A method for calculating a satellite shadow factor

Abstract

The application relates to a satellite earth shadow factor calculation method, which is used for solving the problems of low calculation accuracy and poor spatial applicability of the earth shadow factor. The application calculates half of a sun cone cone angle alpha S , half of an earth cone cone angle alpha E , and an opening angle theta of a satellite center and an earth center to the satellite, and divides the process of whether the earth blocks the sun from the satellite into four types of no blocking, intersecting blocking, full blocking or inner-embedded blocking by using the above angles, in the case of the intersecting blocking, the earth blocking projection is further divided into three cases, i.e. regions surrounded by an ellipse, a parabola and a hyperbola, and the earth shadow factors in various cases are calculated by using the definition of the earth shadow factor v. The application gets rid of the design idea of the existing technology with coarse granularity and overall approximation, carries out refined analysis on the blocking relation of the earth to the sun, is closer to the actual situation, and is higher in calculation accuracy.

Description

Technical Field

[0001] This invention relates to the field of aerospace technology, and in particular to a method for calculating satellite ground shadow factors. Background Technology

[0002] A satellite shadow occurs when, during a satellite's orbit around the Earth, the Earth lies between the sun and the satellite, blocking some or all of the sunlight, preventing the satellite from receiving direct sunlight. During the shadow period, the energy supply from solar arrays is relatively insufficient, or even stops, increasing the likelihood of abnormalities or malfunctions in satellite components. Furthermore, the satellite may be unable to perceive the sun's position, affecting satellite navigation. Similarly, during precise orbit determination, the solar radiation pressure differs when the satellite enters and exits the shadow, resulting in different perturbation forces. Therefore, accurately predicting the timing and duration of satellite shadows and analyzing their shading conditions is crucial.

[0003] Accurate prediction of the Earth's shadow and its precise description are quite complex. In aerospace engineering, it is generally assumed that: the Earth is spherical; there is no atmosphere around the Earth, meaning the refraction effect of the Earth's atmosphere on light is not considered. The Sun is considered a light source of varying size, and the relationship between the Earth's shadow and the Earth and Sun is as follows: Figure 1 As shown.

[0004] During the umbra (also known as the total shadow), satellites cannot see the sun, resulting in a total solar eclipse; during the penumbra, satellites can only see part of the sun, resulting in a partial solar eclipse; and during the annulus, satellites also only see part of the sun, resulting in an annular solar eclipse.

[0005] If we consider the sun as an equivalent, uniformly luminous disk, then the intensity of sunlight received by a satellite is directly proportional to the visible area of ​​this equivalent disk. The scaling factor describing the visible portion of this equivalent disk is known in the industry as the Earth's shadow factor, denoted by v. Typically, the Earth's shadow factor v is used to characterize the satellite's shadow; a larger Earth's shadow factor indicates less influence from the Earth's shadow. Although various methods exist for calculating the Earth's shadow factor, they usually approximate the Earth's occlusion projection as a circle, ignoring the variability of the Earth's occlusion projection. This results in low accuracy in calculating the Earth's shadow factor and makes it unsuitable for high-orbit occlusion scenarios. Summary of the Invention

[0006] To improve the accuracy of Earth's shadow factor calculation and expand its spatial applicability, this invention provides a method for calculating satellite shadow factors. This invention utilizes a conical shadow model to classify the Earth's occlusion relationship with the Sun into four types: no occlusion, full occlusion, embedded occlusion, and intersecting occlusion. In the case of intersecting occlusion, the Earth's occlusion projection is further divided into three cases, with the projection areas being the regions enclosed by ellipses, parabolas, and hyperbolas, respectively. Using the definition of the shadow factor v, the shadow factor is calculated for each case, specifically including the following:

[0007] A method for calculating satellite ground shadow factor uses a cone-shaped ground shadow model to calculate half of the solar cone angle α. S Half the cone angle of the Earth, α E The angle θ between the center of the sun and the center of the earth and the satellite is used to classify the process of whether the earth blocks the sun from the satellite's view into four types: no obstruction, intersecting obstruction, full obstruction, or embedded obstruction. In the case of intersecting obstruction, the earth's obstruction projection is further divided into three cases: the region enclosed by an ellipse, a parabola, and a hyperbola. Using the definition of the earth shadow factor v, the earth shadow factor is calculated for each case.

[0008] Furthermore, when there is embedded occlusion, the formula for calculating the ground shadow factor is as follows:

[0009]

[0010] Furthermore, in the case of intersection, when At that time, the Earth's shadow is the region enclosed by an ellipse. The formula for calculating the Earth's shadow factor is as follows:

[0011]

[0012] in,

[0013]

[0014]

[0015]

[0016]

[0017] Furthermore, in the case of intersection, when At that time, the Earth's shadow is the area enclosed by a parabola. The formula for calculating the Earth's shadow factor is as follows:

[0018]

[0019] in,

[0020]

[0021]

[0022] Furthermore, in the case of intersection, when At that time, the Earth's shadow is the area enclosed by a hyperbola. The formula for calculating the Earth's shadow factor is as follows:

[0023]

[0024] in,

[0025]

[0026]

[0027]

[0028]

[0029]

[0030] Beneficial effects

[0031] 1) This invention further subdivides the intersecting occlusion cases, making the entire occlusion process closer to the actual situation and improving the accuracy of the ground shadow factor calculation.

