A method, system and device for calculating the relative motion period of spacecraft water droplet configuration

Abstract

The present invention proposes a method, system and equipment for calculating the relative motion period of a spacecraft water droplet configuration, which relates to the technical field of spacecraft orbital motion design. The orbital parameters of the target spacecraft and the tracking spacecraft are set, and the orbital elements and operating parameters of the target spacecraft and the tracking spacecraft are calculated respectively based on the orbital parameters; the motion trajectory direction of the water droplet configuration of the tracking spacecraft relative to the target spacecraft is determined based on the orbital parameters, orbital elements and operating parameters; the true anomaly angle difference of the tracking spacecraft is iteratively solved based on the orbital elements, orbital parameters and trajectory data of the motion trajectory direction of the water droplet configuration, and the relative motion period of the water droplet configuration is calculated based on the true anomaly angle difference. The present invention is completely based on the calculation of the spacecraft according to the orbital elements, does not rely on the specific relative motion equation, and directly obtains the relative motion period of the water droplet configuration according to the orbital elements of the spacecraft. The calculation is stable, convenient and accurate, the physical meaning is clear and easy to understand, and it is suitable for practical engineering applications.

Description

Technical Field

[0001] The present invention relates to the technical field of spacecraft orbital motion design, and in particular to a method, system and device for calculating the relative motion period of a spacecraft water droplet configuration. Background Art

[0002] A teardrop configuration refers to a spacecraft's motion trajectory relative to another spacecraft, achieved by applying control at specific locations. This relative motion not only allows two spacecraft to maintain their radial relative positions for extended periods while consuming minimal energy, but also allows for a flyby period shorter than the natural orbital period. Therefore, this configuration holds significant practical value for space applications and has garnered extensive research.

[0003] Traditional research methods rely on the Hill equations to conduct analysis and studies under various application conditions. Specifically, they conduct research based on the equations of motion obtained by linearizing and simplifying the relative motion equations of two spacecraft. This research and calculation approach not only results in a loss of computational accuracy, making the results difficult to directly apply in engineering practice, but also, because this approach, based on the relative motion equations of two spacecraft, inherently ignores the orbital characteristics of the spacecraft themselves, transforming the spacecraft orbital problem, which has intuitive physical properties, into an unintuitive mathematical problem, which somewhat hinders understanding of the mechanism. Furthermore, because the analysis is not based on the orbital elements of the spacecraft, this creates certain inconveniences in practical applications based on orbital elements. For water droplet configurations, the configuration period has a clear correspondence with the orbital elements of the two spacecraft. Studies based on the linearization of the relative motion equations cannot provide a physical relationship between the orbital elements and the configuration period.

[0004] In view of the shortcomings of the existing technology, it is necessary to provide a method, system and equipment for calculating the relative motion period of spacecraft water droplet configuration that can solve the problems raised in the above background technology. Summary of the Invention

[0005] The purpose of the present invention is to provide a method, system and equipment for calculating the relative motion period of water droplet configuration in spacecraft, which can propose solutions to the shortcomings of the existing technology and calculate the relative motion period of water droplet configuration based on the number of spacecraft orbital elements. Compared with the traditional linearization method of relative motion equations, it has the advantages of clear physical meaning, high calculation accuracy, direct and convenient application.

[0006] An embodiment of the present invention provides a method for calculating the relative motion period of a spacecraft water droplet configuration, comprising the following steps:

[0007] Setting orbital parameters of the target spacecraft and the tracking spacecraft, and calculating the orbital elements and operating parameters of the target spacecraft and the tracking spacecraft respectively based on the orbital parameters; wherein the orbital parameters of the target spacecraft include the geocentric distance, and the orbital parameters of the tracking spacecraft include the geocentric distance of perigee and the geocentric distance of apogee;

[0008] determining a motion trajectory direction of the water droplet configuration of the tracking spacecraft relative to the target spacecraft based on the orbital parameters, the number of orbital elements, and the operating parameters, wherein the motion trajectory direction includes a relative direction between a smooth vertex and a direction switching point of the water droplet configuration;

[0009] The true anomaly angle difference of the tracking spacecraft is iteratively solved according to the number of orbital elements, the orbital parameters and the trajectory data of the motion trajectory direction of the water drop configuration, and the relative motion period of the water drop configuration is calculated according to the true anomaly angle difference.

[0010] In some embodiments of the present invention, the steps of setting the orbital parameters of the target spacecraft and the tracking spacecraft, and calculating the orbital elements and operating parameters of the target spacecraft and the tracking spacecraft respectively based on the orbital parameters include:

[0011] Set the target spacecraft's geocentric distance r T , set the perigee distance of the tracking spacecraft Apogee geocentric distance

[0012] According to the tracking spacecraft's perigee distance and apogee geocentric distance Calculate the orbital elements of the tracking spacecraft, wherein the orbital elements include the semi-major axis a C , eccentricity e C and semi-diameter P C Calculate the operating parameters of the tracking spacecraft based on the orbital elements of the tracking spacecraft, wherein the operating parameters include the perigee angular velocity w max and the apogee angular velocity w min ;

[0013] According to the distance r from the center of the Earth of the target spacecraft T Calculate the operating parameters of the target spacecraft, wherein the operating parameters include the angular velocity w T .

