CN103488833B - A kind of heat radiation force modeling method of navigation satellite complex model - Google Patents

Abstract

The invention discloses a thermal radiation force modeling method of a complex model of a navigation satellite. By obtaining a three-dimensional surface model of the satellite to be analyzed, a data information database of surface components that generate thermal radiation force is established; the working conditions of each component are analyzed in The thermal radiation force in the body coordinate system, calculate the thermal radiation force and thermal radiation acceleration of the whole star through the vector synthesis of the thermal radiation force of each surface component, so as to establish the mathematical model of thermal radiation force and thermal radiation acceleration, this modeling method can Establishing a high-precision thermal radiation force model for complex satellites, as a non-conservative force, can improve and improve the dynamic model of high-precision satellites, and further improve the accuracy of orbit determination and orbit prediction.

Description

A thermal radiation force modeling method for complex models of navigation satellites

technical field

The invention relates to a thermal radiation force modeling method, in particular to a thermal radiation force modeling method for a complex model of a navigation satellite, and belongs to the technical field of aircraft design.

Background technique

With the improvement of precision orbit determination and orbit prediction accuracy requirements of navigation satellites, the establishment of accurate satellite dynamic models has become an engineering need. Photopressure perturbation is the most important error source of navigation satellites at present, and its accuracy directly affects the precise orbit determination and orbit prediction of satellites. The perturbation sources that conform to the light pressure perturbation mechanism include sunlight, the satellite's own thermal radiation, and the Earth's return light. At present, there is no published research on the precise modeling of the satellite's own thermal radiation force at home and abroad.

Contents of the invention

The technical problem of the present invention is: to overcome the deficiencies of the prior art, to provide a thermal radiation force modeling method of the complex model of the navigation satellite, and to improve the accuracy of orbit determination and orbit prediction.

The technical solution of the present invention is: a thermal radiation force modeling method of a navigation satellite complex model, the steps are as follows:

(1) Obtain the surface three-dimensional model of the satellite to be analyzed based on the coordinate system of the satellite body, mark all surface components of the satellite as i, where i is 1, ..., N, and judge the surface state of each surface component;

(2) Establish a thermal radiation force analysis database including each surface component of the satellite. The thermal radiation force information of each surface component includes: surface area A _i , thermal emissivity ε _i , and external normal of the surface component in the body coordinate system. Unit vector P _i in the axial direction = (x _i , y _i , z _i ) ^T ;

(3) Call the thermal radiation force analysis database, and calculate the thermal radiation force of all surface components under the working conditions according to the surface state of each surface component determined in step (1):

For a surface component with only one surface exposed to the space environment, its thermal radiation force F _thermali :

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}\mathrm{<span\; class="notranslate">\; h</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; l</span>}\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&sigma;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 3</span>}\mathrm{<span\; class="notranslate">\; c</span>}}$

In the formula, ε _i , A _i , T _i are the thermal emissivity, surface area, and average temperature of the i-th surface component, respectively;

ε ₀ is the thermal radiation rate of the space environment where the satellite is located, and ε ₀ =1;

T ₀ is the space ambient temperature, take T ₀ =4K;

σ is Stefan-Boltzmann constant, take σ=5.6699×10 ^-8 Wm ^-2 K ^-4 ;

c is the speed of light, take c=3×10 ⁸ m/s;

For a surface component with both sides in the space environment, its thermal radiation force F _thermali :

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}\mathrm{<span\; class="notranslate">\; h</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; l</span>}\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&sigma;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; f</span>}}{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; f</span>}}^{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; b</span>}}{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; b</span>}}^{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 3</span>}\mathrm{<span\; class="notranslate">\; c</span>}}$

In the formula, ε _if and ε _ib are the thermal emissivity of the positive and negative surfaces of the surface component i respectively;

T _if , T _ib are the average temperatures of the positive and negative surfaces of the surface part i under the surrounding environment;

(4) According to the unit vector P _i of the external normal of each surface component in the three-axis direction of the body coordinate system, the thermal radiation force F _thermali of each surface component is decomposed into a thermal radiation force vector along the three-axis direction of the body coordinate system, They are respectively recorded as (F _xi , F _yi , F _zi ), where:

