remote sensing
Article Effects of Solar Invasion on Earth Observation Sensors at a Moon-Based Platform
Hanlin Ye 1, Wei Zheng 1,*, Huadong Guo 2,3, Guang Liu 2,3 and Jinsong Ping 3,4
1 Qian Xuesen Laboratory of Space Technology, China Academy of Space Technology, Beijing 100094, China; [email protected] 2 Key Laboratory of Digital Earth Science, Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100094, China; [email protected] (H.G.); [email protected] (G.L.) 3 University of Chinese Academy of Sciences, No.19(A) Yuquan Road, Shijingshan District, Beijing 100049, China; [email protected] 4 Key Laboratory of Lunar and Planetary Exploration, National Astronomical Observatories, Chinese Academy of Sciences, No.20 Datun Road, Chaoyang District, Beijing 100101, China * Correspondence: [email protected]; Tel.: +86-10-6811-1077
Received: 5 October 2019; Accepted: 23 November 2019; Published: 25 November 2019
Abstract: The solar invasion to an Earth observation sensor will cause potential damage to the sensor and reduce the accuracy of the measurements. This paper investigates the effects of solar invasion on the Moon-based Earth observation sensors. Different from the space-borne platform, a Moon-based sensor can be equipped anywhere on the near-side of the Moon, and this makes it possible to reduce solar invasion effects by selecting suitable regions to equip sensors. In this paper, methods for calculating the duration of the Sun entering of the sensor’s field of view (FOV) and the solar invasion radiation at the entrance pupil of the sensor are proposed. By deducing the expressions of the proposed geometrical relationship between the Sun, Earth, and Moon-based platform, it has been found that the key parameter to the effects of solar invasion is the angle between the Sun direction and the line-of-sight vector. Based on this parameter, both the duration and radiation can be calculated. In addition, an evaluation approach based on the mean value and standard deviation has been established to compare the variation of solar invasion radiation at different positions on the lunar surface. The results show that the duration is almost the same wherever the sensor is placed in the permanent Earth-observation region. Further, by comparing the variation of solar invasion radiation at different positions on the near-side of the Moon, we suggest that equipping sensors on the mid–high latitude regions within the permanent Earth-observation region will result in less solar invasion affects.
Keywords: solar invasion; Moon-based Earth observation platform; geometric modeling; remote sensing
1. Introduction With the development of space science and technology, Earth observation systems have been established gradually [1,2]. Various Earth observation platforms, including air-borne and space-borne platforms, have played important roles in many fields and are organized as systems to provide numerous datasets of our living planet. In recent years, the Moon, as the only natural satellite of the Earth, has gained great interest as a potential Earth observation platform [3–6]. The first Moon-based sensor can be dated back to 1972, when Apollo 16 sent men to the Moon for the fifth time [7]. A far-ultraviolet camera was operated on the lunar surface, and imagery of the terrestrial atmosphere and the geocorona was obtained [8]. Forty-one-years later, in 2013, an extreme
Remote Sens. 2019, 11, 2775; doi:10.3390/rs11232775 www.mdpi.com/journal/remotesensing Remote Sens. 2019, 11, 2775 2 of 17 ultraviolet camera (EUVC) onboard the Chang’E-3 (CE-3) lander observed the Earth’s plasmasphere from the lunar surface [9]. In recent years, many countries and organizations have initiated programs to set up a base on the Moon, which includes establishing an Earth observation platform [10]. Some pioneer research has been carried out to investigate the Moon-based Earth observations, including scientific goals [3,11], observation geometry analysis [12–15], and Moon-based synthetic aperture radar (SAR) parameters [4,5,16]. According to their research conclusion, a Moon-based Earth observation platform is characterized by longevity, integrity, stability, and uniqueness. Equipping sensors on the lunar surface can be used to monitor the Earth-space environment, the dynamics of solid Earth, the Earth’s radiation budget at the top of atmosphere, and other issues of large-scale phenomena of the Earth. Further, a Moon-based Earth observation platform could be complementary to the existing Earth observation systems. For the Moon to serve as an Earth observation platform, it is essential to evaluate its observation geometry. Compared to traditional Earth observation platforms, equipping sensors on the lunar surface has some special characteristics in observation geometry. First, since the distance between the Earth and the Moon is very large, a sensor installed on the lunar surface could observe nearly half of the Earth, which could extend the existing Earth observations to longer time scales and larger space scales [12]. Additionally, it is possible to realize integrative measurements for the Earth [11]. Second, combining the orbit of the Moon and the seasonal change in relative Earth orientation, a Moon-based platform can realize simultaneous and integral observation of the high latitudes, which will help carry out the contrastive study of the polar regions [17]. Third, due to the vast places of the lunar surface, different kinds of sensors can be installed. They can work together and acquire data from the Earth’s surface to the plasmasphere simultaneously. Many scholars have conducted research on the observation geometry. He et al. [18] simulated the Moon-based extreme ultraviolet images and demonstrated that equipping sensors on the regions where they can observe the Earth is beneficial for acquiring high quality images. Ren et al. [12] proposed simulation technologies of Moon-based Earth observations and evaluated the line-of-sight condition to the Earth. In addition to the consideration of the line-of-sight condition to the Earth, Ye et al. [13] studied the pointing error of a Moon-based sensor and noted that the mid–high latitude regions on the lunar surface are suitable places to equip Earth observation sensors. Guo et al. [14] analyzed the errors of the exterior orientation elements of Moon-based sensors. They also suggested that equipping sensors on the mid–high latitude region helps to reduce the pointing error. As an Earth observation platform, the requirements of acquiring high-quality data need to be considered. Solar invasion for a sensor refers to the sunlight hitting the lens of the sensor directly, which may damage the sensor, reduce the quality of the measurements, and ultimately affect the accuracy of the data [19–21]. When observing the Earth from the lunar surface, the effect of solar invasion also exists. As shown in Figure1, the Sun moves into the FOV of the sensor. At that moment, the Sun moves to the other side of the Earth and the lens of the sensor will be directly exposed to the Sun. From the experiences of space-borne platforms, the effects of the solar invasion depend on the geometric relationships between the Sun, the Earth, and the platforms. The solar invasion does not seem to be an issue in the Sun-synchronous orbit because the satellites will pass over the Earth’s surface at the same local mean solar time [22]. It is an orbit that always maintains the same relationship with the Sun. Another common one is the geostationary orbit. Since the geostationary orbit is a circular orbit above the Earth’s Equator and follows the direction of the Earth’s rotation, the solar invasion will occur near midnight at local time daily, which might lead to the damage of the sensors. A method to solve this problem is to avoid the solar invasion by adjusting the satellite attitude [19]. When observing the Earth from a Moon-based platform, since the relative position of the Sun, the Earth, and the Moon is unfixed, the sensor’s line-of-sight vector would be close to the Sun direction at some time. Such a complex geometrical relationship will no doubt complicate the evaluation of the solar invasion effects. Remote Sens. 2019, 11, 2775 3 of 17 Remote Sens. 2019, 11, x FOR PEER REVIEW 3 of 17
FigureFigure 1.1. Schematic representing thethe solarsolar invasion.invasion.