[0014] In some embodiments of the present invention, the step of determining the direction of the motion trajectory of the water droplet configuration of the tracking spacecraft relative to the target spacecraft based on the orbital parameters, the orbital element number, and the operating parameters includes:

[0015] determining, based on a magnitude relationship between operating parameters of the tracking spacecraft and the target spacecraft, whether the motion trajectory of the tracking spacecraft forms a water droplet configuration;

[0016] When the motion trajectory of the tracking spacecraft forms a water drop configuration, the direction of the motion trajectory of the tracking spacecraft relative to the target spacecraft is determined based on the relationship between the semi-major axis of the tracking spacecraft and the distance from the center of the earth to the target spacecraft.

[0017] In some embodiments of the present invention, the step of determining whether the motion trajectory of the tracking spacecraft forms a water droplet configuration based on the magnitude relationship between the operating parameters of the tracking spacecraft and the target spacecraft includes:

[0018] When w min >w T or w max <w T , then the motion trajectory of the tracking spacecraft cannot form a water droplet configuration;

[0019] When w min ≤w T or w max ≥w T , then the motion trajectory of the tracking spacecraft can form a water droplet configuration.

[0020] In some embodiments of the present invention, the step of determining the direction of the motion trajectory of the water droplet configuration of the tracking spacecraft relative to the target spacecraft based on the relationship between the semi-major axis of the tracking spacecraft and the distance from the center of the Earth to the target spacecraft includes:

[0021] When the semi-major axis a of the tracking spacecraft C Less than the distance r from the center of the Earth to the target spacecraft T , the smooth vertex of the water drop configuration is located above the direction switching point;

[0022] When the semi-major axis a of the tracking spacecraft C Greater than the distance r from the center of the Earth to the target spacecraft T , the smooth vertex of the water drop configuration is located below the direction switching point.

[0023] In some embodiments of the present invention, the step of iteratively solving the true anomaly difference of the tracking spacecraft based on the number of orbital elements, the orbital parameters, and the trajectory data of the motion trajectory direction of the water droplet configuration, and calculating the relative motion period of the water droplet configuration based on the true anomaly difference includes:

[0024] When the smooth vertex of the water droplet configuration is above the direction switching point, the true anomaly Δf of the tracking spacecraft is iteratively solved according to the orbital elements, the orbital parameters and the trajectory data of the water droplet configuration. down , the calculation formula is:

[0025]

[0026] in,

[0027]

[0028]

[0029]

[0030]

[0031] Among them, α and β represent intermediate variables, s represents half of the perimeter of the triangle connecting the starting point, end point and the center of the earth, c represents the straight-line distance between the starting point and end point of the water droplet configuration orbit transfer, r down Represents the distance from the center of the earth at the direction switching point, μ e represents the Earth's gravitational constant;

[0032] The relative motion period T of the water droplet configuration is calculated based on the true anomaly angle difference, and the calculation formula is:

[0033]

[0034] In some embodiments of the present invention, the step of iteratively solving the true anomaly error of the tracking spacecraft based on the number of orbital elements, the orbital parameters, and the trajectory data of the motion trajectory direction of the water droplet configuration, and calculating the relative motion period of the water droplet configuration based on the true anomaly error, further includes:

[0035] When the smooth vertex of the water droplet configuration is below the direction switching point, the true anomaly Δf of the tracking spacecraft is iteratively solved according to the orbital elements, the orbital parameters and the trajectory data of the water droplet configuration. up , the calculation formula is:

[0036]

[0037] in,

[0038]

[0039]

[0040]

[0041]

[0042]

[0043] Among them, α and β represent intermediate variables, s represents half of the perimeter of the triangle connecting the starting point, end point and the center of the earth, c represents the straight-line distance between the starting point and end point of the water droplet configuration orbit transfer, r up Represents the distance from the center of the earth at the direction switching point, μ e represents the Earth's gravitational constant;

[0044] The relative motion period T of the water droplet configuration is calculated based on the true anomaly angle difference, and the calculation formula is:

[0045]

[0046] In some embodiments of the present invention, the Δf down and the Δf up The initial value of the iteration is selected as 90°.

[0047] An embodiment of the present invention further provides a system for calculating the relative motion period of a spacecraft water droplet configuration based on orbital elements, comprising:

[0048] a parameter calculation module, configured to set the orbital parameters of the target spacecraft and the tracking spacecraft, and to calculate the orbital elements and operating parameters of the target spacecraft and the tracking spacecraft respectively based on the orbital parameters; wherein the orbital parameters of the target spacecraft include the geocentric distance, and the orbital parameters of the tracking spacecraft include the geocentric distance of perigee and the geocentric distance of apogee;

[0049] a motion trajectory direction determination module, configured to determine a motion trajectory direction of the water droplet configuration of the tracking spacecraft relative to the target spacecraft based on the orbital parameters, the number of orbital elements, and the operating parameters, wherein the motion trajectory direction includes the relative direction of the smooth vertex and the direction switching point of the water droplet configuration;

[0050] The relative motion period calculation module is used to iteratively solve the true anomaly angle difference of the tracking spacecraft based on the number of orbital elements, the orbital parameters and the trajectory data of the motion trajectory direction of the water droplet configuration, and calculate the relative motion period of the water droplet configuration based on the true anomaly angle difference.

[0051] An embodiment of the present invention further provides a device, characterized in that it includes a processor, a memory, and a computer program stored in the memory and capable of running on the processor, and when the computer program is executed by the processor, it implements the method according to any one of claims 1 to 8.

