A method for calculating the apparent magnitude of targets in lunar space optical observation

Abstract

This invention discloses a method for calculating the apparent magnitude of a target in lunisolar space optical observations, addressing the problem of improving the accuracy of apparent magnitude calculations for lunisolar space target observations. It belongs to the field of apparent magnitude calculation and includes: simulating target characteristics using a Lambertian sphere that simultaneously exhibits specular and diffuse reflection; constructing a target apparent magnitude model based on the relationship between irradiance and apparent magnitude; obtaining the target's first irradiance (using direct sunlight), second irradiance (using Earth's reflected light), and third irradiance (using moonlight) from the irradiance reaching the target using direct sunlight, Earth's reflected light, and moonlight, respectively; summing the first, second, and third irradiances to obtain the irradiance of the reflected light received by the sensor; and obtaining the apparent magnitude of the lunisolar space optical observation target based on the target apparent magnitude model. This invention improves the accuracy of brightness estimation for lunisolar space target observations.

Description

Technical Field

[0001] This invention belongs to the field of apparent magnitude calculation technology, and relates to a method for calculating the apparent magnitude of a lunar optical observation target. Background Technology

[0002] With the continuous improvement of aerospace technology capabilities, countries are vying to focus their aerospace development efforts on the Earth-Moon space.

[0003] Space situational awareness can be defined as "the identification, characterization, and understanding of any factors, whether passive or active, related to the space domain." Its significance lies in maintaining the safe operation of spacecraft in orbit, providing early warning of potential collisions, and detecting and cataloging unknown spacecraft.

[0004] With increasingly frequent human activities in the Earth-Moon space, the need for optical observation capabilities in this space is becoming increasingly urgent. Current detection capabilities are insufficient to cover the vast Earth-Moon space. Currently, situational awareness equipment is primarily used for low-Earth orbit, medium-Earth orbit, and geostationary orbit spacecraft. However, facing the distant Moon and the vast Earth-Moon space, relying solely on ground-based observation equipment is insufficient to meet the growing future demands for situational awareness in this region. Target detection in the Earth-Moon space suffers from problems such as a large observation space, short observation arc, high error sensitivity, and slow convergence in orbit determination calculations. Deploying space-based observation platforms for patrols in the Earth-Moon space can effectively increase the capacity of the observation space and the length of the observation arc, thereby enhancing situational awareness capabilities in this region.

[0005] The most common method for evaluating observation results is to calculate apparent magnitude using sunlight. For example, the apparent magnitude calculation method used in application number 202011292546.0, publication number CN112417670A, entitled "A Calculation Model for the Photometric Characteristics of a GEO Target Considering the Effect of Solar Panel Migration," only considers the solar irradiance on the target. While this is feasible for GEO targets, targets in the Earth-Moon space are closer to the Moon, and calculating apparent magnitude using only the Sun as a light source is not accurate enough. Furthermore, calculating only the solar irradiance on the target fails to determine the contributions of the Moon and Earth to the target's irradiance. Summary of the Invention

[0006] To address the technical challenge of improving the accuracy of apparent magnitude calculations for Earth-Moon space target observations, this invention proposes a method for calculating the apparent magnitude of Earth-Moon space optical observation targets, taking into account sunlight, moonlight, and Earth's albedo. This method includes the Moon and Earth in the calculation of light sources, simultaneously calculating the contributions of sunlight, moonlight, and Earth's albedo to the target's irradiance. This yields more accurate apparent magnitude calculation results, solving the problems of inaccurate target apparent magnitude calculations without considering the influence of moonlight and Earth's albedo, and the inability to calculate target apparent magnitude under conditions without sunlight. Through the optimized scheme, the contribution rates of moonlight and Earth's albedo to target brightness are effectively evaluated, and the impact of moonlight and Earth's albedo on Earth-Moon space-based optical observations is effectively determined, thus improving the accuracy of brightness estimation for Earth-Moon space target observations.

[0007] The objective of this invention is specifically achieved through the following technical solutions:

[0008] This invention discloses a method for calculating the apparent magnitude of a target in Earth-Moon space optical observation, comprising:

[0009] Step 1: Integrate the solar irradiance in the visible light band to obtain the irradiance of visible sunlight reaching the Earth; use the irradiance of visible sunlight reaching the Earth as the irradiance of direct sunlight reaching the target.

