CN110826224A - Method for determining spherical harmonic coefficient of small celestial body gravitational field based on gravitational acceleration - Google Patents
Method for determining spherical harmonic coefficient of small celestial body gravitational field based on gravitational acceleration Download PDFInfo
- Publication number
- CN110826224A CN110826224A CN201911074154.4A CN201911074154A CN110826224A CN 110826224 A CN110826224 A CN 110826224A CN 201911074154 A CN201911074154 A CN 201911074154A CN 110826224 A CN110826224 A CN 110826224A
- Authority
- CN
- China
- Prior art keywords
- celestial body
- small celestial
- spherical harmonic
- gravitational
- gravitational acceleration
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
Images
Landscapes
- Complex Calculations (AREA)
Abstract
The invention discloses a method for determining a spherical harmonic coefficient of a small celestial body gravitational field based on gravitational acceleration, and belongs to the field of aerospace. The implementation method of the invention comprises the following steps: the method comprises the steps of selecting sampling points near a small celestial body through a polyhedron shape model of the small celestial body, calculating gravitational acceleration of the sampling points by adopting a polyhedron method, establishing a gravitational acceleration expression according to a calculation method of a spherical harmonic gravitational field, solving simultaneous equations to obtain corresponding spherical harmonic coefficients, applying the obtained spherical harmonic coefficients to the construction of an orbit observed by the small celestial body, realizing primary orbit design of the orbit observed by the small celestial body, and improving design precision and efficiency of the orbit observed by the small celestial body. The method has the advantages of high calculation efficiency and high precision, is suitable for preliminary analysis of the movement near the small celestial body, realizes the design of the task track, and saves the resource consumption of the task track.
Description
Technical Field
The invention relates to a shape description and gravitational field modeling method for small irregular celestial bodies, in particular to a gravitational field spherical harmonic coefficient determination method for small celestial bodies with polyhedral shape models, which is suitable for the initial design of a probe orbit of a probe for the small celestial bodies and belongs to the field of aerospace.
Background
The surrounding and landing detection of the small celestial body is a key link of the small celestial body detection. In the design of the detection task, the influence of the gravitational field of the small celestial body on the track design needs to be considered. Because the small celestial bodies are small in size and mass and different in shape, the gravitational field modeling of the small celestial bodies is difficult greatly. The motion of the detector near the small celestial body is obviously disturbed by the small celestial body, and the small celestial body needs to be described more accurately.
For the surrounding orbit, the gravitational field representation method adopting the spherical harmonic coefficient has good effect. However, the small celestial bodies are different from the large planets, the irregular degree of the shapes is high, the large planets are generally spherical or quasi-spherical, the spherical harmonic coefficients of lower orders can be well described, but the small celestial bodies require the spherical harmonic coefficients of higher orders, and cannot be directly obtained through astronomical observation. In the developed modeling of small celestial gravity fields, prior art [1] (see Miller J K, Konopliv A S, Antrea PG, et al. determination of shape, gradient, and rotational state of absolute 433Eros [ J ]. Icarous, 2002,155(1):3-17) provides a method for accounting for small celestial high order spherical harmonics using on-orbit measured position velocity information, but this method requires that the detector already perform surround detection on small celestial bodies and cannot accurately estimate undetected targets.
In the prior art [2] (see Zhang Yangjiang, Cuzu, Yun Peak, irregular-shaped asteroid gravitational environment modeling and spherical harmonic coefficient solving method [ J ]. spacecraft environment engineering, 2010 (3)), a method for solving the spherical harmonic coefficient by adopting gravitational potential energy of a polyhedral model is provided, and the method solves the spherical harmonic coefficient by establishing an equality relation of the gravitational potential energy and a simultaneous equation. However, the gravitational potential energy points required by the method are more and large in calculation amount, and the gravitational potential energy is a scalar quantity and has multivalue, so that ambiguity may exist in the solved spherical harmonic coefficient.