TheThe aimaim of of this this paper paper is tois analyzeto analyze the solarthe solar invasion invasion effects effects at diff aterent different positions positions on the lunaron the surface lunar sosurface as to giveso as support to give to thesupport site selection to the forsite a Moon-basedselection for platform. a Moon-based We make platform. three contributions We make inthree this paper.contributions The first in contribution this paper. isThe to makefirst acontribution geometrical is description to make a of geometrical solar invasion description for a Moon-based of solar sensor.invasion By for analyzing a Moon-based the geometrical sensor. By relationship, analyzing thethe degreegeometrical of solar relationship, invasion is foundthe degree to be relativeof solar toinvasion the angle is found between to be the relative Sun and to line-of-sight the angle between vector direction,the Sun and aswell line-of-sight as the position vector thedirection, sensor as is equippedwell as the on. position Second, the according sensor tois theequipped geometric on. analysis,Second, theaccording method to to the calculate geometric the solar analysis, invasion the durationmethod andto calculate radiation the is proposed.solar invasion Different durati fromon Burinskayaand radiation et al. is [23 proposed.] and Song Different et al. [24], from who calculatedBurinskaya the et solaral. [23] radiation and Song on et the al. lunar [24], surface,who calculated the theoretical the solar expression radiation of on solar the invasion lunar surface, radiation the considerstheoretical the expression radiation of at solar the entranceinvasion pupilradiation of a considers sensor. The the third radiation is to evaluateat the entrance the eff ectspupil of of the a solarsensor. invasion The third duration is to evaluate and radiation the effects for a of sensor the so onlar the invasion near-side duration of the and Moon. radiation Since the for eaff sensorect of the on variationthe near-side of the of orbit the ofMoon. the Moon Since on the the effect solar invasionof the variation radiation of is the diff erent,orbit of to evaluatethe Moon the on di thefferences solar atinvasion different radiation positions is on different, the lunar to surface, evaluate the the mean diffe valuerences and at standarddifferent deviationpositions needon the to lunar be calculated. surface, Thethe standardmean value deviation and standard could be deviation combined withneed theto meanbe calculated. value to measureThe standard the variation deviation amplitude could be of thecombined solar invasion with the radiation. mean value to measure the variation amplitude of the solar invasion radiation. TheThe remainderremainder ofof thisthis paperpaper isis arrangedarranged asas follows.follows. Section2 2 first first introduces introduces the the theoretical theoretical geometricgeometric modelmodel forfor Moon-basedMoon-based EarthEarth observations.observations. Based on the geometricgeometric model,model, twotwo typicaltypical observationalobservational cyclescycles areare demonstrated.demonstrated. A geometric description of solar invasioninvasion isis introducedintroduced inin SectionSection3 ,3, and and the the angle angle between between the Sunthe directionSun direction and line-of-sight and line-of-sight vector are vector found are to befound an important to be an factorimportant in determining factor in determining the effects of the solar effects invasion of solar on a sensor.invasion Then, on thea sensor. calculation Then, methods the calculation of solar invasionmethods durationof solar andinvasion radiation duration are established. and radiation In Section are established.4, the results In of Section the simulations 4, the results conducted of the aresimulations presented conducted to illustrate are the presented effects of solarto illustrate invasion the on effects the near-side of solar of invasion the Moon on from the near-side the perspective of the ofMoon duration from and the radiation. perspective Finally, of duration some discussion and radiat aboution. the Finally, site selection some issuediscussion of Moon-based about the Earth site observationselection issue sensors of Moon-based is provided Earth in Section observ5.ation sensors is provided in Section 5.
2. Theoretical Geometric Model 2. Theoretical Geometric Model The analysis of solar invasion effects on sensors at a Moon-based platform requires a theoretical The analysis of solar invasion effects on sensors at a Moon-based platform requires a theoretical model of the Moon-based Earth observation geometry. The theoretical geometric model presented in model of the Moon-based Earth observation geometry. The theoretical geometric model presented in thisthis paperpaper isis basedbased onon thethe modelmodel publishedpublished by Ye etet al.al. [[13]13] andand andand GuoGuo etet al.al. [[14].14]. In this section, thethe theoreticaltheoretical geometricgeometric modelmodel ofof aa Moon-basedMoon-based platformplatform isis introducedintroduced briefly.briefly. The corecore ofof thisthis modelmodel isis thethe processprocess toto transformtransform thethe Moon-basedMoon-based platform,platform, thethe Sun,Sun, andand thethe EarthEarth intointo thethe samesame coordinatecoordinate system.system. All All of of them them should should be transformedbe transformed through through a series a ofseries complex of complex coordinate coordinate systems. Figuresystems.2 summarizes Figure 2 summarizes the general the procedures general procedur of the coordinatees of the systemcoordinate transformations. system transformations. Since the MoonSince the is simplified Moon is simplified as a sphere as witha sphere a radius with 1738a radius km, 1738 the position km, the canposition be expressed can be expressed as latitude, as latitude, longitude, and altitude in the selenographic coordinate system. Additionally, the coordinates of a Moon-based platform can be transformed to a Cartesian coordinate system, i.e.,
Remote Sens. 2019, 11, 2775 4 of 17 longitude, and altitude in the selenographic coordinate system. Additionally, the coordinates of aRemote Moon-based Sens. 2019,platform 11, x FOR PEER can REVIEW be transformed to a Cartesian coordinate system, i.e., Moon-centered4 of 17 Moon-fixed coordinate system (MCMF). For the description of the Moon-based platform’s orientation, Moon-centered Moon-fixed coordinate system (MCMF). For the description of the Moon-based the Euler angles of the lunar libration are used to transform the MCMF to the Selenocentric Celestial platform’s orientation, the Euler angles of the lunar libration are used to transform the MCMF to the Reference System (SCRS). According to the lunar positions derived from the planetary ephemeris, the Selenocentric Celestial Reference System (SCRS). According to the lunar positions derived from the position of the Moon is defined in the Geocentric Celestial Reference System (GCRS), which shares planetary ephemeris, the position of the Moon is defined in the Geocentric Celestial Reference the same orientation with SCRS. Thus, in the inertial reference system, the transformation between System (GCRS), which shares the same orientation with SCRS. Thus, in the inertial reference system, the SCRS and GCRS can be treated as the translation of the barycenter between the Moon and the the transformation between the SCRS and GCRS can be treated as the translation of the barycenter Earth. Similarly, the coordinates of the Sun can be transformed to GCRS by translating its barycenter between the Moon and the Earth. Similarly, the coordinates of the Sun can be transformed to GCRS toby the translating Earth. For its the barycenter transformation to the Earth. of the For point the ontransformation Earth, the position of the point of the on point Earth, on the Earth, position defined of inthe the point International on Earth, Terrestrial defined Referencein the Internationa System (ITRS),l Terrestrial needs toReference transform System to GCRS (ITRS), and twoneeds sets to of transformationtransform to GCRS models and can two be sets used of totransformation transform it mo fromdels ITRS can tobe GCRS, used to i.e., transform the classical it from model ITRS andto non-rotatingGCRS, i.e., the origin classical model model [25]. and non-rotating origin model [25].
FigureFigure 2. 2.General General proceduresprocedures of the coordinatecoordinate system transformations. transformations.
AccordingAccording to theto theoreticalthe theoretical geometric geometric model, model, two fundamental two fundamental observation observation periods of Moon-basedperiods of EarthMoon-based observation Earth can observation be found. Onecan be is afound. 29.5-day One cycle is acalled 29.5-day the cycle orbital called period. the As orbital the Moon period. rotates As aroundthe Moon the Earth,rotates its around declination the Earth, also its changes, declination completing also changes, a cycle completing once every 29.5a cycle days. once Another every 29.5 is an 18.6-yeardays. Another cycle, which is an is18.6-year much longer cycle, than which the is orbital much period. longer The than extreme the orbital values period. of one The orbital extreme period values of one orbital period vary about 5° with respect to the ecliptic plane, and the obliquity of the vary about 5◦ with respect to the ecliptic plane, and the obliquity of the ecliptic is about 23.5◦. The value ofecliptic the orbit is ofabout the Moon 23.5°. to The ecliptic value gradually of the orbit changes of the over Moon an 18.6-year to ecliptic cycle gradually due to the changes precession over of an the lunar18.6-year inclination, cycle due alternately to the precession adding to orof subtracting the lunar inclination, from the obliquity alternately of the adding ecliptic. to Therefore,or subtracting there arefrom two the extreme obliquity cases, of includingthe ecliptic. the Therefore, adding case ther (showne are two in extreme Figure3a) cases, and subtractingincluding the case adding (shown case in (shown in Figure 3a) and subtracting case (shown in Figure 3b). In the adding case, the Moon will Figure3b). In the adding case, the Moon will change its declination during the variation about 28.5◦ to change its declination during the variation about −28.5° to +28.5°, for a total range of 57°.− Then, +28.5◦, for a total range of 57◦. Then, 9.3-years later, during the subtracting case, the Moon will change 9.3-years later, during the subtracting case, the Moon will change its declination from −18.5° to its declination from 18.5◦ to +18.5◦, which totals 37◦ in range. In this paper, we mainly analyzed the +18.5°, which totals− 37° in range. In this paper, we mainly analyzed the effects of the solar invasion effects of the solar invasion duration based on these two fundamental observation periods. duration based on these two fundamental observation periods.