[0010] Step two: Simplify the Earth as a diffuse Lambertian sphere with a completely diffuse reflective surface, and obtain the irradiance of the Earth's reflected light reaching the target through the Lambertian reflection law;

[0011] Step 3: Integrate the irradiance of the moon's reflected light reaching the target in the visible light band to obtain the irradiance of the moonlight reaching the target.

[0012] Step 4: Use a Lambertian sphere that has both specular and diffuse reflection to simulate the target characteristics, and construct a target apparent magnitude model based on the relationship between irradiance and apparent magnitude.

[0013] Step 5: Based on the target apparent magnitude model, obtain the target's first irradiance when sunlight is the light source by obtaining the irradiance of direct sunlight reaching the target, the target's second irradiance when Earth's albedo is the light source by obtaining the irradiance of Earth's albedo reaching the target, and the target's third irradiance when moonlight is the light source by obtaining the irradiance of moonlight reaching the target.

[0014] Step six: Summing the first, second, and third irradiance of the target to obtain the irradiance of the target reflected light received by the sensor. Based on the target apparent magnitude model, the apparent magnitude of the Earth-Moon space optical observation target is obtained from the irradiance of the target reflected light received by the sensor.

[0015] In step one, the method for calculating the irradiance of direct sunlight reaching the target is as follows:

[0016] ;

[0017] In the formula, The irradiance of direct sunlight reaching the target. The irradiance of visible sunlight reaching Earth. The radius of the sun, The average distance between the Earth and the Sun. Let be Planck's constant. The speed of light in a vacuum. The wavelength of light It is a natural constant. Boltzmann's constant, This is the absolute temperature of the solar blackbody.

[0018] In step two, the method for calculating the irradiance of the Earth's reflected light reaching the target is as follows:

[0019] ;

[0020] In the formula, The irradiance of light reflected from Earth reaching the target. The angle between the Sun, Earth, and the target. For the Earth's radius, The distance between Earth and the target. This refers to Earth's reflectivity.

[0021] In step three, the method for calculating the irradiance of moonlight reaching the target is as follows:

[0022] ;

[0023] In the formula, The irradiance of moonlight reaching the target. For lunar reflectivity, The radius of the moon, This represents the distance from the moon to the target. The lunar phase function is used to represent the phases of the moon and stars. In Replace with The obtained; among them, The angle between the sun, the moon, and the target. The lunar phase angle is observed from the top layer of Earth's atmosphere.

[0024] In step three, the method for calculating the irradiance of lunar reflected light reaching the target is as follows:

[0025] ;

[0026] In the formula, The irradiance of lunar reflected light reaching the target. For wavelength The irradiance of sunlight reaching the moon.

[0027] In step three, the method for constructing the lunar magnitude phase function is as follows:

[0028] ;

[0029] In the formula, For the magnitude of the moon, ; The first fitting coefficient for the phase angle, The second fitting coefficient for the phase angle.

[0030] In step four, the target apparent magnitude model is as follows:

[0031] ;

[0032] In the formula, For the target apparent magnitude, The apparent magnitude of the sun, The irradiance of the light reflected from the target reaching the sensor. This refers to the irradiance of direct sunlight reaching the target.

[0033] In step five, the method for calculating the first irradiance of the target is as follows:

[0034] ;

[0035] The method for calculating the second irradiance of the target is as follows:

[0036] ;

[0037] The method for calculating the target's third irradiance is as follows:

[0038] ;

[0039] In the formula, For the target first irradiance, For the target second irradiance, The target is the third irradiance; The average reflectance, Let be the cross-sectional area of ​​the Lambert sphere. For the target observation distance, The scaling factor for diffuse and specular reflection of the target;

[0040] The first diffuse reflection phase angle function, Let be the phase angle function of the first mirror reflection. The solar phase angle formed between the sensor and the target relative to the sun;

[0041] This is the second diffuse reflection phase angle function. The phase angle function of the second mirror reflection. The Earth phase angle formed by the sensor and target relative to the Earth;

[0042] This is the third diffuse reflection phase angle function. The phase angle function of the third mirror reflection. The lunar phase angle formed by the sensor and target relative to the moon.

[0043] In step six, the irradiance of the target-reflected light received by the sensor is calculated as follows:

[0044] ;

[0045] In the formula, The irradiance of the light reflected from the target received by the sensor. This refers to the distance between the target and the sensor.

[0046] In step six, the method for calculating the apparent magnitude of the Earth-Moon space optical observation target is as follows:

[0047] ;

[0048] In the formula, Apparent magnitude for targets in Earth-Moon space optical observation. Let be the radius of the Lambert sphere. This is the phase function, which is the angle function formed by the Sun, Earth, and target.

