A Design Method for Circular Satellite Formation Configuration in an Elliptic Reference Orbit Plane

Abstract

The present invention discloses a method for designing the configuration of a circular satellite formation in an elliptical reference orbit plane, including: S1, selecting the orbital elements of the reference satellite for the planar circular formation; S2, selecting the RIC coordinate system of the reference satellite in the elliptical orbit; S3, establishing the relative dynamics equation for the formation flight of the satellites in the elliptical reference orbit; S4, establishing the periodic solution of the linearized relative dynamics equation for the elliptical reference orbit; S5, giving the constraint conditions for the circular formation configuration in the elliptical orbit plane; S6, designing the parameters of the planar circular formation; S7, calculating the relative position and velocity parameters of the accompanying satellite at the initial moment in the RIC coordinate system of the reference satellite; S8, calculating the position and velocity parameters of the accompanying satellite at the initial moment in the geocentric inertial coordinate system; S9, calculating the orbital elements of the accompanying satellite at the initial moment to complete the design of the configuration of the planar circular formation satellites.

Description

Technical Field

[0001] The present invention belongs to the technical field of satellite technology integrated application systems, and particularly relates to a method for designing a circular satellite formation configuration in an elliptical reference orbit plane. Background Art

[0002] Satellite formation refers to a number of spacecraft flying in a certain configuration in space by using natural orbital characteristics or with slight control, working together to form a virtual instrument to complete specific functions. It is a new type of satellite integrated application technology, and the corresponding satellite group is called distributed satellites or formation satellites.

[0003] The proposal of satellite formation has opened up a new space for the application of satellites, especially small satellites. It breaks the concept of traditional spacecraft combined by hardware, puts forward an innovative idea of combining spacecraft according to mission requirements, expands the application scope of small satellites, and can complete many tasks that traditional spacecraft could not complete before, bringing revolutionary changes to the future space field.

[0004] Classical satellite formation configurations are designed using the C-W equation. Common configurations include serial formation, space circle formation, and horizontal circle formation. However, the C-W equation is only applicable to the case where the reference satellite orbit is a circular orbit.

[0005] Based on the C-W equation, an elliptical formation configuration of 2:1 can be designed in the reference satellite orbit plane, but a planar circular formation configuration cannot be designed. Summary of the Invention

[0006] In order to solve the technical problems existing in the background art, the present invention aims to provide a method for designing a circular satellite formation configuration in an elliptical reference orbit plane. By establishing the relative dynamic equation of satellite formation flight in an elliptical reference orbit and the periodic solution of the linearized relative dynamic equation in the elliptical reference orbit, combined with the constraints of the planar circular formation configuration, using the radius of the planar circular formation as the input parameter, the design of the planar circular formation configuration parameters is completed; the planar circular configuration parameters are converted into the relative position and velocity of the accompanying satellite relative to the reference satellite at the initial moment in the RIC coordinate system of the reference satellite in the elliptical orbit, and the position, velocity, and orbital elements of the accompanying satellite in the geocentric inertial coordinate system are calculated to complete the construction of the planar circular formation configuration.

[0007] In order to solve the technical problems, the technical solution of the present invention is as follows:

[0008] A method for designing a circular satellite formation configuration in an elliptical reference orbit plane, the method comprising:

[0009] S1: Select the orbital elements of the reference satellite of the planar circular formation;

[0010] S2: Select the RIC coordinate system of the reference satellite in the elliptical orbit;

[0011] S3: Based on steps S1 and S2, establish the relative dynamic equation for the formation flying of satellites in an elliptical reference orbit;

[0012] S4: Based on steps S1 and S2, establish the periodic solution of the linearized relative dynamic equation for the elliptical reference orbit;

[0013] S5: Construct the constraint conditions for the circular formation configuration in the elliptical orbit plane;

[0014] S6: Design the parameters for the circular formation in the plane;

[0015] S7: Based on steps S3 and S4 and the parameters of the circular formation in the plane, calculate the relative position and velocity parameters of the accompanying satellite at the initial moment in the RIC coordinate system of the reference satellite;

[0016] S8: Based on steps S1 and S7, calculate the position and velocity parameters of the accompanying satellite at the initial moment in the geocentric inertial coordinate system;

[0017] S9: Based on the position and velocity parameters obtained in step S8, calculate the orbital elements of the accompanying satellite at the initial moment to complete the design of the satellite configuration for the circular formation in the plane.