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}\mathrm{<span\; class="notranslate">\; h</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; l</span>}\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&CenterDot;</span>\frac{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}{\sqrt{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}}$

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}\mathrm{<span\; class="notranslate">\; h</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; l</span>}\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&CenterDot;</span>\frac{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}{\sqrt{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}}$

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}\mathrm{<span\; class="notranslate">\; h</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; l</span>}\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\frac{{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}{\sqrt{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}}$

(5) Superimpose the thermal radiation force vectors of all surface components along the three-axis direction of the body coordinate system to obtain the thermal radiation force and thermal radiation acceleration of the whole star in the three-axis direction of the body coordinate system, thereby forming a model of acceleration;

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; i</span>}}$

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; Y</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}\mathrm{<span\; class="notranslate">\; i</span>}}$

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; Z</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}\mathrm{<span\; class="notranslate">\; i</span>}}$

${\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}}{\mathrm{<span\; class="notranslate">\; m</span>}}$

${\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; Y</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; Y</span>}}}{\mathrm{<span\; class="notranslate">\; m</span>}}$

${\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; Z</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; Z</span>}}}{\mathrm{<span\; class="notranslate">\; m</span>}}$

m is the mass of the whole star;

(6) The model including thermal radiation force and thermal radiation acceleration is used as a perturbation term of the satellite dynamic model for satellite orbit determination and orbit prediction.

The beneficial effects of the present invention compared with the prior art are: the present invention establishes the data information database of the surface components that generate thermal radiation force by obtaining the surface three-dimensional model of the satellite to be analyzed; the working condition of each component is analyzed in the body coordinate system Under the thermal radiation force, the thermal radiation force and thermal radiation acceleration of the whole star are calculated by vector synthesis of the thermal radiation force of each surface component, so as to establish the mathematical model of thermal radiation force and thermal radiation acceleration. This modeling method can establish a complex satellite. The high-precision thermal radiation force model, as a non-conservative force, can improve and improve the dynamic model of high-precision satellites, and further improve the accuracy of orbit determination and orbit prediction.

Description of drawings

Fig. 1 is the realization flowchart of the present invention;

Fig. 2 is a schematic diagram of the satellite body coordinate system;

Figure 3 is a schematic diagram of a satellite orbit arc;

Fig. 4 is a temperature bin distribution map of satellite surface components.

detailed description

The realization train of thought of the present invention is: (1) obtain the surface three-dimensional model of the satellite to be analyzed, mark as i to all surface parts numbering of satellite, i is 1, ..., N, obtain the temperature analysis report of each surface part of satellite, as input; (2) Based on the coordinate system of the satellite body, establish the data information database of the surface components that generate thermal radiation force; (3) Analyze the working conditions of each component, and call the surface temperature data of the components under different working conditions; (4) Calculate all The thermal radiation force of the surface components in the body coordinate system; (5) Calculate the thermal radiation force and thermal radiation acceleration of the whole star through the vector synthesis of the thermal radiation forces of each surface component; thus establish the mathematics of thermal radiation force and thermal radiation acceleration Model.

The specific implementation process is shown in Figure 1:

1) Obtain the surface 3D model of the satellite to be analyzed based on the coordinate system of the satellite body, mark all the surface parts of the satellite as i, i is 1, ..., N; record the number of all surface parts of the satellite as i, i is 1, ... , N, and judge the surface state of each surface component, such as solar panels and antennas, both sides are exposed to the space, while only one side of the six panels of the box is in contact with the space environment.

2) Establish a thermal radiation force analysis database including each satellite surface component, and the thermal radiation force information of each surface component includes: surface area A _i , thermal emissivity ε _i , external normal of the surface component in the three-axis body coordinate system The unit vector P _i of the direction = (x _i , y _i , z _i ) ^T ;

According to the attitude control law of the satellite, it is assumed that the origin of the satellite system coincides with the center of mass of the satellite, the Z axis is parallel to the central axis of the antenna field of view, the Y axis extends along a certain solar wing, and the X axis, Y, and Z axes satisfy the right-handed rotation rule, as shown in the figure 2 shown. For the convenience of analysis, it is defined that the three axes of the satellite mechanical coordinate system are parallel to the three axes of the star body coordinate system, and the coordinate origin is located at the center of the separation plane of the satellite and arrow, so the mechanical coordinate system has a translation vector relative to the body system Record the installation position of each component relative to the mechanical coordinate system as (r _xi0 , r _yi0 , r _zi0 ) ^T , and the normal vector P _i0 . For fixed surface components, the installation position of the component in the system: Normal vector: P _i =P _i0 .