[0049] The beneficial effects of this invention are:

[0050] 1. To simplify calculations, this invention integrates the solar irradiance in the visible light band to obtain the irradiance of visible sunlight reaching the Earth. Since the average distance from the Earth to the Moon is much smaller than the average distance between the Earth and the Sun, this invention uses the irradiance of visible sunlight reaching the Earth as the irradiance of direct sunlight reaching the target.

[0051] 2. In remote sensing observation of the Earth, the Earth itself exhibits different reflectivities due to different surface coverings. However, in this invention, the target is very far away from the Earth, and the influence of different surface coverings on reflectivity is very limited. Simplifying the Earth into a diffuse Lambertian sphere with a completely diffuse reflective surface can effectively simulate the Earth's reflected light at a relatively long distance scale. By using the Lambertian reflection law, the irradiance of the Earth's reflected light reaching the target can be quickly obtained.

[0052] 3. After sunlight shines directly on the lunar surface, it is reflected into space to form moonlight. By referencing and fitting the lunar phase function coefficients, the irradiance of the lunar reflected light reaching the target is integrated in the visible light band to obtain a more accurate irradiance of the moonlight reaching the target.

[0053] 4. Space debris is an object that has both specular and diffuse reflection properties. Therefore, the present invention uses a Lambertian sphere that has both specular and diffuse reflection properties to better simulate the characteristics of space debris, thereby enabling the construction of a target apparent magnitude model based on the relationship between irradiance and apparent magnitude.

[0054] 5. The target apparent magnitude model constructed in this invention considers the irradiance of the reflected light from the target reaching the sensor simultaneously with the irradiance contributions of sunlight, Earth's albedo, and moonlight. Compared with the second apparent magnitude model in the prior art that only considers the irradiance contribution of sunlight, the calculation results of the target apparent magnitude model constructed in this invention are more accurate.

[0055] 6. This invention considers the conditions of sunlight, moonlight, and Earth's albedo, and includes the moon and Earth in the calculation of light sources. That is, it simultaneously calculates the irradiance of sunlight, moonlight, and Earth's albedo. Based on the target apparent magnitude model, it obtains the target's first irradiance when sunlight is the light source by obtaining the irradiance of direct sunlight reaching the target, the target's second irradiance when Earth's albedo is the light source by obtaining the irradiance of Earth's albedo reaching the target, and the target's third irradiance when moonlight is the light source by obtaining the irradiance of moonlight reaching the target. Since the irradiance of sunlight, moonlight, and Earth's albedo is calculated separately, the contribution rate of moonlight and Earth's albedo to the target brightness can be evaluated. This optimization scheme effectively determines the impact of moonlight and Earth's albedo on Earth-Moon space-based optical observations.

[0056] 7. The irradiance of the target is obtained by summing the first, second, and third irradiances of the target. Based on the target apparent magnitude model, the apparent magnitude of the Earth-Moon space optical observation target obtained from the irradiance of the target reflected light received by the sensor is a more accurate result. This solves the problem that the apparent magnitude of the target cannot be accurately obtained without considering the influence of moonlight and Earth's albedo, and that the apparent magnitude of the target cannot be calculated under conditions without sunlight. This improves the accuracy of brightness estimation for Earth-Moon space target observations.

[0057] 8. Under conditions where the sun is blocked or other unfavorable observation conditions, the feasibility of using moonlight and Earth's reflected light to observe a target can be determined by the calculation results of this invention. Attached Figure Description

[0058] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments.

[0059] Figure 1 This is a schematic diagram illustrating the relative positional relationship between the Sun, Earth, Moon, target, and sensor, provided for an embodiment of the present invention.

[0060] Figure 2 This is a schematic diagram illustrating the relative positional relationship between the sun, moon, target, and sensor, provided in an embodiment of the present invention.

[0061] Figure 3 This is a schematic diagram illustrating the relative positional relationship between the Sun, Earth, target, and sensor, provided in an embodiment of the present invention.

[0062] Figure 4 This is a schematic diagram illustrating the relative positional relationship between the sun, the target, and the sensor, provided for an embodiment of the present invention.

[0063] Figure 5 This is a schematic diagram illustrating the variation of target star magnitude with distance for different light sources, provided in an embodiment of the present invention.