[0018] Furthermore, the selection method for the orbital elements of the reference satellite in step S1 includes:

[0019] S101: The semi-major axis a of the reference satellite's orbit has a value range of [6678 km, 43000 km], including low Earth orbits, medium Earth orbits, and high Earth orbits;

[0020] S102: The eccentricity e of the reference satellite's orbit has a value range of [0.01, 0.99];

[0021] S103: The inclination i of the reference satellite's orbit has a value range of [0°, 180°];

[0022] S104: The right ascension of the ascending node Ω of the reference satellite has a value range of [0°, 360°];

[0023] S105: The argument of perigee ω of the reference satellite has a value range of [0°, 360°];

[0024] S106: The true anomaly f of the reference satellite has a value range of [0°, 360°];

[0025] S107: The mean anomaly M of the reference satellite has a value range of [0°, 360°];

[0026] S108: The eccentric anomaly E of the reference satellite has a value range of [0°, 360°];

[0027] S109: Any combination of S101 - S108.

[0028] Furthermore, the step S2 of selecting the reference satellite RIC coordinate system in the elliptical orbit includes:

[0029] S201: The coordinate origin of the coordinate system is the centroid of the reference satellite;

[0030] S202: The x-axis direction of the coordinate system is the direction from the geocenter to the centroid of the reference satellite;

[0031] S203: The z-axis direction of the coordinate system is the normal direction of the reference satellite orbit;

[0032] S204: The y-axis direction of the coordinate system is determined by the right-hand rule.

[0033] Furthermore, the step S3 includes:

[0034] The mathematical model of the relative motion of the satellite formation in the elliptical reference orbit is:

[0035]

[0036] where μ is the Earth's gravitational constant, a is the semi-major axis of the reference satellite orbit selected in S1, e is the eccentricity of the reference satellite orbit selected in S1, f is the true anomaly of the reference satellite orbit selected in S1, [x y z] T is the projection of the position vector of the accompanying satellite relative to the reference satellite in the satellite formation on the x, y, and z axes of the RIC coordinate system, is the second derivative of x, y, and z with respect to time.

[0037] Furthermore, the step S4 includes:

[0038] The mathematical model of the periodic solution of the linearized relative dynamics equation in the elliptical reference orbit is:

[0039]

[0040]

[0041]

[0042]

[0043] where, e is the eccentricity of the reference satellite orbit selected in S1, f is the true anomaly of the reference satellite orbit selected in S1, [xy z] T is the projection of the position vector of the accompanying satellite relative to the reference satellite in the satellite formation on the x, y, and z axes of the RIC coordinate system, [x′y′z′] T is the first derivative of x, y, and z with respect to the true anomaly of the near-Earth point, and the subscript 0 is the initial time.

[0044] Further, the constraint conditions for constructing the circular formation configuration in the elliptical orbit plane in step S5 include:

[0045] The constraint conditions for the circular formation configuration in the elliptical orbit plane are:

[0046] x 2 +y 2 =R 2

[0047] where R is the radius of the circular formation in the plane, and x and y are the projections of the position vector of the accompanying satellite relative to the reference satellite in the formation on the x and y axes of the RIC coordinate system of the reference satellite.

[0048] Further, the parameters for designing the circular formation in the plane in step S6 include:

[0049] S601: Select the radius R of the circular formation in the plane, where the value range of R is [0.1 km, 200 km];

[0050] S602: The calculation formula for the position vector of the center of the circular formation in the plane relative to the reference satellite in the RIC coordinate system of the reference satellite is:

[0051]

[0052] where R is the radius of the circular formation selected in S601, e is the eccentricity of the orbit of the reference satellite selected in S1, + represents the positive direction of the y-axis of the RIC coordinate system of the reference satellite, and - represents the negative direction of the y-axis of the RIC coordinate system of the reference satellite.