Taking the navigation satellite as an example, according to the attitude control law of the satellite, the +Z axis points to the center of the earth, and the yaw rotation of the satellite around the Z axis makes the sun in the XOZ plane of the star system, and the +X axis faces the sun, so remember that the sun is on the body The included angle between the center and the +Z axis is θ _EPS . The solar panel is rotated by θ _EPS angle around the Y axis, so that the sunlight is vertically incident. Therefore, the normal vector P _i of the solar panel = (sinθ _EPS ,0, cosθ _EPS ).

3) Call the thermal radiation force analysis database to calculate the thermal radiation force of all surface components under the working conditions; the direction is along the external normal direction of the component.

For a surface component with only one surface exposed to the space environment, its thermal radiation force F _thermali :

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}\mathrm{<span\; class="notranslate">\; h</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; l</span>}\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&sigma;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 3</span>}\mathrm{<span\; class="notranslate">\; c</span>}}$

In the formula, ε _i , A _i , T _i are the thermal emissivity, surface area, and average temperature of the i-th surface component, respectively;

ε ₀ is the thermal radiation rate of the space environment where the satellite is located, and ε ₀ =1;

T ₀ is the space ambient temperature, take T ₀ =4K;

σ is Stefan-Boltzmann constant, take σ=5.6699×10 ^-8 Wm ^-2 K ^-4 ;

c is the speed of light, take c=3×10 ⁸ m/s;

For a surface component with both sides in the space environment, its thermal radiation force F _thermali :

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}\mathrm{<span\; class="notranslate">\; h</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; l</span>}\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&sigma;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; f</span>}}{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; f</span>}}^{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; b</span>}}{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; b</span>}}^{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 3</span>}\mathrm{<span\; class="notranslate">\; c</span>}}$

In the formula, ε _if and ε _ib are the thermal emissivity of the positive and negative surfaces of the surface component i respectively;

T _if , T _ib are the average temperatures of the positive and negative surfaces of the surface part i under the surrounding environment;

Example: the temperature distribution of each surface component is divided into different temperature bins, denoted as T _ij , which represents the temperature of the jth bin of the i-th part, where j is 1 to M, and the corresponding bin area is A _ij , Fig. 4 shows the schematic diagram of the temperature bin distribution of the satellite box panel and the solar panel.

For case 1, take the floor as an example, and record it as component 1: firstly, judge the environment of the satellite, the sunlight area: θ _EPS ≤ 90°, component 1 is illuminated by the sun, θ _EPS > 90°, component 1 is not illuminated by the sun, penumbra area The entire star is partially illuminated, and the umbra area is not illuminated by the sun. The temperature data of the components is selected according to different illumination conditions.

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}\mathrm{<span\; class="notranslate">\; h</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&sigma;</span>}<span\; class="notranslate">\; (</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}\mathrm{<span\; class="notranslate">\; j</span>}\mathrm{<span\; class="notranslate">\; f</span>}}^{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 3</span>}\mathrm{<span\; class="notranslate">\; c</span>}}$

For case 2, take a certain solar panel as an example, which is recorded as component 7: the solar panel always maintains the vertical incidence of sunlight during the non-terrestrial shadow period, so the environment where the solar panel is located is divided into sunshine area, penumbra area, and umbra area. According to different lighting conditions, select the temperature data input of the solar panel.

