Lunar large elliptical orbit satellite-borne orbit forecasting method
By using the linear extrapolation method of Delaunay canonical orbit elements, the problem of three-body gravitational perturbation in the lunar highly elliptical orbit was solved, achieving efficient and accurate orbit prediction, which is suitable for on-orbit calculation and autonomous tracking pointing by spaceborne computers.
Patent Information
- Application Number
- CN202411371846.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-09-29
- Publication Date
- 2025-01-07
AI Technical Summary
Existing orbit prediction models cannot effectively handle the three-body gravitational perturbation in the Moon's highly elliptical orbit, resulting in large prediction errors. Furthermore, existing methods are either slow to compute or consume excessive resources.
A linear extrapolation method based on Delaunay canonical orbital elements is adopted, combined with analytical functions for orbital correction, which avoids numerical integration and improves calculation speed and accuracy.
It achieves orbit prediction with low computational load, high speed and high accuracy, and is suitable for on-orbit computing by spaceborne computers. In particular, it is used for autonomous tracking and pointing of lunar probes and lunar relay satellites, and has broad application potential.
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Figure CN119271947A_ABST
Abstract
Description
Technical Field
[0001] The invention belongs to the technical field of deep space exploration orbit design, and in particular relates to a satellite-borne orbit prediction method for a highly elliptical orbit around the moon. Background Art
[0002] Autonomous orbit prediction on the probe is a basic function to ensure the autonomous operation of spacecraft. The lunar probe will play a basic role in ensuring the relay satellite to complete autonomous attitude maneuvers to track the lunar lander, the lander's directional data transmission antenna to autonomously track the on-orbit relay satellite and other on-orbit real-time on-board computing tasks. It will also have a good guiding role in the relay satellite's subsequent long-term stable operation on a large elliptical frozen orbit and the autonomous generation of the required orbit correction strategy. Traditional on-board autonomous orbit prediction methods usually use a simple two-body model or a long-term orbit prediction model based on the J2 term of the non-spherical gravitational field, which is generally applicable to the prediction of low-orbit near-circular orbits around the moon or the orbit prediction of Mars orbiters. However, for the lunar large elliptical orbit, the main factor of the main gravitational perturbation has changed from non-spherical gravitational perturbation to the three-body perturbation of the earth. The main contradiction of its perturbation is different from that of the low-orbit lunar orbit and the Mars orbit, which makes the existing analytical prediction model inapplicable. For a 24-hour large elliptical orbit around the moon, the three-body gravitational perturbation acceleration will account for more than 95% of the total perturbation acceleration and is the primary perturbation term. However, the existing forecast model does not model this, resulting in forecast errors. To solve this problem, the existing methods are: 1) using multiple sets of orbital parameters to frequently inject short arc segment forecast splicing, but there are problems such as occupying the storage space of the onboard computer and uplink measurement and control resources, and multiple sets of orbital parameters are prone to input data errors; 2) or directly using numerical integration methods to solve it, but the main problem is that the calculation speed is slow and the onboard computing resources cannot meet the requirements of the calculation amount. Summary of the invention
[0003] The technical problem solved by the present invention is: to overcome the deficiencies of the prior art and provide a satellite-borne orbit prediction method for a large elliptical orbit around the moon, which has the advantages of small calculation amount, fast calculation speed and high calculation accuracy.
[0004] The object of the present invention is achieved by the following technical solution: A method for predicting a satellite-borne orbit of a lunar highly elliptical orbit, comprising: 0 The average classical orbital element at the time is converted into the initial average Delaunay canonical orbital element; according to the preset initial t 0Auxiliary variables are obtained from the classical orbit elements at time t and the initial average Delaunay canonical orbit elements; the proportional coefficient required for linear extrapolation is obtained based on the auxiliary variables; the average Delaunay canonical orbit elements at time t are obtained based on the proportional coefficient required for linear extrapolation and the preset extrapolation duration; the corrected average Delaunay canonical orbit elements at time t are obtained based on the average Delaunay canonical orbit elements at time t; the corrected average Delaunay canonical orbit elements at time t are converted into the classical orbit elements at time t; the position and velocity at time t are obtained based on the corrected average Delaunay canonical orbit elements at time t and the classical orbit elements at time t.
[0005] In the above-mentioned satellite-borne orbit prediction method for a highly elliptical orbit around the moon, the preset initial t 0 The average classical orbital element at the time is K″0=(a″0 , e″ 0 ,I″ 0 ,Ω″ 0 ,ω″ 0 ,M″0 ) ; where K″ 0 is the initial t 0 The classical orbital element of time, a″ 0 is the average semi-major axis, e″ 0 is the average eccentricity, I″ 0 is the average orbital inclination, Ω″ 0 is the right ascension of the mean ascending node, ω″ 0 is the average perigee argument, M″ 0 is the mean anomaly angle.