[0053] Further, step S7 includes:

[0054] S701: In the RIC coordinate system of the reference satellite, the calculation formula for the initial position of the accompanying satellite in the x direction is:

[0055] x0 = Rsinf0

[0056] where R is the radius of the circular formation selected in S601, and f0 is the initial true anomaly of the orbit of the reference satellite selected in S1;

[0057] S702: In the RIC coordinate system of the reference satellite, the calculation formula for the initial position of the accompanying satellite in the y direction is:

[0058]

[0059] where R is the radius of the circular formation selected in S601, f0 is the initial true anomaly of the orbit of the reference satellite selected in S1, e is the eccentricity of the orbit of the reference satellite selected in S1, + represents the positive direction of the y-axis of the RIC coordinate system of the reference satellite, and - represents the negative direction of the y-axis of the RIC coordinate system of the reference satellite;

[0060] S703: In the RIC coordinate system of the reference satellite, the formula for calculating the initial position of the accompanying satellite in the y direction is:

[0061] z0 = 0

[0062] S704: In the RIC coordinate system of the reference satellite, the formula for calculating the initial velocity of the accompanying satellite in the x direction is:

[0063]

[0064] where R is the radius of the planar circular formation selected in S601, μ is the gravitational constant of the earth, a is the semi-major axis of the reference satellite orbit selected in S1, e is the eccentricity of the reference satellite orbit selected in S1, and f0 is the initial true anomaly of the reference satellite orbit selected in S1;

[0065] S705: In the RIC coordinate system of the reference satellite, the formula for calculating the initial velocity of the accompanying satellite in the y direction is:

[0066]

[0067] S706: In the RIC coordinate system of the reference satellite, the formula for calculating the initial position of the accompanying satellite in the z direction is:

[0068]

[0069] Furthermore, the step S8 includes:

[0070] S801: The formula for calculating the direction cosine matrix from the geocentric inertial coordinate system of the reference satellite to the RIC coordinate system is:

[0071]

[0072] where r and v are the position vector and velocity vector of the center of mass of the reference satellite in the geocentric inertial coordinate system at the initial moment, respectively;

[0073] S802: The formula for calculating the position vector of the accompanying satellite in the geocentric inertial coordinate system is:

[0074] r B = r + R T [x0 y0 z0] T

[0075] where r is the position vector of the center of mass of the reference satellite in the geocentric inertial coordinate system at the initial moment, R T is the transpose of the direction cosine matrix from the geocentric inertial coordinate system of the reference satellite to the RIC coordinate system in S801, and [x0 y0 z0] T is the relative position vector of the accompanying satellite at the initial moment in the RIC coordinate system of the reference satellite in S7;

[0076] S803: The calculation formula for the velocity vector of the accompanying satellite in the geocentric inertial coordinate system is as follows:

[0077]

[0078] where v is the position vector of the centroid of the reference satellite at the initial moment in the geocentric inertial coordinate system, and R T is the transpose of the direction cosine matrix from the geocentric inertial coordinate system of the reference satellite to the RIC coordinate system in S801, and [x0 y0 z0] T is the relative position vector of the accompanying satellite at the initial moment in the RIC coordinate system of the reference satellite in S7, is the relative velocity vector of the accompanying satellite at the initial moment in the RIC coordinate system of the reference satellite in S7, μ is the gravitational constant of the earth, a is the semi-major axis of the reference satellite orbit selected in S1, e is the eccentricity of the reference satellite orbit selected in S1, and f0 is the initial true anomaly of the reference satellite orbit selected in S1.

[0079] Furthermore, the step S9 includes:

[0080] S901: The calculation formula for the orbital angular momentum of the accompanying satellite is as follows:

[0081] h = r B × v B

[0082] where r B and v B are respectively the position vector and velocity vector of the centroid of the accompanying satellite at the initial moment in the geocentric inertial coordinate system in S8;

[0083] S902: The calculation formula for the orbital eccentricity of the accompanying satellite is as follows:

[0084]

[0085] e = |e|

[0086] where μ is the gravitational constant of the earth, h is the orbital angular momentum of the accompanying satellite in S901, and r B and v B are respectively the position vector and velocity vector of the centroid of the accompanying satellite at the initial moment in the geocentric inertial coordinate system in S8, and |·| represents taking the modulus of the vector;

[0087] S903: The calculation formula for the orbital inclination of the accompanying satellite is as follows:

[0088]