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FigureFigure 3. 3. ((aa)) The The extreme extreme case of thethe valuevalue ofof thethe orbit orbit of of the the Moon Moon to to ecliptic ecliptic adding adding to to the the obliquity obliquity of ofthe the ecliptic. ecliptic. (b )(b The) The extreme extreme case case of of the the value valu ofe of the the orbit orbit of theof the Moon Moon to eclipticto ecliptic subtracting subtracting from from the theobliquity obliquity of the of the ecliptic. ecliptic. 3. Solar Invasion of a Moon-based Sensor 3. Solar Invasion of a Moon-based Sensor The objective of this paper was to investigate the effects of solar invasion, and to analyze it in The objective of this paper was to investigate the effects of solar invasion, and to analyze it in terms of both duration and radiation. The geometric description of solar invasion was first introduced. terms of both duration and radiation. The geometric description of solar invasion was first The Boolean matrix method was then used to calculate the duration when the Sun entered the FOV. introduced. The Boolean matrix method was then used to calculate the duration when the Sun Finally, the method of solar invasion radiation at the pupil entrance of a sensor was constructed. entered the FOV. Finally, the method of solar invasion radiation at the pupil entrance of a sensor was3.1. Geometricconstructed. Description of Solar Invasion
3.1. GeometricThe impact Description of solar invasionof Solar Invasion on a sensor essentially reflects the geometric relationship between the line-of-sight vector and the Sun direction vector. In this section, we parameterized the line-of-sight vectorThe and impact the Sun of directionsolar invasion vector, on and a sensor then obtained essentially the anglereflects between the geometric these two relationship vectors. The between smaller thethe angleline-of-sight is, the longer vector the and solar the invasion Sun direction duration onvector. a sensor In this will be.section, we parameterized the line-of-sightAccording vector to the and theoretical the Sun geometricdirection modelvector, in and Section then2 ,obtained we need tothe transform angle between the coordinates these two of vectors.the Moon-based The smaller platform, the angle the Sun,is, the and longer the Earththe solar into invasion the same duration coordinate on system.a sensor Figure will be.4 illustrates the solarAccording invasion to the geometry. theoretical Diff geometricerent positions model on in the Section lunar 2, surface we need will to havetransform different the line-of-sightcoordinates ofvectors the Moon-based [13,26]. This factplatform, dictates the that Sun, the and position the ofEa therth Moon-basedinto the same sensor coordinate cannot besystem. simplified Figure as at4 illustratesthe barycenter the solar of the invasion Moon. Thus,geometry. theline-of-sight Different po vectorsitions shouldon the belunar from surface the position will have on thedifferent lunar line-of-sightsurface to the vectors Earth. [13,26]. This fact dictates that the position of the Moon-based sensor cannot be simplifiedTo clearly as at demonstrate the barycenter the calculationof the Moon. process Thus, of the line-of-sightline-of-sight vectorvector andshould the Sunbe from direction the positionvector, it on is necessarythe lunar surface to introduce to the three Earth. related transformation matrixes. To clearly demonstrate the calculation process of the line-of-sight vector and the Sun direction vector,1. Constant it is necessary matrix to [C introduce]: The location three related of a Moon-based transformation sensor matrixes. on the lunar surface are given by 1. Constantcoordinates matrix expressed [C]: The in thelocation MCMF, of a where Moon-based the X-axis sens pointsor on tothe the lunar mean surface Earth directionare given and by coordinatesthe Z-axis points expressed to the in mean the MCMF, rotation where axis direction. the X-axis However, points to the the data mean derived Earth from direction planetary and theephemeris Z-axis points is defined to the in mean another rotation coordinate axis direct system,ion. However, and the Principle the data Axisderived coordinate from planetary system ephemeris(PA), and theis defined PA and in MCMF another rotation coordinate axes dosyst notem, coincide. and the Thus,Principle the Axis differences coordinate of these system two (PA), and the PA and MCMF rotation axes do not coincide. Thus, the differences of these two coordinate systems can be described by applying the constant matrix. Coordinates in the MCMF are converted to PA by:
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coordinate systems can− be described by applying the constant matrix. Coordinates in the MCMF cosCC11 sin 0 0 cos C 2 0 sin C 2 0 1 0 0 0 are converted to PA by: sinCC cos 00 0 1 0 00cos C− sin C 0 []C = 11 3 3 − (1), cos C 0sin C 00 1 0 0cos sinCCC22 00 cos sin C 00 01 sin CC 33 0 cos 0 0 0 1 1 2 2 000100010001− sinC1 cos C1 0 0 0 1 0 0 0 cos C3 sin C3 0 [C] = − , , (1) 0 0 1 0 sin C 0 cos C 0 0 sin C cos C 0 where C1, C2, and C3 are three different constants.− 2 It is worth2 noticing that different3 versions3 of the 0 0 0 1 0 0 0 1 0 0 0 1 development ephemeris have different values [27,28]. 2. Lunarwhere C1,libration C2, and matrix C3 are three[L]: The diff erentlunar constants. libration It ismatrix worth describes noticingthat the di fflunarerent versionsorientation of parameterizedthe development by ephemeristhree Euler have angles, different ϕm, θ valuesm, and [ψ27m,.28 These]. three parameters can be obtained 2. fromLunar planetary libration matrixephemeris. [L]: The The lunar lunar libration libration matrix matrix describes from thePA lunar to SCRS orientation can be parameterized expressed as [29]: by three Euler angles, φm, θm, and ψm. These three parameters can be obtained from planetary φφ−− ψψ ephemeris. Thecos lunarmm libration sin 0matrix 0 1 from 0 PA to SCRS 0 can 0 be cos expressed m sin as m[29]: 0 0 sinφφ cos 000cos θ− sin θ 0 sin ψψ cos 00 []L = mm m m m m cosφm00100sincos00010sin φm 0 0 1θθ 0 0 0 cos ψm sin ψm 0 0 (2). − mm − sinφ cos φ 0 0 0 cos θ sin θ 0 sin ψ cos ψ 0 0 [ ] = m000100010001m m m m m L − , , 0 0 1 0 0 sin θm cos θm 0 0 0 1 0 3. Translation matrix0 [T 0]: Translation 0 1 0matrix 0 was used 0 to 1transform0 the coordinates 0 0 1 of a Moon-based sensor from SCRS to GCRS. The parameters xm, ym, and zm are the coordinates(2) of 3. theTranslation barycenter matrix of the [T ]:Moon Translation in the GCRS, matrix which was used can to be transform derived from the coordinates planetary ephemeris. of a Moon-based Thus, thesensor translation from SCRS matrix to GCRS. can be The written parameters as: xm, ym, and zm are the coordinates of the barycenter of the Moon in the GCRS, which can be derived100 from planetaryx ephemeris. Thus, the translation matrix can be written as: m 0101 0 0 yxm []T = 0 1 0 y (3). [ ] =001z m T m , (3) 0 0 1 zm 000 1 0 0 0 1 , As shown in Figure 4, the coordinates of the Moon-based sensor can be related to its As shown in Figure4, the coordinates of the Moon-based sensor can be related to its selenographic selenographic coordinates φm and λm. Therefore, its position vector p(xp, yp, zp) in the GCRS are given coordinates ϕ and λ . Therefore, its position vector p(x , y , z ) in the GCRS are given by by m m p p p xR cos(ϕλ )cos( ) xp pmmm R m cos(ϕm) cos(λm) yp yR Rm coscos((ϕϕλm) )sin(sin(λm )) =pmmm [=T][[][][]TLCL][C] , (4) z R sin(ϕ ) (4), p zRpmm m sin(m ) 1 111 , wherewhere thethe subscriptsubscript pp refersrefers toto thethe point.point. RRmm represents the radius of the Moon.