[0064] Figure 6 This is a schematic diagram illustrating the variation of the irradiance ratio of different light sources with distance, provided in an embodiment of the present invention. Detailed Implementation

[0065] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0066] This invention provides a method for calculating the apparent magnitude of targets in Earth-Moon space optical observations, including:

[0067] Step 1: Integrate the solar irradiance in the visible light band to obtain the irradiance of visible sunlight reaching the Earth; use the irradiance of visible sunlight reaching the Earth as the irradiance of direct sunlight reaching the target.

[0068] Step two: Simplify the Earth as a diffuse Lambertian sphere with a completely diffuse reflective surface, and obtain the irradiance of the Earth's reflected light reaching the target through the Lambertian reflection law;

[0069] Step 3: Integrate the irradiance of the moon's reflected light reaching the target in the visible light band to obtain the irradiance of the moonlight reaching the target.

[0070] Step 4: Use a Lambertian sphere that has both specular and diffuse reflection to simulate the target characteristics, and construct a target apparent magnitude model based on the relationship between irradiance and apparent magnitude.

[0071] Step 5: Based on the target apparent magnitude model, obtain the target's first irradiance when sunlight is the light source by obtaining the irradiance of direct sunlight reaching the target, the target's second irradiance when Earth's albedo is the light source by obtaining the irradiance of Earth's albedo reaching the target, and the target's third irradiance when moonlight is the light source by obtaining the irradiance of moonlight reaching the target.

[0072] Step six: Summing the first, second, and third irradiance of the target to obtain the irradiance of the target reflected light received by the sensor. Based on the target apparent magnitude model, the apparent magnitude of the Earth-Moon space optical observation target is obtained from the irradiance of the target reflected light received by the sensor.

[0073] Because Earth's orbit around the sun is not perfectly circular, the distance between the sun and Earth varies throughout the year, causing solar irradiance to constantly change as Earth revolves. The solar irradiance at Earth ranges from 1320 to 1412 W / m². 2 The values ​​fluctuate between these values. To simplify calculations, the solar constant is taken as the irradiance projected by the sun onto a unit area 1 AU from the sun and perpendicular to the direction of sunlight per unit time. The approximate average value is... .

[0074] This invention considers the case of visible light detection, which requires integrating the solar irradiance within the visible light band (0.4~0.7 μm) and taking the average Earth-Sun distance. Solar radius We approximate sunlight as parallel rays of blackbody radiation. By integration, we obtain the solar visible light irradiance to Earth as:

[0075] ;

[0076] The average distance from the Earth to the Moon is The distance is much smaller than the average distance between the Earth and the Sun, therefore the irradiance of visible sunlight reaching the Earth can be approximated as the irradiance of direct sunlight reaching the target. This invention will... The irradiance constant of visible sunlight in the Earth-Moon space, which is the irradiance of direct sunlight reaching a target, is denoted as […]. Therefore, in step one, the method for calculating the irradiance of direct sunlight reaching the target is as follows:

[0077] ;

[0078] In the formula, The irradiance of direct sunlight reaching the target. The irradiance of visible sunlight reaching Earth. The radius of the sun, The average distance between the Earth and the Sun. Let be Planck's constant. The speed of light in a vacuum. The wavelength of light It is a natural constant. Boltzmann's constant, This is the absolute temperature of the solar blackbody.

[0079] Sunlight, after hitting the Earth's surface directly, is reflected into space, forming Earth's albedo. Compared to the solar irradiance received by a target, the irradiance of Earth's albedo is much smaller. Simplifying the Earth as a diffuse Lambertian sphere with perfectly diffuse reflectivity, and taking the reflectivity of visible light as 0.4, the irradiance of Earth's albedo is:

[0080] ;

[0081] in, The irradiance of light reflected from Earth reaching the target. For the Earth's radius, The distance between Earth and the target. For reflectivity, For land phase functions, Let be the angle between the Sun, Earth, and the target. For Earth, simplified as a diffuse Lambertian sphere, the geomorphic function is:

[0082] ;but,

[0083] In step two, the method for calculating the irradiance of the Earth's reflected light reaching the target is as follows:

[0084] ;

[0085] In the formula, The irradiance of light reflected from Earth reaching the target. The angle between the Sun, Earth, and the target. For the Earth's radius, The distance between Earth and the target. This refers to Earth's reflectivity.