[0089] where h is the orbital angular momentum of the accompanying satellite in S901, and h z is the component of h on the z-axis in the geocentric inertial coordinate system;

[0090] S904: The formula for calculating the right ascension of the ascending node of the accompanying satellite upgrade point is:

[0091] Ω = arctan(h x , -h y )

[0092] where h x and h y are the components of the orbital angular momentum h of the accompanying satellite in the x and y axes of the geocentric inertial coordinate system in S901, respectively;

[0093] S905: The formula for calculating the semi-major axis of the accompanying satellite orbit is:

[0094]

[0095] where μ is the gravitational constant of the Earth, h is the magnitude of the orbital angular momentum h of the accompanying satellite in S901, and e is the orbital eccentricity of the accompanying satellite in S902;

[0096] S906: The formula for calculating the argument of perigee of the accompanying satellite is:

[0097] i n = [0 0 1] × h

[0098]

[0099] where h is the orbital angular momentum of the accompanying satellite in S901, and e is the eccentricity vector of the accompanying satellite in S902;

[0100] S906. The formula for calculating the true anomaly of the accompanying satellite is:

[0101]

[0102] where r B is the position vector of the centroid of the accompanying satellite at the initial moment in the geocentric inertial coordinate system in S8, e is the eccentricity vector of the accompanying satellite in S902, and |·| represents taking the modulus of the vector.

[0103] Compared with the prior art, the advantages of the present invention are:

[0104] The present invention proposes a method for designing the formation configuration of circular satellites in an elliptical reference orbit plane. Through the proposed method, the satellite orbits for flying in formation in the elliptical reference orbit plane can be designed, breaking through the traditional method of designing the formation satellite configuration based on the C-W equation, and designing a brand-new formation configuration. The designed circular formation configuration in the plane can be used in and is not limited to fields such as the observation of space targets, the remote sensing of ground resources, and the close inspection of target satellites.

[0105] Accuracy and systematicness: Through detailed steps and mathematical models, from selecting orbital parameters to calculating initial conditions and then determining orbital elements, the entire process ensures the accuracy of design and calculation.

[0106] Wide applicability: This method covers various orbital types, including low Earth orbits, medium orbits, and high orbits, and is applicable to the design of satellite formations with various orbital eccentricities and orbital inclinations.

[0107] Utilization of reference frame: By introducing the RIC coordinate system, the relative motion of the accompanying satellite is described more intuitively, and the derivation and solution of the dynamic model are simplified.

[0108] Establishment of periodic solutions: Using the periodic solutions of the linearized relative dynamic equations helps to understand and design the periodic motion characteristics of the formation, making it more feasible to maintain the formation under dynamic conditions.

[0109] Design flexibility: By introducing various parameter selections and calculation methods in the steps, this method allows for customized design of specific formation configurations according to different mission requirements.

[0110] Efficiency improvement: Through systematic steps and a clear sequence, designers can complete the formation design efficiently, reducing the cost of trial and error and the need for complex calculations.

[0111] Generally speaking, the present invention provides an efficient and accurate solution for the design of satellite formations in elliptical orbits through clear steps and detailed mathematical models, and is particularly suitable for space missions that require precise control and long-term stability. These advantages are of great significance in improving the success rate and service life of spacecraft formation missions. Brief description of the drawings

[0112] Figure 1 A flowchart of the design of a circular formation satellite configuration in the elliptical orbit plane according to an embodiment of the present invention;

[0113] Figure 2 An example diagram of the left-side plane circular formation configuration according to an embodiment of the present invention;

[0114] Figure 3 An example diagram of the right-side plane circular formation configuration according to an embodiment of the present invention;

[0115] Figure 4 An example diagram of the bilateral plane circular formation configuration according to an embodiment of the present invention. Detailed implementation manners

[0116] The following describes the specific implementation manners of the present invention in conjunction with embodiments:

[0117] It should be noted that the structures, ratios, sizes, etc. shown in this specification are only used to cooperate with the content disclosed in the specification for those familiar with this technology to understand and read, and are not used to limit the implementation conditions of the present invention. Any modification of the structure, change of the proportional relationship or adjustment of the size, without affecting the effects that the present invention can produce and the purposes that can be achieved, should still fall within the scope covered by the technical content disclosed in the present invention.

