector of vector b from the orbital plane normal vector n, b / ||b||2=(a×n) / ||a×n||2;

[0041] Based on the vector a, we can determine the initial parameters of the relative orbit x0, and z0;

[0042] According to x0 calculated in S3.3, z0 calculates the first and second elements of vector b.

[0043] Furthermore, S4 is specifically:

[0044] S4.1. Take the third element of vector b as the unknown quantity and solve for the third element of vector b by combining the relationship between vector b and its unit vector. Finally, determine the initial parameters of the relative orbit.

[0045] S4.2. Periodic conditions of relative flyby orbits and no offset conditions Finally determine all the initial parameters of the relative flyby orbit.

[0046] Compared with the prior art, the present invention has the following beneficial effects:

[0047] The present invention provides a space station companion satellite orbit design method for space debris threat warning. By combining the parametric equations of a space ellipse, the CW equation is parametrically expressed. The geometric meaning of the parameters is then combined with azimuth and distance constraints to produce an orbit design result. The proposed design method fully utilizes the geometric characteristics of the CW equation and mathematical geometry methods, offering the advantages of intuitiveness, clear physical meaning, and ease of calculation. On the one hand, it considers the constraints of actual scenarios, freeing orbit design from the previous simple orbit design. On the other hand, the method is intuitive, physically clear, and easy to calculate, and has the potential for engineering application. The present invention enables a satellite to approach a threat at a specific azimuth and distance. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 This is a flow chart of a method for designing a relative flyby orbit for a space station aimed at warning of space debris impact threats according to the present invention;

[0049] Figure 2 is a flow chart of the relative orbit parameterization representation method based on the CW equation of the present invention;

[0050] Figure 3 This is a flow chart of a relative orbit design method based on parameterized relative motion equations of the present invention that takes into account the space debris threat orientation and desired detection distance constraints;

[0051] Figure 4 This is a schematic diagram of a scenario in which satellites near a space station are used to observe and warn of collision threats in a specific direction;

[0052] Figure 5 It is a schematic diagram of the geometric characteristics of the periodic solution of the CW equation of the present invention and the geometric meaning of the undetermined parameters in the parameterized expression;

[0053] Figure 6 It is the relative flyby orbit design result of the specific implementation method of the present invention. DETAILED DESCRIPTION

[0054] In order to enable those skilled in the art to better understand the solutions of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the embodiments described are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts should fall within the scope of protection of the present invention.

[0055] It should be noted that the terms "first", "second", etc. in the description and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that the numbers used in this way can be interchanged where appropriate, so that the embodiments of the present invention described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions. For example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0056] The present invention utilizes the geometric characteristics of the CW equation and provides a relative flyby orbit design method under the conditions of considering specific orientation constraints and detection distance constraints.

[0057] When a high probability of a space debris impact threat is detected in a certain direction near the space station, a satellite is required to approach the threat direction at a certain period and distance to achieve early warning; the present invention gives the approximate direction of the impact threat and the expected distance to approach the threat, and outputs a set of relative fly-by orbit initial parameters that meet the requirements; the fly-by orbit is built based on the calculated parameters, and the calculated set of relative initial states describes a fly-by orbit; traditional relative orbit design methods are based on the geometric properties of the CW equation itself to design fly-by orbits of regular geometric shapes (such as space circles, plane ellipses, etc.), while the present invention further utilizes the geometric properties of the CW equation, combined with mathematical methods, to design fly-by orbits under arbitrary direction and distance constraints.

[0058] The present invention is described in further detail below with reference to the accompanying drawings:

[0059] See also Figure 1 , Figure 1 This is a flow chart of a method for designing a relative flyby orbit for a space station for space debris impact threat warning according to the present invention. The method comprises the following steps: S1, inputting the impact threat azimuth coordinates and the expected detection distance; S2, establishing a parameterized expression for the relative flyby orbit; S3, calculating the undetermined parameters in the parameterized expression according to the impact threat azimuth coordinates and the expected detection distance; and S4, determining a set of initial relative states of the flyby orbit according to the undetermined parameters.

[0060] See also Figure 2 , Figure 2 It is a flow chart of the method for establishing a relative orbit parameterized expression based on the CW equation of the present invention; a method for establishing a relative orbit parameterized expression based on the CW equation, comprising the following steps: S2.1, analyzing the geometric characteristics of the periodic solution of the CW equation; S2.2, establishing the parametric equation of the space ellipse; S2.3, establishing the parametric expression of the relative fly-by orbit based on the parametric equation of the space ellipse. Specifically: S2.1, according to the geometric characteristics of the periodic solution of the CW equation, the relative fly-by orbit can be regarded as a set Φ consisting of the intersection lines of a plane P passing through the origin and an elliptical cylinder C, and the bottom surface of the elliptical cylinder C is an ellipse with a ratio of the major semi-axis a to the minor semi-axis b of 2:1. Therefore, any relative motion orbit near the space platform can be obtained using three independent variables (α x ,α y ,a) to uniquely determine. Among them, α x and α y They represent the angles between the normal vector of plane P and the positive directions of the x-axis and y-axis, respectively, and their value range is [-90°, 90°]; a is the major semi-axis of the base ellipse of the elliptical cylinder C.