Figure 4. Geometrical relationship of solar invasion.
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As far as the line-of-sight vector is concerned, we assume that the line-of-sight vector (v) always points to the Earth barycenter. v is then given by: xp xe v = y y p e , (5) − zp ze where (xe, ye, and ze) are the coordinates of the Earth barycenter in the GCRS. Since the distance between the Sun and the Moon is too large, the Sun is treated as a disk and the received sunlight of a Moon-based sensor can be assumed to be parallel light. Letting Os (xs, ys, and zs) represent the direction of the Sun in the GCRS, the vector s can be written as: xp xs s = y y p s , (6) − zp zs
It is worth noting that the barycenter of the Sun (Os) can also be derived from planetary ephemeris. Therefore, the angle θ can be given by: v s θ = arccos( · ), (7) v s | || | 3.2. Solar Invasion Duration Calculation Solar invasion duration means the duration when the Sun enters the sensor’s FOV. We use the Boolean matrix method to calculate the solar invasion duration at a certain time period. Previous studies evaluating the solar invasion duration of Geostationary Earth Orbit (GEO) platforms mainly first calculated the Earth shadow region and then judged whether the satellite was within that region (e.g., Ye et al. [30]). The GEO’s orbit is a circle in the GCRS and the solar invasion usually occured at midnight, where the duration is relatively regular. The calculation of solar invasion duration will be more difficult in a Moon-based platform. Previous work has used the Boolean matrix method to calculate the observation duration of a Moon-based platform [15]. They formed a ‘0–10 matrix to describe the visibility of Earth during the time period. Each element in the matrix indicates the visibility of Earth at that moment. If the Earth target was visible, the element was marked ‘10, otherwise the element was marked ‘00. Figure5 shows the scheme, which is divided into two phases. The proposed processing phases are designed to calculate the Boolean matrix of solar invasion duration. Through processing the Boolean matrix, some important statistics, such as the distribution and the length of the solar invasion duration, can be achieved. In the preprocessing phase, the time period and step size need to be set. In this study, the step size was set to 1 min to reflect the solar invasion duration variation, while at the same time considering the computational burden. After setting the time period and step size, the planetary ephemeris was used to acquire the position and orientation of the Moon. The conventional coordinate system transformations were applied to unify the positions of the Moon-based platform, the Earth, and the Sun. The next phase of the scheme mainly presented the generation of the Boolean matrix. As the established geometric relationship does not incorporate the sight condition, i.e., the Earth is not visible all the time when equipping sensors at the limb of the lunar disk, it was necessary to consider the visibility of the Earth for a Moon-based platform first. Then, the angle θ between the line-of-sight vector and Sun direction vector could be acquired. If the parameter θ was larger than the field of view, the Sun would not appear in the observational scope and the sensor would not be affected by direct sunlight. The elements in the Boolean matrix represents whether the Sun direction was in the field of view of the sensor. If the parameter θ was less than half of the FOV, the element was marked ‘10, Remote Sens. 2019, 11, 2775 8 of 17 Remote Sens. 2019, 11, x FOR PEER REVIEW 8 of 17
‘1′, otherwise the ‘0′ value was assigned. Thus far, the solar invasion determination process at a otherwise the ‘00 value was assigned. Thus far, the solar invasion determination process at a certain timecertain was time finished. was finished. In this phase, In this the phase, process the was proc repeatedess was until repeated all the until calculations all the calculations were finished. were finished.
Figure 5. Schematic diagram of solar invasion duration calculation. Figure 5. Schematic diagram of solar invasion duration calculation.
FollowingFollowing allall thethe calculationscalculations forfor thethe timetime period,period, the Boolean matrix was was generated. generated. As As the the elementselements were were calculated calculated at aat fixed a fixed step step size size during during the time the period,time period, the element the element numbers numbers of the Booleanof the Boolean matrix recorded the time information. The start and finish time of each duration were matrix recorded the time information. The start and finish time of each duration were indicated by the indicated by the start and finish element numbers and the total observation time was the product of start and finish element numbers and the total observation time was the product of the sum of the the sum of the Boolean matrix and the step size. Boolean matrix and the step size.
3.3.3.3. Solar Solar Invasion Invasion Radiation Radiation CalculationCalculation The solar invasion radiation refers to the solar radiation at the entrance pupil of a sensor. For a The solar invasion radiation refers to the solar radiation at the entrance pupil of a sensor. For a sensor on the lunar surface, in essence, the magnitude of the solar invasion radiation was the sensor on the lunar surface, in essence, the magnitude of the solar invasion radiation was the component component of the solar radiation on the lunar surface along the sensor’s line-of-sight direction. of the solar radiation on the lunar surface along the sensor’s line-of-sight direction. Thus, the calculation Thus, the calculation of the solar invasion radiation was dealt with in two steps. The first was to of the solar invasion radiation was dealt with in two steps. The first was to calculate the solar radiation calculate the solar radiation on the lunar surface. After that, the component along the line-of-sight on the lunar surface. After that, the component along the line-of-sight direction could be achieved. direction could be achieved. On the basis of the energy conservation principle and ignoring the attenuation of the energy On the basis of the energy conservation principle and ignoring the attenuation of the energy emitted from the Sun in the interplanetary space, the radiation emitted from the Sun needed to remain emitted from the Sun in the interplanetary space, the radiation emitted from the Sun needed to the same at the lunar surface. Thus, remain the same at the lunar surface. Thus, 2 2 F4πRs = E4πR0 , (8) F4πRER22= 4π s0, (8),
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where F denotes the solar emittance, Rs the radius of the Sun, E the total solar energy reaching to the Moon-based platform, and R0 the instantaneous distance between the Sun and the Moon-based platform. The solar constant was defined as the solar energy across a unit area on the top of the atmosphere of the Earth, which was normal to the solar beam at the mean distance between the Sun and the Earth. The solar constant S0 can be written as R 2 S = F s , (9) 0 R where R denotes the mean distance between the Sun and the Earth. The total solar radiation on the lunar surface can be obtained by modifying the distance in the case of the solar constant. We had !2 R E = S0 , (10) R0 where S0 denotes the solar constant. Since the solar constant is a quantity denoting the amount of total solar energy reaching the top of the atmosphere of the Earth, R/R0 is essentially the ratio of the between the distance from the Sun to the Earth and to the Moon-based platform. The effective solar radiation is defined as the actual radiation received by the position on the lunar surface at a given time. It depends primarily on the local solar zenith angle and on the variable distance of the position on the lunar surface to the Sun. Hence, the effective solar radiation at a specific position on the lunar surface can be written as:
I = E cos i, (11) where i denotes the solar zenith angle at the specific position on the lunar surface when the instantaneous total solar radiation is E. The solar invasion radiation of a Moon-based sensor can be calculated by resolving the effective solar radiation into the component along the line-of-sight direction of the sensor. We obtained
Is = I sin is, (12) where is denotes the sensor’s elevation angle.
