CN111483619B - Spacecraft gravitational acceleration calculation method and orbit control method - Google Patents
Spacecraft gravitational acceleration calculation method and orbit control method Download PDFInfo
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- CN111483619B CN111483619B CN202010309856.2A CN202010309856A CN111483619B CN 111483619 B CN111483619 B CN 111483619B CN 202010309856 A CN202010309856 A CN 202010309856A CN 111483619 B CN111483619 B CN 111483619B
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- B64—AIRCRAFT; AVIATION; COSMONAUTICS
- B64G—COSMONAUTICS; VEHICLES OR EQUIPMENT THEREFOR
- B64G1/00—Cosmonautic vehicles
- B64G1/22—Parts of, or equipment specially adapted for fitting in or to, cosmonautic vehicles
- B64G1/24—Guiding or controlling apparatus, e.g. for attitude control
- B64G1/242—Orbits and trajectories
Abstract
The invention provides a spacecraft gravitational acceleration calculation method and an orbit control method, and provides a spacecraft gravitational acceleration calculation method for eliminating singularity, aiming at the situation that the spacecraft gravitational acceleration calculated by a traditional method is singular. The dynamic model is the basis of spacecraft orbit design and control, wherein the earth gravity is an important part for forming the near-earth orbit dynamic model. When the gravity acceleration of the spacecraft is calculated by using the traditional calculation method, a singular condition exists when the geocentric latitude of the spacecraft is close to 90 degrees. In order to enhance the robustness of the algorithm and avoid the occurrence of singular conditions, a new calculation method is provided.
Description
Technical Field
The invention relates to the technical field of spacecraft power, in particular to a spacecraft gravitational acceleration calculation method and a spacecraft orbit control method.
Background
The dynamic model is the basis of spacecraft orbit design and control, wherein the earth gravity is an important part for forming the near-earth orbit dynamic model. Since the earth is an ellipsoid, the gravitational force of the earth has non-spherical gravitational components in addition to the central gravitational force. The gravitational force is typically determined using a spherical harmonic model.
The spherical harmonic expansion of the gravitational potential of the earth is
Wherein: GM (GM)eIs the constant of the earth's gravity; reIs the earth mean radius; r, phi and lambda are respectivelyGeocentric distance, geocentric latitude, and geocentric longitude;
and
is a completely normalized spherical harmonic coefficient;
is a fully normalized associative legendre function.
The acceleration of the earth gravity can be obtained by calculating the first derivative of the earth gravity position to the position, but the spherical harmonic expansion formula of the earth gravity position takes the geocentric height r, the geocentric longitude phi and the geocentric latitude lambda under the earth-fixed relation as parameters, and usually an orbit integral equation is described by rectangular coordinates under the earth-fixed relation, so that the derivative of the earth gravity position to the position of the spacecraft under the earth-fixed relation needs to be calculated firstly, and then the derivative is converted into the earth-fixed relation. Then
Wherein:
δijis Kronecker operator.
According to the expression and the spherical harmonic coefficient of the earth gravity field model, the earth gravity acceleration under the earth-solid relation can be calculated, but when the geocentric latitude of the spacecraft is close to 90 degrees, the expression is singular, so that a novel calculation method is provided for enhancing the robustness of the algorithm and avoiding the occurrence of the singular condition.
Disclosure of Invention
The invention aims to provide a spacecraft gravitational acceleration calculation method and an orbit control method, and aims to solve the problem that spacecraft gravitational acceleration under earth-fixed connection calculated by the existing method is singular.
In order to solve the technical problem, the invention provides a spacecraft gravitational acceleration calculation method, which relates to a parameter acquisition module, a spacecraft gravitational acceleration calculation module and a near-earth orbit dynamics model generation module, wherein:
the parameter acquisition module acquires the spherical harmonic coefficient of the earth gravitational field
And
transformation matrix from earth inertia system to earth solid relation
And the position r of the spacecraft in the inertial system of the earthECIAnd sending the acceleration to the spacecraft gravitational acceleration calculation module;
the spacecraft gravitational acceleration calculation module converts the earth inertial system into the earth-solid system according to the transformation matrix
And the position r of the spacecraft in the inertial system of the earthECIAnd calculating the position of the spacecraft under the earth-fixed connection:
the spacecraft gravitational acceleration calculation module calculates the position r according to the earth contactECEFCalculating the geocentric height r, the geocentric latitude phi and the geocentric longitude lambda of the spacecraft under earth-fixed connection;
calculating a first auxiliary variable by the spacecraft gravitational acceleration calculation module
The spacecraft gravitational acceleration calculation module calculates the spherical harmonic coefficient according to the earth gravitational field
And
geocentric altitude r, geocentric latitude phi, geocentric longitude lambda and first auxiliary variable of spacecraft in earth-solid connection
Calculating the gravitational acceleration a of the spacecraft under the earth-solid connectionECEF；
The spacecraft gravitational acceleration calculation module converts the earth inertial system into the earth-solid system according to the transformation matrix
And the gravitational acceleration a of the spacecraft under the earth-solid connectionECEFTo calculate the groundGravitational acceleration of spacecraft under ball inertial system
And generating a near-earth orbit dynamic model by the near-earth orbit dynamic model generating module according to the gravitational acceleration of the spacecraft under the earth inertial system to serve as orbit determination navigation data of the spacecraft.