[0086] In step three, the method for constructing the lunar magnitude phase function is as follows:

[0087] ;

[0088] In the formula, For the magnitude of the moon, ; The first fitting coefficient for the phase angle, This represents the second fitting coefficient for the phase angle. Sunlight, after directly hitting the lunar surface, is reflected into space to form moonlight. By referencing the fitted lunar phase function coefficients, the lunar reflected irradiance received by the target at different angles to the moon can be obtained. This is first achieved by observing the lunar phase angle (the angle between the sun, moon, and earth) from the upper atmosphere of Earth. Interpolation yields lunar magnitudes corresponding to the phase angle and wavelength. ;in , As shown in Table 1:

[0089] Table 1

[0090]

[0091] Ignoring the differences in distance between the Sun and Earth and between the Sun and Moon, the irradiance of lunar albedo reaching the top of Earth's atmosphere is:

[0092] ;

[0093] in, The radius of the moon, This is the distance from the Moon to the Earth. The radius is the Earth's radius. The lunar reflectivity is taken as 0.116. For targets in the Earth-Moon space, this represents the irradiance of lunar reflected light reaching the top of Earth's atmosphere. Replace with the distance from the moon to the target. The lunar phase angle is replaced by the angle between the sun, the moon, and the target. The irradiance of the lunar reflected light reaching the target is obtained as follows:

[0094] ;

[0095] In the formula, The irradiance of lunar reflected light reaching the target. For wavelength The irradiance of sunlight reaching the moon. The lunar phase function is used to represent the phases of the moon and stars. In Replace with The obtained; among them, The angle between the sun, the moon, and the target. The lunar phase angle is observed from the top layer of Earth's atmosphere.

[0096] Integrating the lunar irradiance reaching the target from the visible light band (0.4 μm to 0.7 μm) yields a function of the lunar irradiance received by the target as a function of the angle between the target and the moon and the sun, i.e., the irradiance of moonlight reaching the target:

[0097] ;

[0098] In the formula, The irradiance of moonlight reaching the target. For lunar reflectivity, The radius of the moon, This represents the distance from the moon to the target.

[0099] The target irradiance received by the sensor needs to be determined by the angles between the sun, earth, moon, target, and sensor, and their interrelationships are as follows: Figure 1 As shown. Figure 1 In the diagram, S is the Sun's center of mass, M is the Moon's center of mass, E is the Earth's center of mass, T is the target, and O is the observer. For ease of subsequent calculations, let ∠STO = , ∠ETO= , ∠MTO= , ∠SMT= , ∠SET= .

[0100] The optical properties of the target, i.e., space debris, are affected by factors such as the material of the debris and its relative position. To simplify the calculation, a Lambertian sphere with both specular and diffuse reflection is used to simulate the target characteristics, so that the reflectivity of the target is the same in all directions.

[0101] In step four, the target apparent magnitude model is as follows:

[0102] ;

[0103] In the formula, For the target apparent magnitude, The apparent magnitude of the sun, The irradiance of the light reflected from the target reaching the sensor. This refers to the irradiance of direct sunlight reaching the target.

[0104] Furthermore, in existing technologies, considering only sunlight as the light source, the resulting second apparent magnitude model is as follows:

[0105] ;

[0106] In the formula, The target's apparent magnitude is calculated using the second apparent magnitude model. The apparent magnitude of the sun, The average reflectance, Let be the cross-sectional area of ​​the Lambert sphere. For the target observation distance, The ratio of diffuse reflection to specular reflection of the target. The diffuse reflection phase angle function, Let be the phase angle function of the mirror reflection; where,

[0107] ;

[0108] ;

[0109] The irradiance of the target reflected light reaching the sensor in the target apparent magnitude model constructed in this invention. The target apparent magnitude model constructed using this invention takes into account the irradiance contributions of sunlight, Earth's albedo, and moonlight. Compared to the second apparent magnitude model in the prior art that only considers the irradiance contribution of sunlight, the calculation results are more accurate.

[0110] In step five, the method for calculating the first irradiance of the target is as follows:

[0111] ;

[0112] The method for calculating the second irradiance of the target is as follows:

[0113] ;

[0114] The method for calculating the target's third irradiance is as follows:

[0115] ;

[0116] In the formula, For the target first irradiance, For the target second irradiance, The target is the third irradiance; The average reflectance, Let be the cross-sectional area of ​​the Lambert sphere. For the target observation distance, The scaling factor for diffuse and specular reflection of the target;

[0117] Let be the first diffuse reflection phase angle function, and let be In Replace with Obtained; Let be the phase angle function of the first mirror reflection, and let be the phase angle function of the first mirror reflection. In Replace with Obtained; The solar phase angle formed between the sensor and the target relative to the sun;

[0118] Let be the second diffuse reflection phase angle function, and let be In Replace with Obtained; Let be the phase angle function of the second mirror reflection, and let be the phase angle function of the second mirror reflection. In Replace with Obtained; The Earth phase angle formed by the sensor and target relative to the Earth;

[0119] The third diffuse reflection phase angle function is used to... In Replace with Obtained; Let be the phase angle function of the third mirror reflection, and let be In Replace with Obtained; The lunar phase angle formed by the sensor and target relative to the moon.