[0006] In the above-mentioned satellite-borne orbit prediction method for a highly elliptical orbit around the moon, the initial average Delaunay canonical orbit element is:
[0007] D″ 0 =(L″ 0 ,G″ 0 ,H″ 0 ,l″ 0 ,g″ 0 ,h″ 0 );
[0008] in,
[0009] Among them, D 0 is the initial average Delaunay canonical orbital element, μ M is the lunar gravitational constant, L″ 0 is the first element of the initial average Delaunay canonical orbit, G″ 0is the second element of the initial average Delaunay canonical orbit, H″ 0 is the third element of the initial average Delaunay canonical orbit, l″ 0 is the fourth element of the initial average Delaunay canonical orbit, g″ 0 is the fifth element of the initial average Delaunay canonical orbit, h″ 0 is the sixth element of the initial average Delaunay canonical orbit, a″ 0 is the average semi-major axis, e″ 0 is the average eccentricity, I″ 0 is the average orbital inclination, Ω″ 0 is the right ascension of the mean ascending node, ω″ 0 is the average perigee argument, M″ 0 is the mean anomaly angle.
[0010] In the above-mentioned satellite-borne orbit prediction method for a highly elliptical orbit around the moon, the auxiliary variables include: in,
[0011]
[0012]
[0013] in, is the first auxiliary variable, is the second auxiliary variable, is the third auxiliary variable, is the fourth auxiliary variable, n′ is the average orbital angular velocity of the probe; n M is the angular velocity of the moon; is the angular velocity of the moon's rotation; n E is the angular velocity of the Earth’s revolution; is the angular velocity of the Earth's rotation; b is the lunar equatorial radius; J 2 is the second-order harmonic coefficient of the non-spherical gravitational perturbation of the moon; J 22 is the second-order field harmonic coefficient of the non-spherical gravitational perturbation of the moon; ε is the coefficient of the mass ratio of the earth and the moon, L″ 0 is the first element of the initial average Delaunay canonical orbit, G″ 0 is the second element of the initial average Delaunay canonical orbit, H″ 0 is the third element of the initial average Delaunay canonical orbit, l″ 0 is the fourth element of the initial average Delaunay canonical orbit, g″ 0 is the fifth element of the initial average Delaunay canonical orbit, h″0 is the sixth element of the initial average Delaunay canonical orbit, a″ 0 is the average semi-major axis, e″ 0 is the average eccentricity, I″ 0 is the average orbital inclination, Ω″ 0 is the right ascension of the mean ascending node, ω″ 0 is the average perigee argument, M″ 0 is the mean anomaly angle.
[0014] In the above-mentioned satellite-borne orbit prediction method for a highly elliptical orbit around the moon, the proportional coefficients required for linear extrapolation include: in,
[0015]
[0016] is the first proportionality factor required for linear extrapolation, is the second proportionality factor required for linear extrapolation, is the third proportionality factor required for linear extrapolation, is the first auxiliary variable, is the second auxiliary variable, is the third auxiliary variable, μ M is the lunar gravitational constant, a″ 0 is the average semi-major axis, e″ 0 is the average eccentricity, I″ 0 is the average orbital inclination.
[0017] In the above-mentioned satellite-borne orbit prediction method for a highly elliptical orbit around the moon, the average Delaunay canonical orbit element D″ at time t is D″=(L″,G″,H″,l″,g″,h″); where,
[0018]
[0019] Δt=tt 0 ;
[0020] Among them, Δt is the extrapolation time, is the first proportionality factor required for linear extrapolation, is the second proportionality factor required for linear extrapolation, is the third proportionality factor required for linear extrapolation, is the fourth auxiliary variable, n′ is the average orbital angular velocity of the probe; n Mis the angular velocity of the moon’s revolution; L″ is the first element of the average Delaunay canonical orbit at time t, G″ is the second element of the average Delaunay canonical orbit at time t, H″ is the third element of the average Delaunay canonical orbit at time t, l″ is the fourth element of the average Delaunay canonical orbit at time t, g″ is the fifth element of the average Delaunay canonical orbit at time t, h″ is the sixth element of the average Delaunay canonical orbit at time t, L″ 0 is the first element of the initial average Delaunay canonical orbit, H″ 0 is the third element of the initial average Delaunay canonical orbit.
[0021] In the above-mentioned satellite-borne orbit prediction method for the lunar highly elliptical orbit, the average Delaunay canonical orbit element D′ at time t after correction is D′=(L′,G′,H′,l′,g′,h′); where,
[0022] L′=L″;
[0023]
[0024]
[0025] h′=h″;
[0026] Where n′ is the average orbital angular velocity of the probe; n M is the angular velocity of the moon's rotation, is the angular velocity of the moon's revolution; b is the lunar equatorial radius; J 22 is the coefficient of the second-order field harmonic term of the non-spherical gravitational perturbation of the moon; L′ is the first element of the average Delaunay canonical orbit at time t after correction, G′ is the second element of the average Delaunay canonical orbit at time t after correction, H′ is the third element of the average Delaunay canonical orbit at time t after correction, l′ is the fourth element of the average Delaunay canonical orbit at time t after correction, g′ is the fifth element of the average Delaunay canonical orbit at time t after correction, h′ is the sixth element of the average Delaunay canonical orbit at time t after correction, L″ is the first element of the average Delaunay canonical orbit at time t, G″ is the second element of the average Delaunay canonical orbit at time t, H″ is the third element of the average Delaunay canonical orbit at time t, l″ is the fourth element of the average Delaunay canonical orbit at time t, g″ is the fifth element of the average Delaunay canonical orbit at time t, h″ is the sixth element of the average Delaunay canonical orbit at time t, L″ 0is the first element of the initial average Delaunay canonical orbit, H″ 0 is the third element of the initial average Delaunay canonical orbit.