[0052] Compared with the prior art, the embodiments of the present invention have at least the following advantages or beneficial effects:

[0053] The present invention sets the orbital parameters of a target spacecraft and a tracking spacecraft, and calculates the orbital elements and operating parameters of the target spacecraft and the tracking spacecraft respectively based on the orbital parameters; wherein the orbital parameters of the target spacecraft include the distance from the center of the Earth, and the orbital parameters of the tracking spacecraft include the distance from the center of the Earth to the center of the Earth at perigee and the distance from the center of the Earth to the center of the Earth at apogee; determines the motion trajectory direction of the water droplet configuration of the tracking spacecraft relative to the target spacecraft based on the orbital parameters, the orbital elements, and the operating parameters, wherein the motion trajectory direction includes the relative direction of the smooth vertex and the direction switching point of the water droplet configuration; iteratively solves the true anomaly angle difference of the tracking spacecraft based on the orbital elements, the orbital parameters, and the trajectory data of the motion trajectory direction of the water droplet configuration, and calculates the relative motion period of the water droplet configuration based on the true anomaly angle difference. The present invention is completely based on the calculation of the spacecraft based on the orbital elements, does not rely on the specific relative motion equation, and directly obtains the relative motion period of the water droplet configuration based on the orbital elements of the spacecraft. The calculation is stable, convenient, and accurate, the physical meaning is clear and easy to understand, and is suitable for practical engineering applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments. It should be understood that the following drawings only illustrate certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other relevant drawings can be obtained based on these drawings without paying any creative work.

[0055] Figure 1 Flowchart of the steps of the method for calculating the relative motion period of a spacecraft water droplet configuration in an embodiment of the present invention;

[0056] Figure 2 is the semi-major axis a of the tracking spacecraft in the embodiment of the present invention C Less than the distance r from the center of the Earth to the target spacecraft T Schematic diagram of the water droplet configuration when ;

[0057] Figure 3 is the semi-major axis a of the tracking spacecraft in the embodiment of the present invention C Greater than the distance r from the center of the Earth to the target spacecraft T Schematic diagram of the water droplet configuration when ;

[0058] Figure 4 This is a structural block diagram of a spacecraft water droplet configuration relative motion period calculation system based on orbital elements provided by an embodiment of the present application;

[0059] Figure 5It is a structural diagram of a computer device provided in one embodiment of the present application. DETAILED DESCRIPTION

[0060] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings herein can be arranged and designed in various different configurations.

[0061] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention as claimed, but rather merely represents selected embodiments of the present invention. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without creative effort shall fall within the scope of protection of the present invention.

[0062] It should be noted that similar reference numerals and letters denote similar items in the following drawings, and therefore, once an item is defined in one drawing, it does not need to be further defined or explained in subsequent drawings.

[0063] In the description of the embodiments of the present invention, it should be noted that if the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", etc. appear, the orientation or position relationship indicated is based on the orientation or position relationship shown in the accompanying drawings, or the orientation or position relationship in which the product of the invention is usually placed when in use. It is only for the convenience of describing the present invention and simplifying the description, and does not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operate in a specific orientation. Therefore, it should not be understood as limiting the present invention. In addition, the terms "first", "second", "third", etc. are only used to distinguish the description and should not be understood as indicating or implying relative importance.

[0064] In the description of the embodiments of the present invention, it should be noted that, unless otherwise expressly specified or limited, the terms "disposed," "installed," "connected," and "connected" should be understood in a broad sense. For example, they can refer to fixed connections, detachable connections, or integral connections; they can refer to mechanical connections or electrical connections; they can refer to direct connections or indirect connections through an intermediate medium; and they can refer to internal connections between two components. Those skilled in the art will understand the specific meanings of the above terms in the present invention based on specific circumstances.

[0065] Example

[0066] Reference Figure 1-Figure 3 , Figure 1Flowchart of the steps of the method for calculating the relative motion period of a spacecraft water droplet configuration in an embodiment of the present invention; Figure 2 is the semi-major axis a of the tracking spacecraft in the embodiment of the present invention C Less than the distance r from the center of the Earth to the target spacecraft T Schematic diagram of the water droplet configuration when ; Figure 3 is the semi-major axis a of the tracking spacecraft in the embodiment of the present invention C Greater than the distance r from the center of the Earth to the target spacecraft T Schematic diagram of the water droplet configuration when ;

[0067] The specific steps include:

[0068] S110: Set the orbital parameters of the target spacecraft and the tracking spacecraft, and calculate the orbital elements and operating parameters of the target spacecraft and the tracking spacecraft respectively based on the orbital parameters; wherein the orbital parameters of the target spacecraft include the geocentric distance, and the orbital parameters of the tracking spacecraft include the geocentric distance of perigee and the geocentric distance of apogee;

[0069] S120, determining a motion trajectory direction of the water droplet configuration of the tracking spacecraft relative to the target spacecraft based on the orbital parameters, the number of orbital elements, and the operating parameters, wherein the motion trajectory direction includes the relative direction of the smooth vertex and the direction switching point of the water droplet configuration;

[0070] S130, iteratively solving the true anomaly angle difference of the tracking spacecraft based on the number of orbital elements, orbital parameters and trajectory data of the motion trajectory direction of the water drop configuration, and calculating the relative motion period of the water drop configuration based on the true anomaly angle difference.

