Method for designing relay mission orbit of lunar back sampling task
Through iterative calculation and full perturbation term consideration, we quickly solve the track design parameters of the lunar back sampling task relay mission with high precision, solve the problems of insufficient accuracy and influence of long-term inclination in the existing technology, and achieve high track design Accuracy and quick solution.
Patent Information
- Application Number
- CN202411494455.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-10-24
- Publication Date
- 2025-02-18
AI Technical Summary
The prior art is difficult to quickly solve the design parameters of the mission track of the lunar back sampling task with high accuracy, and the destructive effect of long-term terms caused by inclination on the frozen track conditions is not considered.
By determining the initial parameters of the large elliptical orbit of the moon, substituting a system of nonlinear equations that consider the total perturbation term, solving the deviation amount of the orbital semi-major axis, eccentricity and orbital inclination, calculating the sensitivity matrix and correction amount, and iteratively compute until the convergence criterion is met. , and pre-bias processing is performed considering the amount of change in the inclination angle for a long period.
High-precision and rapid solution of mission tracks for the lunar back sampling task is realized, which enhances the accuracy of the calculation model, reduces the increment of track maintenance speed, and simplifies the initial value calculation method.
Smart Images
Figure CN119475703A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the field of deep space exploration orbit design, and is a method for designing a relay mission orbit for a lunar far side sampling mission. Background Art
[0002] In order to cope with various uncertainties in the implementation of the project, my country's unmanned sampling and return mission on the far side of the moon has designed a multi-window launch plan for multiple years, multiple months, and multiple days per month to ensure the reliable implementation of the mission. The lunar sampling times corresponding to these windows are different, and the spatial geometric relationships corresponding to the lunar surface work in each window are also different. The large elliptical frozen sun-synchronous tracking and control regression orbit is a good choice for the mission orbit. How to give the design parameters of such an orbit with high precision is an urgent problem to be solved in engineering.
[0003] The iterative initial value calculation of the existing method is relatively complex and not easy to implement in engineering; moreover, the existing method considers fewer perturbation factors, and the calculation results cannot meet the requirements of high-precision engineering implementation; in addition, the existing method does not consider the destructive effect of the long-period term caused by the inclination on the frozen orbit condition. Summary of the invention
[0004] The technical problem solved by the present invention is: to overcome the deficiencies of the prior art, to propose a method for designing a relay mission orbit for a lunar far side sampling mission, and to solve the problem of high-precision and rapid solution of the relay mission orbit for the sampling mission.
[0005] The technical solution of the present invention is: a method for designing a relay mission orbit for a lunar back sampling mission, comprising: 1) Determine the initial parameters of the lunar elliptical orbit, including the initial values of the semi-major axis, eccentricity, and inclination of the orbit; 2) Substitute the initial parameters of the lunar great elliptical orbit into the nonlinear equations taking into account all perturbations to obtain the current orbital semi-major axis, eccentricity and orbital inclination, and solve for the deviation from the target orbital parameters; 3) Calculate the sensitivity matrix required to convert the deviation between the current orbit parameters and the target orbit parameters into the orbit element correction; 4) Calculate the corrections for the semi-major axis, eccentricity and orbital inclination based on the obtained deviation and sensitivity matrix; 5) Using the obtained correction, obtain the new semi-major axis, eccentricity and orbital inclination, and update the orbital semi-major axis, eccentricity and orbital inclination in step 1); 6) Determine whether the correction value meets the convergence criterion. If so, proceed to step 7). If not, return to step 2) and repeat steps 2)-5) to iteratively calculate the semi-major axis, eccentricity and orbital inclination until the convergence criterion is met; 7) Based on the convergence results, the orbital semi-major axis, eccentricity, orbital inclination and perigee argument are obtained; 8) Calculate the long-period variation of the inclination, pre-bias the mission orbit inclination, and obtain the final orbit inclination design value.
[0006] The step of determining the initial value of the lunar large elliptical orbit iteration comprises: According to the moon's own return cycle to the domestic deep space tracking and control station , calculate the initial value of the orbital angular velocity as:
[0007] According to the initial value of the average orbital angular velocity , and further obtain the initial value of the orbital semi-major axis ; Initial value of eccentricity ;in It represents the initial value of the perigee height of the lunar great elliptical orbit; Initial value of inclination .
[0008] The perturbations considered include the lunar non-spherical gravitational perturbation item, terms, the first-order terms and second-order terms of the earth's three-body gravitational perturbations, and the sun's gravitational perturbations.
