Lunar Coordinates Research Articles

Analysis of the First Optical Detection of a Meteoroidal Impact on the Lunar Surface Recorded from Brazil

Two lunar flashes are reported and fully analyzed, with one of them fulfilling every criterion preconized in the literature for the characterization of an impact, including confirmation by two simultaneous observations. It happened at 07:13:46 UT on 14 December 2017, at the selenographic coordinates of 9.79° (±0.06°)N and 45.42 (±0.07°)E. The peak magnitudes in the R and V bands vary from 6.3 to 7.9 and from 7.4 to 9.0, respectively, depending on the observatory, as the cameras’ exposure times were considerably different. The impactor mass is estimated to be between 1.6 and 2.0 kg, with a diameter of 10 to 11 cm, having produced a crater of 8.4 to 8.9 m in diameter. Results for the second flash are also presented and discussed, although the confirmation of an impact was not possible due to a pause in the recordings at one of the sites. The observations took place as part of an inaugural observing campaign in Brazil for lunar impact flash (LIF) detection conceived by the Brazilian Meteor Observation Network (BRAMON) and were carried out by two teams located in different states in the Northeast Region of Brazil, about 353 km apart from each other, at a time when the Moon was crossing the densest part of the Geminid meteoroid stream in 2017. The observing setups included 0.13 m and 0.2 m telescopes, both equipped with sensitive cameras. The Maceió setup probably delivered the finest definition ever reported in the literature for lunar impact monitoring, resulting in high-accuracy positioning. This will certainly aid in finding the associated crater from orbiter images, which will substantiate another work, aimed at performing a comparative analysis between the results from our photometry and the data retrieved by the LRO images. These observations were also very likely the first and the only one so far made by a normal framerate camera and a long-exposure camera simultaneously. The associated benefits are commented on. The source of the impactors is also discussed. In view of the successful results of this experience, national observing campaigns of this kind will be given continuation.

Fundamental parameters modeling for the lunar telescope

The powerful flow of highly accurate and multiparameter information produced by spacecrafts has caused a surge interest in the industrial robotic exploration of the Moon and manned flight to Mars after the creation of long-term lunar bases. The modern level of both ongoing and planned lunar studies is characterized by a high level of observation accuracy and a large variety of observation methods. The study of the Moon’s rotational parameters (MRP) is of important value. For this reason, new methods for analyzing big data sets on observation of MRP and extracting the highest possible amount of scientific information from them are needed. Such space technologies require the creation of in-situ telescopes on the Moon. The long-term laser measurements have supplied comprehensive observational information about the Moon. This allows for a description of the Moon’s dynamics with the accuracy required at the current stage - the error of determining the distance to the Moon should be less than a meter, while the one of establishing rotational parameters - arc milliseconds. Nevertheless, there is a necessity to obtain observation data independent of laser measurements. One of the ways to do it is to place on the lunar surface one or several optical telescopes, that will allow determining lunar rotational parameters by measuring the trajectories of the stars and will also be used to solve astrophysical and astrometric problems in the future. This work considers the results of computer modeling of observations taken by lunar in-situ telescopes located at various selenographic latitudes. The sensitivity of MRP to the observed selenographic coordinates of the stars is assessed. Based on the analysis of the simulation results, the optimum location of the telescope is concluded to be at a latitude of 30–45°. The constructive suggestions on the described experiment’s implementation are presented in the paper. The details that will allow implementing or declining the practical implementation of the in-situ telescope are discussed.

Development of Methods for Navigational Referencing of Circumlunar Spacecrafts to the Selenocentric Dynamic Coordinate System

The initial form of present-day space optical observations contain considerable geometrical and brightness distortions. This problem can be solved based on geometrical correction and transformation of reference object coordinates into commonly accepted cartographic projections. In this work, the method of coordinate transformation to the reference selenocentric dynamic system by using a base of reference selenographic objects as electronic maps is considered. The transformation process presupposes the formation of a photogrammetrically corrected image and identification of observed objects included into the electronic maps. Height data of on the Moon’s surface are determined from known observed selenographic coordinates with respect to reference objects by software tools. Preliminary selenographic coordinates can be determined using both ground positional observations and onboard goniometric devices such as a laser interferometer.