Optionally, in the method for calculating gravitational acceleration of spacecraft, the spacecraft gravitational acceleration calculation module calculates the gravitational acceleration of spacecraft according to a position r under earth contactECEFCalculating the geocentric altitude r, the geocentric latitude phi and the geocentric longitude lambda of the spacecraft under the earth-fixed connection comprises the following steps:
wherein x, y and z are positions r of the spacecraft in earth-fixed connectionECEFThree-dimensional coordinates of (1).
Optionally, in the method for calculating gravitational acceleration of spacecraft, the calculation module for gravitational acceleration of spacecraft may calculate the height of the earth's center of the spacecraft in earth-fixed connectionrThe geocentric latitude phi and the geocentric longitude lambda are calculated to calculate the gravitational acceleration a of the spacecraft under the earth-solid connectionECEFThe method comprises the following steps:
wherein:
optionally, in the method for calculating gravitational acceleration of spacecraft, the spacecraft gravitational acceleration calculation module calculates a first auxiliary variable
The method comprises the following steps:
introducing said first auxiliary variable
The first auxiliary variable
And associated legendre function
The relationship of (a) to (b) is as follows:
the first auxiliary variable
Satisfies the following recursion relational expression:
optionally, in the method for calculating gravitational acceleration of spacecraft, the second auxiliary variable cmAnd a third auxiliary variable smThe specific definition of (A) is as follows:
optionally, in the method for calculating gravitational acceleration of spacecraft, the second auxiliary variable c is calculatedmAnd the third auxiliary variable smAnd the recurrence relation satisfies:
optionally, in the method for calculating gravitational acceleration of spacecraft, the earth gravitational field spherical harmonic coefficient
And
and obtaining by inquiring the earth gravity field model.
The invention also provides a spacecraft orbit control method, which comprises the spacecraft gravitational acceleration calculation method.
In the spacecraft gravitational acceleration computing method and the orbit control method provided by the invention, an earth gravitational field spherical harmonic coefficient, a conversion matrix from an earth inertia system to an earth solid relation and a position of a spacecraft under the earth inertia system are obtained by a parameter obtaining module and are sent to a spacecraft gravitational acceleration computing module, the spacecraft gravitational acceleration computing module computes the position of the spacecraft under the earth solid relation according to the conversion matrix from the earth inertia system to the earth solid relation and the position of the spacecraft under the earth inertia system, the spacecraft gravitational acceleration computing module computes the geocentric altitude, the geocentric latitude and the geocentric longitude of the spacecraft under the earth solid relation according to the position under the earth solid relation, the spacecraft gravitational acceleration computing module computes the geocentric altitude, the geocentric latitude and the geocentric longitude of the spacecraft under the earth solid relation according to the spacecraft gravitational field spherical harmonic coefficient, the geocentric altitude, the geocentric latitude and the geocentric longitude, the spacecraft gravitational acceleration calculation method based on the earth-fixed relation can be used for calculating the spacecraft gravitational acceleration under the earth-fixed relation according to a transformation matrix from the earth inertial system to the earth-fixed relation and the spacecraft gravitational acceleration under the earth-fixed relation.
Drawings
Fig. 1 is a schematic flow chart of a spacecraft gravitational acceleration calculation method according to an embodiment of the present invention.
Detailed Description
The spacecraft gravitational acceleration calculation method and the orbit control method provided by the invention are further described in detail below with reference to the accompanying drawings and specific embodiments. Advantages and features of the present invention will become apparent from the following description and from the claims. It is to be noted that the drawings are in a very simplified form and are not to precise scale, which is merely for the purpose of facilitating and distinctly claiming the embodiments of the present invention.