[0027] In the above-mentioned satellite-borne orbit prediction method for a highly elliptical orbit around the moon, the classical orbit element K′ at time t is K′=(a′,e′,I′,Ω′,ω′,M′); where,
[0028]
[0029] Among them, μ M is the lunar gravitational constant, L′ is the first element of the average Delaunay canonical orbit at time t after correction, G′ is the second element of the average Delaunay canonical orbit at time t after correction, H′ is the third element of the average Delaunay canonical orbit at time t after correction, l′ is the fourth element of the average Delaunay canonical orbit at time t after correction, g′ is the fifth element of the average Delaunay canonical orbit at time t after correction, h′ is the sixth element of the average Delaunay canonical orbit at time t after correction, a′ is the first-average semi-major axis, e′ is the first-average eccentricity, I′ is the first-average orbital inclination, Ω′ is the first-average ascending node right ascension, ω′ is the first-average perigee argument, and M′ is the first-average mean anomaly.
[0030] In the above-mentioned satellite-borne orbit prediction method for the highly elliptical orbit around the moon, the position at time t (R x ,R y ,R z ) is obtained by the following formula:
[0031]
[0032] Among them, R x is the x-axis component of the position at time t, R y is the y-axis component of the position at time t, R z is the z-axis component of the position at time t, E is the anomaly angle, e is the eccentricity, A x , B x , A y , B y , A z and B zare all elements of the transformation matrix, L′ is the first element of the average Delaunay canonical orbit at time t after correction, G′ is the second element of the average Delaunay canonical orbit at time t after correction, H′ is the third element of the average Delaunay canonical orbit at time t after correction, l′ is the fourth element of the average Delaunay canonical orbit at time t after correction, g′ is the fifth element of the average Delaunay canonical orbit at time t after correction, h′ is the sixth element of the average Delaunay canonical orbit at time t after correction, a′ is the first-average semi-major axis, e′ is the first-average eccentricity, I′ is the first-average orbital inclination, Ω′ is the first-average ascending node right ascension, ω′ is the first-average perigee argument, and M′ is the first-average mean anomaly.
[0033] In the above-mentioned satellite-borne orbit prediction method for a highly elliptical orbit around the moon, the velocity at time t is It is obtained by the following formula:
[0034]
[0035] in, is the x-axis component of the velocity at time t, is the y-axis component of the velocity at time t, is the z-axis component of the velocity at time t, E is the anomaly angle, e is the eccentricity, A x , B x , A y , B y , A z and B z are all elements of the transformation matrix, L′ is the first element of the average Delaunay canonical orbit at time t after correction, G′ is the second element of the average Delaunay canonical orbit at time t after correction, H′ is the third element of the average Delaunay canonical orbit at time t after correction, l′ is the fourth element of the average Delaunay canonical orbit at time t after correction, g′ is the fifth element of the average Delaunay canonical orbit at time t after correction, h′ is the sixth element of the average Delaunay canonical orbit at time t after correction, a′ is the first-average semi-major axis, e′ is the first-average eccentricity, I′ is the first-average orbital inclination, Ω′ is the first-average ascending node right ascension, ω′ is the first-average perigee argument, and M′ is the first-average mean anomaly.
[0036] Compared with the prior art, the present invention has the following beneficial effects:
[0037] The present invention does not require integration, the entire calculation process is an analytical function, the amount of calculation is small, the calculation speed is two orders of magnitude faster than numerical integration, the calculation accuracy is high, and it is particularly suitable for on-orbit calculations of satellite computers. It has direct use and reference significance for the design of satellite-borne software algorithms required for mutual autonomous tracking and pointing between lunar probes and lunar relay satellites; it has great potential application value in the long-term autonomous operation management of future large elliptical frozen orbit spacecraft or constellations. BRIEF DESCRIPTION OF THE DRAWINGS
[0038] Various other advantages and benefits will become apparent to those of ordinary skill in the art by reading the detailed description of the preferred embodiments below. The accompanying drawings are only for the purpose of illustrating the preferred embodiments and are not to be considered as limiting the present invention. Moreover, the same reference symbols are used throughout the accompanying drawings to represent the same components. In the accompanying drawings:
[0039] Figure 1 It is a flow chart of a satellite-borne orbit prediction method for a highly elliptical orbit around the moon provided in an embodiment of the present invention. DETAILED DESCRIPTION
[0040] Exemplary embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. Although exemplary embodiments of the present disclosure are shown in the accompanying drawings, it should be understood that the present disclosure can be implemented in various forms and should not be limited by the embodiments set forth herein. On the contrary, these embodiments are provided in order to enable a more thorough understanding of the present disclosure and to be able to fully convey the scope of the present disclosure to those skilled in the art. It should be noted that, in the absence of conflict, the embodiments of the present invention and the features described in the embodiments can be combined with each other. The present invention will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.
