Satellite orbit prediction method

Abstract

The invention relates to a satellite orbit prediction method. The method comprises the following steps: constructing an expression of gravity borne by a satellite according to the mass of the satellite and the distance between the satellite and the earth; constructing a differential equation of the acceleration of the satellite according to the Newton's second law and the expression of the gravity borne by the satellite; solving the differential equation according to conservative force field characteristics of mechanics, calculating a gravitational potential energy function and a derivative expression of the gravitational potential energy function relative to time, and converting the derivative expression based on a mechanical conservation law that the sum of derivatives of kinetic energy and gravitational potential energy relative to time is zero to obtain a derivative expression of acceleration; according to the angular momentum conservation principle, the time relation in the derivative expression of the acceleration is converted into the radial position relation, integration is conducted on the radial position relation, and an orbital equation of the satellite is obtained. By adopting the method, satellite orbit prediction can be realized.

Description

Technical Field

[0001] The present application relates to the technical field of satellite orbit prediction, and in particular to a satellite orbit prediction method. Background Art

[0002] In recent years, with the progress of aerospace industry, more and more satellites have been launched into space to operate in predetermined orbits to perform various tasks. During the operation of satellites, they will be affected by various factors, making it extremely difficult to accurately predict the satellite orbit. At the same time, the engine used to control the satellite's motion state cannot be extremely accurate when working. Therefore, how to predict the orbit has become an urgent problem to be solved. Summary of the invention

[0003] Based on this, it is necessary to provide a satellite orbit prediction method that can realize satellite orbit prediction in response to the above technical problems.

[0004] A satellite orbit prediction method, the method comprising:

[0005] Obtain the mass and launch angle of the satellite; construct the expression of the gravity on the satellite based on the mass of the satellite and the distance between the satellite and the earth; construct the differential equation of the satellite's acceleration based on Newton's second law and the expression of the gravity on the satellite;

[0006] Solve the differential equation according to the conservative force field characteristics of mechanics, calculate the gravitational potential energy function and the derivative expression of the gravitational potential energy function with respect to time, transform the derivative expression based on the mechanical conservation law that the sum of the derivatives of kinetic energy and gravitational potential energy with respect to time is zero, and obtain the derivative expression of acceleration;

[0007] According to the principle of conservation of angular momentum, the time relationship in the derivative expression of acceleration is converted into a radial position relationship. The radial position relationship is integrated to obtain the orbital equation of the satellite.

[0008] In one embodiment, the expression for the gravity on the satellite is calculated based on the mass of the satellite and the distance between the satellite and the earth, including:

[0009] The gravity expression of the satellite is calculated based on the mass of the satellite and the distance between the satellite and the earth:

[0010]

[0011] Among them, G represents the gravitational constant, M represents the mass of the earth, m represents the mass of the satellite, and r represents the distance between the earth and the satellite.

[0012] In one embodiment, a differential equation for the acceleration of the satellite is constructed based on Newton's second law and an expression for the gravity acting on the satellite, including:

[0013] According to Newton's second law and the gravity expression of the satellite, the differential equation of the satellite's acceleration is constructed as follows:

[0014]

[0015] Among them, F represents the expression of the gravity acting on the satellite, G represents the gravitational constant, M represents the mass of the earth, m represents the mass of the satellite, and r represents the distance between the earth and the satellite.

[0016] In one embodiment, calculating the gravitational potential energy function and the derivative of the gravitational potential energy function with respect to time includes:

[0017] The gravitational potential energy function and the derivative of the gravitational potential energy function with respect to time are calculated as

[0018]

[0019] Among them, F is the expression of the gravity acting on the satellite, G is the gravitational constant, M is the mass of the earth, m is the mass of the satellite, r is the distance between the earth and the satellite, and t is the launch time.

[0020] In one embodiment, the process expression based on the sum of the derivatives of kinetic energy and gravitational potential energy with respect to time being zero is: Among them, F is the expression of the gravity acting on the satellite, m is the mass of the satellite, a is the acceleration of the satellite, r is the distance between the earth and the satellite, and t is the launch time.

[0021] In one embodiment, the derivative expression is converted based on the mechanical conservation law that the sum of the derivatives of kinetic energy and gravitational potential energy with respect to time is zero, so as to obtain the derivative expression of acceleration, including:

[0022] because Where F = ma, that is Then the derivative expression of acceleration is:

[0023]

[0024] Among them, C represents the integration constant and G represents the gravitational constant.

