CN116361597A - Satellite ground shadow factor calculation method - Google Patents

Satellite ground shadow factor calculation method Download PDF

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CN116361597A
CN116361597A CN202310140246.8A CN202310140246A CN116361597A CN 116361597 A CN116361597 A CN 116361597A CN 202310140246 A CN202310140246 A CN 202310140246A CN 116361597 A CN116361597 A CN 116361597A
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earth
shielding
shadow
satellite
sun
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张延鑫
黄建余
赵华
刘也
王东丽
杨迪
朱肇昆
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63921 Troops of PLA
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Abstract

The invention relates to a satellite ground shadow factor calculation method which is used for solving the problems of low ground shadow factor calculation accuracy and poor space applicability. The invention calculates half alpha of the cone angle of the sun cone by using the cone ground shadow model S Half alpha of cone angle of earth cone E And the aperture angle theta of the sun center and the earth center to the satellite, dividing the process of observing whether the earth shields the sun from the satellite into four types of non-shielding, intersecting shielding, full shielding or embedded shielding by utilizing the angle, and further dividing the earth shielding projection into three cases under the condition of intersecting shielding, namely, areas surrounded by ellipses, parabolas and hyperbolas, and respectively calculating the earth shadow factors under various conditions by utilizing the definition of the earth shadow factors v. The invention gets rid of the design ideas of coarse granularity and integral approximation in the prior art, carries out refinement analysis on the shielding relation of the earth to the sun, is closer to reality, and has higher calculation accuracy.