[0071] The present invention sets the orbital parameters of the target spacecraft and the tracking spacecraft, and calculates the orbital elements and operating parameters of the target spacecraft and the tracking spacecraft respectively based on the orbital parameters; wherein the orbital parameters of the target spacecraft include the distance from the center of the earth, and the orbital parameters of the tracking spacecraft include the distance from the center of the earth to the center of the perigee and the distance from the center of the earth to the apogee; determines the motion trajectory direction of the water droplet configuration of the tracking spacecraft relative to the target spacecraft based on the orbital parameters, the orbital elements and the operating parameters, wherein the motion trajectory direction includes the relative direction of the smooth vertex and the direction switching point of the water droplet configuration; iteratively solves the true anomaly angle difference of the tracking spacecraft based on the orbital elements, the orbital parameters and the trajectory data of the motion trajectory direction of the water droplet configuration, and calculates the relative motion period of the water droplet configuration based on the true anomaly angle difference. The present invention is completely based on the calculation of the spacecraft based on the orbital elements, does not rely on the specific relative motion equation, and directly obtains the relative motion period of the water droplet configuration based on the orbital elements of the spacecraft. The calculation is stable, convenient and accurate, the physical meaning is clear and easy to understand, and is suitable for practical engineering applications.

[0072] Next, the method for calculating the relative motion period of the spacecraft water droplet configuration in this exemplary embodiment will be further described.

[0073] In an embodiment of the present application, as described in step S110, the orbital parameters of the target spacecraft and the tracking spacecraft are set, and the orbital elements and operating parameters of the target spacecraft and the tracking spacecraft are calculated respectively based on the orbital parameters; wherein, the orbital parameters of the target spacecraft include the geocentric distance, and the orbital parameters of the tracking spacecraft include the perigee geocentric distance and the apogee geocentric distance.

[0074] It should be noted that the above-mentioned orbital elements are parameters that characterize the orbital shape, position and motion, and can be used to determine the orbit and position of the spacecraft at any time. The above-mentioned orbital elements include the semi-major axis, eccentricity and true anomaly.

[0075] Specifically, the target spacecraft's geocentric distance r is set T , set the perigee distance of the tracking spacecraft Apogee geocentric distance Based on the tracking spacecraft's perigee distance and apogee geocentric distance Calculate the orbital elements of the tracking spacecraft, where the orbital elements include the semi-major axis a C , eccentricity e C and semi-diameter P C , the calculation formula is as follows:

[0076] Tracking spacecraft semi-major axis a C for:

[0077] Tracking spacecraft eccentricity e C for:

[0078] Tracking spacecraft semi-diameter P C for:

[0079] The operating parameters of the tracking spacecraft are calculated based on the orbital elements of the tracking spacecraft, where the operating parameters include the perigee angular velocity w max and the apogee angular velocity w min , the calculation formula is as follows:

[0080] Tracking spacecraft perigee angular velocity w max for:

[0081] Tracking the spacecraft apogee angular velocity w min for:

[0082] According to the distance r from the center of the target spacecraft T Calculate the operating parameters of the target spacecraft, including the angular velocity w T , the calculation formula is:

[0083] In an embodiment of the present application, as described in step S120, the motion trajectory direction of the water droplet configuration of the tracking spacecraft relative to the target spacecraft is determined based on the orbital parameters, the number of orbital roots and the operating parameters, where the motion trajectory direction includes the relative direction of the smooth vertex and the direction switching point of the water droplet configuration.

[0084] It should be noted that Determines the orbital period of the tracking spacecraft, r T Determines the orbital period of the target spacecraft. When , the tracking spacecraft and the target spacecraft have the same orbital period, so the relative motion trajectory of the two will not diverge over time, but form a periodic closed loop curve, which is an elliptical configuration, that is, when When , the water droplet configuration is specialized into an elliptical configuration.

[0085] This application gives , the calculation of the relative motion period of the water droplet configuration; as shown in the following steps, based on the relationship between the operating parameters of the tracking spacecraft and the target spacecraft, it is determined whether the motion trajectory of the tracking spacecraft forms a water droplet configuration.

[0086] Specifically, when w min >w T or w max <w T In the relative motion of the water droplet configuration, the angular velocity of the tracking spacecraft relative to the angular velocity of the target spacecraft has a periodic change process from greater to less, and then from less to greater. Therefore, if the minimum angular velocity of the tracking spacecraft is greater than that of the target spacecraft, or the maximum angular velocity is less than that of the target spacecraft, the water droplet configuration cannot be formed. That is, when w min >w T or w max <w T When the spacecraft's trajectory is tracked, the water droplet configuration cannot be formed; on the contrary, when w min ≤w T or w max ≥w T , then tracking the motion trajectory of the spacecraft can form a water droplet configuration.

[0087] As described in the following steps, when the motion trajectory of the tracking spacecraft forms a water droplet configuration, the direction of the motion trajectory of the tracking spacecraft relative to the target spacecraft is determined based on the relationship between the semi-major axis of the tracking spacecraft and the distance from the center of the earth to the target spacecraft.

[0088] Specifically, when tracking the semi-major axis a of the spacecraft C Less than the distance r from the center of the Earth to the target spacecraft T, the smooth vertex of the water droplet configuration is located above the direction switching point. When it is less than , the average angular velocity of the tracking spacecraft is large, and the relative motion trajectory spirals forward from the bottom of the target spacecraft, forming a relative motion trajectory with the smooth vertex above. When the semi-major axis a of the tracking spacecraft is C Greater than the target spacecraft's distance from the Earth's center r T , the smooth vertex of the water droplet configuration is located below the direction switching point; when it is greater than , the average angular velocity of the tracking spacecraft is small, and the relative motion trajectory spirals backward from above the target spacecraft, forming a relative motion trajectory with the smooth vertex below.