[0120] Taking into account sunlight, Earth's albedo, and moonlight, the method for calculating the irradiance of the target-reflected light received by the sensor in step six is ​​as follows:

[0121] ;

[0122] In the formula, The irradiance of the light reflected from the target received by the sensor. This refers to the distance between the target and the sensor.

[0123] Taking the sun as the denomination In step six, the method for calculating the apparent magnitude of the Earth-Moon space optical observation target is as follows:

[0124] ;

[0125] In the formula, Apparent magnitude for targets in Earth-Moon space optical observation. Let be the radius of the Lambert sphere. This is the phase function, which is the angle function formed by the Sun, Earth, and target.

[0126] The following are verification examples to demonstrate the effectiveness of the method disclosed in this invention.

[0127] Example 1: The effect of reflected light on the target

[0128] The irradiance of Earth's albedo and moonlight is much less than that of sunlight, and is often ignored in simulation calculations. However, in situations such as solar eclipses or when the angle of sunlight is unfavorable for observation, Earth's albedo and moonlight can be used to observe targets. Since the target's irradiance and apparent magnitude are affected by multiple variables, such as the relative positions of the Sun, Moon, Earth, target, and probe, three fixed scenarios were assumed to determine the impact of albedo on the target's irradiance and apparent magnitude.

[0129] like Figure 2 , Figure 3 and Figure 4 As shown, S is the Sun's center of mass, M is the Moon's center of mass, E is the Earth's center of mass, T is the target, and O is the observer. Assume the target is located on the line connecting the Earth and the Moon, with a radius of... For a Lambert sphere with a diameter of 1m, the cross-sectional area of ​​the Lambert sphere is... average reflectivity The distance is 0.175. (This refers to the distance between the Moon and the target.) Set as Distance between Earth and target Set as ,and Distance between the sun and the target Set as Keeping the Earth-Sun distance constant, the distance between the probe and the target The distance remains constant at 5000km. Assume the angle between the sun, moon, and target is ∠SMT ( ), the angle between the moon, the target, and the probe ∠MTO ( ), the angle between the sun, the earth, and the target ∠SET ( ), the angle between Earth, target, and probe ∠ETO ( ), the angle between the sun, the target, and the probe ∠STO ( All angles are 20° to ensure that the included angles are the same.

[0130] The first irradiance of the target observed with the sun as the light source was calculated. And the first sight star, etc. for:

[0131] ;

[0132] ;

[0133] The second irradiance of the target observed with Earth as the light source was calculated. And the target second star, etc. for:

[0134] ;

[0135] ;

[0136] ;

[0137] The third irradiance of the target observed with the moon as the light source was calculated. and target third-party star etc. for:

[0138] ;

[0139] ;

[0140] ;

[0141] In summary, the irradiance of the target reflected light observed using the sun, earth, and moon as light sources was calculated. Apparent magnitude of targets for optical observation in Earth-Moon space for:

[0142] ;

[0143] ;

[0144] in, , and Follow Changes such as Figure 5 As shown, and respectively with The ratio value, that is , , Changes such as Figure 6 As shown.

[0145] Figure 5 and Figure 6 In the diagram, the x-axis represents the distance between the moon and the target. The range is 10,000km to 250,000km. Figure 5 In the diagram, the y-axis represents the apparent magnitude of the detected target. Figure 6 In the diagram, the y-axis represents the ratio between target irradiance values. From... Figure 5 It can be observed that, under the hypothetical scenario, the target is within approximately 17,500 km of the moon. Less than 18, approximately 162,500 km from the moon. Less than 18; and Figure 6 The proportional values ​​in the figure indicate that, under the same observation angle, and much smaller This means that when observations can be made using sunlight, the effects of moonlight and Earth's reflected light can be ignored, while when observations cannot be made using sunlight, there is an opportunity to make observations using moonlight and Earth's reflected light.