Disclosure of Invention
Aiming at the following technical problems in the prior art: and describing the spherical harmonic coefficient gravitational field of the small irregular celestial body, and obtaining a gravitational field model with a higher order. The method for solving the polyhedral gravitational potential energy is large in calculation amount and limited in precision, and is not suitable for estimating the high-order spherical harmonic coefficient of the small celestial body. The invention discloses a method for determining a spherical harmonic coefficient of a small celestial body gravitational field based on gravitational acceleration, which aims to solve the technical problems that: the method for calculating the spherical harmonic gravitational field model coefficient by using the gravitational acceleration as an invariant and the polyhedral model is provided, a gravitational field model with a higher order is not required to be obtained, the calculated amount can be reduced, the precision can be improved, and the method is further suitable for estimating the small celestial body high-order spherical harmonic coefficient. The method has the advantages of high calculation efficiency, high precision and the like, can be suitable for constructing the orbit for observing the small celestial body, and saves the orbit task resource consumption for observing the small celestial body.
The purpose of the invention is realized by the following technical scheme.
The invention discloses a method for determining a spherical harmonic coefficient of a small celestial body gravitational field based on gravitational acceleration, which comprises the steps of selecting sampling points near a small celestial body through a polyhedral shape model of the small celestial body, calculating the gravitational acceleration of the sampling points by adopting a polyhedral method for the sampling points, establishing a gravitational acceleration expression according to a calculation method of the spherical harmonic gravitational field, solving simultaneous equations to obtain corresponding spherical harmonic coefficients, applying the obtained spherical harmonic coefficients to the construction of an encircling track observed by the small celestial body, realizing the initial track design of the encircling track observed by the small celestial body, and improving the design precision and efficiency of the encircling track observed by the small celestial body. The method has the advantages of high calculation efficiency and high precision, is suitable for preliminary analysis of the movement near the small celestial body, realizes the design of the task track, and saves the resource consumption of the task track.
The invention discloses a method for determining a spherical harmonic coefficient of a small celestial body gravitational field based on gravitational acceleration, which comprises the following steps:
the method comprises the following steps: according to the polyhedral model of the selected target, a small celestial body fixed connection coordinate system is established, the space near the small celestial body is divided into a plurality of regions, and sampling points are selected in each region and used for calculating gravitational acceleration.
And establishing a fixed connection coordinate system of the small celestial body according to the polyhedral shape model of the selected target, wherein an X axis is a minimum inertia main shaft of the small celestial body, a Z axis is a maximum inertia main shaft of the small celestial body, and a Y axis forms a complete right-hand coordinate system. And determining the maximum radius of the small celestial body, and converging the spherical harmonic gravitational field model in a convergence domain which is larger than the maximum radius from the origin of the coordinate system. In a convergence domain near the small celestial body, the space is divided into a plurality of regions according to the longitude and latitude, and sample points are randomly selected in the regions and used for solving the gravitational acceleration.
Step two: and (5) solving the gravitational acceleration of the sample points determined in the step one by adopting a polyhedral method.
The polyhedral model is a small celestial body gravitational field modeling method, and can accurately describe the gravitational field of the small homogeneous irregular celestial body. The polyhedral model simulates the surface of a small celestial body into a series of small triangles, and the gravitational potential energy and the specific gravitational acceleration of the polyhedral model are solved by an integral transformation method. Note the position of the sample point P under the celestial fixation as P (x, y, z). The three coordinates from the point to the vertex of the small triangle ABC on the surface are r respectivelyPA、rPBAnd rPCThe edge connecting the two vertices AB is defined as:
eABthe length of the edge AB. For triangular face ABC, define:
the gravitational acceleration corresponding to the sample point is
Wherein G is the gravity coefficient, σ is the density of the small celestial body, and reIs the vector from any point in the gravitational field to any point on the edge, rfThe vector from any point in the gravitational field to any point on the triangular surface ABC is defined as nfFor each edge, defining the normal vector n of the edgeeIts position is perpendicular to nfPointing out of plane, then
And sequentially calculating the gravitational acceleration of all the sample points and recording the result.
And step three, establishing a spherical harmonic gravitational field model to solve an expression corresponding to gravitational acceleration.