4. Results The theoretical framework for solar invasion geometric characteristics and radiation calculation was introduced in Section3. Here, experiments were set up to reveal the e ffects of the solar invasion for a Moon-based sensor. First, the characteristics of the angle between the Sun direction and line-of-sight vector are analyzed. According to the variation of the angle, the solar invasion duration for a sensor at different positions on the lunar surface was presented. The effects of the solar invasion were finally evaluated.
4.1. Characteristic Analysis of the Angle between the Sun Direction and Line-of-Sight Vector Figure6 demonstrates the case of equipping sensors on the origin of the selenographic coordinate system, i.e., (0◦N, 0◦E). With the relation between the Earth and the Sun changing, the angle between the Earth and the Sun shows periodic variations. This is because, taking the Moon as a reference, the angular velocity of the Earth and the Sun is different, resulting in different relative position relations between the Sun and the Earth. From Figure6, the angle between the Earth and the Sun presents a 29.5-day cyclical fluctuation, corresponding to one orbital period of the Moon-based Earth observations and it will reach the minimum when the Earth passes the Sun direction. The ranges of oscillation periods were not all the same throughout the entire year. For each oscillation period, larger variations could range from approximately 0◦ to 180◦, while shorter variations only ranged from 5◦ to 170◦. Remote Sens. 2019, 11, 2775 10 of 17
In Figure6b, we set three lines as thresholds, representing the FOV of 5 ◦, 10◦, and 15◦, respectively. The lens was exposed to the Sun when the angle was smaller than the threshold. For the case of the same threshold, the lower minimum value in each oscillation period led to a longer solar invasion duration.Remote Sens. According 2019, 11, x FOR to thesePEER REVIEW characteristics, we found that the solar invasion duration was subject 10 ofto 17 the size of the FOV and the minimum value of each period together. EarthIn observations the following, and we it mainly will reach concentrated the minimu on them when characteristics the Earth of passes minimum the Sun value. direction. In Figure The6, weranges found of thatoscillation all of the periods minimum were values not all were the same as low throughout as 5◦ and some the entire of the year. values For were each even oscillation lower thanperiod, 2◦. larger It means variations that the could lens ofrange the sensorfrom approximately would probably 0° beto 180°, directly while exposed shorter to variations the Sun every only orbitalranged period from 5° when to 170°. the size of FOV is larger than 10◦. Further, there are some distinctions in the orbitalIn period Figure of 6b, diff erentwe set years. three Figure lines 7as presents thresholds the minimum, representing value the of oneFOV orbital of 5°, period 10°, and during 15°, 18.6-years.respectively. It can The be lens seen was clearly exposed that the to trendsthe Sun are when cyclical the andangle the was period smaller is about than half the of threshold. one year. WeFor alsothe case noticed of the that same all the threshold, minimum the values lower wereminimum lower value than 5in◦ andeach some oscillation lower period values led were to actuallya longer downsolar invasion to the level duration. of 0.1◦ Accordingin the following to these 18.6-years. characteri Thatstics, means, we found if the that size the of solar FOV invasion was larger duration than 10was◦, the subject Sun willto the enter size the of the FOV FOV every and orbital the minimum period. value of each period together.
(a)
(b)
Figure 6. The variation of (a) angle θ (b) angle θ less than 15° during one year—assuming that the Figure 6. The variation of (a) angle θ (b) angle θ less than 15◦ during one year—assuming that the Moon-basedMoon-based sensor sensor is is at at (0 (0°N◦N,, 0 0°E)◦E)on onthe thelunar lunarsurface. surface.
Figure 7. The variation of minimum values of angle θ in one orbital period during 18.6-years.
Remote Sens. 2019, 11, x FOR PEER REVIEW 10 of 17
In Figure 6b, we set three lines as thresholds, representing the FOV of 5°, 10°, and 15°, respectively. The lens was exposed to the Sun when the angle was smaller than the threshold. For the case of the same threshold, the lower minimum value in each oscillation period led to a longer solar invasion duration. According to these characteristics, we found that the solar invasion duration was subject to the size of the FOV and the minimum value of each period together.
Figure 6. The variation of (a) angle θ (b) angle θ less than 15° during one year—assuming that the Moon-based sensor is at (0°N, 0°E) on the lunar surface.
In the following, we mainly concentrated on the characteristics of minimum value. In Figure 6, we found that all of the minimum values were as low as 5° and some of the values were even lower than 2°. It means that the lens of the sensor would probably be directly exposed to the Sun every orbital period when the size of FOV is larger than 10°. Further, there are some distinctions in the orbital period of different years. Figure 7 presents the minimum value of one orbital period during 18.6-years. It can be seen clearly that the trends are cyclical and the period is about half of one year. We also noticed that all the minimum values were lower than 5° and some lower values were actuallyRemote Sens. down2019, 11to, 2775the level of 0.1° in the following 18.6-years. That means, if the size of FOV11 was of 17 larger than 10°, the Sun will enter the FOV every orbital period.
FigureFigure 7. 7. TheThe variation variation of of minimum minimum values values of of angle angle θθ inin one one orbital orbital period period during during 18.6-years. 18.6-years.
4.2.4.2. Solar Solar Invasion Invasion Duration Duration Analysis Analysis AccordingAccording toto the the description description in Sectionin Section 4.1, the4.1, angle the betweenangle between the Sun directionthe Sun and direction line-of-sight and line-of-sightvector was the vector determinative was the determinative factor for the solar factor invasion for the duration. solar invasion The smaller duration. the minimum The smaller value the of minimumtheRemote angle Sens. in value2019 one, 11 of orbital, x theFOR angle PEER period, REVIEWin one the longer orbital theperiod, solar th invasione longer durationthe solar wouldinvasion last. duration In this would subsection, 11 last. of 17 Inwe this mainly subsection, investigated we the mainly variations investigated of solar invasion the variations duration of during solar 18.6-years invasionand duration its distribution during 18.6-yearscharacteristicsFor the and solar onits distribution theinvasion near-side duration characteristics of the analysis, Moon. on the the concern near-side was of its the duration Moon. and frequency. The solar invasionFor theduration solar invasion can be calculated duration analysis, by using the th concerne Boolean was matrix its duration method and in frequency.Section 3. TheFrom solar the invasiongeometric duration description can beabove, calculated we know by usingthat the the Su Booleann will matrixenter the method FOV, inat Sectionmost, once3. From in every the geometricorbital period, description and the above, solar we invasion know thatduration the Sun and will frequency enter the FOV,mainly at most,depends once on in the every FOV orbital and period,angle θ andvariation the solar patterns. invasion duration and frequency mainly depends on the FOV and angle θ variationFigure patterns. 8 shows the solar invasion duration during 18.6-years. To compare the solar invasion durationFigure variation8 shows under the solar different invasion FOV duration conditions, during we calculated 18.6-years. the To solar compare invasion the solarduration invasion of 5°, duration10°, and variation15°-FOV undersensor, di ffrespectively.erent FOV conditions, From the wemagnitude calculated of the solar solar invasion invasion duration, duration ofa 5°-FOV 5◦, 10◦, andsensor 15◦ will-FOV suffer sensor, from respectively. solar invasion From for the approximately magnitude of solar500 min. invasion However, duration, it will a 5◦ -FOVnot occur sensor in willevery su orbitalffer from period. solar invasionIt usually for appears approximately twice a year 500 min.and the However, durations it will are not extremely occur in small every at orbital some period.time. For It usuallythe caseappears of 10°-FOV, twice the a year solar and invasion the durations duration are ranges extremely from small200 to at 1200 some min, time. while For thethe caseduration of 10 of◦-FOV, a 15°-FOV the solar sensor invasion is from duration 1200 to ranges 1900 min. from It 200 is toclear 1200 that, min, in whilethe case the of duration the 10° ofand a 1515°-FOV◦-FOV sensorsensor, is solar from invasion 1200 to 1900duration min. also It is displays clear that, cyclic in the variations case of the over 10 ◦time.and 15We◦-FOV also noticed sensor, solarthat there invasion was duration no significant also displays interannual cyclic difference variations in over the time.solar Weinvasion also noticed durations that for there the was 10° noor significant15°-FOV sensor. interannual difference in the solar invasion durations for the 10◦ or 15◦-FOV sensor.