[0041] Aiming at the needs of autonomous prediction of satellite-borne orbits, a typical and widely used orbit type, the lunar large elliptical frozen orbit, a new analytical and fast orbit prediction algorithm is proposed. This algorithm comprehensively considers the calculation speed of the satellite computer and the requirements of orbit prediction accuracy, and fully considers the special characteristics of the large elliptical frozen orbit that multiple average orbital elements are constants. A new analytical orbit extrapolation method based on the linear extrapolation of the average regular orbit elements and the superposition of the correction of the orbital element periodic term is proposed, thereby solving the implementation difficulties caused by frequent orbit injection or the unbearable problem of large calculation amount caused by numerical integration. This algorithm is an analytical algorithm, which can greatly reduce the calculation amount of numerical integration and is very suitable for on-orbit calculation of satellite-borne computers. Due to its high extrapolation accuracy and small calculation amount, it has direct use and reference significance for the design of satellite-borne software algorithms required for autonomous tracking and pointing between lunar probes and relay satellites; it has great potential application value in the long-term autonomous operation management of spacecraft or constellations in future large elliptical frozen orbits.
[0042] Figure 1 It is a flow chart of a satellite-borne orbit prediction method for a highly elliptical orbit around the moon provided in an embodiment of the present invention.
[0043] like Figure 1 As shown, the method comprises the following steps:
[0044] Set the preset initial t 0 The average classical orbital element at the time is converted into the initial average Delaunay canonical orbital element;
[0045] According to the preset initial t 0 The classical orbital elements at the time and the initial average Delaunay canonical orbital elements are used to obtain auxiliary variables;
[0046] Obtain the proportional coefficient required for linear extrapolation based on the auxiliary variables
[0047] According to the proportional coefficient required for linear extrapolation and the preset extrapolation time Δt=tt 0 Get the average Delaunay canonical orbit element D″=(L″,G″,H″,l″,g″,h″) at time t;
[0048] According to the average Delaunay canonical orbit element D″=(L″,G″,H″,l″,g″,h″) at time t, the corrected average Delaunay canonical orbit element D′=(L′,G′,H′,l′,g′,h′) at time t is obtained;
[0049] Convert the corrected average Delaunay canonical orbital element D′=(L′,G′,H′,l′,g′,h′) at time t into the classical orbital element K′=(a′,e′,I′,Ω′,ω′,M′) at time t;
[0050] According to the average Delaunay canonical orbital element D′=(L′,G′,H′,l′,g′,h′) at time t after correction and the classical orbital element K′=(a′,e′,I′,Ω′,ω′,M′) at time t, the position (R x ,R y ,R z ) and speed
[0051] The preset initial t 0 The classical orbital element at the moment is K″ 0 =(a″ 0 ,e″ 0 ,I″ 0 ,Ω″ 0 ,ω″ 0 ,M″0 ), where K″ 0 is the initial t 0 The classical orbital element of time, a″ 0 is the average semi-major axis, e″ 0 is the average eccentricity, I″ 0 is the average orbital inclination, Ω″ 0 is the right ascension of the mean ascending node, ω″ 0 is the average perigee argument, M 0 is the mean anomaly angle.
[0052] The initial average Delaunay canonical orbital element is:
[0053] D″ 0 =(L″ 0 ,G″ 0 ,H″ 0 ,l″ 0 ,g″ 0 ,h″ 0 );
[0054] in,
[0055] Among them, D 0 is the initial average Delaunay canonical orbital element, μ M is the lunar gravitational constant, L″ 0 , G″ 0 , H″ 0 , l″ 0 , g″ 0 and h″ 0 They are all average Delaunay canonical orbital elements, and have a fixed mapping relationship with the classical orbital elements. L″ 0 is the first element of the initial average Delaunay canonical orbit, G″ 0 is the second element of the initial average Delaunay canonical orbit, H″ 0 is the third element of the initial average Delaunay canonical orbit, l″0 is the fourth element of the initial average Delaunay canonical orbit, g″ 0 is the fifth element of the initial average Delaunay canonical orbit, h″ 0 is the sixth element of the initial average Delaunay canonical orbit.