The form of the gravitational field of the small celestial body is represented by spherical harmonic functions, and the gravitational potential energy of the celestial body is approximated by Legendre polynomials. According to the spherical harmonic formula, the corresponding gravitational acceleration at the sampling point P is:
wherein:
Vlm,Wlmonly with respect to the position of the sample point P, solved by a recurrence formula. Wherein
Is that
Associated Legendre polynomials of
ReAnd (3) representing the reference radius of the small celestial body, taking the maximum radius of the small celestial body, wherein R represents the distance from a sampling point to the mass center of the small celestial body, and M is the mass of the small celestial body.
And step four, establishing an equality relation of the gravitational acceleration, solving the equation, and determining the coefficient of the small celestial body spherical harmonic gravitational field.
According to the second step and the third step, the gravitational acceleration obtained by adopting different modes for the same sampling point is the same, so that an equality relation of the gravitational acceleration is established. And (5) constructing an equation set to obtain spherical harmonic coefficients in the spherical harmonic functions.
For any sample point, add ClmAnd SlmFor variables, a 3 × 1 linear equation was constructed:
wherein
Is an equation
The three-axis component of (a).
Considering the geometrical significance of the spherical harmonic coefficient, if the coordinate system is established on the centroid of the small celestial body, the number of unknowns in the above formula is N (N +2), and the number of equations is 3, so that only N (N +2)/3 check points need to be selected to construct a linear equation set with dimension N (N +2), and the linear equation set is written into the form of Ax ═ b. Solving the equation system to obtain the spherical harmonic coefficient ClmAnd Slm。
An N (N +2) -dimensional linear equation set is constructed according to the formula (11), and the spherical harmonic coefficient C can be uniquely solvedlmAnd SlmHowever, in order to prevent the linear correlation of equations caused by the values of the check points, the number of the check points is increased to change the equation set into an over-determined equation set, and the least square solution of the over-determined equation set is solved to be used as the gravitational field spherical harmonic coefficient ClmAnd SlmThe optimal estimated value of (a). Solving the over-determined equation set to obtain the generalized inverse matrix A+And further by x ═ A+And b, solving the equation to obtain the spherical harmonic coefficient of the small celestial body spherical harmonic gravitational field. Preferably, the overdetermined equation set is solved in the fourth step preferably by using a singular value decomposition theory.
Further comprises the following steps: and D, applying the spherical harmonic coefficient obtained in the step four to the construction of the surrounding orbit observed by the small celestial body, realizing the initial orbit design of the surrounding orbit observed by the small celestial body, and improving the design precision and efficiency of the surrounding orbit observed by the small celestial body.
Has the advantages that:
1. the method for determining the spherical harmonic coefficient of the gravitational field of the small celestial body based on the gravitational acceleration only needs to obtain a high-order solving coefficient by approximation through a polyhedral shape model of the small celestial body, is simple to operate, and does not need to actually measure orbit data.
2. The invention discloses a method for determining a spherical harmonic coefficient of a small celestial body gravitational field based on gravitational acceleration.
3. The method for determining the spherical harmonic coefficient of the small celestial body gravitational field based on the gravitational acceleration directly fits the gravitational acceleration without differentiating the spherical harmonic coefficient again in the track design, and has high calculation precision.
4. The method for determining the spherical harmonic coefficient of the small celestial body gravitational field based on the gravitational acceleration disclosed by the invention has the advantages that the obtained spherical harmonic coefficient is applied to the construction of the surrounding orbit observed by the small celestial body, the primary orbit design of the surrounding orbit observed by the small celestial body is realized, and the design precision and efficiency of the surrounding orbit of the small celestial body are improved.
Drawings
FIG. 1 is a schematic flow chart of a method for determining a spherical harmonic coefficient of a small celestial body gravitational field based on gravitational acceleration.
FIG. 2 is a polyhedral model diagram of a minor planet 6489 in an embodiment of the present invention.
FIG. 3 is a graph of acceleration error in the X direction of a test using a spherical harmonic coefficient model determined using gravitational acceleration and gravitational potential in an example of the invention.
FIG. 4 is a graph of acceleration error in the Y direction of a test using a spherical harmonic coefficient model determined using gravitational acceleration and gravitational potential in an example of the invention.
FIG. 5 is a graph of acceleration error in the Z direction of a test using a spherical harmonic coefficient model determined using gravitational acceleration and gravitational potential in an example of the invention.