[0025] In one embodiment, converting the time relationship in the derivative expression of acceleration into the radial position relationship according to the principle of conservation of angular momentum includes:

[0026] The derivative expression of acceleration is expressed as in is the radial velocity, is the angular velocity; according to the law of conservation of angular momentum, is a constant, where L is the angular momentum, so Therefore That is, the radial position relationship is: C represents the integration constant, m represents the mass of the satellite, G represents the gravitational constant, r represents the distance between the earth and the satellite, t represents the launch time, and M represents the mass of the earth.

[0027] In one embodiment, the radial position relationship is integrated to obtain the orbit equation of the satellite, including:

[0028] Integrating the radial position relationship, the orbit equation of the satellite is obtained as follows:

[0029]

[0030] or

[0031] Where C is the integration constant, m is the mass of the satellite, G is the gravitational constant, r is the distance between the earth and the satellite, θ is the launch angle, M is the mass of the earth, L is the angular momentum, and r is the gravitational constant. 0 Represents the radius of the Earth.

[0032] The above-mentioned satellite orbit prediction method first constructs an expression of the gravity received by the satellite according to the mass of the satellite and the distance between the satellite and the earth; constructs a differential equation of the satellite's acceleration according to Newton's second law and the expression of the gravity received by the satellite; solves the differential equation according to the conservative force field characteristics of mechanics, calculates the gravitational potential energy function and the derivative expression of the gravitational potential energy function with respect to time, and transforms the derivative expression based on the mechanical conservation law that the sum of the derivatives of kinetic energy and gravitational potential energy with respect to time is zero to obtain the derivative expression of acceleration; according to the principle of conservation of angular momentum, the time relationship in the derivative expression of acceleration is converted into a radial position relationship, and the radial position relationship is integrated to obtain the satellite's orbit equation. The present application realizes satellite orbit prediction by utilizing conservative positions, Newton's second law and the law of conservation of momentum, and transforms the relevant equations based on the law. The calculation process is simple, fast and concise, with high accuracy, and is more suitable for satellite orbit prediction for scheme design or engineering tasks. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 A schematic diagram of a flow chart of a satellite orbit prediction method in an embodiment;

[0034] Figure 2 FIG. 4 is a diagram showing the internal structure of a computer device in one embodiment. DETAILED DESCRIPTION

[0035] In order to make the purpose, technical solution and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0036] In one embodiment, Figure 1 As shown, a satellite orbit prediction method is provided, comprising the following steps:

[0037] Step 102, obtain the mass and launch angle of the satellite; construct an expression for the gravity on the satellite based on the mass of the satellite and the distance between the satellite and the earth; and construct a differential equation for the acceleration of the satellite based on Newton's second law and the expression for the gravity on the satellite.

[0038] First, calculate the gravity on the satellite at any time t. In the polar coordinate system, we can construct the gravity expression on the satellite based on the mass of the satellite and the distance between the satellite and the earth. Then, according to Newton's second law, the acceleration of the satellite in the radial direction can be expressed as:

[0039]

[0040] Step 104, solving the differential equation according to the conservative force field characteristics of mechanics, calculating the gravitational potential energy function and the derivative expression of the gravitational potential energy function with respect to time, converting the derivative expression based on the mechanical conservation law that the sum of the derivatives of kinetic energy and gravitational potential energy with respect to time is zero, and obtaining the derivative expression of acceleration.

[0041] The differential equation is an equation related to the distance between the satellite and the earth, that is, the position r. This application solves it through the properties of the conservative force field. In the conservative force field, the potential energy function satisfies the following relationship:

[0042]

[0043] Where U(r) is the potential energy function, which can be found from the gravitational potential energy function. The gravitational potential energy function is Therefore, the total mechanical energy of the satellite can be expressed as the sum of kinetic energy and potential energy:

[0044]

[0045] The derivatives of kinetic energy and potential energy with respect to time are:

[0046]

[0047] According to the law of conservation of mechanics, because Where F = ma, that is

[0048] Then the derivative expression of acceleration is:

[0049]

[0050] Among them, C represents the integration constant and G represents the gravitational constant.

[0051] Step 106, according to the principle of conservation of angular momentum, the time relationship in the derivative expression of acceleration is converted into a radial position relationship, and the radial position relationship is integrated to obtain the orbit equation of the satellite.

[0052] The derivative expression of acceleration is expressed as in is the radial velocity, is the angular velocity; according to the law of conservation of angular momentum, is a constant, where L is the angular momentum, so Therefore That is, the radial position relationship is: C represents the integration constant, m represents the mass of the satellite, G represents the gravitational constant, r represents the distance between the earth and the satellite, t represents the launch time, and M represents the mass of the earth.