[0056] Auxiliary variables include: in,
[0057]
[0058]
[0059] in, is the first auxiliary variable, is the second auxiliary variable, is the third auxiliary variable, is the fourth auxiliary variable, n′ is the average orbital angular velocity of the probe; n M is the angular velocity of the moon; is the angular velocity of the moon's rotation; n E is the angular velocity of the Earth’s revolution; is the angular velocity of the Earth's rotation; b is the lunar equatorial radius; J 2 is the second-order harmonic coefficient of the non-spherical gravitational perturbation of the moon; J 22 is the second-order field harmonic coefficient of the non-spherical gravitational perturbation of the moon; ε is the coefficient of the mass ratio of the earth and the moon, ε=1+μ M / μ E , μ E and μ M are the gravitational constants of the Earth and the Moon respectively.
[0060] The scaling factors required for linear extrapolation are: in,
[0061]
[0062] is the first proportionality factor required for linear extrapolation, is the second proportionality factor required for linear extrapolation, is the third proportionality factor required for linear extrapolation, is the first auxiliary variable, is the second auxiliary variable, is the third auxiliary variable, μ M is the lunar gravitational constant, a″ 0 is the average semi-major axis, e″ 0 is the average eccentricity, I″ 0 is the average orbital inclination.
[0063] The average Delaunay canonical orbital element D″ at time t is D″=(L″,G″,H″,l″,g″,h″); where,
[0064]
[0065] Δt=tt 0 ;
[0066] Among them, Δt is the extrapolation time, is the first proportionality factor required for linear extrapolation, is the second proportionality factor required for linear extrapolation, is the third proportionality factor required for linear extrapolation, is the fourth auxiliary variable, n′ is the average orbital angular velocity of the probe; n M is the angular velocity of the moon’s revolution; L″ is the first element of the average Delaunay canonical orbit at time t, G″ is the second element of the average Delaunay canonical orbit at time t, H″ is the third element of the average Delaunay canonical orbit at time t, l″ is the fourth element of the average Delaunay canonical orbit at time t, g″ is the fifth element of the average Delaunay canonical orbit at time t, h″ is the sixth element of the average Delaunay canonical orbit at time t, L″ 0 is the first element of the initial average Delaunay canonical orbit, and H″0 is the third element of the initial average Delaunay canonical orbit.
[0067] The average Delaunay canonical orbit element D′ at time t after correction is D′=(L′,G′,H′,l′,g′,h′); where,
[0068] L′=L″;
[0069]
[0070]
[0071] h′=h″;
[0072] Where n′ is the average orbital angular velocity of the probe; n M is the angular velocity of the moon's rotation, is the angular velocity of the moon's revolution; b is the lunar equatorial radius; J 22is the coefficient of the second-order field harmonic term of the non-spherical gravitational perturbation of the moon; L′ is the first element of the average Delaunay canonical orbit at time t after correction, G′ is the second element of the average Delaunay canonical orbit at time t after correction, H′ is the third element of the average Delaunay canonical orbit at time t after correction, l′ is the fourth element of the average Delaunay canonical orbit at time t after correction, g′ is the fifth element of the average Delaunay canonical orbit at time t after correction, h′ is the sixth element of the average Delaunay canonical orbit at time t after correction, L″ is the first element of the average Delaunay canonical orbit at time t, G″ is the second element of the average Delaunay canonical orbit at time t, H″ is the third element of the average Delaunay canonical orbit at time t, l″ is the fourth element of the average Delaunay canonical orbit at time t, g″ is the fifth element of the average Delaunay canonical orbit at time t, h″ is the sixth element of the average Delaunay canonical orbit at time t, L″ 0 is the first element of the initial average Delaunay canonical orbit, H″ 0 is the third element of the initial average Delaunay canonical orbit.
[0073] The classical orbital element K′ at time t is K′=(a′,e′,I′,Ω′,ω′,M′); where,
[0074]
[0075] Among them, μ M is the lunar gravitational constant, L′, G′, H′, l′, g′ and h′ are the averaged Delaunay canonical orbit elements, a′ is the averaged semi-major axis, e′ is the averaged eccentricity, I′ is the averaged orbital inclination, Ω′ is the averaged right ascension of the ascending node, ω′ is the averaged argument of perigee, and M′ is the averaged mean anomaly.
[0076] The position at time t (R x ,R y ,R z ) is obtained by the following formula:
[0077]
[0078] Among them, R x is the x-axis component of the position at time t, R y is the y-axis component of the position at time t, R z is the z-axis component of the position at time t, E is the anomaly angle, e is the eccentricity, A x , B x , Ay , B y , A z and B z are the elements of the transformation matrix, L′, G′, H′, l′, g′ and h′ are the first-average Delaunay canonical orbit elements, a′ is the first-average semi-major axis, e′ is the first-average eccentricity, I′ is the first-average orbit inclination, Ω′ is the first-average right ascension of the ascending node, ω′ is the first-average argument of perigee, and M′ is the first-average mean anomaly.
[0079] Speed at time t It is obtained by the following formula:
[0080]
[0081] in, is the x-axis component of the velocity at time t, is the y-axis component of the velocity at time t, is the z-axis component of the velocity at time t, E is the anomaly angle, e is the eccentricity, A x , B x , A y , B y , A z and B z are the elements of the transformation matrix, L′, G′, H′, l′, g′ and h′ are the first-average Delaunay canonical orbit elements, a′ is the first-average semi-major axis, e′ is the first-average eccentricity, I′ is the first-average orbit inclination, Ω′ is the first-average right ascension of the ascending node, ω′ is the first-average argument of perigee, and M′ is the first-average mean anomaly.