FigureFigure 8.8. Solar invasion durationduration during oneone year.year.
Further, we analyzed the solar invasion duration of a sensor at different positions on the lunar surface. Owing to the elliptical orbit of the Moon and the phenomenon of physical libration, a sensor at different positions on the lunar surface is not all the same.
Figure 9 shows the results in the case of the 5°, 10°, and 15°-FOV sensor at different positions on the lunar surface. As shown in this figure, whatever the FOV of a sensor, the distribution of annual solar invasion duration can be divided into two parts. One is near the center of the lunar disk, covering almost 80% of the near-side of the Moon. The boundary of the region has a longitude between 80°W and 80°E and latitude between 80°S and 80°N. In this region, the annual solar invasion duration of a sensor is relatively consistent. The reason is that the maximum difference of the angle between the Earth and the Sun direction at this region is about 0.5°. Such a small angular difference cannot make significant changes in solar invasion duration. The annual solar invasion duration is about 1860, 9000, and 18,000 min, respectively, for a 5°, 10°, and 15°-FOV sensor in this region. Another covers the limb of the lunar disk. Solar invasion duration in this region is lower, in only half the cases near the center of the Moon. The major reason is the sight condition to the Earth.
Remote Sens. 2019, 11, 2775 12 of 17
Further, we analyzed the solar invasion duration of a sensor at different positions on the lunar surface. Owing to the elliptical orbit of the Moon and the phenomenon of physical libration, a sensor at different positions on the lunar surface is not all the same. Figure9 shows the results in the case of the 5 ◦, 10◦, and 15◦-FOV sensor at different positions on the lunar surface. As shown in this figure, whatever the FOV of a sensor, the distribution of annual solar invasion duration can be divided into two parts. One is near the center of the lunar disk, covering Remote Sens. 2019, 11, x FOR PEER REVIEW 12 of 17 almost 80% of the near-side of the Moon. The boundary of the region has a longitude between 80◦W andbetween 80◦E 80 and °W latitude and 80 between °E and 80latitude◦S and between 80◦N. In 80 this °S region,and 80 the °N. annual In this solar region, invasion the annual duration solar of a sensorinvasion is relativelyduration of consistent. a sensor is The relatively reason consistent. is that the The maximum reason is di thatfference the maximum of the angle difference between of the Earththe angle and between the Sun directionthe Earth atand this the region Sun direction is about 0.5at this◦. Such region a small is about angular 0.5°. diSuchfference a small cannot angular make significantdifference changescannot make in solar significant invasion changes duration. in Thesolar annual invasion solar duration. invasion The duration annual is aboutsolar invasion 1860, 9000, andduration 18,000 is min,about respectively, 1860, 9000, forand a 18000 5◦, 10◦ min,, and respec 15◦-FOVtively, sensor for a in 5°, this 10°, region. and 15°-FOV Another sensor covers in the this limb ofregion. the lunar Another disk. covers Solar invasionthe limb of duration the lunar in thisdisk. region Solar invasion is lower, duration in only half in this the casesregion near is lower, the center in ofonly the half Moon. the cases The major near the reason center is theof the sight Moon. condition The major to the reason Earth. is the sight condition to the Earth.
(a) (b) (c)
Figure 9. Distribution of annual solar invasion duration by using (a) 5°, (b) 10°, and (c) 15°-FOV Figure 9. Distribution of annual solar invasion duration by using (a) 5◦,(b) 10◦, and (c) 15◦-FOV Earth Earth observation sensor. (Unit: min). observation sensor. (Unit: min). In general, within the region of the longitude between 80 °W and 80 °E and latitude between In general, within the region of the longitude between 80◦W and 80◦E and latitude between 80 °S and 80 °N, there is almost no difference among the annual solar invasion duration for a sensor, 80◦S and 80◦N, there is almost no difference among the annual solar invasion duration for a sensor, regardlessregardless ofof thethe sensor’s position position and and FOV. FOV.
4.3.4.3. Solar Invasion Radiation Effect Effect Analysis Analysis InIn orderorder toto understandunderstand thethe solarsolar invasioninvasion radiationradiation eeffectsffects onon aa sensorsensor onon thethe lunarlunar surfacesurface andand its distributionits distribution on theon near-sidethe near-side of the of Moon, the Moon, we first we simulatedfirst simulated the solar the invasionsolar invasion radiation radiation on the on diff theerent positionsdifferent atpositions the lunar at surface, the lunar and surface, then its and distribution then its anddistribution variation and could variation be found. could According be found. to the According to the variation characteristics of the solar invasion radiation, two metrics, including the variation characteristics of the solar invasion radiation, two metrics, including the mean value and mean value and standard deviation were set to compare the amplitude and fluctuation of solar standard deviation were set to compare the amplitude and fluctuation of solar invasion radiation for a invasion radiation for a sensor on the near-side of the Moon. sensor on the near-side of the Moon. Figure 10 shows composite images of solar invasion radiation distribution. In this figure, large Figure 10 shows composite images of solar invasion radiation distribution. In this figure, large solar invasion radiation occurs near the center of the lunar disk—nearly 1200 W m-2. This result is solar invasion radiation occurs near the center of the lunar disk—nearly 1200 W m 2. This result is close close to the theoretical value of solar radiation at the lunar surface. At this moment,− if there was a to the theoretical value of solar radiation at the lunar surface. At this moment, if there was a sensor sensor near the center of the lunar disk, the Sun would be at mid-sky position. Additionally, when near the center of the lunar disk, the Sun would be at mid-sky position. Additionally, when the Earth the Earth was at the mid-sky position, the lens of a sensor will be directly exposed to the Sun. wasTherefore, at the mid-skythe solar position,invasion radiation the lens ofwill a sensorbe larger will in bethis directly region. exposed In addition, to the this Sun. value Therefore, is close to the solarthe most invasion serious radiation solar invasion will be larger radiation in this for region. a Moon-based In addition, sensor this due value to isthe close mid-sky to the position most serious of solarthe Sun. invasion In contrast, radiation at forthe amid–high Moon-based latitude sensor region, due to the the solar mid-sky invasion position radiation of the was Sun. relatively In contrast, atsmall, themid–high much less latitude than that region, at the the low solar latitude invasion region. radiation While the was lens relatively of the sensor small, muchwas still less exposed than that atto thethe lowSunlatitude directly, region. the solar While radiation the lens in ofthis the regi sensoron was was much still exposedless than toth theose Sunin the directly, low latitude the solar radiationregion. Additionally, in this region we was note much that less the thanpattern those does in thenot lowshow latitude obvious region. change Additionally, from Figure we 10a–10g. note that theThat pattern means does that not there show is obviousno significant change change from Figure of solar 10 a–g.invasion That meansradiation that for there a sensor is nosignificant during changeone-day. of We solar then invasion listed the radiation variation for of a solar sensor invasion during radiation one-day. di Westribution then listed for theone variationorbital period. of solar From Figure 11a–11d, with the changes between the Earth and the Sun, the solar invasion radiation became lower and lower, until it disappeared. This is because the near-side of the Moon gradually goes into night. After solar invasion radiation entirely disappears in the near-side of the Moon, the Sun rises in the limb of the lunar disk. Several days later, the pattern turns back into the origin.