[0089] In an embodiment of the present application, as described in step S130, the true anomaly angle difference of the tracking spacecraft is iteratively solved based on the number of orbital elements, orbital parameters and trajectory data of the motion trajectory direction of the water droplet configuration, and the relative motion period of the water droplet configuration is calculated based on the true anomaly angle difference.

[0090] It's important to note that the relative motion period of the droplet configuration is the flight time it takes for the spacecraft to reach the direction switching point again after passing through the smooth vertex of the relative motion trajectory of the droplet configuration. The true anomaly angle is one of the six orbital elements, describing the geocentric angle of the spacecraft's current position relative to its perigee position. The true anomaly difference is the difference in the spacecraft's anomaly angle between two points. The true anomaly angle corresponds one-to-one with the flight time, and the true anomaly difference is used to calculate the flight time from one point to another.

[0091] As described in the following steps, when tracking the spacecraft's semi-major axis a C Less than the distance r from the center of the Earth to the target spacecraft T , that is, when When the smooth vertex of the water droplet configuration is at the bottom and the direction switching point is at the top, the true anomaly angle Δf of the tracking spacecraft is iteratively solved according to the number of orbital elements, orbital parameters and trajectory data of the water droplet configuration. down , that is, the iterative method is used to solve the true anomaly angle difference Δf when the tracking spacecraft flies from the smooth vertex of the water droplet configuration to the switching point of the relative motion trajectory direction down , the calculation formula is as follows: in,

[0092]

[0093]

[0094]

[0095]

[0096]

[0097] Among them, α and β represent intermediate variables, s represents half of the perimeter of the triangle connecting the starting point, end point and the center of the earth, c represents the straight-line distance between the starting point and end point of the water droplet configuration orbit transfer, r down Represents the distance from the center of the earth at the direction switching point, μ e Represents the Earth's gravitational constant. In the above formula, only Δf down is an unknown quantity and can be solved numerically by Newton's iteration method;

[0098] Since Δf down =0 also meets the requirements of the formula, but Δf down = 0 is not the desired solution, so the initial value of the iteration cannot be selected arbitrarily, and the numerical solution must not converge to Δf down =0. After verification by calculation practice, the initial value of iteration is selected as Δf down =90° can ensure the correct convergence result;

[0099] Calculate the relative motion period T of the water drop configuration based on the true anomaly difference, Δf down After solving, the calculation formula is: That is, the semi-major axis a of the tracking spacecraft is obtained. C Less than the distance r from the center of the Earth to the target spacecraft T Track the relative motion period of the spacecraft's water droplet configuration.

[0100] As described in the following steps, when tracking the spacecraft's semi-major axis a C Greater than the target spacecraft's distance from the Earth's center r T , the smooth vertex of the water droplet configuration is below the direction switching point, that is, when When the smooth vertex of the water droplet configuration is at the bottom and the direction switching point is at the top, the true anomaly angle Δf of the tracking spacecraft is iteratively solved according to the number of orbital elements, orbital parameters and trajectory data of the water droplet configuration. up , that is, the iterative method is used to solve the true anomaly angle difference Δf when the tracking spacecraft switches from the relative motion trajectory direction to the smooth vertex of the water droplet configuration up , the calculation formula is as follows: in,

[0101]

[0102]

[0103]

[0104]

[0105]

[0106] Among them, α and β represent intermediate variables, s represents half of the perimeter of the triangle connecting the starting point, end point and the center of the earth, c represents the straight-line distance between the starting point and end point of the water droplet configuration orbit transfer, r up Represents the distance from the center of the earth at the direction switching point, μ e Represents the Earth's gravitational constant. In the above formula, only Δf up is an unknown quantity and can be solved numerically by Newton's iteration method;

[0107] Since Δf up =0 also meets the requirements of the formula, but Δf up =0 is not the desired solution, Δf up The initial value of the iteration cannot be selected arbitrarily to avoid the numerical solution converging to Δf up =0. After calculation practice, the initial value of iteration is selected as Δf up =90° can ensure correct convergence results.

[0108] Calculate the relative motion period T of the water drop configuration based on the true anomaly difference, Δf up After solving, the calculation formula is: That is, the semi-major axis a of the tracking spacecraft is obtained. C Greater than the target spacecraft's distance from the Earth's center r T Track the relative motion period of the spacecraft's water droplet configuration.

[0109] Beneficial effects of the embodiments of the present application:

[0110] This patent provides a method for calculating the relative motion period of water drop configurations that is suitable for practical engineering tasks. Traditional methods use a simplified method of linearizing the relative motion equations. In addition to the loss of calculation accuracy, it is difficult to directly apply to engineering practice. After converting the physical problem into a mathematical problem, the intuitive and clear physical characteristics of the spacecraft orbit itself are abandoned. When applied to actual engineering, the characteristic parameters of the water drop configuration cannot be directly obtained based on the main characteristic parameters of the orbit. The calculation method based on the number of spacecraft orbit elements proposed in this patent can not only obtain higher-precision calculation results, but also directly obtain the relative motion period of the water drop configuration based on the number of spacecraft orbit elements. The calculation is stable, convenient, accurate, and the physical meaning is clear and easy to understand, making it suitable for practical engineering applications.