FIG. 6 the inventive example was designed to achieve a asteroid 6489 freeze orbit using the determined spherical harmonics.
Detailed Description
To better illustrate the objects and advantages of the present invention, the present invention is explained in detail below by solving the coefficients of the spherical harmonic gravitational field of the asteroid 6478.
Example 1:
as shown in fig. 1, taking a small celestial body 6489 as an example, for a gravitational field spherical harmonic coefficient, the method for determining a small celestial body gravitational field spherical harmonic coefficient based on gravitational acceleration disclosed in this embodiment specifically includes the following steps:
the method comprises the following steps: according to the polyhedron shape model of the selected target, a small celestial body fixed connection coordinate system is established, the space near the small celestial body is divided into a plurality of regions, and sampling points are selected in each region and used for calculating the gravitational acceleration.
A model of 4092 faces polyhedron shape is used, and the model diagram is shown in FIG. 2. The density of the small celestial body is 2.7g/cm3Mass 2.1X 1011And kg, establishing a small celestial body fixed connection coordinate system. The maximum radius of the small celestial body is 175m, the longitude of the area near the small celestial body is at intervals of 30 degrees, the latitude is at intervals of 10 degrees, the area near the small celestial body is divided into 216 grids, the longitude and the latitude are randomly selected in each grid, and sampling points are randomly selected at a distance of 175m to 525m and used for solving gravitational acceleration.
Step two: and (5) solving the gravitational acceleration of the sample points determined in the step one by adopting a polyhedral method.
Calculating the polyhedral model of the small celestial body 6489 according to a formula
And obtaining gravitational acceleration vectors of all sample points, and recording the result.
And step three, establishing an expression for solving the corresponding gravitational acceleration by adopting a spherical harmonic gravitational field model.
The form of the gravitational field of the small celestial body is represented by spherical harmonic functions, and the gravitational potential energy of the celestial body is approximated by Legendre polynomials. According to the spherical harmonic formula, the corresponding gravitational acceleration at the sampling point P is:
wherein:
selecting a reference radius of 175m, solving for V based on the position of each sample pointlm,WlmAnd establishing a spherical harmonic function form gravity expression.
And step four, establishing an equality relation of the gravitational acceleration, solving the equation, and determining the coefficient of the small celestial body spherical harmonic gravitational field.
According to the third step and the fourth step, the gravitational acceleration obtained by adopting different modes for the same sampling point is the same, so that an equality relation of the gravitational acceleration can be established. And (5) constructing an equation set to obtain spherical harmonic coefficients in the spherical harmonic functions.
Selecting the order of the spherical harmonic coefficient as 8, totally 80 coefficients, establishing an overdetermined equation set, and solving a generalized inverse matrix A by adopting a singular value decomposition theory+And further by x ═ A+And b, solving the equation to obtain the spherical harmonic coefficient of the small celestial body spherical harmonic gravitational field. The results obtained are shown in table 1.
TABLE 1 asteroid 6489 spherical harmonic coefficient (8X 8 th order)
Randomly selecting 1000 check points in an area with the radius of 0.2-0.6km near the asteroid, calculating by using a spherical harmonic coefficient model solved by adopting two modes of gravitational acceleration and gravitational potential energy, and comparing with an accurate value, wherein acceleration errors in three directions are shown in figures 3-5. The maximum deviation and mean for both models are shown in table 2.
TABLE 2 error comparison of two models
3-5 and Table 2 show that the fitting effect of the gravitational field model using gravitational acceleration is better than that of the gravitational field model using gravitational potential fitting, and that the gravitational field model has a plurality of inspection points with abnormally increased errors only using gravitational potential. The result shows that the model obtained by solving the gravitational acceleration has higher precision.
Step five: and D, applying the spherical harmonic coefficient obtained in the step four to the construction of the surrounding orbit observed by the small celestial body, realizing the initial orbit design of the surrounding orbit observed by the small celestial body, and improving the design precision and efficiency of the surrounding orbit observed by the small celestial body.