Remote Sens. 2019, 11, x FOR PEER REVIEW 12 of 17
Figure 9. Distribution of annual solar invasion duration by using (a) 5°, (b) 10°, and (c) 15°-FOV Earth observation sensor. (Unit: min).
In general, within the region of the longitude between 80°W and 80°E and latitude between 80°S and 80°N, there is almost no difference among the annual solar invasion duration for a sensor, regardless of the sensor’s position and FOV.
4.3. Solar Invasion Radiation Effect Analysis In order to understand the solar invasion radiation effects on a sensor on the lunar surface and its distribution on the near-side of the Moon, we first simulated the solar invasion radiation on the different positions at the lunar surface, and then its distribution and variation could be found. According to the variation characteristics of the solar invasion radiation, two metrics, including the mean value and standard deviation were set to compare the amplitude and fluctuation of solar invasion radiation for a sensor on the near-side of the Moon. Figure 10 shows composite images of solar invasion radiation distribution. In this figure, large solar invasion radiation occurs near the center of the lunar disk—nearly 1200 W m−2. This result is close to the theoretical value of solar radiation at the lunar surface. At this moment, if there was a sensor near the center of the lunar disk, the Sun would be at mid-sky position. Additionally, when the Earth was at the mid-sky position, the lens of a sensor will be directly exposed to the Sun. Therefore, the solar invasion radiation will be larger in this region. In addition, this value is close to the most serious solar invasion radiation for a Moon-based sensor due to the mid-sky position of the Sun. In contrast, at the mid–high latitude region, the solar invasion radiation was relatively small, much less than that at the low latitude region. While the lens of the sensor was still exposed Remoteto the Sens. Sun2019 directly,, 11, 2775 the solar radiation in this region was much less than those in the low latitude13 of 17 region. Additionally, we note that the pattern does not show obvious change from Figure 10a–10g. That means that there is no significant change of solar invasion radiation for a sensor during invasion radiation distribution for one orbital period. From Figure 11a–d, with the changes between one-day. We then listed the variation of solar invasion radiation distribution for one orbital period. the Earth and the Sun, the solar invasion radiation became lower and lower, until it disappeared. This From Figure 11a–11d, with the changes between the Earth and the Sun, the solar invasion radiation isbecame because lower the near-side and lower, of theuntil Moon it disappeared. gradually goes This intois because night. Afterthe near-side solar invasion of the Moon radiation gradually entirely disappearsgoes into night. in the After near-side solar of invasion the Moon, radiation the Sun en risestirely in disappears the limb of in the the lunar near-side disk. of Several the Moon, days later,the theSun pattern rises in turns the limb back of into the the lunar origin. disk. Several days later, the pattern turns back into the origin.
FigureFigure 10. Solar10. Solar invasion invasion radiation radiation variation variation during during one-day. one-day. (a–g ()a respectively)–(g) respectively represent represent solar invasionsolar Remoteradiation Sens. 2019 at, 00:0011, x invasionFOR UTC- PEER 24:00 radiation REVIEW UTC, at the 00:00 interval UTC- is 24:00 four UTC, hours. the interval is four hours. 13 of 17
FigureFigure 11. 11.Solar Solar invasion invasion radiation radiation during during one one orbital orbital period. period. (a (–ag)–() correspondsg) corresponds to theto the case case in in the the date during the orbital period respectively.date during the orbital period respectively.
ToTo clearly clearly illustrate illustrate the the cycles cycles ofof thethe solarsolar invasioninvasion radiation, the solar solar invasion invasion radiation radiation from from 20102010 to to 2050 2050 is equippedis equipped with with a sensor a sensor at the at lunar the lu equator,nar equator, 60◦S, and 60°S, the and lunar the South lunar Pole South is presented. Pole is Aspresented. shown in As Figure shown 12 ,in the Figure solar 12, invasion the solar radiation invasion displays radiation some displays cycles some with cycles different with time different scales. Fromtime thescales. mathematical From the mathematical description indescription Section3, thein Section solar invasion 3, the solar radiation invasion varies radiation with varies the relative with positionthe relative between position the Sun,between the Earth,the Sun, and the the Eart Moon-basedh, and the sensor.Moon-based The fundamental sensor. The cyclefundamental is about 29.5-days,cycle is correspondingabout 29.5-days, to onecorresponding orbital period. to Thisone cycleorbital comes period. from This the illuminationcycle comes period from ofthe the positionillumination on the period lunar of surface. the position The second on the cycle lunar is surface. about one-year. The second The cycle reason is about is due one-year. to the cycle The of reason is due to the cycle of the Earth orbital period. Further, there is a cycle about 9.3-years long. This cycle corresponds to a half cycle of lunar declination variation. This cycle will be more obvious in the region of the middle latitude on the lunar surface.
Figure 12. The variation of solar invasion radiation from 2010 to 2050.
To compare the variation characteristics of the solar invasion radiation at the near-side of the Moon, two metrics, including the mean value and standard deviation, are proposed. The mean value represents the magnitude of the solar invasion effects and high mean value means larger effects. However, mean value is not enough to reveal the variation characteristics. For example, there are some cycles with different time scales and different amplitudes. Larger variations of solar invasion radiation will increase the difficulties of Earth observations. Therefore, another metric, standard deviation was proposed to measure the fluctuation of solar invasion radiation variation.
Remote Sens. 2019, 11, x FOR PEER REVIEW 13 of 17
Figure 11. Solar invasion radiation during one orbital period. (a)–(g) corresponds to the case in the date during the orbital period respectively.
To clearly illustrate the cycles of the solar invasion radiation, the solar invasion radiation from 2010 to 2050 is equipped with a sensor at the lunar equator, 60°S, and the lunar South Pole is presented. As shown in Figure 12, the solar invasion radiation displays some cycles with different time scales. From the mathematical description in Section 3, the solar invasion radiation varies with the relative position between the Sun, the Earth, and the Moon-based sensor. The fundamental RemotecycleSens. is 2019about, 11 , 277529.5-days, corresponding to one orbital period. This cycle comes from14 ofthe 17 illumination period of the position on the lunar surface. The second cycle is about one-year. The reason is due to the cycle of the Earth orbital period. Further, there is a cycle about 9.3-years long. the Earth orbital period. Further, there is a cycle about 9.3-years long. This cycle corresponds to a RemoteThis cycleSens. 2019 corresponds, 11, x FOR PEER to a REVIEWhalf cycle of lunar declination variation. This cycle will be more obvious 14 of 17 half cycle of lunar declination variation. This cycle will be more obvious in the region of the middle in the region of the middle latitude on the lunar surface. latitude on the lunar surface.