[0009] Substituting the initial parameters of the lunar great elliptical orbit into the non-spherical gravitational perturbation of the moon item, The current orbital semi-major axis, eccentricity and orbital inclination are obtained from the nonlinear equations of the full perturbation model of the three-body gravitational perturbation of the Earth, the first-order term and the second-order term of the three-body gravitational perturbation of the Earth, and the solar gravitational perturbation, and the deviation from the target orbital parameters is solved, including: The initial values of the orbital semi-major axis, eccentricity and orbital inclination cosine are , substitute into the following nonlinear equations:
[0010] in, is the rate of change of right ascension of ascending node; is the rate of change of the argument of perigee; is the rate of change of the mean anomaly; is the angular velocity of the sun's rotation around the moon; Calculate the deviation between the orbit state and the right ascension of the target ascending node, the argument of perigee and the rate of change of the mean anomaly under the iterative initial value condition:
[0011] in, is the difference in the rate of change of the right ascension of the ascending node, is the difference of the rate of change of the perigee angle, is the difference in the rate of change of the mean anomaly angle.
[0012] The changing rates of the ascending node right ascension, perigee argument and mean anomaly are expressed as
[0013] Subscript represents the first-order term of the Earth's three-body gravity; Subscript represents the second-order term of the Earth's three-body gravity; Subscript The second-order band harmonics representing the non-spherical gravity of the moon; Subscript The second-order field harmonic term representing the non-spherical gravity of the moon; Subscript represents the solar gravitational term;
[0014]
[0015]
[0016]
[0017]
[0018] in, is the average angular velocity of the probe around the moon; is the average angular velocity of the moon’s revolution; is the average rotation angular velocity of the moon; is the Earth-Moon mass characteristic ratio coefficient; is the radius of the moon; is the coefficient of the second-order harmonic term of the moon’s non-spherical gravitational field.
[0019] The step 3) calculates the sensitivity matrix required for converting the deviation between the current orbit parameter and the target orbit parameter into the orbit element correction value, including: Calculate the target variable For the design variables The partial derivative matrix of as follows:
[0020] The expressions are as follows:
[0021]
[0022] .
[0023] The corrections for calculating the orbital average angular velocity, eccentricity and orbital inclination are as follows:
[0024] in, is the correction of the mean angular velocity of the orbit, is the correction value of eccentricity, is the correction value of the orbital inclination cosine, is the difference in the rate of change of right ascension of the ascending node, is the difference of the rate of change of the perigee angle, is the difference in the rate of change of the mean anomaly angle. The convergence criterion is: .
[0025] According to the convergence results, the orbital semi-major axis, eccentricity, orbital inclination and perigee argument are obtained, including: The calculated orbital semi-major axis , eccentricity , orbital inclination , and the argument of perigee , calculate the long-period rate of change of the inclination :
[0026] in, ; is the latitude argument of the sun in the lunar equatorial inertial coordinate system; the orbital semi-major axis, eccentricity and inclination are ; Maintaining cycle according to orbit , calculate the long-period variation of the inclination :
[0027] Calculate the tilt pre-bias :
[0028] After pre-biasing the inclination of the designed track, the final track inclination design value is obtained. : .
[0029] The advantages of the present invention compared with the prior art are: 1) Based on the traditional perturbation model that only considers the first-order term of the three-body gravity of the earth and the J2 term of the moon, this invention further adds the non-spherical gravitational perturbation of the moon. More perturbation factors, such as the second-order term of the earth's three-body gravitational perturbation and the solar gravitational perturbation, make the calculation model more accurate and the results can be directly used in engineering implementation.
[0030] 2) Compared with traditional methods, this invention considers for the first time the influence of the long-period term of solar gravitational perturbation on the inclination of the lunar orbit, proposes a strategy for pre-biasing the initial value of the inclination, and reduces the orbit maintenance velocity increment.
[0031] 3) Compared with the traditional method, the initial value calculation method of the present invention is simpler, has less calculation amount, and the result is easier to verify. BRIEF DESCRIPTION OF THE DRAWINGS
[0032] Figure 1 A flow chart showing the algorithm of the present invention. DETAILED DESCRIPTION
[0033] A method for designing the orbit of the relay mission of the unmanned sampling mission on the far side of the moon is proposed. First, the iterative initial conditions are obtained by considering only the first-order solution of the three-body perturbation of the earth. Then, the simplified analytical partial derivative matrix is calculated using the first-order solution of the three-body perturbation of the earth. Secondly, the second-order band harmonic term of the non-spherical gravitational perturbation of the moon is taken into consideration. , second-order field harmonic term , the first-order and second-order terms of the three-body gravitational perturbation of the Earth, the solar gravitational perturbation and other full perturbation models, and obtain high-precision numerical solutions through the nonlinear equation root-finding method; finally, according to the long-term evolution of the inclination, the mission orbit inclination is pre-biased. The specific steps are as follows: 1 Obtain the initial parameters of the lunar great elliptical orbit 1) Determine the initial value of the semi-major axis of the large elliptical orbit : According to the characteristics of the moon's own return period to the domestic deep space tracking and control station of about 24 hours, 50 minutes and 40 seconds, the period , based on which the initial value of the orbital angular velocity is calculated as: (1) According to the initial value of the average orbital angular velocity , we can further get the initial value of the orbital semi-major axis .