Description

Satellite ground shadow factor calculation method
Technical Field
The invention relates to the technical field of aerospace, in particular to a satellite earth shadow factor calculating method.
Background
Satellite ground shadow refers to the phenomenon that during the satellite flying around the earth, the earth is positioned between the sun and the satellite, part or all of solar rays are shielded, and the satellite cannot be irradiated by the solar rays. The solar array energy supply is relatively insufficient during the ground shadow, and even the power supply is stopped, the possibility of abnormality or failure of satellite components increases. During the earth shadow, the satellite star may not sense the sun position, which affects satellite navigation. Also, in the precise orbit determination, the satellite has different solar pressure and different power for shooting when entering and exiting the ground shadow. Therefore, it is important to accurately predict the occurrence time and duration of satellite earth shadow and analyze the shielding situation of satellite earth shadow.
Accurate descriptions of accurate forecast ground shadows are complex. In aerospace engineering it can generally be assumed that: the earth is spherical; the earth's surroundings are free of atmosphere, i.e. the refractive effect of the earth's atmosphere on light is not considered. The sun is considered as a large and small light source, and the relationship between the earth and the sun is shown in fig. 1.
In the full-view area (also called the present-view area), the satellite cannot see the sun and is in a daily full-view state; part of the sun is seen by the satellite in the penumbra area, and the satellite is in a solar food preference state; also seen in the artifact area is part of the sun, a solar ring food condition.
If the sun is equivalent to a uniformly luminous disk, the intensity of sunlight received by the satellite is proportional to the visible area of the sun equivalent disk. The scale factor describing the visible portion of this solar equivalent disk is referred to in the industry as ground shadow factor, denoted v. Generally, the satellite ground shadow is characterized by a ground shadow factor v, and the larger the ground shadow factor is, the smaller the influence of the ground shadow on the satellite is. Although various methods for calculating the earth shadow factors exist, the earth shielding projection is generally regarded as a circle approximately, and the variability of the earth shielding projection is ignored, so that the earth shadow factors have low calculation accuracy and are not suitable for the situation of high orbit shielding.
Disclosure of Invention
In order to improve the calculation accuracy of the ground shadow factors and the space applicability of the extended ground shadow factors, the invention provides a satellite ground shadow factor calculation method. The invention utilizes a cone-shaped ground shadow model to divide the earth's shielding relation to the sun into four types of non-shielding, full shielding, embedded shielding and intersecting shielding, under the condition of intersecting shielding, earth shielding projection is divided into three cases, projection areas are respectively areas surrounded by ellipses, parabolas and hyperbolas, and the definition of ground shadow factors v is utilized to respectively calculate the ground shadow factors under various conditions, and the method specifically comprises the following steps:
satellite earth shadow factor calculation method for calculating half alpha of solar cone angle by using cone earth shadow model S Half alpha of cone angle of earth cone E And the aperture angle theta of the sun center and the earth center to the satellite, dividing the process of observing whether the earth shields the sun from the satellite into four types of non-shielding, intersecting shielding, full shielding or embedded shielding by utilizing the angle, dividing the earth shielding projection into three cases under the condition of intersecting shielding, namely areas surrounded by ellipses, parabolas and hyperbolas, and respectively calculating the earth shadow factors under various conditions by utilizing the definition of the earth shadow factor v.
Further, when the occlusion is embedded, the calculation formula of the ground shadow factor is as follows,
Figure BDA0004087254320000021
further, in the case of intersection, when
Figure BDA0004087254320000022
When the earth shadow is an area surrounded by an ellipse, the earth shadow factor calculation formula is as follows:
Figure BDA0004087254320000023
wherein,,
Figure BDA0004087254320000024
Figure BDA0004087254320000025
Figure BDA0004087254320000026
Figure BDA0004087254320000027
further, in the case of intersection, when
Figure BDA0004087254320000028
When the earth shadow is a region surrounded by parabolas, the earth shadow factor calculation formula is as follows:
Figure BDA0004087254320000029
wherein,,
Figure BDA00040872543200000210
Figure BDA00040872543200000211
further, in the case of intersection, when
Figure BDA00040872543200000212
When the earth shadow is an area surrounded by hyperbolas, the earth shadow factor calculation formula is as follows:
Figure BDA0004087254320000031
wherein,,
Figure BDA0004087254320000032
Figure BDA0004087254320000033
Figure BDA0004087254320000034
Figure BDA0004087254320000035
Figure BDA0004087254320000036
advantageous effects
1) According to the invention, the intersecting shielding condition is subdivided, so that the whole shielding process is more close to the actual condition, and the calculation accuracy of the ground shadow factor is improved.
2) The invention is more suitable for the situation when the high orbit satellite is blocked.
3) The invention can ensure that the perturbation of the calculated light pressure is more accurate, the power supply of the calculated solar sailboard is more accurate,
drawings
Figure 1 satellite ground shadow schematic diagram
FIG. 2 schematic view of a solar cone and an earth cone
Detailed Description
In satellite optical measurement, the solar light intensity irradiated to the satellite surface needs to be calculated by taking the astronomical shadows into consideration; in the satellite precise orbit calculation, the perturbation of the sunlight pressure on the orbit needs to be considered, and the sunlight intensity irradiated to the satellite needs to be calculated; when calculating satellite solar cell power, it is also necessary to calculate the intensity of solar light impinging on the electromagnetic panel. In one state, if the sun is equivalent to a uniformly luminous disk, the sun exposure intensity of the satellite is proportional to the visible area of the sun equivalent disk. The scale factor describing the visible portion of this solar equivalent disk is referred to in the industry as ground shadow factor, denoted v. The following description describes the implementation of the invention:
1. basic angle calculation using cone-shaped ground shadow model
As shown in FIG. 2, the sun and the earth each form a cone with the satellite, and the half of the cone angle (the included angle between the axis and the generatrix) of the sun cone is denoted as alpha S Half of the cone angle of the earth is alpha E And (3) recording the opening angles of the sun center and the earth center to the satellite as theta, wherein the calculation formulas of the angles are as follows:
Figure BDA0004087254320000041
wherein R is S Is the radius of the sun, R E For the radius of the earth,
Figure BDA0004087254320000042
is the position vector of the sun, ">
Figure BDA0004087254320000043
Is a position vector of the earth and,
Figure BDA0004087254320000044
is a position vector of the satellite, wherein the three position vectors are descriptions in the same coordinate system.
2. Occlusion determination
The process of determining whether the earth is looking at the sun from the satellite is as follows:
1) When theta is greater than or equal to alpha E +α S When the shielding is not performed;
2) When |alpha S -α E |＜θ＜α E +α S When there is a shade, the intersection (daily food preference);
3) When theta is less than or equal to |alpha S -α E When I, if alpha E ≥α S Complete shielding (Riquan)Food) or embedded occlusion (daily diet, which does not occur in the near-earth orbit).
3. Ground shadow factor calculation
According to the definition of the ground shadow factor v, the calculation formula is as follows:
Figure BDA0004087254320000045
1) When there is no occlusion, v=1;
2) When fully occluded (full day), v=0;
3) When the shade is embedded (solar ring food),
Figure BDA0004087254320000046
4) When |alpha S -α E |＜θ＜α E +α S When the earth is in the state of intersection, earth shielding projection is divided into three cases, wherein the projection areas are respectively areas surrounded by ellipses, parabolas and hyperbolas. The eccentricity of the corresponding elliptic, parabolic and hyperbolic three conic is:
Figure BDA0004087254320000047
(1) when (when)
Figure BDA0004087254320000048
When e is less than 1, the earth shadow is an area surrounded by ellipses, and the earth shadow factor calculation formula is as follows:
Figure BDA0004087254320000049
wherein,,
Figure BDA0004087254320000051
Figure BDA0004087254320000052
Figure BDA0004087254320000053
(2) when (when)
Figure BDA0004087254320000054
When e=1, the earth shadow is an area surrounded by parabolas, and the ground shadow factor calculation formula is as follows:
Figure BDA0004087254320000055
wherein,,
Figure BDA0004087254320000056
Figure BDA0004087254320000057
(3) when (when)
Figure BDA0004087254320000058
When e is more than 1, the earth shadow is an area surrounded by hyperbolas, and the earth shadow factor calculation formula is as follows:
Figure BDA0004087254320000059
wherein,,
Figure BDA00040872543200000510
Figure BDA00040872543200000511
Figure BDA00040872543200000512
Figure BDA00040872543200000513