[0118] At the same time, the terms such as "upper", "lower", "left", "right", "middle" and "one" cited in this specification are only for the convenience of clear narration, and are not used to limit the scope of implementation of the present invention. The change or adjustment of their relative relationship, without substantial change in the technical content, should also be regarded as the scope of implementation of the present invention.

[0119] Embodiment 1:

[0120] The present invention provides a method for designing the configuration of a circular satellite formation in an elliptical reference orbit plane. By establishing the relative dynamic equation of satellite formation flight in an elliptical reference orbit and the periodic solution of the linearized relative dynamic equation in the elliptical reference orbit, it breaks through the traditional method of designing the formation satellite configuration based on the C-W equation. Combining the constraints of the planar circular formation configuration, taking the radius of the planar circular formation as the input parameter, completing the design of the planar circular formation configuration parameters, converting the planar circular configuration parameters into the relative position and velocity of the accompanying satellite relative to the reference satellite at the initial moment in the RIC coordinate system of the reference satellite in the elliptical orbit, and calculating the orbital elements of the accompanying satellite, a new formation configuration is designed.

[0121] According to this method, the left planar circular formation configuration, the right planar circular formation configuration, and the bilateral planar circular formation configuration can be quickly designed. This configuration can be used in, but not limited to, the fields of observing space targets, remote sensing of ground resources, and approaching inspection of target satellites.

[0122] In this embodiment, taking a formation satellite in an elliptical reference orbit as an example, the left planar circular, right planar circular, and bilateral planar circular formation configurations are designed. The orbital elements of the elliptical reference orbit at the initial moment are: semi-major axis of the orbit 20000 km, orbital eccentricity 0.6, orbital inclination 30°, right ascension of the ascending node 0°, argument of perigee 0°, true anomaly 0°, and radius of the planar circle 10 km.

[0123] As Figure 1 shown, an embodiment of the present invention provides a flowchart for designing the configuration of a circular formation satellite in an elliptical orbit. The specific steps include:

[0124] S1. Select the orbital elements of the reference satellite of the planar circular formation.

[0125] In an embodiment of the present invention, the initial elliptical reference orbit elements are as follows: the semi-major axis of the orbit is 20,000 km, the orbital eccentricity is 0.6, the orbital inclination is 30°, the right ascension of the ascending node is 0°, the argument of perigee is 0°, and the true anomaly is 0°

[0126] S2. Select the reference satellite RIC coordinate system of the elliptical orbit.

[0127] In an embodiment of the present invention, the origin of the RIC coordinate system is the center of mass of the reference satellite. The x-axis direction of the coordinate system is the direction from the Earth's center to the center of mass of the reference satellite, the z-axis direction of the coordinate system is the normal direction of the reference satellite's orbit, and the y-axis direction of the coordinate system is determined by the right-hand rule.

[0128] S3. Establish the relative dynamics equation for the formation flight of satellites in the elliptical reference orbit.

[0129] In an embodiment of the present invention, the relative dynamics equation is:

[0130]

[0131] S4. Establish the periodic solution of the linearized relative dynamics equation for the elliptical reference orbit.

[0132] In an embodiment of the present invention, the periodic solution of the linearized relative dynamics equation for the elliptical reference orbit is:

[0133]

[0134]

[0135]

[0136]

[0137] S5. Give the constraint conditions for the circular formation configuration in the elliptical orbit plane.

[0138] In an embodiment of the present invention, the constraint conditions for the circular formation configuration are:

[0139] x 2 +y 2 =R 2

[0140] S6. Design the parameters of the circular formation in the plane.

[0141] In an embodiment of the present invention, the radius R of the circular formation in the plane is taken as 10 km;

[0142] The calculation formula for the position vector of the center of the circular formation in the plane relative to the reference satellite in the RIC coordinate system of the reference satellite is:

[0143]

[0144] In one embodiment of the present invention, the position vector of the center of the planar circular formation is The ‘+’ indicates the right-side planar circular formation configuration, the ‘-’ indicates the left-side planar circular formation configuration, and the ‘±’ indicates the bilateral planar circular formation configuration.

[0145] S7. Calculate the relative position and velocity parameters of the accompanying satellite at the initial moment in the reference satellite RIC coordinate system.