[0082] Specifically, the method comprises the following steps:
[0083] (1) Obtaining the initial t 0 The average Kepler ian orbital element K″ 0 =(a″ 0 ,e″ 0 ,I″ 0 ,Ω″ 0 ,ω″ 0 ,M″ 0 );
[0084] (2) K″ 0 Transformed into Delaunay regularized variable D″ 0 =(L″ 0 ,G″ 0 ,H″ 0 ,l″ 0 ,g″ 0 ,h″ 0), the specific conversion relationship is as follows:
[0085]
[0086] (3) According to K″ 0 =(a″ 0 ,e″ 0 ,I″ 0 ,Ω″ 0 ,ω″ 0 ,M″ 0 ) and D″ 0 =(L″ 0 ,G″ 0 ,H″ 0 ,l″ 0 ,g″ 0 ,h″ 0 ) Calculate t 0 The following auxiliary variables for the moment:
[0087]
[0088] in,
[0089] n′ is the mean orbital angular velocity of the probe;
[0090] n M is the angular velocity of the moon;
[0091] is the angular velocity of the Moon’s rotation;
[0092] n E is the angular velocity of the Earth’s revolution;
[0093] is the angular velocity of the Earth’s rotation;
[0094] b is the lunar equatorial radius;
[0095] J 2 is the second-order harmonic coefficient of the non-spherical gravitational perturbation of the moon;
[0096] J 22 is the coefficient of the second-order field harmonic term of the non-spherical gravitational perturbation of the moon;
[0097] ε is the Earth-Moon mass characteristic ratio coefficient, ε=1+μ M / μ E , μ E and μM are the gravitational constants of the Earth and the Moon respectively.
[0098] (4) Based on auxiliary variables The proportionality factor required for linear extrapolation is calculated as follows:
[0099]
[0100] (5) According to the proportionality coefficient and the extrapolation time Δt = tt 0 , calculate the average orbital element D″=(L″,G″,H″,l″,g″,h″):
[0101]
[0102] (6) Based on the average orbit element D″=(L″,G″,H″,l″,g″,h″) obtained from the forecast at time t, the orbit element is periodically corrected according to the following equations (8) to (12) to obtain the corrected regular orbit element D′=(L′,G′,H′,l′,g′,h′):
[0103] L′=L″ (8)
[0104]
[0105]
[0106] h′=h″
[0107] in,
[0108]
[0109] (7) The period-corrected orbital element D′=(L′, G′, H′, l′, g′, h′) at time t is converted into the classical orbital element K′=(a′, e′, I′, Ω′, ω′, M′) at time t. The conversion formula is as follows:
[0110]
[0111] (8) Convert D′=(L′,G′,H′,l′,g′,h′) and K′=(a′,e′,I′,Ω′,ω′,M′) into the position R(x,y,z) and velocity at time t The components of a vector, the process is as follows:
[0112] a) First, calculate the following variables:
[0113]
[0114] b) Then, calculate the components of the position vector R(x,y,z):
[0115]
[0116] Where E is the eccentric anomaly angle, which can be obtained by solving the following Kepler equation based on the known e and M:
[0117] Ee sin E=M (17)
[0118] c) Finally, the velocity vector Calculate as follows:
[0119]
[0120] Thus, the position R(x, y, z) and velocity at time t can be obtained As the forecast result of orbit forecast.
[0121] This embodiment uses the average Delaunay canonical orbit element as a parameter for the dynamic characteristics of the lunar large elliptical orbit mainly affected by the three-body gravity of the Earth, and transforms the traditional three-body orbit dynamics prediction problem that requires numerical integration into a linear superposition problem of the analytical prediction results of the average orbit element and the periodic vibration results, thereby avoiding the time-consuming problem of solving the problem by the numerical integration method. Under the condition of ensuring the long-term prediction accuracy, the calculation efficiency is improved by more than 2 orders of magnitude compared with numerical integration.
[0122] This embodiment does not require integration, the entire calculation process is an analytical function, the amount of calculation is small, the calculation speed is two orders of magnitude faster than numerical integration, the calculation accuracy is high, and it is particularly suitable for on-orbit calculations of satellite-borne computers. It has direct use and reference significance for the design of satellite-borne software algorithms required for mutual autonomous tracking and pointing between lunar probes and lunar relay satellites; it has great potential application value in the long-term autonomous operation management of future large elliptical frozen orbit spacecraft or constellations.
[0123] Although the present invention has been disclosed as above in the form of a preferred embodiment, it is not intended to limit the present invention. Any person skilled in the art may make possible changes and modifications to the technical solution of the present invention by using the methods and technical contents disclosed above without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention shall fall within the protection scope of the technical solution of the present invention.