And designing to obtain a task orbit track near the small celestial body 6489 by adopting the obtained spherical harmonic coefficient, so as to realize surrounding observation of the small celestial body. Taking the freezing orbit as an example, the semimajor axis of the orbit is 380m, the inclination angle is 45 degrees, the amplitude angle of the paraxial point is 90 degrees, the eccentricity of the freezing orbit is 0.0439 calculated according to the spherical harmonic coefficient, and the freezing orbit is shown in fig. 6. By adopting the determined spherical harmonic coefficient, a task orbit can be designed before the detector reaches the asteroid, and the method is used for determining the initial observation and the on-orbit accurate orbit of the asteroid and improving the design precision and efficiency of the orbit observed by the asteroid.
The above detailed description is intended to illustrate the objects, aspects and advantages of the present invention, and it should be understood that the above detailed description is only exemplary of the present invention and is not intended to limit the scope of the present invention, and any modifications, equivalents, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (7)
1. A method for determining a spherical harmonic coefficient of a small celestial body gravitational field based on gravitational acceleration is characterized by comprising the following steps: comprises the following steps of (a) carrying out,
the method comprises the following steps: establishing a small celestial body fixed connection coordinate system according to a polyhedral shape model of a selected target, dividing a space near the small celestial body into a plurality of regions, and selecting sampling points in each region for calculating gravitational acceleration;
step two: solving the gravitational acceleration of the sample points determined in the step one by adopting a polyhedral method;
step three, establishing a spherical harmonic gravitational field model to solve an expression corresponding to gravitational acceleration;
and step four, establishing an equality relation of the gravitational acceleration, solving the equation, and determining the coefficient of the small celestial body spherical harmonic gravitational field.
2. The method for determining the spherical harmonic coefficient of the gravitational field of the small celestial body based on the gravitational acceleration as claimed in claim 1, wherein: and step five, applying the spherical harmonic coefficient obtained in the step four to the construction of the surrounding orbit observed by the small celestial body, realizing the initial orbit design of the surrounding orbit observed by the small celestial body, and improving the design precision and efficiency of the surrounding orbit observed by the small celestial body.
3. The method for determining the spherical harmonic coefficient of the gravitational field of the small celestial body based on gravitational acceleration as claimed in claim 1 or 2, wherein: the first implementation method comprises the following steps of,
establishing a fixed connection coordinate system of the small celestial body according to a polyhedral shape model of the selected target, wherein an X axis is a minimum inertia main shaft of the small celestial body, a Z axis is a maximum inertia main shaft of the small celestial body, and a Y axis forms a complete right-hand coordinate system; determining the maximum radius of the small celestial body, and converging the spherical harmonic gravitational field model in a convergence domain with the distance from the origin of the coordinate system larger than the maximum radius; in a convergence domain near the small celestial body, the space is divided into a plurality of regions according to the longitude and latitude, and sample points are randomly selected in the regions and used for solving the gravitational acceleration.
4. The method for determining the spherical harmonic coefficient of the gravitational field of the small celestial body based on gravitational acceleration as claimed in claim 3, wherein: the second step is realized by the method that,
the polyhedral model is a small celestial body gravitational field modeling method, and can accurately describe the gravitational field of the small homogeneous irregular celestial body; the polyhedral model simulates the surface of a small celestial body into a series of small triangles, and solves the gravitational potential energy and the specific gravitational acceleration of the polyhedral model by an integral transformation method; recording the position of the sample point P under the small celestial body fixed connection system as P (x, y, z); the three coordinates from the point to the vertex of the small triangle ABC on the surface are r respectivelyPA、rPBAnd rPCThe edge connecting the two vertices AB is defined as:
eABis the length of the edge AB; for triangular face ABC, define:
the gravitational acceleration corresponding to the sample point is
Wherein G is the gravity coefficient, σ is the density of the small celestial body, and reIs the vector from any point in the gravitational field to any point on the edge, rfThe vector from any point in the gravitational field to any point on the triangular surface ABC is defined as nfFor each edge, defining the normal vector n of the edgeeIts position is perpendicular to nfPointing out of plane, then
And sequentially calculating the gravitational acceleration of all the sample points and recording the result.