[0146] S8. Calculate the position and velocity parameters of the accompanying satellite at the initial moment in the geocentric inertial coordinate system.

[0147] In one embodiment of the present invention, the calculation method of the position and velocity parameters;

[0148] The calculation method of the initial position of the accompanying satellite in the x direction is:

[0149] x0 = Rsinf0

[0150] The calculation method of the initial position of the accompanying satellite in the y direction is:

[0151]

[0152] The calculation method of the initial position of the accompanying satellite in the y direction is:

[0153] z0 = 0

[0154] The calculation method of the initial velocity of the accompanying satellite in the x direction is:

[0155]

[0156] The calculation method of the initial velocity of the accompanying satellite in the y direction is:

[0157]

[0158] The calculation method of the initial position of the accompanying satellite in the z direction is:

[0159]

[0160] S9. Calculate the orbital elements of the accompanying satellite at the initial moment, and complete the design of the planar circular formation satellite configuration.

[0161] In one embodiment of the present invention, the designed left-side planar circular formation configuration is as Figure 2 shown.

[0162] In one embodiment of the present invention, the designed right-side planar circular formation configuration is as Figure 3 shown.

[0163] In one embodiment of the present invention, the designed bilateral planar circular formation configuration is asFigure 4 as shown

[0164] Those skilled in the art should understand that the embodiments of the present invention can be provided as a method, a system, or a computer program product. Therefore, the present invention can take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present invention can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk memory, CD-ROM, optical memory, etc.) containing computer-usable program code.

[0165] The present invention is described with reference to the flowcharts and / or block diagrams of methods, apparatuses (systems), and computer program products according to embodiments of the present invention. It should be understood that each flow and / or block in the flowcharts and / or block diagrams, and the combination of flows and / or blocks in the flowcharts and / or block diagrams, can be realized by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing devices generate means for realizing the functions specified in Figure 1 one or more of the flows Figure 1 or a plurality of flows and / or blocks

[0166] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer-readable memory generate a manufactured article including instruction means, and the instruction means realizes the functions specified in Figure 1 one or more of the flows Figure 1 or a plurality of flows and / or blocks

[0167] These computer program instructions can also be loaded onto a computer or other programmable data processing device, so that a series of operation steps are executed on the computer or other programmable device to generate a computer-implemented process, and thus the instructions executed on the computer or other programmable device provide steps for realizing the functions specified in Figure 1 one or more of the flows Figure 1 or a plurality of flows and / or blocks

[0168] The preferred embodiments of the present invention are described in detail above, but the present invention is not limited to the above embodiments. Within the knowledge scope of those of ordinary skill in the art, various changes can be made without departing from the gist of the present invention.

[0169] Many other changes and modifications can be made without departing from the spirit and scope of the present invention. It should be understood that the present invention is not limited to the specific embodiments, and the scope of the present invention is defined by the appended claims.

Claims

1. A method for designing a circular satellite formation configuration in an elliptical reference orbit plane, characterized in that: The method comprises: S1: Select the orbital elements of the reference satellite of the plane circle formation; S2: Select the elliptical orbit reference satellite RIC coordinate system; S3: Based on steps S1 and S2, a relative dynamic equation of the satellite formation flying in the elliptical reference orbit is established; The step S3 comprises: The mathematical model of the relative motion of satellite formations in an elliptical reference orbit is: where μ is the Earth's gravitational constant, a is the semi-major axis of the reference satellite orbit selected by S1, e is the eccentricity of the reference satellite orbit selected by S1, f is the true anomaly angle of the reference satellite orbit selected by S1, [x yz] T is the projection of the position vector of the companion satellite in the formation relative to the reference satellite on the x, y, and z axes of the RIC coordinate system, is the second-order derivative of x, y, and z with respect to time; S4: Based on steps S1 and S2, a periodic solution of the linearized relative dynamic equation of the elliptical reference orbit is established; S5: Constraints for constructing the plane circle formation configuration of elliptical orbits; S6: Design plane circle formation parameters; S7: Based on the steps S3 and S4 and the plane circle formation parameters, the relative position velocity parameters of the companion satellite in the reference satellite RIC coordinate system at the initial moment are calculated; S8: Based on steps S1 and S7, calculate the position and velocity parameters of the companion satellite in the geocentric inertial coordinate system at the initial moment; S9: Based on the position and velocity parameters obtained in step S8, the orbital elements of the companion satellite at the initial moment are calculated to complete the satellite configuration design of the plane circular formation.