[0053] By integrating the radial position relationship, the orbit equation of the satellite is obtained, including:

[0054] Integrating the radial position relationship, the orbit equation of the satellite is obtained as follows:

[0055]

[0056] or Where C is the integration constant, m is the mass of the satellite, G is the gravitational constant, r is the distance between the earth and the satellite, θ is the launch angle, M is the mass of the earth, L is the angular momentum, and r is the gravitational constant. 0 Represents the radius of the Earth.

[0057] In one embodiment, the expression for the gravity on the satellite is calculated based on the mass of the satellite and the distance between the satellite and the earth, including:

[0058] The gravity expression of the satellite is calculated based on the mass of the satellite and the distance between the satellite and the earth:

[0059]

[0060] Among them, G represents the gravitational constant, M represents the mass of the earth, m represents the mass of the satellite, and r represents the distance between the earth and the satellite.

[0061] In one embodiment, a differential equation for the acceleration of the satellite is constructed based on Newton's second law and an expression for the gravity acting on the satellite, including:

[0062] According to Newton's second law and the gravity expression of the satellite, the differential equation of the satellite's acceleration is constructed as follows:

[0063]

[0064] Among them, F represents the expression of the gravity acting on the satellite, G represents the gravitational constant, M represents the mass of the earth, m represents the mass of the satellite, and r represents the distance between the earth and the satellite.

[0065] In one embodiment, calculating the gravitational potential energy function and the derivative of the gravitational potential energy function with respect to time includes:

[0066] The gravitational potential energy function and the derivative of the gravitational potential energy function with respect to time are calculated as

[0067]

[0068]

[0069] Among them, F is the expression of the gravity acting on the satellite, G is the gravitational constant, M is the mass of the earth, m is the mass of the satellite, r is the distance between the earth and the satellite, and t is the launch time.

[0070] In one embodiment, the process expression based on the sum of the derivatives of kinetic energy and gravitational potential energy with respect to time being zero is: Among them, F is the expression of the gravity acting on the satellite, m is the mass of the satellite, a is the acceleration of the satellite, r is the distance between the earth and the satellite, and t is the launch time.

[0071] In one embodiment, the derivative expression is converted based on the mechanical conservation law that the sum of the derivatives of kinetic energy and gravitational potential energy with respect to time is zero, so as to obtain the derivative expression of acceleration, including:

[0072] because Where F = ma, that is Then the derivative expression of acceleration is:

[0073]

[0074] Among them, C represents the integration constant and G represents the gravitational constant.

[0075] In one embodiment, converting the time relationship in the derivative expression of acceleration into the radial position relationship according to the principle of conservation of angular momentum includes:

[0076] The derivative expression of acceleration is expressed as in is the radial velocity, is the angular velocity; according to the law of conservation of angular momentum, is a constant, where L is the angular momentum, so Therefore That is, the radial position relationship is: C represents the integration constant, m represents the mass of the satellite, G represents the gravitational constant, r represents the distance between the earth and the satellite, t represents the launch time, and M represents the mass of the earth.

[0077] In one embodiment, the radial position relationship is integrated to obtain the orbit equation of the satellite, including:

[0078] Integrating the radial position relationship, the orbit equation of the satellite is obtained as follows:

[0079]

[0080] or

[0081] Where C is the integration constant, m is the mass of the satellite, G is the gravitational constant, r is the distance between the earth and the satellite, θ is the launch angle, M is the mass of the earth, L is the angular momentum, and r is the gravitational constant. 0 Represents the radius of the Earth.

[0082] It should be understood that although Figure 1 The steps in the flowchart are shown in sequence as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified in this document, there is no strict order restriction for the execution of these steps, and these steps can be executed in other orders. Moreover, Figure 1 At least part of the steps may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily executed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least part of the sub-steps or stages of other steps.

[0083] In one embodiment, a computer device is provided. The computer device may be a terminal, and its internal structure diagram may be as follows: Figure 2As shown. The computer device includes a processor, a memory, a network interface, a display screen and an input device connected through a system bus. Among them, the processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and a computer program. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The network interface of the computer device is used to communicate with an external terminal through a network connection. When the computer program is executed by the processor, a satellite orbit prediction method is implemented. The display screen of the computer device can be a liquid crystal display screen or an electronic ink display screen, and the input device of the computer device can be a touch layer covering the display screen, or a key, trackball or touchpad set on the computer device housing, or an external keyboard, touchpad or mouse, etc.