5. The method for determining the spherical harmonic coefficient of the gravitational field of the small celestial body based on gravitational acceleration as claimed in claim 4, wherein: the third step is to realize the method as follows,
the form of the gravitational field of the small celestial body is represented by a spherical harmonic function, and the gravitational potential energy of the celestial body is approximated by a Legendre polynomial; according to the spherical harmonic formula, the corresponding gravitational acceleration at the sampling point P is:
wherein:
Vlm,Wlmonly related to the position of the sample point P, and solving through a recurrence formula; wherein
Is that
Associated Legendre polynomials of
ReAnd (3) representing the reference radius of the small celestial body, taking the maximum radius of the small celestial body, wherein R represents the distance from a sampling point to the mass center of the small celestial body, and M is the mass of the small celestial body.
6. The method for determining the spherical harmonic coefficient of the gravitational field of the small celestial body based on gravitational acceleration as claimed in claim 5, wherein: the implementation method of the fourth step is that,
according to the second step and the third step, the gravitational acceleration obtained by adopting different modes for the same sampling point is the same, so that an equality relation of the gravitational acceleration is established; establishing an equation set to obtain spherical harmonic coefficients in the spherical harmonic functions;
for any sample point, add ClmAnd SlmFor variables, a 3 × 1 linear equation was constructed:
wherein
Is an equation
The three-axis component of (a);
considering the geometric meaning of the spherical harmonic coefficient, if the coordinate system is established on the centroid of the small celestial body, the number of the unknowns in the above formula is N (N +2), and the number of the equations is 3, so that only N (N +2)/3 check points need to be selected to construct an N (N +2) -dimensional linear equation set, and the Ax is written into a form of b; solving the equation system to obtain the spherical harmonic coefficient ClmAnd Slm；
An N (N +2) -dimensional linear equation set is constructed according to the formula (11), and the spherical harmonic coefficient C can be uniquely solvedlmAnd SlmHowever, in order to prevent the linear correlation of equations caused by the values of the check points, the number of the check points is increased to change the equation set into an over-determined equation set, and the least square solution of the over-determined equation set is solved to be used as the gravitational field spherical harmonic coefficient ClmAnd SlmThe optimal estimated value of (a); solving the over-determined equation set to obtain the generalized inverse matrix A+And further by x ═ A+And b, solving the equation to obtain the spherical harmonic coefficient of the small celestial body spherical harmonic gravitational field.
7. The method for determining the spherical harmonic coefficient of the gravitational field of the small celestial body based on gravitational acceleration as claimed in claim 6, wherein: solving the over-determined equation set in the fourth step adopts a singular value decomposition theory to solve.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201911074154.4A CN110826224A (en) | 2019-11-06 | 2019-11-06 | Method for determining spherical harmonic coefficient of small celestial body gravitational field based on gravitational acceleration |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201911074154.4A CN110826224A (en) | 2019-11-06 | 2019-11-06 | Method for determining spherical harmonic coefficient of small celestial body gravitational field based on gravitational acceleration |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN110826224A true CN110826224A (en) | 2020-02-21 |
Family
ID=69552815
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201911074154.4A Pending CN110826224A (en) | 2019-11-06 | 2019-11-06 | Method for determining spherical harmonic coefficient of small celestial body gravitational field based on gravitational acceleration |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN110826224A (en) |
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111483619A (en) * | 2020-04-20 | 2020-08-04 | 中国科学院微小卫星创新研究院 | Spacecraft gravitational acceleration calculation method and orbit control method |
| CN111695239A (en) * | 2020-05-14 | 2020-09-22 | 南京航空航天大学 | Asteroid landing segment gravitation calculation method based on dynamic polyhedral hybrid model |
| CN116819637A (en) * | 2023-07-25 | 2023-09-29 | 华中科技大学 | Gravitation effect compensation method and system |
Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105631099A (en) * | 2015-12-23 | 2016-06-01 | 北京工业大学 | Landing dynamic simulation system of small celestial body probe |
| CN106778012A (en) * | 2016-12-29 | 2017-05-31 | 北京理工大学 | A kind of small feature loss attachment detection descending trajectory optimization method |
-
2019
- 2019-11-06 CN CN201911074154.4A patent/CN110826224A/en active Pending
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105631099A (en) * | 2015-12-23 | 2016-06-01 | 北京工业大学 | Landing dynamic simulation system of small celestial body probe |
| CN106778012A (en) * | 2016-12-29 | 2017-05-31 | 北京理工大学 | A kind of small feature loss attachment detection descending trajectory optimization method |
Non-Patent Citations (3)
| Title |
|---|
| ZHANG ZHENJIANG 等: "Modeling and Analysis of Gravity Field of 433Eros Using Polyhedron Model Method", 《2010 2ND INTERNATIONAL CONFERENCE ON INFORMATION ENGINEERING AND COMPUTER SCIENCE》 * |
| 张振江 等: "不规则形状小行星引力环境建模及球谐系数求取方法", 《航天器环境工程》 * |
| 郭延宁 等: "小行星重力场全球及局部球谐系数计算与仿真", 《哈尔滨工业大学学报》 * |
Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111483619A (en) * | 2020-04-20 | 2020-08-04 | 中国科学院微小卫星创新研究院 | Spacecraft gravitational acceleration calculation method and orbit control method |
| CN111695239A (en) * | 2020-05-14 | 2020-09-22 | 南京航空航天大学 | Asteroid landing segment gravitation calculation method based on dynamic polyhedral hybrid model |
| CN111695239B (en) * | 2020-05-14 | 2024-02-13 | 南京航空航天大学 | Dynamic polyhedron hybrid model-based asteroid landing segment gravitation calculation method |
| CN116819637A (en) * | 2023-07-25 | 2023-09-29 | 华中科技大学 | Gravitation effect compensation method and system |
| CN116819637B (en) * | 2023-07-25 | 2024-05-28 | 华中科技大学 | Gravitation effect compensation method and system |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN110826224A (en) | Method for determining spherical harmonic coefficient of small celestial body gravitational field based on gravitational acceleration | |
| Park et al. | Estimating small-body gravity field from shape model and navigation data | |
| Karimi et al. | Initial orbit determination using multiple observations | |
| Takahashi et al. | Morphology driven density distribution estimation for small bodies | |
| Gao et al. | Efficient gravity field modeling method for small bodies based on Gaussian process regression | |
| CN106646645B (en) | A kind of gravity forward modeling accelerated method | |
| Gong et al. | Pursuit–evasion game for satellites based on continuous thrust reachable domain | |
| CN110609972A (en) | Free trajectory construction method for appointed launching elevation angle | |
| CN109974749A (en) | A kind of assessment method of the comprehensive error in pointing of three-axle table | |
| JP2023517146A (en) | System and method for measuring high speed wind flow with LiDAR in complex terrain | |
| Panou et al. | Fitting a triaxial ellipsoid to a geoid model | |
| Zeng et al. | An error similarity-based error-compensation method for measurement in the nonuniform temperature field | |
| Izzo et al. | Geodesy of irregular small bodies via neural density fields: geodesynets | |
| US9851441B2 (en) | Method and system for generating a distance velocity azimuth display | |
| CN113722958A (en) | Efficient modeling method for irregular-shaped small celestial body gravitational field | |
| CN110231619B (en) | Radar handover time forecasting method and device based on Enk method | |
| CN112001099A (en) | Method for quickly measuring and calculating pulsating wind pressure of antenna panel of large radio telescope | |
| Dechambre et al. | Transformation of spherical harmonic coefficients to ellipsoidal harmonic coefficients | |
| Riwanto et al. | Particle swarm optimization for magnetometer calibration with rotation axis fitting using in-orbit data | |
| CN116299740A (en) | Space domain gravity multi-parameter analysis forward modeling method of rotary rectangular prism | |
| Andrle et al. | Deterministic relative attitude determination of three-vehicle formations | |
| CN110967778A (en) | Dynamic coordinate system polyhedral subdivision gravity grid distribution correction method | |
| US9990335B2 (en) | Universal and automated monte carlo method code for uncertainty propagation in metrology databases | |
| Tanygin | Closed-form solution for lost-in-space visual navigation problem | |
| Ray et al. | Improved drag coefficient modeling with spatial and temporal Fourier coefficient expansions: theory and application |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| WD01 | Invention patent application deemed withdrawn after publication |
Application publication date: 20200221 |
|
| WD01 | Invention patent application deemed withdrawn after publication |