[0146] The beneficial effects of this invention are:

[0147] 1. To simplify calculations, this invention integrates the solar irradiance in the visible light band to obtain the irradiance of visible sunlight reaching the Earth. Since the average distance from the Earth to the Moon is much smaller than the average distance between the Earth and the Sun, this invention uses the irradiance of visible sunlight reaching the Earth as the irradiance of direct sunlight reaching the target.

[0148] 2. In remote sensing observation of the Earth, the Earth itself exhibits different reflectivities due to different surface coverings. However, in this invention, the target is very far away from the Earth, and the influence of different surface coverings on reflectivity is very limited. Simplifying the Earth into a diffuse Lambertian sphere with a completely diffuse reflective surface can effectively simulate the Earth's reflected light at a relatively long distance scale. By using the Lambertian reflection law, the irradiance of the Earth's reflected light reaching the target can be quickly obtained.

[0149] 3. After sunlight shines directly on the lunar surface, it is reflected into space to form moonlight. By referencing and fitting the lunar phase function coefficients, the irradiance of the lunar reflected light reaching the target is integrated in the visible light band to obtain a more accurate irradiance of the moonlight reaching the target.

[0150] 4. Space debris is an object that has both specular and diffuse reflection properties. Therefore, the present invention uses a Lambertian sphere that has both specular and diffuse reflection properties to better simulate the characteristics of space debris, thereby enabling the construction of a target apparent magnitude model based on the relationship between irradiance and apparent magnitude.

[0151] 5. The target apparent magnitude model constructed in this invention considers the irradiance of the reflected light from the target reaching the sensor simultaneously with the irradiance contributions of sunlight, Earth's albedo, and moonlight. Compared with the second apparent magnitude model in the prior art that only considers the irradiance contribution of sunlight, the calculation results of the target apparent magnitude model constructed in this invention are more accurate.

[0152] 6. This invention considers the conditions of sunlight, moonlight, and Earth's albedo, and includes the moon and Earth in the calculation of light sources. That is, it simultaneously calculates the irradiance of sunlight, moonlight, and Earth's albedo. Based on the target apparent magnitude model, it obtains the target's first irradiance when sunlight is the light source by obtaining the irradiance of direct sunlight reaching the target, the target's second irradiance when Earth's albedo is the light source by obtaining the irradiance of Earth's albedo reaching the target, and the target's third irradiance when moonlight is the light source by obtaining the irradiance of moonlight reaching the target. Since the irradiance of sunlight, moonlight, and Earth's albedo is calculated separately, the contribution rate of moonlight and Earth's albedo to the target brightness can be evaluated. This optimization scheme effectively determines the impact of moonlight and Earth's albedo on Earth-Moon space-based optical observations.

[0153] 7. The irradiance of the target is obtained by summing the first, second, and third irradiances of the target. Based on the target apparent magnitude model, the apparent magnitude of the Earth-Moon space optical observation target obtained from the irradiance of the target reflected light received by the sensor is a more accurate result. This solves the problem that the apparent magnitude of the target cannot be accurately obtained without considering the influence of moonlight and Earth's albedo, and that the apparent magnitude of the target cannot be calculated under conditions without sunlight. This improves the accuracy of brightness estimation for Earth-Moon space target observations.

[0154] 8. Under conditions where the sun is blocked or other unfavorable observation conditions, the feasibility of using moonlight and Earth's reflected light to observe a target can be determined by the calculation results of this invention.

[0155] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for calculating the apparent magnitude of a target in a lunar space optical observation, characterized in that, include: Step 1: Integrate the solar irradiance in the visible light band to obtain the solar visible light irradiance reaching the Earth. The irradiance of visible sunlight reaching the Earth is taken as the irradiance of direct sunlight reaching the target; Step two: Simplify the Earth as a diffuse Lambertian sphere with a completely diffuse reflective surface, and obtain the irradiance of the Earth's reflected light reaching the target through the Lambertian reflection law; Step 3: Integrate the irradiance of the moon's reflected light reaching the target in the visible light band to obtain the irradiance of the moonlight reaching the target. Step 4: Use a Lambertian sphere that has both specular and diffuse reflection to simulate the target characteristics, and construct a target apparent magnitude model based on the relationship between irradiance and apparent magnitude. Step 5: Based on the target apparent magnitude model, obtain the target's first irradiance when sunlight is the light source by obtaining the irradiance of direct sunlight reaching the target, the target's second irradiance when Earth's albedo is the light source by obtaining the irradiance of Earth's albedo reaching the target, and the target's third irradiance when moonlight is the light source by obtaining the irradiance of moonlight reaching the target. Step six: Summing the first, second, and third irradiance of the target to obtain the irradiance of the target reflected light received by the sensor. Based on the target apparent magnitude model, the apparent magnitude of the Earth-Moon space optical observation target is obtained from the irradiance of the target reflected light received by the sensor.