Claims
1. A method for predicting a highly elliptical orbit around the moon, characterized in that include: Convert the average classical orbital element at the preset initial time t0 into the initial average Delaunay canonical orbital element; Auxiliary variables are obtained according to the preset classical orbital elements at the initial time t0 and the initial average Delaunay canonical orbital elements; Obtain the proportionality coefficient required for linear extrapolation based on the auxiliary variables; The average Delaunay canonical orbit element at time t is obtained according to the proportional coefficient required for linear extrapolation and the preset extrapolation time; According to the average Delaunay canonical orbital element at time t, the average Delaunay canonical orbital element at time t after correction is obtained; Convert the corrected average Delaunay canonical orbital element at time t into the classical orbital element at time t; The position and velocity at time t are obtained based on the corrected average Delaunay canonical orbital element at time t and the classical orbital element at time t.
2. The satellite-borne orbit prediction method for a highly elliptical orbit around the moon according to claim 1, characterized in that: The preset average classical orbit element at the initial time t0 is K0″=(a′0′, e′0′, I0″, Ω′0′, ω0″, M0″); wherein, K0″ is the classical orbit element at the initial time t0, a″0 is the average semi-major axis, e″0 is the average eccentricity, I″0 is the average orbit inclination, Ω″0 is the average right ascension of the ascending node, ω″0 is the average perigee argument, and M″0 is the average mean anomaly.
3. The satellite-borne orbit prediction method for a highly elliptical orbit around the moon according to claim 1, characterized in that: The initial average Delaunay canonical orbital element is: D0″=(L0″,G0″,H0″,l0″,g′0′,h0″); in, Where D0″ is the initial average Delaunay canonical orbit element, μ M is the lunar gravitational constant, L0″ is the first element of the initial average Delaunay canonical orbit, G0″ is the second element of the initial average Delaunay canonical orbit, H0″ is the third element of the initial average Delaunay canonical orbit, l″0 is the fourth element of the initial average Delaunay canonical orbit, g″0 is the fifth element of the initial average Delaunay canonical orbit, h″0 is the sixth element of the initial average Delaunay canonical orbit, a″0 is the average semi-major axis, e″0 is the average eccentricity, I″0 is the average orbital inclination, Ω″0 is the average ascending node right ascension, ω″0 is the average perigee argument, and M″0 is the mean mean anomaly.
4. The satellite-borne orbit prediction method for a highly elliptical orbit around the moon according to claim 1, characterized in that: Auxiliary variables include: in, in, is the first auxiliary variable, is the second auxiliary variable, is the third auxiliary variable, is the fourth auxiliary variable, n′ is the average orbital angular velocity of the probe; n M is the angular velocity of the moon; is the angular velocity of the moon's rotation; n E is the angular velocity of the Earth’s revolution; is the rotational angular velocity of the Earth; b is the lunar equatorial radius; J2 is the second-order harmonic coefficient of the lunar non-spherical gravitational perturbation; J 22 is the coefficient of the second-order field harmonic term of the non-spherical gravitational perturbation of the moon; ε is the coefficient of the Earth-Moon mass characteristic ratio, L″0 is the first element of the initial average Delaunay canonical orbit, G″0 is the second element of the initial average Delaunay canonical orbit, H″0 is the third element of the initial average Delaunay canonical orbit, l″0 is the fourth element of the initial average Delaunay canonical orbit, g″0 is the fifth element of the initial average Delaunay canonical orbit, h″0 is the sixth element of the initial average Delaunay canonical orbit, a″0 is the average semi-major axis, e″0 is the average eccentricity, I″0 is the average orbital inclination, Ω″0 is the average ascending node right ascension, ω″0 is the average perigee argument, and M″0 is the average mean anomaly.
5. The satellite-borne orbit prediction method for a highly elliptical orbit around the moon according to claim 1, characterized in that: The scaling factors required for linear extrapolation are: in, is the first proportionality factor required for linear extrapolation, is the second proportionality factor required for linear extrapolation, is the third proportionality factor required for linear extrapolation, is the first auxiliary variable, is the second auxiliary variable, is the third auxiliary variable, μ M is the lunar gravitational constant, a0″ is the mean semi-major axis, e0″ is the mean eccentricity, and I0″ is the mean orbital inclination.
6. The satellite-borne orbit prediction method for a highly elliptical orbit around the moon according to claim 1, characterized in that: The average Delaunay canonical orbital element D″ at time t is D″=(L″,G″,H″,l″,g″,h″); where, Δt=t-t0; Among them, Δt is the extrapolation time, is the first proportionality factor required for linear extrapolation, is the second proportionality factor required for linear extrapolation, is the third proportionality factor required for linear extrapolation, is the fourth auxiliary variable, n′ is the average orbital angular velocity of the probe; n M is the angular velocity of the moon’s revolution; L″ is the first element of the average Delaunay canonical orbit at time t, G″ is the second element of the average Delaunay canonical orbit at time t, H″ is the third element of the average Delaunay canonical orbit at time t, l″ is the fourth element of the average Delaunay canonical orbit at time t, g″ is the fifth element of the average Delaunay canonical orbit at time t, h″ is the sixth element of the average Delaunay canonical orbit at time t, L″0 is the first element of the initial average Delaunay canonical orbit, and H″0 is the third element of the initial average Delaunay canonical orbit.