[0111] Reference Figure 4 , shows a block diagram of the system for calculating the relative motion period of a spacecraft water droplet configuration based on orbital elements provided by an embodiment of the present application, specifically including:

[0112] The parameter calculation module 110 is used to set the orbital parameters of the target spacecraft and the tracking spacecraft, and calculate the orbital elements and operating parameters of the target spacecraft and the tracking spacecraft respectively based on the orbital parameters. The orbital parameters of the target spacecraft include the geocentric distance, and the orbital parameters of the tracking spacecraft include the perigee geocentric distance and the apogee geocentric distance.

[0113] A motion trajectory direction determination module 120 is configured to determine the motion trajectory direction of the water droplet configuration of the tracking spacecraft relative to the target spacecraft based on the orbital parameters, the number of orbital elements, and the operating parameters, wherein the motion trajectory direction includes the relative direction between the smooth vertex and the direction switching point of the water droplet configuration;

[0114] The relative motion period calculation module 130 is used to iteratively solve the true anomaly angle difference of the tracking spacecraft based on the number of orbital elements, orbital parameters and trajectory data of the motion trajectory direction of the water drop configuration, and calculate the relative motion period of the water drop configuration based on the true anomaly angle difference.

[0115] Reference Figure 5 , showing the spacecraft water droplet configuration relative motion period computer device based on orbital elements of the present application, which may specifically include the following:

[0116] The computer device 12 is a general-purpose computing device. The components of the computer device 12 may include but are not limited to: one or more processors or processing units 16, memory 28, and a bus 18 connecting different system components (including memory 28 and processing unit 16).

[0117] The bus 18 represents one or more of several types of bus 18 structures, including a memory bus 18 or memory controller, a peripheral bus 18, an accelerated graphics port, a processor, or a local bus 18 that utilizes any of a variety of bus 18 architectures. Examples of such architectures include, but are not limited to, an Industry Standard Architecture (ISA) bus 18, a Micro Channel Architecture (MAC) bus 18, an Enhanced ISA bus 18, an Audio Video Electronics Standards Association (VESA) local bus 18, and a Peripheral Component Interconnect (PCI) bus 18.

[0118] The computer device 12 typically includes a variety of computer system readable media. These media can be any available media that can be accessed by the computer device 12, including volatile and non-volatile media, removable and non-removable media.

[0119] Memory 28 may include computer system readable media in the form of volatile memory, such as random access memory 30 and / or cache memory 32. Computer device 12 may further include other removable / non-removable, volatile / non-volatile computer system storage media. By way of example only, storage system 34 may be configured to read and write to non-removable, non-volatile magnetic media (commonly referred to as a "hard drive"). Although Figure 4 Not shown, a disk drive for reading and writing to a removable non-volatile disk (such as a "floppy disk"), and an optical drive for reading and writing to a removable non-volatile optical disk (such as a CD-ROM, DVD-ROM, or other optical media) can be provided. In these cases, each drive can be connected to the bus 18 via one or more data medium interfaces. The memory may include at least one program product having a set (e.g., at least one) of program modules 42, which are configured to perform the functions of the various embodiments of the present application.

[0120] A program / utility 40 having a set (at least one) of program modules 42 may be stored, for example, in a memory. Such program modules 42 include, but are not limited to, an operating system, one or more application programs, other program modules 42, and program data, each of which, or some combination thereof, may include an implementation of a network environment. The program modules 42 generally perform the functions and / or methods of the embodiments described herein.

[0121] The computer device 12 may also communicate with one or more external devices 14 (e.g., a keyboard, a pointing device, a display 24, a camera, etc.), one or more devices that enable an operator to interact with the computer device 12, and / or any device that enables the computer device 12 to communicate with one or more other computing devices (e.g., a network card, a modem, etc.). Such communication may be performed through an I / O interface 22. Furthermore, the computer device 12 may also communicate with one or more networks (e.g., a local area network (LAN)), a wide area network (WAN), and / or a public network (e.g., the Internet) through a network adapter 20. Figure 4 As shown, the network adapter 20 communicates with the other modules of the computer device 12 via the bus 18. Figure 4 Not shown, other hardware and / or software modules may be used in conjunction with the computer device 12, including but not limited to microcode, device drivers, redundant processing units 16, external disk drive arrays, RAID systems, tape drives, and data backup storage systems 34.

[0122] The processing unit 16 executes various functional applications and data processing by running the programs stored in the memory 28, such as implementing the method for calculating the relative motion period of the spacecraft water droplet configuration provided in the embodiment of the present application.

[0123] That is, when the processing unit 16 executes the program, it realizes: setting the orbital parameters of the target spacecraft and the tracking spacecraft, and calculating the orbital elements and operating parameters of the target spacecraft and the tracking spacecraft respectively based on the orbital parameters; wherein, the orbital parameters of the target spacecraft include the geocentric distance, and the orbital parameters of the tracking spacecraft include the geocentric distance of the perigee and the geocentric distance of the apogee; determining the motion trajectory direction of the water droplet configuration of the tracking spacecraft relative to the target spacecraft based on the orbital parameters, the orbital elements and the operating parameters, wherein the motion trajectory direction includes the relative direction of the smooth vertex and the direction switching point of the water droplet configuration; iteratively solving the true anomaly angle difference of the tracking spacecraft based on the orbital elements, orbital parameters and the trajectory data of the motion trajectory direction of the water droplet configuration, and calculating the relative motion period of the water droplet configuration based on the true anomaly angle difference.