[0084] Those skilled in the art will understand that Figure 1 The structure shown in the figure is only a block diagram of a part of the structure related to the solution of the present application, and does not constitute a limitation on the computer device to which the solution of the present application is applied. The specific computer device may include more or fewer components than those shown in the figure, or combine certain components, or have a different arrangement of components.

[0085] Those skilled in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be completed by instructing the relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to memory, storage, database or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM) or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. As an illustration and not limitation, RAM is available in many forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link (Synchlink) DRAM (SLDRAM), memory bus (Rambus) direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM).

[0086] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0087] The above-mentioned embodiments only express several implementation methods of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the invention patent. It should be pointed out that, for a person of ordinary skill in the art, several variations and improvements can be made without departing from the concept of the present application, and these all belong to the protection scope of the present application. Therefore, the protection scope of the patent of the present application shall be subject to the attached claims.

Claims

1. A satellite orbit prediction method, characterized in that: The method comprises: Obtaining the mass and launch angle of the satellite; constructing an expression of the gravity on the satellite according to the mass of the satellite and the distance between the satellite and the earth; constructing a differential equation of the acceleration of the satellite according to Newton's second law and the expression of the gravity on the satellite; Solving the differential equation according to the conservative force field characteristics of mechanics, calculating the gravitational potential energy function and the derivative expression of the gravitational potential energy function with respect to time, converting the derivative expression based on the mechanical conservation law that the sum of the derivatives of kinetic energy and gravitational potential energy with respect to time is zero, and obtaining the derivative expression of acceleration; According to the principle of conservation of angular momentum, the time relationship in the derivative expression of acceleration is converted into a radial position relationship, and the radial position relationship is integrated to obtain the orbit equation of the satellite.

2. The method according to claim 1, characterized in that The expression for calculating the gravity on the satellite according to the mass of the satellite and the distance between the satellite and the earth includes: The gravity expression of the satellite is calculated according to the mass of the satellite and the distance between the satellite and the earth: Among them, G represents the gravitational constant, M represents the mass of the earth, m represents the mass of the satellite, and r represents the distance between the earth and the satellite.

3. The method according to claim 1, characterized in that The differential equation of the satellite's acceleration is constructed based on Newton's second law and the expression of the gravity on the satellite, including: According to Newton's second law and the gravity expression of the satellite, the differential equation of the satellite's acceleration is constructed as follows: Among them, F represents the expression of the gravity acting on the satellite, G represents the gravitational constant, M represents the mass of the earth, m represents the mass of the satellite, and r represents the distance between the earth and the satellite.

4. The method according to claim 1, characterized in that: Calculating the gravitational potential energy function and the derivative of the gravitational potential energy function with respect to time includes: The calculated gravitational potential energy function and the derivative of the gravitational potential energy function with respect to time are respectively Among them, F is the expression of the gravity acting on the satellite, G is the gravitational constant, M is the mass of the earth, m is the mass of the satellite, r is the distance between the earth and the satellite, and t is the launch time.

5. The method according to claim 1, characterized in that: The process expression based on the sum of the derivatives of kinetic energy and gravitational potential energy with respect to time being zero is: Among them, F is the expression of the gravity acting on the satellite, m is the mass of the satellite, a is the acceleration of the satellite, r is the distance between the earth and the satellite, and t is the launch time.

6. The method according to claim 5, characterized in that The derivative expression is converted based on the mechanical conservation law that the sum of the derivatives of kinetic energy and gravitational potential energy with respect to time is zero, and the derivative expression of acceleration is obtained, including: because Where F = ma, that is Then the derivative expression of acceleration is: Among them, C represents the integration constant and G represents the gravitational constant.

7. The method according to claim 1, characterized in that According to the principle of conservation of angular momentum, the time relationship in the derivative expression of acceleration is converted into the radial position relationship, including: The derivative expression of acceleration is expressed as in is the radial velocity, is the angular velocity; according to the law of conservation of angular momentum, is a constant, where L is the angular momentum, so Therefore That is, the radial position relationship is: C represents the integration constant, m represents the mass of the satellite, G represents the gravitational constant, r represents the distance between the earth and the satellite, t represents the launch time, and M represents the mass of the earth.

8. The method according to claim 1, characterized in that Integrating the radial position relationship to obtain the orbit equation of the satellite includes: By integrating the radial position relationship, the orbit equation of the satellite is obtained as follows: or Among them, C represents the integration constant, m represents the mass of the satellite, G represents the gravitational constant, r represents the distance between the earth and the satellite, θ represents the launch angle, M represents the mass of the earth, L represents the angular momentum, and r0 represents the radius of the earth.

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