The core idea of the invention is to provide a spacecraft gravitational acceleration calculation method and an orbit control method, so as to solve the problem that the spacecraft gravitational acceleration calculated by the existing method under earth-fixed connection is singular.
In order to realize the above thought, the invention provides a spacecraft gravitational acceleration calculation method and an orbit control method, wherein the spacecraft gravitational acceleration calculation method relates to a parameter acquisition module and a spacecraft gravitational acceleration calculation module, wherein: the parameter acquisition module acquires the spherical harmonic coefficient of the earth gravitational field
And
transformation matrix from earth inertia system to earth solid relation
And the position r of the spacecraft in the inertial system of the earthECIAnd sent to the spacecraft for gravitational accelerationA degree calculation module; the spacecraft gravitational acceleration calculation module converts the earth inertial system into the earth-solid system according to a conversion matrix
And the position r of the spacecraft in the inertial system of the earthECIAnd calculating the position of the spacecraft under the earth-fixed connection:
the spacecraft gravitational acceleration calculation module is used for calculating the gravitational acceleration of the spacecraft according to the position r under the earth contactECEFCalculating the geocentric height r, the geocentric latitude phi and the geocentric longitude lambda of the spacecraft under earth-fixed connection; the spacecraft gravitational acceleration calculation module calculates a first auxiliary variable
The spacecraft gravitational acceleration calculation module calculates the spherical harmonic coefficient according to the spacecraft gravitational field
And
geocentric altitude r, geocentric latitude phi, geocentric longitude lambda and first auxiliary variable of spacecraft in earth-solid connection
Calculating the gravitational acceleration a of the spacecraft under the earth-solid connectionECEF(ii) a The spacecraft gravitational acceleration calculation module converts the earth inertial system into the earth-solid system according to a conversion matrix
And the gravitational acceleration a of the spacecraft under the earth-solid connectionECEFAnd calculating the gravitational acceleration of the spacecraft under the earth inertial system
The near-earth orbit dynamics model generation moduleAnd generating a near-earth orbit dynamic model according to the gravitational acceleration of the spacecraft under the earth inertial system to serve as orbit determination navigation data of the spacecraft.
< example one >
The embodiment provides a spacecraft gravitational acceleration calculation method, as shown in fig. 1, the spacecraft gravitational acceleration calculation method relates to a spacecraft orbit control system, that is, the spacecraft gravitational acceleration calculation method is completed by the spacecraft orbit control system, the spacecraft orbit control system includes a parameter acquisition module and a spacecraft gravitational acceleration calculation module, wherein: the parameter acquisition module acquires the spherical harmonic coefficient of the earth gravitational field
And
transformation matrix from earth inertia system to earth solid relation
And the position r of the spacecraft in the inertial system of the earthECIAnd sending the acceleration to the spacecraft gravitational acceleration calculation module; the spacecraft gravitational acceleration calculation module converts the earth inertial system into the earth-solid system according to a conversion matrix
And the position r of the spacecraft in the inertial system of the earthECIAnd calculating the position of the spacecraft under the earth-fixed connection:
the spacecraft gravitational acceleration calculation module is used for calculating the gravitational acceleration of the spacecraft according to the position r under the earth contactECEFCalculating the geocentric height r, the geocentric latitude phi and the geocentric longitude lambda of the spacecraft under earth-fixed connection; the spacecraft gravitational acceleration calculation module calculates a first auxiliary variable
The spacecraft gravitational acceleration calculation module calculates the spherical harmonic coefficient according to the earth gravitational field
And
geocentric altitude r, geocentric latitude phi, geocentric longitude lambda and first auxiliary variable of spacecraft in earth-solid connection
Calculating the gravitational acceleration a of the spacecraft under the earth-solid connectionECEF(ii) a The spacecraft gravitational acceleration calculation module converts the earth inertial system into the earth-solid system according to a conversion matrix
And the gravitational acceleration a of the spacecraft under the earth-solid connectionECEFAnd calculating the gravitational acceleration of the spacecraft under the earth inertial system
And the near-earth orbit dynamics model generation module generates a near-earth orbit dynamics model according to the gravitational acceleration of the spacecraft under the earth inertial system, and the near-earth orbit dynamics model is used as orbit determination navigation data of the spacecraft.
Specifically, in the spacecraft orbit control system, the spacecraft gravitational acceleration calculation module calculates the position r according to the earth contactECEFCalculating the geocentric altitude r, the geocentric latitude phi and the geocentric longitude lambda of the spacecraft under the earth-fixed connection comprises the following steps:
wherein x, y and z are positions r of the spacecraft in earth-fixed connectionECEFThree-dimensional coordinates of (1).