[0061] S2.2, based on the analysis in S2.1, the orbit around the space station can be described mathematically by the equation of a space ellipse, and the parametric equation of the space ellipse can be written as:

[0062]

[0063] In the formula, (C x ,C y ,C z ) represents the coordinates of the center of the space ellipse, a = (a1, a2, a3) represents the space vector located within the space ellipse, and b = (b1, b2, b3) represents the space vector located within the space ellipse and perpendicular to a. Combining the above formula, the periodic solution of the CW equation can be rewritten as follows:

[0064]

[0065] S2.3, by comparing equations (1) and (2), we can obtain the parameterized expression of the relative flyby orbit:

[0066]

[0067] in:

[0068]

[0069] At the same time, the triple variable (α) describing the size and direction of the relative orbit x ,α y ,a) is also represented by a and b:

[0070]

[0071] See also Figure 3 , Figure 3 This is a flow chart of the relative orbit design method based on the parameterized relative motion equation of the present invention, which takes into account the space debris threat orientation and the expected detection distance constraints; a relative orbit design method based on the parameterized relative motion equation, which takes into account the space debris threat orientation and the expected detection distance constraints, and its main steps are: S3.1, input the impact threat orientation coordinates and the expected detection distance; S3.2, first determine the first undetermined parameter a according to the threat orientation coordinates and the expected detection distance; S3.3, calculate the normal vector n of the relative fly-by orbit plane according to a; S3.4, determine the second undetermined parameter b according to n. Specifically, input the approximate orientation vector Treaten of the approximate impact orientation relative to the origin of the space platform LVLH coordinate system and the expected detection distance d; calculate the vector a in the parameterized relative motion equation according to the vector Treaten and the distance d, and its specific expression is a=(||Threaten||2-d)·(Threaten / ||Threaten||2); according to the vector a, the x0, x1 and x2 in the initial parameters of the relative fly-by orbit can be determined according to formula (4). And z0; according to the perpendicularity theorem of straight lines and planes in space, if there exists a vector n perpendicular to vector a, then vector n is the normal vector of the orbital plane. From this, the property of vector product is used to calculate the orbital plane normal vector n, that is, n = a×i or n = a×j; the unit vector of vector b is calculated from the orbital plane normal vector n as b / ||b||2 = (a×n) / ||a×n||2.

[0072] S4. Determine a set of initial relative states of the orbit according to the undetermined parameters. Specifically, according to formula (4), the x0, z0 can be used to calculate the first and second elements of vector b; taking the third element of vector b as the unknown quantity, the third element of vector b is solved by combining the relationship between vector b and its unit vector, and finally the initial parameters of the relative orbit are determined. The periodic conditions of relative orbits and no offset conditions Finally determine all the initial parameters of the relative flyby orbit.

[0073] Figure 4 This is a schematic diagram of a scenario in which satellites near a space station are used to observe and warn of collision threats in a specific direction; Figure 4 In the figure, there is a space debris impact threat with a known direction near the space station (as shown by the triangle in the figure). By designing the relative orbit shown in the figure, the satellite can achieve close observation and early warning of the impact threat direction at a fixed time period and a certain distance d.

[0074] Figure 5 It is a schematic diagram of the geometric characteristics of the periodic solution of the CW equation of the present invention and the geometric meaning of the undetermined parameters in the parameterized expression; Figure 5 In the figure, the real-space elliptical plane above represents the plane formed by the actual space flyby orbit. Vector a and vector b in this plane represent any pair of parameter vectors in the parametric expression of the relative flyby orbit. The shaded part below is a plane ellipse with a major-minor axis ratio of 2:1, which represents that the projection of the relative flyby orbit on the horizontal plane is an ellipse with a major-minor axis ratio of 2:1.

[0075] Figure 6 It is the relative flyby orbit design result of the specific implementation method of the present invention. Figure 6 In the figure, the central pentagon represents the space station, the pentagons around the space station represent possible space debris impact threat points, the dotted line represents the line connecting the space station and the possible impact threat points, the three elliptical solid lines represent the designed relative flyby orbits, and the circles represent positions on the relative flyby orbits that can approach the impact threat points at the expected distance.

[0076] Example

[0077] Assuming the space station is operating in a circular orbit at an altitude of 400 km, preliminary detection indicates that three approximate locations (Table 1) have a high probability of space debris impact threats. Three satellites are required to provide early warning monitoring for these threats, with their expected observation distances shown in Table 1. To avoid repetition, this section details the orbit design process for impact threat No. 1.