[0124] In one embodiment of the present application, a computer-readable storage medium is further provided, on which a computer program is stored. When the program is executed by a processor, the method for calculating the relative motion period of a spacecraft water droplet configuration provided in all embodiments of the present application is implemented.

[0125] That is, when the program is executed by the processor, it is implemented as follows: setting the orbital parameters of the target spacecraft and the tracking spacecraft, and calculating the orbital elements and operating parameters of the target spacecraft and the tracking spacecraft respectively based on the orbital parameters; wherein the orbital parameters of the target spacecraft include the geocentric distance, and the orbital parameters of the tracking spacecraft include the geocentric distance of the perigee and the geocentric distance of the apogee; determining the motion trajectory direction of the water droplet configuration of the tracking spacecraft relative to the target spacecraft based on the orbital parameters, the orbital elements and the operating parameters, wherein the motion trajectory direction includes the relative direction of the smooth vertex and the direction switching point of the water droplet configuration; iteratively solving the true anomaly angle difference of the tracking spacecraft based on the orbital elements, orbital parameters and the trajectory data of the motion trajectory direction of the water droplet configuration, and calculating the relative motion period of the water droplet configuration based on the true anomaly angle difference.

[0126] Any combination of one or more computer-readable media may be employed. A computer-readable medium may be a computer-readable signal medium or a computer-readable storage medium. A computer-readable storage medium may be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples (a non-exhaustive list) of computer-readable storage media include: an electrical connection having one or more wires, a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination thereof. In this document, a computer-readable storage medium may be any tangible medium containing or storing a program that may be used by or in conjunction with an instruction execution system, apparatus, or device.

[0127] A computer-readable signal medium may include a data signal propagated in baseband or as part of a carrier wave, which carries computer-readable program code. Such a propagated data signal may take a variety of forms, including, but not limited to, electromagnetic signals, optical signals, or any suitable combination thereof. A computer-readable signal medium may also be any computer-readable medium other than a computer-readable storage medium that can transmit, propagate, or transport a program for use by or in conjunction with an instruction execution system, apparatus, or device.

[0128] The computer program code for performing the operations of the present application can be written in one or more programming languages or a combination thereof, including object-oriented programming languages such as Java, Smalltalk, C++, and conventional procedural programming languages such as "C" language or similar programming languages. The program code can be executed entirely on the operator's computer, partially on the operator's computer, as a separate software package, partially on the operator's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving a remote computer, the remote computer can be connected to the operator's computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or can be connected to an external computer (for example, using an Internet service provider to connect through the Internet). The various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same and similar parts between the various embodiments can be referenced to each other.

[0129] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention shall be included within the scope of protection of the present invention.

Claims

1. A method for calculating the relative motion period of a spacecraft water droplet configuration, characterized in that: The steps include: Setting orbital parameters of the target spacecraft and the tracking spacecraft, and calculating the orbital elements and operating parameters of the target spacecraft and the tracking spacecraft respectively based on the orbital parameters; wherein the orbital parameters of the target spacecraft include the geocentric distance, and the orbital parameters of the tracking spacecraft include the geocentric distance of perigee and the geocentric distance of apogee; determining a motion trajectory direction of the water droplet configuration of the tracking spacecraft relative to the target spacecraft based on the orbital parameters, the number of orbital elements, and the operating parameters, wherein the motion trajectory direction includes a relative direction between a smooth vertex and a direction switching point of the water droplet configuration; Iteratively solving the true anomaly difference of the tracking spacecraft based on the number of orbital elements, the orbital parameters, and the trajectory data of the motion trajectory direction of the water droplet configuration, and calculating the relative motion period of the water droplet configuration based on the true anomaly difference; comprising: When the smooth vertex of the water droplet configuration is above the direction switching point, the true anomaly Δf of the tracking spacecraft is iteratively solved according to the orbital elements, the orbital parameters and the trajectory data of the water droplet configuration. down , the calculation formula is: in, Among them, α and β represent intermediate variables, s represents half of the perimeter of the triangle connecting the starting point, end point and the center of the earth, c represents the straight-line distance between the starting point and end point of the water droplet configuration orbit transfer, r down Represents the distance from the center of the earth at the direction switching point, μ e represents the Earth's gravitational constant, r T represents the distance from the center of the Earth; represents the perigee distance, represents the distance from the apogee to the center of the earth, a C represents the semi-major axis; e C represents eccentricity; The relative motion period T of the water droplet configuration is calculated based on the true anomaly angle difference, and the calculation formula is: When the smooth vertex of the water droplet configuration is below the direction switching point, the true anomaly Δf of the tracking spacecraft is iteratively solved according to the orbital elements, the orbital parameters and the trajectory data of the water droplet configuration. up , the calculation formula is: in, Among them, α and β represent intermediate variables, s represents half of the perimeter of the triangle connecting the starting point, end point and the center of the earth, c represents the straight-line distance between the starting point and end point of the water droplet configuration orbit transfer, r up Represents the distance from the center of the earth at the direction switching point, μ e represents the Earth's gravitational constant; The relative motion period T of the water droplet configuration is calculated based on the true anomaly angle difference, and the calculation formula is:

2. The method for calculating the relative motion period of a spacecraft water droplet configuration according to claim 1, characterized in that: The steps of setting the orbital parameters of the target spacecraft and the tracking spacecraft, and respectively calculating the orbital elements and operating parameters of the target spacecraft and the tracking spacecraft based on the orbital parameters include: Set the target spacecraft's geocentric distance r T , set the perigee distance of the tracking spacecraft Apogee geocentric distance According to the tracking spacecraft's perigee distance and apogee geocentric distance Calculate the orbital elements of the tracking spacecraft, wherein the orbital elements include the semi-major axis a C , eccentricity e C and semi-diameter P C Calculate the operating parameters of the tracking spacecraft based on the orbital elements of the tracking spacecraft, wherein the operating parameters include the perigee angular velocity w max and the apogee angular velocity w min ; According to the distance r from the center of the Earth of the target spacecraft T Calculate the operating parameters of the target spacecraft, wherein the operating parameters include the angular velocity w T .