Figure 12. The variation of solar invasion radiation from 2010 to 2050. Figure 12. The variation of solar invasion radiation from 2010 to 2050. Figure 12. The variation of solar invasion radiation from 2010 to 2050. To compare the variation characteristics of the solar invasion radiation at the near-side of the To compare the variation characteristics of the solar invasion radiation at the near-side of the Moon,To two compare metrics, the including variation thecharacteristics mean value of andthe solarstandard invasion deviation, radiation are atproposed. the near-side The meanof the Moon, two metrics, including the mean value and standard deviation, are proposed. The mean value valueMoon, represents two metrics, the includingmagnitude the of meanthe solar value inva andsion standard effects anddeviation, high mean are proposed.value means The larger mean represents the magnitude of the solar invasion effects and high mean value means larger effects. effects.value representsHowever, themean magnitude value is notof the enough solar toinva revealsion effectsthe variation and high characteristics. mean value Formeans example, larger However, mean value is not enough to reveal the variation characteristics. For example, there are thereeffects. are However, some cycles mean with value different is not time enough scales to an reveald different the variationamplitudes. characteristics. Larger variations For example, of solar some cycles with different time scales and different amplitudes. Larger variations of solar invasion invasionthere are radiationsome cycles will with increase different the timedifficulties scales anofd Earth different observations. amplitudes. Therefore, Larger variations another metric,of solar radiation will increase the difficulties of Earth observations. Therefore, another metric, standard standardinvasion deviationradiation waswill proposedincrease the to measuredifficulties the of fluctuation Earth observations. of solar invasion Therefore, radiation another variation. metric, deviation was proposed to measure the fluctuation of solar invasion radiation variation. Figure 13 Figurestandard 13 showsdeviation the wasdistribution proposed of to these measure two me thetrics fluctuation in the near-side of solar ofinvasion the Moon. radiation The maximum variation. showsmean thesolar distribution invasion radiation of these two is metricsabout 500 in theW near-sidem−2 (Figure of the 13a), Moon. and The the maximum maximum mean standard solar 2 invasiondeviation radiation was about is about 520 W500 m W−2 (Figure m− (Figure 13b). 13Thea), andpattern the maximumpresents a standardconcentric deviation circle distribution, was about 2 520for Wboth m− the(Figure mean 13 valueb). The and pattern standard presents deviation. a concentric The circlevalue distribution,decreases with for boththe theincrease mean of value the anddistance standard to the deviation. center of Thethe valuelunar decreasesdisk. In the with limb the of increase the lunar of thedisk, distance specifically to the in center the high of the latitude lunar disk.region In of the the limb Moon, of the both lunar the disk,mean specifically value and the in the standard high latitude deviation region were of lower. the Moon, both the mean value and the standard deviation were lower.
(a) (b)
FigureFigure 13.13. (a) The mean and (b) standard deviationdeviation ofof solarsolar invasioninvasion radiationradiation variationvariation receivedreceived byby aa Moon-basedMoon-based sensorsensor atat didifferentfferent positionspositionson onthe thenear-side near-side of of the the Moon. Moon.
5. Discussion In this study, the solar invasion effects on a Moon-based sensor are analyzed systematically. The geometric description of solar invasion was established based on the theoretical geometric model of the Moon-based Earth observations. From the geometric analysis, we found that the angle between the Sun and the Earth direction was an important factor. If this angle was too small, the
Remote Sens. 2019, 11, 2775 15 of 17
5. Discussion In this study, the solar invasion effects on a Moon-based sensor are analyzed systematically. The geometric description of solar invasion was established based on the theoretical geometric model of the Moon-based Earth observations. From the geometric analysis, we found that the angle between the Sun and the Earth direction was an important factor. If this angle was too small, the Sun would probably enter the field of view, and the solar invasion radiation would reach a maximum. According to this parameter, the solar invasion duration when the Sun enters the FOV and the solar invasion radiation at the entrance pupil of the sensor were calculated. Since a Moon-based sensor can be equipped on the whole near-side of the Moon, and the changes of the orbit of the Moon are complicated, it is necessary to evaluate the solar invasion effects for a sensor on the different positions of the near-side of the Moon. In other words, by comparing the solar invasion effects at different positions on the near-side of the Moon, a suitable place to equip an Earth observation sensor can be suggested to avoid the solar invasion effects as much as possible. In establishing a lunar base, site selection is an extraordinarily significant issue, especially for Earth observations. They need a good line-of-sight condition to the Earth, high-precision pointing control, and low stray light. In the mission of Apollo 16, a far-ultraviolet camera was installed on the Descartes Highlands, located in the low latitude region of the Moon [8]. In the mission of CE-3, an extreme ultraviolet camera (EUVC) was installed on the Northwest of Mare Imbrium [9], and many scholars have investigated the landing area [31]. However, the main reason to land on these two sites is to deepen the understanding of the local region, rather than the requirements of Earth observations. Therefore, this site selection strategy is not suitable for Earth observation sensors. According to the analysis of the line-of-sight condition to the Earth and pointing accuracy, the site selection issue of a Moon-based sensor have been discussed in References [13,14,26]. However, the site selection issue, considering the stray light of the sensor, was not mentioned. The stray light of the Moon-based sensor was mainly caused by solar invasion and background contamination in the FOV. In this paper, we mainly investigated how to select a suitable region to equip an Earth observation sensor in view of reducing the effects of solar invasion. We first investigated the solar invasion duration and its distribution at the near-side of the Moon. The solar invasion duration depended on the FOV of the sensor. Within the permanently Earth-observing region, the solar invasion duration for a sensor did not change appreciably, regardless of the sensor’s position and FOV (Figure9). However, when considering the solar invasion radiation, the differences among different positions on the permanently Earth-observing region were revealed. The solar invasion radiation of a sensor mainly depended on the angle between the Sun direction and the line-of-sight vector. Due to the geometric relationship between the Sun and the Moon, the solar radiation in the mid–high latitude region would be lower than that in the low latitude region, leading to differences in the solar invasion radiation (Figures 11 and 12). Since the variation of lunar inclination to the ecliptic plane induces the relevant changes of solar invasion radiation (Figure3), solar invasion radiation at a certain position is not consistent. To evaluate these variations more scientifically and rationally, two metrics, including the mean and the standard deviation, are proposed to measure the mean value and amplitude of solar invasion radiation variation (Figure 13). As shown in Figure 13, compared to the low latitude region, equipping a sensor at the mid–high latitude region would not only have a lower solar invasion radiation, but also have a relatively stable variation. Our study suggests that equipping sensors on the mid–high latitude of the permanently Earth-observing region will lessen the effects of the solar invasion on a sensor.
6. Conclusions The effect of solar invasion on an Earth observation sensor on the near-side of the Moon has been investigated. Through parameterization of the Moon-based Earth observation geometry, considering the coordinate transformations of the Earth, the Sun, and the Moon-based sensor, the solar invasion duration of the Sun entering the FOV and solar invasion radiation at the entrance pupil of the sensor was calculated. Remote Sens. 2019, 11, 2775 16 of 17
It was found that the angle between the Sun direction and the line-of-sight vector was a dominant factor in determining whether the Sun was in the FOV of the sensor. The variation of this angle showed a 29.5-day cycle and the major reason to affect the solar invasion duration was the FOV of the sensor. When the FOV was larger than 10◦, the Sun enters the FOV every orbital period. Further, the solar invasion duration was almost the same when equipping sensors on the permanently Earth-observation region (i.e., 81◦S–81◦N, 80◦W–80◦E, as described in the selenographic coordinate system). As for solar invasion radiation, the results showed that both the mean and the standard deviation of the solar invasion radiation variation at the entrance pupil of the sensor was lower at the mid–high latitude regions. In conclusion, as a consequence of the solar invasion effect analysis, we suggest that the mid–high latitude regions within the permanently Earth-observing region are suitable for equipping Earth observation sensors.
Author Contributions: Conceptualization, H.Y. and H.G.; methodology, H.Y., J.P. and G.L.; validation, H.Y., J.P. and W.Z.; writing—Original draft preparation, H.Y. and W.Z.; writing—Review and editing, H.Y., J.P., G.L., and W.Z.; visualization, H.Y. Funding: This research was supported by the National Natural Science Foundation of China, grant number 41590851, 41590852, 41574014 and 41774014, the Open Research Fund of Key Laboratory of Digital Earth Science, Chinese Academy of Sciences, the Key Research Program of Frontier Sciences, CAS, grant number QYZDY-SSW-DQC026, the Frontier Science and Technology Innovation Project and the Innovation Workstation Project of the Science and Technology Commission of the Central Military Commission, and the Outstanding Youth Fundation of the China Academy of Space Technology. Conflicts of Interest: The authors declare no conflict of interest.
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