[0078] Table 1 Collision threat direction information

[0079]

[0080] S3.1. Input the approximate impact direction of the space debris relative to the origin of the LVLH coordinate system of the space platform. Treaten = [300, 150, 250] T and the expected detection distance d = 200;

[0081] S3.2. Calculate the vector a in the parameterized relative motion equation based on the vector Treaten and the distance d = [156.5726, 78.2863, 130.4771] T ;

[0082] S3.3, according to the vector a, the initial parameters of the relative orbit can be determined according to formula (4): x0 = 156.5726, and z0 = 130.4771;

[0083] S3.4. According to the perpendicularity theorem between lines and planes in space, if there exists a vector n perpendicular to vector a, then vector n is the normal vector to the orbital plane. Therefore, using the properties of the vector product, we can calculate the normal vector to the orbital plane as n = [0, 0.8575, -0.5145] T ;

[0084] S3.5. Calculate the unit vector b from the orbital plane normal vector n: b / ||b||2 = [-0.6969, 0.3690, 0.6149] T ;

[0085] S3.6, according to formula (4) obtained from the calculation in step 3, z0 can be calculated to obtain the first element of vector b as 39.1413 and the second element as -313.1451;

[0086] S3.7. Take the third element of vector b as the unknown quantity, and combine the relationship between vector b and its unit vector to solve the third element of vector b to be -34.5381, and finally determine the initial parameters of the relative orbit.

[0087] S3.8. Determined by the periodic conditions of the relative flyby orbit And the no-offset condition determines y0=-0.3392, and finally all the initial parameters of the relative flyby orbit are obtained.

[0088] The above content is only for explaining the technical idea of ​​the present invention and cannot be used to limit the protection scope of the present invention. Any changes made on the basis of the technical solution in accordance with the technical idea proposed by the present invention shall fall within the protection scope of the claims of the present invention.

Claims

1. A space station companion satellite orbit design method for space debris threat warning, characterized in that: The following steps are involved: S1. Obtaining the azimuth coordinates of space debris with a collision risk, and determining a corresponding expected detection distance based on the azimuth coordinates; S2. Establish a parameterized expression of relative orbit based on the CW equation; S3. Calculating undetermined parameters in a parameterized expression of a relative flyby orbit according to the azimuth coordinates of the space debris with a collision risk and the corresponding constraints of an expected detection distance; S4. Determine a set of relative initial states of the relative flyby orbit based on the calculated undetermined parameters; launching a satellite into the orbit; S2 is specifically: S2.

1. Analyze the geometric characteristics of periodic solutions of CW equations; S2.

2. Establish the parametric equation of the space ellipse; S2.

3. Establish a parametric expression for the relative flyby orbit based on the parametric equation of the space ellipse; S2 includes the following steps: S2.

1. Based on the geometric characteristics of the periodic solution of the CW equation, the relative orbit is considered to be a plane passing through the origin. With elliptical cylinder The set of intersections of , so any relative motion trajectory around the space platform can be controlled using three independent variables To uniquely determine, and Represents planes The normal vector and Axis and The angle in the positive direction of the axis is in the range of ; Elliptical cylinder The semi-major axis of the base ellipse; S2.

2. The orbit around the space station is described by the parametric equation of the space ellipse. The parametric equation of the space ellipse is: （1） Where, represents the coordinates of the center of the space ellipse, represents a space vector located within the space ellipse, Indicates that it is located within the elliptical surface of space and is mutually perpendicular space vectors; Combining formula (1), the periodic solution of the CW equation can be rewritten as follows: （2） S2.

3. By comparing equations (1) and (2), the parameterized expression of the relative flyby orbit is obtained as follows: （3） in: （4）； The elliptical cylinder The bottom surface is a major semi-axis With the minor axis The ratio is ellipse; S2.3 also includes: The triplet variable describing the size and direction of the relative orbit use and express: （5）； S3 specifically: S3.

1. Obtain the collision threat azimuth coordinates and expected detection range; S3.

2. Determine the first undetermined parameter based on the collision threat azimuth coordinates and the expected detection range ; S3.3, according to Calculate the normal vector relative to the orbit plane ; S3.4, according to Determine the second pending parameter ; The S3 implementation steps are as follows: S3.

1. Obtain the azimuth vector of the impact direction of the space debris relative to the origin of the LVLH coordinate system of the space platform And the expected detection distance ; S3.2, according to the orientation vector And the expected detection distance Evaluate vectors in parameterized relative motion equations , ; S3.

3. Calculate the normal vector of the orbital plane using the properties of the vector product , or ; S3.4, by the normal vector of the orbital plane Calculating vectors The unit vector of ; Vector-based Substitute into formula (4) to determine the initial parameters of the relative flyby orbit 、 as well as ; According to the calculation 、 、 Calculate the vector The first and second elements of ; S4 is specifically: S4.

1. Vector The third element of the vector is taken as the unknown quantity, combined with Solve for the vector by its relationship to its unit vector The third element of the relative orbital initial parameters is determined ; S4.

2. Periodic conditions of relative flyby orbits and no offset conditions , and finally determine all the initial parameters of the relative flyby orbit.

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