2. The method for calculating the apparent magnitude of a lunar optical observation target as described in claim 1, characterized in that, In step one, the method for calculating the irradiance of direct sunlight reaching the target is as follows: ； In the formula, The irradiance of direct sunlight reaching the target. The irradiance of visible sunlight reaching Earth. The radius of the sun, The average distance between the Earth and the Sun. is Planck's constant. The speed of light in a vacuum. The wavelength of light It is a natural constant. Boltzmann's constant, This is the absolute temperature of the solar blackbody.

3. The method for calculating the apparent magnitude of a lunar optical observation target as described in claim 2, characterized in that, In step two, the method for calculating the irradiance of the Earth's reflected light reaching the target is as follows: ； In the formula, The irradiance of light reflected from Earth reaching the target. The angle between the Sun, Earth, and the target. For the Earth's radius, The distance between Earth and the target. This refers to Earth's reflectivity.

4. The method for calculating the apparent magnitude of a lunar optical observation target as described in claim 3, characterized in that, In step three, the method for calculating the irradiance of moonlight reaching the target is as follows: ； In the formula, The irradiance of moonlight reaching the target. For lunar reflectivity, The radius of the moon, This represents the distance from the moon to the target. The lunar phase function is used to represent the phases of the moon and stars. In Replace with The obtained; among them, The angle between the sun, the moon, and the target. The lunar phase angle is observed from the top layer of Earth's atmosphere.

5. The method for calculating the apparent magnitude of a lunar optical observation target as described in claim 4, characterized in that, In step three, the method for calculating the irradiance of lunar reflected light reaching the target is as follows: ； In the formula, The irradiance of lunar reflected light reaching the target. For wavelength The irradiance of sunlight reaching the moon.

6. A method for calculating the apparent magnitude of a lunar optical observation target as described in claim 4 or 5, characterized in that, In step three, the method for constructing the lunar magnitude phase function is as follows: ； In the formula, For the magnitude of the moon, ; The first fitting coefficient for the phase angle. The second fitting coefficient for the phase angle.

7. The method for calculating the apparent magnitude of a lunar optical observation target as described in claim 6, characterized in that, In step four, the target apparent magnitude model is as follows: ； In the formula, For the target apparent magnitude, The apparent magnitude of the sun, The irradiance of the target reflected light reaching the sensor. This refers to the irradiance of direct sunlight reaching the target.

8. The method for calculating the apparent magnitude of a lunar optical observation target as described in claim 7, characterized in that, In step five, the method for calculating the first irradiance of the target is as follows: ； The method for calculating the second irradiance of the target is as follows: ； The method for calculating the target's third irradiance is as follows: ； In the formula, For the target first irradiance, For the target second irradiance, The target is the third irradiance; The average reflectance, Let be the cross-sectional area of ​​the Lambert sphere. For the target observation distance, The scaling factor for diffuse and specular reflection of the target; The first diffuse reflection phase angle function, Let be the phase angle function of the first mirror reflection. The solar phase angle formed between the sensor and the target relative to the sun; This is the second diffuse reflection phase angle function. The phase angle function of the second mirror reflection. The Earth phase angle formed by the sensor and target relative to the Earth; This is the third diffuse reflection phase angle function. The phase angle function of the third mirror reflection. The lunar phase angle formed by the sensor and target relative to the moon.

9. The method for calculating the apparent magnitude of a lunar optical observation target as described in claim 8, characterized in that, In step six, the irradiance of the target-reflected light received by the sensor is calculated as follows: ； In the formula, The irradiance of the light reflected from the target received by the sensor. This refers to the distance between the target and the sensor.

10. The method for calculating the apparent magnitude of a lunar optical observation target as described in claim 9, characterized in that, In step six, the method for calculating the apparent magnitude of the Earth-Moon space optical observation target is as follows: ； In the formula, Apparent magnitude for targets in Earth-Moon space optical observation. Let be the radius of the Lambert sphere. This is the phase function, which is the angle function formed by the Sun, Earth, and target.

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