Claims (5)

1. satellite earth shadow factor calculation method for calculating half alpha of solar cone angle by using cone earth shadow model S Half alpha of cone angle of earth cone E And the sun center and the earth center are used for forming an opening angle theta to the satellite, and the process of observing whether the earth shields the sun from the satellite is divided into four types of non-shielding, intersecting shielding, full shielding or embedded shielding by utilizing the angle, and the method is characterized in that: under the condition of intersecting shielding, earth shielding projection is divided into three cases, namely an area surrounded by an ellipse, a parabola and a hyperbola, and the earth shadow factors under various conditions are calculated by utilizing the definition of the earth shadow factor v.
2. The method for calculating satellite ground shadow factor according to claim 1, wherein: when the occlusion is embedded, the calculation formula of the ground shadow factor is as follows,
Figure FDA0004087254310000011
3. a satellite ground shadow factor calculating method according to claim 1 or 2, wherein: in the case of intersection, when
Figure FDA0004087254310000012
When the earth shadow is an area surrounded by an ellipse, the earth shadow factor calculation formula is as follows:
Figure FDA0004087254310000013
wherein,,
Figure FDA0004087254310000014
Figure FDA0004087254310000015
Figure FDA0004087254310000016
Figure FDA0004087254310000017
4. a satellite ground shadow factor calculating method according to claim 1 or 2, wherein: in the case of intersection, when
Figure FDA0004087254310000018
When the earth shadow is a region surrounded by parabolas, the earth shadow factor calculation formula is as follows:
Figure FDA0004087254310000021
wherein the method comprises the steps of
Figure FDA0004087254310000022
Figure FDA0004087254310000023
5. A satellite ground shadow factor calculating method according to claim 1 or 2, wherein: in the case of intersection, when
Figure FDA0004087254310000024
When the earth shadow is an area surrounded by hyperbolas, the earth shadow factor calculation formula is as follows:
Figure FDA0004087254310000025
wherein the method comprises the steps of
Figure FDA0004087254310000026
Figure FDA0004087254310000027
Figure FDA0004087254310000028
Figure FDA0004087254310000029
Figure FDA00040872543100000210
CN202310140246.8A 2023-02-08 2023-02-08 Satellite ground shadow factor calculation method Pending CN116361597A (en)

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Application Number Priority Date Filing Date Title
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