Further, in the spacecraft orbit controlIn the system, the spacecraft gravitational acceleration calculation module calculates the spacecraft gravitational acceleration a under earth-solid connection according to the geocentric altitude r, the geocentric latitude phi and the geocentric longitude lambda of the spacecraft under earth-solid connectionECEFThe method comprises the following steps:
wherein:
in addition, in the spacecraft orbit control system, the spacecraft gravitational acceleration calculation module calculates a first auxiliary variable
The method comprises the following steps: introducing said first auxiliary variable
The first auxiliary variable
And associated legendre function
The relationship of (a) to (b) is as follows:
the above-mentionedFirst auxiliary variable
Satisfies the following recursion relational expression:
in particular, in the spacecraft orbit control system, the second auxiliary variable cmAnd a third auxiliary variable smThe specific definition is as follows:
further, in the spacecraft orbit control system, the second auxiliary variable c is calculatedmAnd the third auxiliary variable smAnd the recurrence relation satisfies:
in addition, in the spacecraft orbit control system, the earth gravitational field spherical harmonic coefficient
And
and obtaining by inquiring the earth gravity field model.
In summary, the above embodiments have described in detail different configurations of the spacecraft gravitational acceleration calculation method, and it is understood that the present invention includes, but is not limited to, the configurations listed in the above embodiments, and any modifications made on the configurations provided in the above embodiments are within the scope of the present invention. One skilled in the art can take the contents of the above embodiments to take a counter-measure.
< example two >
The embodiment provides a spacecraft orbit control method based on a spacecraft orbit control system in the previous embodiment, where the spacecraft orbit control method includes a spacecraft gravitational acceleration calculation method in the previous embodiment, and specifically includes: the parameter acquisition module acquires the spherical harmonic coefficient of the earth gravitational field
And
transformation matrix from earth inertia system to earth solid relation
And the position r of the spacecraft in the inertial system of the earthECIAnd sending the acceleration to a spacecraft gravitational acceleration calculation module; the spacecraft gravitational acceleration calculation module converts the earth inertial system into the earth-solid system according to a conversion matrix
And the position r of the spacecraft in the inertial system of the earthECIAnd calculating the position of the spacecraft under the earth-fixed connection:
the spacecraft gravitational acceleration calculation module is used for calculating the gravitational acceleration of the spacecraft according to the position r under the earth contactECEFCalculating the geocentric height r, the geocentric latitude phi and the geocentric longitude lambda of the spacecraft under earth-fixed connection; the spacecraft gravitational acceleration calculation module calculates a first auxiliary variable
The spacecraft gravitational acceleration calculation module is used for calculating the spherical harmonic of the gravitational field of the earthCoefficient of performance
And
earth center height of spacecraft in earth-fixed connectionrGeocentric latitude phi, geocentric longitude lambda and first auxiliary variable
Calculating the gravitational acceleration a of the spacecraft under the earth-solid connectionECEF(ii) a The spacecraft gravitational acceleration calculation module converts the earth inertial system into the earth-solid system according to a conversion matrix
And the gravitational acceleration a of the spacecraft under the earth-solid connectionECEFAnd calculating the gravitational acceleration of the spacecraft under the earth inertial system
And the near-earth orbit dynamics model generation module generates a near-earth orbit dynamics model according to the gravitational acceleration of the spacecraft under the earth inertial system and uses the near-earth orbit dynamics model as orbit determination navigation data of the spacecraft.
In the spacecraft gravitational acceleration computing method and the orbit control method provided by the invention, an earth gravitational field spherical harmonic coefficient, a conversion matrix from an earth inertia system to an earth solid relation and a position of a spacecraft under the earth inertia system are obtained by a parameter obtaining module and are sent to a spacecraft gravitational acceleration computing module, the spacecraft gravitational acceleration computing module computes the position of the spacecraft under the earth solid relation according to the conversion matrix from the earth inertia system to the earth solid relation and the position of the spacecraft under the earth inertia system, the spacecraft gravitational acceleration computing module computes the geocentric altitude, the geocentric latitude and the geocentric longitude of the spacecraft under the earth solid relation according to the position under the earth solid relation, the spacecraft gravitational acceleration computing module computes the geocentric altitude, the geocentric latitude and the geocentric longitude of the spacecraft under the earth solid relation according to the earth gravitational field spherical harmonic coefficient, the spacecraft gravitational acceleration calculation method based on the earth-fixed relation can be used for calculating the spacecraft gravitational acceleration under the earth-fixed relation according to a transformation matrix from the earth inertial system to the earth-fixed relation and the spacecraft gravitational acceleration under the earth-fixed relation.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. For the system disclosed by the embodiment, the description is relatively simple because the system corresponds to the method disclosed by the embodiment, and the relevant points can be referred to the method part for description.