2. The method for designing a circular satellite formation configuration in an elliptical reference orbit plane according to claim 1, characterized in that: The step S1 refers to the satellite orbit element number selection method, including: S101: reference satellite orbit semi-major axis a, value range [6678km, 43000km], including low Earth orbit, medium Earth orbit and high Earth orbit; S102: reference satellite orbit eccentricity e, value range [0.01, 0.99]; S103: Reference satellite orbit inclination angle i, value range [0°, 180°]; S104: right ascension Ω of the reference satellite ascending node, with a value range of [0°, 360°]; S105: reference satellite perigee angle ω, value range [0°, 360°]; S106: reference satellite true anomaly f, value range [0°, 360°]; S107: reference satellite mean anomaly angle M, value range [0°, 360°]; S108: reference satellite anomaly angle E, value range [0°, 360°]; S109: Any combination of S101-S108.

3. The method for designing a circular satellite formation configuration in an elliptical reference orbit plane according to claim 1, characterized in that: The step S2 selects the elliptical orbit reference satellite RIC coordinate system, including: S201: origin of coordinate system, reference satellite mass center; S202: In the x-axis direction of the coordinate system, the center of the earth points to the center of mass of the reference satellite; S203: coordinate system z-axis direction, reference satellite orbit normal direction; S204: The y-axis direction of the coordinate system is determined by the right-hand rule.

4. The method for designing a circular satellite formation configuration in an elliptical reference orbit plane according to claim 1, characterized in that: The step S4 comprises: The mathematical model of the periodic solution of the linearized relative dynamics equation of the elliptical reference orbit is: Where, e is the eccentricity of the reference satellite orbit selected by S1, f is the true anomaly angle of the reference satellite orbit selected by S1, [x yz] T is the projection of the position vector of the companion satellite in the formation relative to the reference satellite on the x, y, and z axes of the RIC coordinate system, [x′ y′z′] T is the first-order derivative of x, y, and z relative to the true perigee angle, and the subscript 0 is the initial moment.

5. The method for designing a circular satellite formation configuration in an elliptical reference orbit plane according to claim 1, characterized in that: The step S5 constructs the constraint conditions of the elliptical orbit plane circle formation configuration, including: The constraints of the elliptical orbit plane circle formation configuration are: x 2 +y 2 =R 2 Where R is the radius of the plane circle formation, and x and y are the projections of the position vector of the companion satellite in the formation relative to the reference satellite on the x and y axes of the RIC coordinate system.

6. The method for designing a circular satellite formation configuration in an elliptical reference orbit plane according to claim 1, characterized in that: The step S6 designs the plane circle formation parameters, including: S601: Select the radius R of the plane circle formation, where R is in the range of [0.1km, 200km]; S602: The calculation formula of the position vector of the center of the plane circle formation relative to the reference satellite in the reference satellite RIC coordinate system is: Where R is the radius of the plane circle formation selected by S601, e is the eccentricity of the reference satellite orbit selected by S1, + represents the positive direction of the y-axis of the reference satellite RIC coordinate system, and - represents the negative direction of the y-axis of the reference satellite RIC coordinate system.

7. The method for designing a circular satellite formation configuration in an elliptical reference orbit plane according to claim 6, characterized in that: The step S7 comprises: S701: In the reference satellite RIC coordinate system, the calculation formula for the initial position of the companion satellite in the x direction is: x0=Rsinf0 Where R is the radius of the plane circle formation selected by S601, and f0 is the initial true anomaly angle of the reference satellite orbit selected by S1; S702: In the reference satellite RIC coordinate system, the calculation formula for the initial position of the companion satellite in the y direction is: Where R is the radius of the plane circle formation selected by S601, f0 is the initial true anomaly of the reference satellite orbit selected by S1, e is the eccentricity of the reference satellite orbit selected by S1, + represents the positive direction of the y-axis of the reference satellite RIC coordinate system, and - represents the negative direction of the y-axis of the reference satellite RIC coordinate system; S703: In the reference satellite RIC coordinate system, the calculation formula for the initial position of the companion satellite in the y direction is: z0＝0 S704: In the reference satellite RIC coordinate system, the calculation formula for the initial velocity of the companion satellite in the x direction is: Where R is the radius of the plane circle formation selected by S601, where μ is the Earth’s gravitational constant, a is the semi-major axis of the reference satellite orbit selected by S1, e is the eccentricity of the reference satellite orbit selected by S1, and f0 is the initial true anomaly angle of the reference satellite orbit selected by S1; S705: In the reference satellite RIC coordinate system, the calculation formula for the initial velocity of the companion satellite in the y direction is: S706: In the reference satellite RIC coordinate system, the calculation formula for the initial position of the companion satellite in the z direction is:

8. The method for designing a circular satellite formation configuration in an elliptical reference orbit plane according to claim 1, characterized in that: The step S8 comprises: S801: The calculation formula of the direction cosine matrix from the reference satellite geocentric inertial coordinate system to the RIC coordinate system is: Where r and v are the position vector and velocity vector of the reference satellite's center of mass in the geocentric inertial coordinate system at the initial moment, respectively; S802: The calculation formula of the position vector of the companion satellite in the Earth-centered inertial coordinate system is: r B =r+R T [x0 y0 z0] T Where r is the position vector of the reference satellite mass center in the geocentric inertial coordinate system at the initial moment, R T is the transpose of the direction cosine matrix from the reference satellite geocentric inertial coordinate system to the RIC coordinate system in S801, [x0 y0 z0] T is the relative position vector of the companion satellite in S7 at the initial time in the reference satellite RIC coordinate system; S803: The velocity vector calculation formula in the Earth-centered inertial coordinate system of the companion satellite is: Where v is the position vector of the reference satellite mass center in the geocentric inertial coordinate system at the initial moment, R T is the transpose of the direction cosine matrix from the reference satellite geocentric inertial coordinate system to the RIC coordinate system in S801, [x0 y0 z0] T is the relative position vector of the companion satellite in S7 at the initial time in the reference satellite RIC coordinate system, is the relative velocity vector of the companion satellite in S7 in the reference satellite RIC coordinate system at the initial moment, μ is the earth's gravitational constant, a is the semi-major axis of the reference satellite orbit selected by S1, e is the eccentricity of the reference satellite orbit selected by S1, and f0 is the initial true anomaly angle of the reference satellite orbit selected by S1.

9. The method for designing a circular satellite formation configuration in an elliptical reference orbit plane according to claim 1, characterized in that: The step S9 comprises: S901: The calculation formula of the companion satellite orbital angular momentum is: h=r B ×v B where r B 、v B are the position vector and velocity vector of the satellite's mass center in the geocentric inertial coordinate system at the initial moment in S8, respectively; S902: The calculation formula for the companion satellite orbit eccentricity is: e=|e| where μ is the Earth's gravitational constant, h is the orbital angular momentum of the companion satellite in S901, and r B 、v B are the position vector and velocity vector of the satellite mass center in the geocentric inertial coordinate system at the initial moment in S8, respectively, and |·| represents the vector modulus; S903: The calculation formula for the companion satellite orbit inclination is: where h is the orbital angular momentum of the companion satellite in S901, h z is the component of h along the z axis in the geocentric inertial coordinate system; S904: The calculation formula for the right ascension of the companion satellite upgrade point is: Ω=arctan(h x ,-h y ) where h x 、h y are the x-axis and y-axis components of the companion satellite orbital angular momentum h in S901 in the geocentric inertial coordinate system; S905: The calculation formula for the semi-major axis of the companion satellite orbit is: Where μ is the Earth's gravitational constant, h is the modulus of the companion satellite's orbital angular momentum h in S901, and e is the companion satellite's orbital eccentricity in S902; S906: The calculation formula for the companion satellite perigee angle is: i n =[0 0 1]×h Where h is the orbital angular momentum of the companion satellite in S901, and e is the eccentricity vector of the companion satellite in S902; S906, the calculation formula of the true anomaly angle of the companion satellite is: where r B is the position vector of the companion satellite mass center in the geocentric inertial coordinate system at the initial moment in S8, e is the companion satellite eccentricity vector in S902, and |·| represents the vector modulus.

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