[0032] 2) This invention is more applicable to situations where high-orbit satellites are obstructed.

[0033] 3) This invention enables more accurate calculation of solar pressure perturbations and more precise calculation of solar panel power supply. Attached Figure Description

[0034] Figure 1 Satellite Earth Shadow Principle Diagram

[0035] Figure 2 Schematic diagram of the solar cone and the Earth cone Detailed Implementation

[0036] In satellite optical measurements, it is necessary to consider the sky and the shadow of the earth, and calculate the intensity of sunlight illuminating the satellite surface; in precise satellite orbit calculations, it is necessary to consider the perturbation of the orbit by solar radiation pressure, and also calculate the intensity of sunlight illuminating the satellite; when calculating the power supply of satellite solar cells, it is also necessary to calculate the intensity of sunlight illuminating the electromagnetic panels. In one scenario, if the sun is considered equivalent to a uniformly emitting disk, then the intensity of sunlight irradiation received by the satellite is proportional to the visible area of ​​this equivalent solar disk. The scaling factor describing the visible portion of this equivalent solar disk is known in the industry as the earth shadow factor, denoted as v. The following describes the specific implementation process of this invention:

[0037] I. Calculating basic angles using a cone-shaped ground shadow model.

[0038] like Figure 2 As shown, the Sun and Earth, along with their respective satellites, form a cone. Let α be half the angle of the Sun's cone (the angle between the axis and the generatrix). S Half of the cone angle of the Earth is α. E Let θ be the angle subtended by the center of the Sun and the center of the Earth relative to the satellite. The formulas for calculating each angle are as follows:

[0039]

[0040] Where R S R is the radius of the sun. E For the Earth's radius, It is the position vector of the sun. It is the Earth's position vector. These are the satellite's position vectors, where the three position vectors are described in the same coordinate system.

[0041] II. Occlusion Judgment

[0042] The process of determining whether the Earth blocks the sun as seen from a satellite is as follows:

[0043] 1) When θ≥α E +α S At that time, there was no obstruction;

[0044] 2) When |α S -α E |<θ<α E +α S At times, there is obstruction, and the two eclipses intersect (partial solar eclipse);

[0045] 3) When θ≤|α S -α E |When, if α E ≥α S A total solar eclipse will completely block out the light, while an annular solar eclipse will be partially blocked (this will not occur in near-Earth orbit).

[0046] III. Calculation of Earth Shadow Factor

[0047] According to the definition of the shadow factor v, its calculation formula is as follows:

[0048]

[0049] 1) When there is no obstruction, v = 1;

[0050] 2) When completely blocked (total solar eclipse), v = 0;

[0051] 3) When there is an embedded obstruction (annular solar eclipse),

[0052] 4) When |α S -α E |<θ<α E +α S During a partial solar eclipse, there is obstruction and intersection. In the case of intersection, the Earth's obstructed projection can be categorized into three types, with the projection areas corresponding to the regions enclosed by an ellipse, a parabola, and a hyperbola, respectively. The eccentricity of the corresponding quadratic curves (ellipse, parabola, and hyperbola) is:

[0053]

[0054] ①When When e < 1, the Earth's shadow is the region enclosed by an ellipse. The formula for calculating the Earth's shadow factor is as follows:

[0055]

[0056] in,

[0057]

[0058]

[0059]

[0060] ②When When e = 1, the Earth's shadow is the area enclosed by the parabola. The formula for calculating the Earth's shadow factor is as follows:

[0061]

[0062] in,

[0063]

[0064]

[0065] ③When When e > 1, the Earth's shadow is the region enclosed by the hyperbola. The formula for calculating the Earth's shadow factor is as follows:

[0066]

[0067] in,

[0068]

[0069]

[0070]

[0071]

Claims

1. A method for calculating satellite ground shadow factor, which uses a cone-shaped ground shadow model to calculate half of the solar cone angle. Half the cone angle of the Earth And the angular subduction of the satellite by the center of the sun and the center of the earth. Using the above perspective, the process of whether the Earth blocks the sun as seen from a satellite is divided into four types: unobstructed, intersecting obstruction, total obstruction, or embedded obstruction. Its characteristics are: In the case of intersecting occlusion, the Earth's occlusion projection can be divided into three cases: the regions enclosed by ellipses, parabolas, and hyperbolas, respectively. The Earth's shadow factor is then used to determine the appropriate projection. The definition of is used to calculate the ground shadow factor under various conditions; In the case of intersection, when At that time, the Earth's shadow is the region enclosed by an ellipse. The formula for calculating the Earth's shadow factor is as follows: in, 。 2. The satellite ground shadow factor calculation method according to claim 1, characterized in that: When there is inset occlusion, the formula for calculating the ground shadow factor is as follows: 。 3. A method for calculating satellite ground shadow factors according to claim 1 or 2, characterized in that: In the case of intersection, when At that time, the Earth's shadow is the area enclosed by a parabola. The formula for calculating the Earth's shadow factor is as follows: in 。 4. A method for calculating satellite ground shadow factors according to claim 1 or 2, characterized in that: In the case of intersection, when At that time, the Earth's shadow is the area enclosed by a hyperbola. The formula for calculating the Earth's shadow factor is as follows: in 。

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