7. The satellite-borne orbit prediction method for a highly elliptical orbit around the moon according to claim 1, characterized in that: The average Delaunay canonical orbit element D′ at time t after correction is D′=(L′,G′,H′,l′,g′,h′); where, L′=L″; h′=h″; Where n′ is the average orbital angular velocity of the probe; n M is the rotational angular velocity of the moon, is the angular velocity of the moon's revolution; b is the lunar equatorial radius; J 22 is the coefficient of the second-order field harmonic term of the non-spherical gravitational perturbation of the moon; L′ is the first element of the average Delaunay canonical orbit at time t after correction, G′ is the second element of the average Delaunay canonical orbit at time t after correction, H′ is the third element of the average Delaunay canonical orbit at time t after correction, l′ is the fourth element of the average Delaunay canonical orbit at time t after correction, g′ is the fifth element of the average Delaunay canonical orbit at time t after correction, h′ is the sixth element of the average Delaunay canonical orbit at time t after correction, and L″ is the average The first element of the Delaunay canonical orbit, G″ is the second element of the average Delaunay canonical orbit at time t, H″ is the third element of the average Delaunay canonical orbit at time t, l″ is the fourth element of the average Delaunay canonical orbit at time t, g″ is the fifth element of the average Delaunay canonical orbit at time t, h″ is the sixth element of the average Delaunay canonical orbit at time t, L″0 is the first element of the initial average Delaunay canonical orbit, and H″0 is the third element of the initial average Delaunay canonical orbit.
8. The satellite-borne orbit prediction method for a highly elliptical orbit around the moon according to claim 1, characterized in that: The classical orbital element K′ at time t is K′=(a′,e′,I′,Ω′,ω′,M′); where, Among them, μ M is the lunar gravitational constant, L′ is the first element of the average Delaunay canonical orbit at time t after correction, G′ is the second element of the average Delaunay canonical orbit at time t after correction, H′ is the third element of the average Delaunay canonical orbit at time t after correction, l′ is the fourth element of the average Delaunay canonical orbit at time t after correction, g′ is the fifth element of the average Delaunay canonical orbit at time t after correction, h′ is the sixth element of the average Delaunay canonical orbit at time t after correction, a′ is the first-average semi-major axis, e′ is the first-average eccentricity, I′ is the first-average orbital inclination, Ω′ is the first-average ascending node right ascension, ω′ is the first-average perigee argument, and M′ is the first-average mean anomaly.
9. The satellite-borne orbit prediction method for a highly elliptical orbit around the moon according to claim 1, characterized in that: The position at time t (R x ,R y ,R z ) is obtained by the following formula: Among them, R x is the x-axis component of the position at time t, R y is the y-axis component of the position at time t, R z is the z-axis component of the position at time t, E is the anomaly angle, e is the eccentricity, A x , B x , A y , B y , A z and B z are all elements of the transformation matrix, L′ is the first element of the average Delaunay canonical orbit at time t after correction, G′ is the second element of the average Delaunay canonical orbit at time t after correction, H′ is the third element of the average Delaunay canonical orbit at time t after correction, l′ is the fourth element of the average Delaunay canonical orbit at time t after correction, g′ is the fifth element of the average Delaunay canonical orbit at time t after correction, h′ is the sixth element of the average Delaunay canonical orbit at time t after correction, a′ is the first-average semi-major axis, e′ is the first-average eccentricity, I′ is the first-average orbital inclination, Ω′ is the first-average ascending node right ascension, ω′ is the first-average perigee argument, and M′ is the first-average mean anomaly.
10. The satellite-borne orbit prediction method for a highly elliptical orbit around the moon according to claim 1, characterized in that: Speed at time t It is obtained by the following formula: in, is the x-axis component of the velocity at time t, is the y-axis component of the velocity at time t, is the z-axis component of the velocity at time t, E is the anomaly angle, e is the eccentricity, A x , B x , A y , B y , A z and B z are all elements of the transformation matrix, L′ is the first element of the average Delaunay canonical orbit at time t after correction, G′ is the second element of the average Delaunay canonical orbit at time t after correction, H′ is the third element of the average Delaunay canonical orbit at time t after correction, l′ is the fourth element of the average Delaunay canonical orbit at time t after correction, g′ is the fifth element of the average Delaunay canonical orbit at time t after correction, h′ is the sixth element of the average Delaunay canonical orbit at time t after correction, a′ is the first-average semi-major axis, e′ is the first-average eccentricity, I′ is the first-average orbital inclination, Ω′ is the first-average ascending node right ascension, ω′ is the first-average perigee argument, and M′ is the first-average mean anomaly.