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}\mathrm{<span\; class="notranslate">\; h</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&sigma;</span>}<span\; class="notranslate">\; (</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; 7</span>}}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; 7</span>}\mathrm{<span\; class="notranslate">\; f</span>}}{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 7</span>}\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 7</span>}\mathrm{<span\; class="notranslate">\; j</span>}\mathrm{<span\; class="notranslate">\; f</span>}}^{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; -</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; 7</span>}}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; 7</span>}\mathrm{<span\; class="notranslate">\; b</span>}}{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 7</span>}\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 7</span>}\mathrm{<span\; class="notranslate">\; j</span>}\mathrm{<span\; class="notranslate">\; b</span>}}^{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 3</span>}\mathrm{<span\; class="notranslate">\; c</span>}}$

F _x ＝F _thermal sinθ _EPS

F _z ＝F _thermal ·cosθ _EPS

In the formula, j is the bin number of part 7, M ₇ is the number of bins divided by the temperature analysis of part 7, ε _7f , ε _7b , A _7j are the thermal emissivity and bin The area of j, T _7jf is the temperature of the sunny side of the jth surface element of the component 7, and T _7jb is the temperature of the backside of the jth surface element of the component 7.

Antennas and other payloads (component i), analyze the working environment of other components according to the attitude and orbit information, and select the temperature data input of the components according to different lighting conditions.

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}\mathrm{<span\; class="notranslate">\; h</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&sigma;</span>}<span\; class="notranslate">\; (</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; f</span>}}{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}\mathrm{<span\; class="notranslate">\; f</span>}}^{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; -</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; b</span>}}{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}\mathrm{<span\; class="notranslate">\; b</span>}}^{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 3</span>}\mathrm{<span\; class="notranslate">\; c</span>}}$

The factors in the formula are the same as above.

The working conditions of the surface components are divided into the whole star is in the non-earth shadow period and the components are illuminated by the sun, the whole star is in the non-earth shadow period and the components are not irradiated by the sun, the penumbra period, and the umbra period. The temperature of the surface components of satellites in different orbital arcs is different. When the satellite enters the penumbra area, the temperature of the components begins to change until it enters the umbra area. In the sunshine state, the orbit of the satellite with the shadow of the earth is shown in Figure 3.

The above is a method for solving the thermal radiation force of a single satellite surface component, where F _thermal =F _n , that is, the direction of the thermal radiation force of a component is along its normal vector direction.

5) According to the unit vector P _i of the external normal of each surface component in the three-axis direction of the body coordinate system, the thermal radiation force F _thermali of each surface component is decomposed into the thermal radiation force vector along the three-axis direction of the body coordinate system, respectively Denoted as (F _xi ,F _yi ,F _zi ), where:

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}\mathrm{<span\; class="notranslate">\; h</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; l</span>}\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&CenterDot;</span>\frac{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}{\sqrt{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}}$

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}\mathrm{<span\; class="notranslate">\; h</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; l</span>}\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\frac{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}{\sqrt{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}}$

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}\mathrm{<span\; class="notranslate">\; h</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; l</span>}\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\frac{{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}{\sqrt{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}}$

Superimpose the thermal radiation force vectors of all surface components along the three-axis direction of the body coordinate system to obtain the thermal radiation force and thermal radiation acceleration of the whole star in the three-axis direction of the body coordinate system, thereby forming a model including thermal radiation force and thermal radiation acceleration ;

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; i</span>}}$

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; Y</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}\mathrm{<span\; class="notranslate">\; i</span>}}$

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; Z</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}\mathrm{<span\; class="notranslate">\; i</span>}}$

${\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}}{\mathrm{<span\; class="notranslate">\; m</span>}}$

${\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; Y</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; Y</span>}}}{\mathrm{<span\; class="notranslate">\; m</span>}}$

${\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; Z</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; Z</span>}}}{\mathrm{<span\; class="notranslate">\; m</span>}}$

m is the mass of the whole star;

(6) The model including thermal radiation force and thermal radiation acceleration is used as a perturbation term of the satellite dynamic model for satellite orbit determination and orbit prediction.

Use the thermal radiation force and thermal radiation acceleration of the whole star in the three-axis direction of the body coordinate system to establish a mathematical model of thermal radiation force and thermal radiation acceleration, and make it a perturbation item of the high-precision satellite dynamic model for precise satellite positioning. orbit, orbit forecast, etc.

The thermal radiation force and thermal radiation acceleration model of the whole star in the three-axis direction of the body coordinate system takes time t as the independent variable, and is described in the form of the following Fourier series, as follows:

F _X (t)＝a ₀ /2+a ₁ cos(t)+b ₁ sin(t)+a ₂ cos(2t)+b ₂ sin(2t)+...