[0034] 2) Determine the initial value of the eccentricity of the large elliptical orbit : Based on the typical initial values of the perigee height for this type of orbit , and the calculated , the initial value of eccentricity can be calculated: (2) in, Determined by step 1), is the radius of the moon.
[0035] 3) Determine the initial value of the inclination cosine of the large elliptical orbit : (3) in, Determined by step 2).
[0036] 2. The initial values of the semi-major axis, eccentricity and orbital inclination of the large elliptical orbit solved in step 1 , substitute into the following nonlinear equations: (4) in, is the rate of change of right ascension of ascending node; is the rate of change of the argument of perigee; is the rate of change of the mean anomaly; is the angular velocity of the sun's rotation around the moon. It takes 365.26 days for the sun to rotate 360° around the moon. Therefore, the average angular velocity of the sun's rotation eastward every day is 0.9856° / d.
[0037] The changing rates of the ascending node right ascension, perigee argument and mean anomaly can be expressed as (5) Subscript represents the first-order term of the Earth's three-body gravity; Subscript represents the second-order term of the Earth's three-body gravity; Subscript The second-order band harmonics representing the non-spherical gravity of the moon.
[0038] Subscript Represents the second-order field harmonic term of the non-spherical gravity of the moon.
[0039] Subscript represents the solar gravitational term.
[0040] The expressions are as follows: (6) (7) (8) (9) (10) in, is the average angular velocity of the probe around the moon; is the average angular velocity of the moon’s revolution; is the average rotation angular velocity of the moon; is the Earth-Moon mass characteristic ratio coefficient, ; is the radius of the moon; is the coefficient of the second-order harmonic term of the non-spherical gravitational field of the moon; Calculate the difference between the orbit state and the right ascension of the target ascending node, the argument of perigee and the rate of change of the mean anomaly under the iterative initial value condition: (11) in, is the difference in the rate of change of the right ascension of the ascending node, is the difference of the rate of change of the perigee angle, is the difference in the rate of change of the mean anomaly angle.
[0041] 3. Calculation right The sensitivity matrix Computing state-space variables Will Calculate the partial derivative matrix for the design variables separately : (12) The expressions are as follows: (13) (14) (15) 4. Calculate the corrections for the semi-major axis, eccentricity and orbital inclination based on the deviation and sensitivity matrix: (16) in, is the correction of the mean angular velocity of the orbit, is the correction value of eccentricity, is the correction for the cosine of the orbital inclination. 5. Calculate the corrections for the semi-major axis, eccentricity and orbital inclination based on the deviation and sensitivity matrix. If , then exit, otherwise return to step 2.
[0042] 6. Output the orbital semi-major axis after calculation , eccentricity , orbital inclination , and the argument of perigee =90° or 270°.
[0043] 7. Pre-bias the initial tilt angle.
[0044] The calculated semi-major axis , eccentricity , orbital inclination , and the argument of perigee = 90° or 270°, calculate the long-period rate of change of the inclination : (17) in, ; is the latitude argument of the sun in the lunar equatorial inertial coordinate system.
[0045] Maintaining cycle according to orbit , generally can be taken , calculate the long-period variation of the inclination : (18) Calculate the tilt pre-bias : (19) After pre-biasing the inclination of the designed track, the final track inclination design value is obtained. : (20) It should be noted that the contents not described in detail in the specification of the present invention are well-known technologies to professionals in the field.
Claims
1. A method for designing a relay mission orbit for a lunar far side sampling mission, characterized in that: include: 1) Determine the initial parameters of the lunar elliptical orbit, including the initial values of the semi-major axis, eccentricity, and inclination of the orbit; 2) Substitute the initial parameters of the lunar great elliptical orbit into the nonlinear equations taking into account all perturbations to obtain the current orbital semi-major axis, eccentricity and orbital inclination, and solve for the deviation from the target orbital parameters; 3) Calculate the sensitivity matrix required to convert the deviation between the current orbit parameters and the target orbit parameters into the orbit element correction; 4) Calculate the corrections for the semi-major axis, eccentricity and orbital inclination based on the obtained deviation and sensitivity matrix; 5) Using the obtained correction, obtain the new semi-major axis, eccentricity and orbital inclination, and update the orbital semi-major axis, eccentricity and orbital inclination in step 1); 6) Determine whether the correction value meets the convergence criterion. If so, proceed to step 7). If not, return to step 2) and repeat steps 2)-5) to iteratively calculate the semi-major axis, eccentricity and orbital inclination until the convergence criterion is met; 7) Based on the convergence results, the orbital semi-major axis, eccentricity, orbital inclination and perigee argument are obtained; 8) Calculate the long-period variation of the inclination, pre-bias the mission orbit inclination, and obtain the final orbit inclination design value.