3. The method for calculating the relative motion period of a spacecraft water droplet configuration according to claim 2, characterized in that: The step of determining the direction of the motion trajectory of the water droplet configuration of the tracking spacecraft relative to the target spacecraft based on the orbital parameters, the orbital element number, and the operating parameters includes: determining, based on a magnitude relationship between operating parameters of the tracking spacecraft and the target spacecraft, whether the motion trajectory of the tracking spacecraft forms a water droplet configuration; When the motion trajectory of the tracking spacecraft forms a water drop configuration, the direction of the motion trajectory of the tracking spacecraft relative to the target spacecraft is determined based on the relationship between the semi-major axis of the tracking spacecraft and the distance from the center of the earth to the target spacecraft.

4. The method for calculating the relative motion period of a spacecraft water droplet configuration according to claim 3, characterized in that: The step of determining whether the motion trajectory of the tracking spacecraft forms a water droplet configuration based on the magnitude relationship between the operating parameters of the tracking spacecraft and the target spacecraft includes: When w min >w T or w max <w T , then the motion trajectory of the tracking spacecraft cannot form a water droplet configuration; When w min ≤w T or w max ≥w T , then the motion trajectory of the tracking spacecraft can form a water droplet configuration.

5. The method for calculating the relative motion period of a spacecraft water droplet configuration according to claim 3, characterized in that: The step of determining the direction of the motion trajectory of the water droplet configuration of the tracking spacecraft relative to the target spacecraft based on the relationship between the semi-major axis of the tracking spacecraft and the distance from the center of the Earth to the target spacecraft comprises: When the semi-major axis a of the tracking spacecraft C Less than the distance r from the center of the Earth to the target spacecraft T , the smooth vertex of the water drop configuration is located above the direction switching point; When the semi-major axis a of the tracking spacecraft C Greater than the distance r from the center of the Earth to the target spacecraft T , the smooth vertex of the water drop configuration is located below the direction switching point.

6. The method for calculating the relative motion period of a spacecraft water droplet configuration according to claim 1, characterized in that: The Δf down and the Δf up The initial value of the iteration is selected as 90°.

7. A spacecraft water droplet configuration relative motion period calculation system based on orbital elements, characterized in that: include: a parameter calculation module, configured to set the orbital parameters of the target spacecraft and the tracking spacecraft, and to calculate the orbital elements and operating parameters of the target spacecraft and the tracking spacecraft respectively based on the orbital parameters; wherein the orbital parameters of the target spacecraft include the geocentric distance, and the orbital parameters of the tracking spacecraft include the geocentric distance of perigee and the geocentric distance of apogee; a motion trajectory direction determination module, configured to determine a motion trajectory direction of the water droplet configuration of the tracking spacecraft relative to the target spacecraft based on the orbital parameters, the number of orbital elements, and the operating parameters, wherein the motion trajectory direction includes the relative direction of the smooth vertex and the direction switching point of the water droplet configuration; A relative motion period calculation module is configured to iteratively solve the true anomaly error of the tracking spacecraft based on the number of orbital elements, the orbital parameters, and the trajectory data of the motion trajectory direction of the water droplet configuration, and calculate the relative motion period of the water droplet configuration based on the true anomaly error; and includes: When the smooth vertex of the water droplet configuration is above the direction switching point, the true anomaly Δf of the tracking spacecraft is iteratively solved according to the orbital elements, the orbital parameters and the trajectory data of the water droplet configuration. down , the calculation formula is: in, Among them, α and β represent intermediate variables, s represents half of the perimeter of the triangle connecting the starting point, end point and the center of the earth, c represents the straight-line distance between the starting point and end point of the water droplet configuration orbit transfer, r down Represents the distance from the center of the earth at the direction switching point, μ e represents the Earth's gravitational constant, r T represents the distance from the center of the Earth; represents the perigee distance, represents the distance from the apogee to the center of the earth, a C represents the semi-major axis; e C represents eccentricity; The relative motion period T of the water droplet configuration is calculated based on the true anomaly angle difference, and the calculation formula is: When the smooth vertex of the water droplet configuration is below the direction switching point, the true anomaly Δf of the tracking spacecraft is iteratively solved according to the orbital elements, the orbital parameters and the trajectory data of the water droplet configuration. up , the calculation formula is: in, Among them, α and β represent intermediate variables, s represents half of the perimeter of the triangle connecting the starting point, end point and the center of the earth, c represents the straight-line distance between the starting point and end point of the water droplet configuration orbit transfer, r up Represents the distance from the center of the earth at the direction switching point, μ e represents the Earth's gravitational constant; The relative motion period T of the water droplet configuration is calculated based on the true anomaly angle difference, and the calculation formula is:

8. A device, characterized in that The method comprises a processor, a memory, and a computer program stored in the memory and capable of running on the processor, wherein the computer program implements the method according to any one of claims 1 to 6 when executed by the processor.

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