The above description is only for the purpose of describing the preferred embodiments of the present invention, and is not intended to limit the scope of the present invention, and any variations and modifications made by those skilled in the art based on the above disclosure are within the scope of the appended claims.
Claims (7)
1. A spacecraft gravitational acceleration calculation method is characterized by involving a parameter acquisition module, a spacecraft gravitational acceleration calculation module and a near-earth orbit dynamics model generation module, wherein:
the parameter acquisition module acquires the spherical harmonic coefficient of the earth gravitational field
And
transformation matrix from earth inertia system to earth solid relation
And spacecraft in the earth's inertial systemPosition rECIAnd sending the acceleration to the spacecraft gravitational acceleration calculation module;
the spacecraft gravitational acceleration calculation module converts the earth inertial system into the earth-solid system according to the transformation matrix
And the position r of the spacecraft in the inertial system of the earthECIAnd calculating the position of the spacecraft under the earth-fixed connection:
the spacecraft gravitational acceleration calculation module calculates the position r according to the earth contactECEFCalculating the geocentric height r, the geocentric latitude phi and the geocentric longitude lambda of the spacecraft under earth-fixed connection;
calculating a first auxiliary variable by the spacecraft gravitational acceleration calculation module
The spacecraft gravitational acceleration calculation module calculates the spherical harmonic coefficient according to the earth gravitational field
And
geocentric altitude r, geocentric latitude phi, geocentric longitude lambda and first auxiliary variable of spacecraft in earth-solid connection
Calculating the gravitational acceleration a of the spacecraft under the earth-solid connectionECEF；
The spacecraft gravitational acceleration calculation module converts the earth inertial system into the earth-solid system according to the transformation matrix
And the gravitational acceleration a of the spacecraft under the earth-solid connectionECEFAnd calculating the gravitational acceleration of the spacecraft under the earth inertial system
And generating a near-earth orbit dynamic model by the near-earth orbit dynamic model generating module according to the gravitational acceleration of the spacecraft under the earth inertial system to serve as orbit determination navigation data of the spacecraft.
2. A spacecraft gravitational acceleration calculation method according to claim 1, wherein said spacecraft gravitational acceleration calculation module is based on a position r under earth contactECEFCalculating the geocentric altitude r, the geocentric latitude phi and the geocentric longitude lambda of the spacecraft under the earth-fixed connection comprises the following steps:
wherein x, y and z are positions r of the spacecraft in earth-fixed connectionECEFThree-dimensional coordinates of (1).
3. A spacecraft gravitational acceleration computing method according to claim 2, wherein said spacecraft gravitational acceleration computing module computes spacecraft gravitational acceleration a in earth-solid relation according to geocentric altitude r, geocentric latitude Φ and geocentric longitude λ of spacecraft in earth-solid relationECEFThe method comprises the following steps:
wherein:
u is a spherical harmonic expansion formula of the earth gravitational potential; GM (GM)eIs the constant of the earth's gravity; delta0mIs a Kronecker operator;
second auxiliary variable cmAnd a third auxiliary variable smThe specific definition of (A) is as follows:
4. a spacecraft gravitational acceleration calculation method according to claim 3, wherein said spacecraft gravitational acceleration calculation module calculates a first auxiliary variable
The method comprises the following steps:
introducing said first auxiliary variable
The first auxiliary variable
And associated legendre function
The relationship of (a) to (b) is as follows:
the first auxiliary variable
Satisfies the following recursion relational expression:
5. a spacecraft gravitational acceleration calculation method according to claim 4, characterized in that said second auxiliary variable c is calculatedmAnd the third auxiliary variable smAnd the recurrence relation satisfies:
c0＝1,s0＝0
6. a spacecraft gravitational acceleration calculation method according to claim 1, characterized in that said earth gravitational field spherical harmonic coefficients
And
and obtaining by inquiring the earth gravity field model.
7. A spacecraft orbit control method, characterized by comprising the spacecraft gravitational acceleration calculation method according to any one of claims 1 to 6.
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