F _Y (t)＝a ₀ /2+a ₁ cos(t)+b ₁ sin(t)+a ₂ cos(2t)+b ₂ sin(2t)+...

F _Z (t)＝a ₀ /2+a ₁ cos(t)+b ₁ sin(t)+a ₂ cos(2t)+b ₂ sin(2t)+...

The content not described in detail in the present invention is well known to those skilled in the art.

Claims (1)

1. the heat radiation force modeling method of a navigation satellite complex model, it is characterised in that step is as follows:

(1) based on satellite body coordinate system, the surface three dimension model of satellite to be analyzed is obtained, to satellite It is 1 that all surface unit number is designated as i, i ..., N, and judge the apparent condition of each surface elements；

(2) foundation includes the heat radiation power analytical database of each satellite surface parts, each surface element The heat radiation force information of part includes: surface area A_i, thermal emissivity rate ε_i, surface elements exterior normal at body Three axial unit vector P in coordinate system_i=(x_i,y_i,z_i)^T；

(3) heat radiation power analytical database is called, according to each surface elements determined by step (1) Apparent condition, calculating all surface parts heat radiation power under residing operating mode:

Only one of which face is exposed to the surface elements of spatial environments, its heat radiation power F_thermali:

$F_{thermali}=-\frac{2\mathrm{\&sigma;}({\mathrm{\&epsiv;}}_i{A}_i{T}_i^4-{\mathrm{\&epsiv;}}_0{A}_i{T}_0^4)}{3c}$

In formula, ε_i, A_i, T_iIt is respectively the thermal emissivity rate of i-th surface elements, surface area, local environment Under mean temperature；

ε₀Residing for satellite, the thermal emissivity rate of spatial environments, takes ε₀=1；

T₀For spatial environments temperature, take T₀=4K；

σ is this special fence-Boltzmann constant, takes σ=5.6699 × 10^-8Wm^-2K^-4；

C is the light velocity, takes c=3 × 10⁸m/s；

For two sides all in the surface elements of spatial environments, its heat radiation power F_thermali:

$F_{thermali}=-\frac{2\mathrm{\&sigma;}({\mathrm{\&epsiv;}}_{if}{A}_i{T}_{if}^4-{\mathrm{\&epsiv;}}_{ib}{A}_i{T}_{ib}^4)}{3c}$

In formula, ε_if、ε_ibIt is respectively the thermal emissivity rate on positive and negative two surfaces of surface elements i；

T_if, T_ibIt is respectively surface elements i positive and negative two surfaces mean temperature under local environment；

(4) according to each surface elements exterior normal three axial unit vector P in body coordinate system_i By heat radiation power F of each surface elements_thermaliIt is decomposed into along body coordinate system three axial heat radiation power Vector, is designated as (F respectively_xi,F_yi,F_zi), wherein:

$F_{xi}=F_{thermali}\&CenterDot;\frac{x_i}{\sqrt{x_i^2+y_i^2+z_i^2}}$

$F_{yi}=F_{thermali}\&CenterDot;\frac{y_i}{\sqrt{x_i^2+y_i^2+z_i^2}}$

$F_{zi}=F_{thermali}\&CenterDot;\frac{z_i}{\sqrt{x_i^2+y_i^2+z_i^2}}$

(5) all surface parts are overlapped along body coordinate system three axial heat radiation force vector, Obtain whole star at body coordinate system three axial heat radiation power and heat radiation acceleration, thus formed and comprise Heat radiation power and the model of heat radiation acceleration；

$F_X=\underset{i=1}{\overset{N}{\&Sigma;}}{F}_{xi}$

$F_Y=\underset{i=1}{\overset{N}{\&Sigma;}}{F}_{yi}$

$F_Z=\underset{i=1}{\overset{N}{\&Sigma;}}{F}_{zi}$

$a_X=\frac{F_X}{m}$

$a_Y=\frac{F_Y}{m}$

$a_Z=\frac{F_Z}{m}$

M is the quality of whole star；

(6) using comprise heat radiation power and heat radiation acceleration model as the one of dynamical model Individual perturbing term is used for orbit determination and the orbit prediction of satellite.