2. The orbit design method for the lunar far side sampling mission relay mission according to claim 1 is characterized in that: The step of determining the initial value of the lunar large elliptical orbit iteration comprises: According to the moon's own return cycle to the domestic deep space tracking and control station , calculate the initial value of the orbital angular velocity as: According to the initial value of the average orbital angular velocity , and further obtain the initial value of the orbital semi-major axis ; Initial value of eccentricity ;in It represents the initial value of the perigee height of the lunar great elliptical orbit; Initial value of inclination .
3. The orbit design method for the lunar far side sampling mission relay mission according to claim 2 is characterized in that: The perturbations considered include the lunar non-spherical gravitational perturbation item, terms, the first-order terms and second-order terms of the earth's three-body gravitational perturbations, and the sun's gravitational perturbations.
4. The orbit design method for the lunar far side sampling mission relay mission according to claim 2 is characterized in that: Substituting the initial parameters of the lunar great elliptical orbit into the non-spherical gravitational perturbation of the moon item, The current orbital semi-major axis, eccentricity and orbital inclination are obtained from the nonlinear equations of the full perturbation model of the three-body gravitational perturbation of the Earth, the first-order term and the second-order term of the three-body gravitational perturbation of the Earth, and the solar gravitational perturbation, and the deviation from the target orbital parameters is solved, including: The initial values of the orbital semi-major axis, eccentricity and orbital inclination cosine are , substitute into the following nonlinear equations: in, is the rate of change of right ascension of ascending node; is the rate of change of the argument of perigee; is the rate of change of the mean anomaly; is the angular velocity of the sun's rotation around the moon; Calculate the deviation between the orbit state and the right ascension of the target ascending node, the argument of perigee and the rate of change of the mean anomaly under the iterative initial value condition: in, is the difference in the rate of change of the right ascension of the ascending node, is the difference of the rate of change of the perigee angle, is the difference in the rate of change of the mean anomaly angle.
5. The orbit design method for the lunar far side sampling mission relay mission according to claim 4 is characterized in that: The changing rates of the ascending node right ascension, perigee argument and mean anomaly are expressed as Subscript represents the first-order term of the Earth's three-body gravity; Subscript represents the second-order term of the Earth's three-body gravity; Subscript The second-order band harmonics representing the non-spherical gravity of the moon; Subscript The second-order field harmonic term representing the non-spherical gravity of the moon; Subscript represents the solar gravitational term; in, is the average angular velocity of the probe around the moon; is the average angular velocity of the moon’s revolution; is the average rotation angular velocity of the moon; is the Earth-Moon mass characteristic ratio coefficient; is the radius of the moon; is the coefficient of the second-order harmonic term of the moon’s non-spherical gravitational field.
6. The orbit design method for the lunar far side sampling mission relay mission according to claim 5 is characterized in that: The step 3) calculates the sensitivity matrix required for converting the deviation between the current orbit parameter and the target orbit parameter into the orbit element correction value, including: Calculate the target variable For the design variables The partial derivative matrix of as follows: The expressions are as follows: 。 7. The orbit design method for the lunar far side sampling relay mission according to claim 6 is characterized in that: The corrections for calculating the orbital average angular velocity, eccentricity and orbital inclination are as follows: in, is the correction of the mean angular velocity of the orbit, is the correction value of eccentricity, is the correction value of the orbital inclination cosine, is the difference in the rate of change of the right ascension of the ascending node, is the difference of the rate of change of the perigee angle, is the difference in the rate of change of the mean anomaly angle.
8. The orbit design method for the lunar far side sampling mission relay mission according to claim 7 is characterized in that: The convergence criterion is: .
9. The method for designing a relay mission orbit for a lunar far side sampling mission according to claim 8, characterized in that: According to the convergence results, the orbital semi-major axis, eccentricity, orbital inclination and perigee argument are obtained, including: The calculated orbital semi-major axis , eccentricity , orbital inclination , and the argument of perigee , calculate the long-period rate of change of the inclination : in, ; is the latitude argument of the sun in the lunar equatorial inertial coordinate system; the orbital semi-major axis, eccentricity and inclination are ; Maintaining cycle according to orbit , calculate the long-period variation of the inclination : Calculate the tilt pre-bias : After pre-biasing the inclination of the designed track, the final track inclination design value is obtained. : 。