Measuring the Earth's Synchrotron Emission From Radiation Belts With a Lunar Near Side Radio Array

AbstractThe high kinetic energy electrons that populate the Earth's radiation belts emit synchrotron emissions because of their interaction with the planetary magnetic field. A lunar near side array would be uniquely positioned to image this emission and provide a near real time measure of how the Earth's radiation belts are responding to the current solar input. The Salammbô code is a physical model of the dynamics of the three‐dimensional phase‐space electron densities in the radiation belts, allowing the prediction of 1‐keV to 100‐MeV electron distributions trapped in the belts. This information is put into a synchrotron emission simulator that provides the brightness distribution of the emission up to 1 MHz from a given observation point. Using Digital Elevation Models from Lunar Reconnaissance Orbiter Lunar Orbiter Laser Altimeter data, we select a set of locations near the Lunar sub‐Earth point with minimum elevation variation over various‐sized patches where we simulate radio receivers to create a synthetic aperture. We consider all realistic noise sources in the low‐frequency regime. We then use a custom Common Astronomy Software Applications code to image and process the data from our defined array, using SPICE to align the lunar coordinates with the Earth. We find that for a moderate lunar surface electron density of 250/cm , the radiation belts may be detected every 12–24 hr with a 16,384‐element array over a 100‐km‐diameter circle. Changing electron density can make measurements 10 times faster at lunar night and 10 times slower at lunar noon.

Insight-building models for lunar range and range rate

The analysis of range or Doppler data between sites on the Earth and Moon requires an accurate computation of the lunar orbit and detailed models of the orientation of the Earth and Moon. Models constructed to understand range and range rate can lack detail, but if they include the largest lunar orbit variations, tracking stations on a rotating Earth, and lunar sites on a synchronously rotating Moon, then they will display the largest effects for orbit elements, Earth orientation, tracking station locations, and lunar site coordinates. The range and range rate are expanded into periodic series. To understand accurate solutions, the largest periodic terms that are sensitive to various solution parameters indicate the sensitivity of data to solution parameters and the time spans needed for their determination. Conclusions include: cylindrical coordinates work well for sites on the rapidly rotating Earth, but Cartesian coordinates are more natural for the synchronously rotating Moon since the series for the three coordinate projections are distinct. For range and range rate data, daily, semimonthly, monthly, and longer periods are present. For Doppler data, the daily periods may be stronger and more useful than the long periods, particularly for terms associated with the terrestrial tracking station. Doppler data do not determine the lander coordinate toward the Earth well. Observational strategies for range and Doppler data are not identical. For all data types, one wishes a variety of hour angles, lunar declinations, times of month, and longer periods. A long span of high-quality range data can improve the lunar orbit, orientation of the Earth’s equator, and physical librations. The locations of new lunar sites or new tracking stations can be determined from shorter spans of data.

A large lunar impact blast on 2013 September 11

On 2013 September 11 at 20h07m28.68 $\pm$ 0.01 s UTC, two telescopes operated in the framework of our lunar impact flashes monitoring project recorded an extraordinary flash produced by the impact on the Moon of a large meteoroid at selenographic coordinates 17.2 $\pm$ 0.2 $^{\circ}$ S, 20.5 $\pm$ 0.2 $^{\circ}$ W. The peak brightness of this flash reached 2.9 $\pm$ 0.2 mag in V and it lasted over 8 seconds. The estimated energy released during the impact of the meteoroid was 15.6 $\pm$ 2.5 tons of TNT under the assumption of a luminous efficiency of 0.002. This event, which is the longest and brightest confirmed impact flash recorded on the Moon thus far, is analyzed here. The likely origin of the impactor is discussed. Considerations in relation to the impact flux on Earth are also made.

Some qualitative manifestations of the physical libration of the Moon by observing stars from the lunar surface

Targets and problems of the future Japanese project ILOM (In situ Lunar Orientation Measurement), which is planned to be realized as one kind of observations of lunar rotation at the second stage of SELENE-2 mission, are briefly described in the article. Inverse problem of lunar physical libration is formulated and solved. Accuracy of libration angles depending on accuracy of measuring selenographic coordinates is estimated. It is shown that selenographic coordinates of polar stars are insensitive to longitudinal librations τ(t). Comparing coordinates calculated for two models of a rigid and deformable Moon is carried out and components sensitive to Love number k2 and to anelastic time delay are revealed.

Book Review: The Hill-Brown Theory: The Hill-Brown Theory of the Moon's Motion: Its Coming-to-Be and Short-Lived Ascendancy (1877–1984)

THE HILL-BROWN THEORY The Hill-Brown Theory of the Moon's Motion: Its Coming-To-Be and Short-Lived Ascendancy (1877-1984). Curtis Wilson (Springer, New York, 2010). Pp. xiv + 323. euro117. ISBN 978-1-4419-5936-2.The Hill-Brown theory has an important place in the history of lunar theory. Based on original methods, it surpassed all the solutions of its time in precision and completeness. It gave rise to tables and for sixty years was used for computing lunar positions in the leading published ephemerides. Simultaneously it provided evidence concerning the contribution of the Earth's rotation to the apparent discrepancies between theories of celestial mechanics and observations, giving rise to the concept of Ephemeris Time, a time measurement independent of the irregularities of Earth rotation, later replaced by Atomic Time.Curtis Wilson gives a magisterial account of all these events. He analyses with great care the numerous scientific publications on which they are based, examining methods, influences and evolutions. Neither biographical nor institutional matters are ignored. In particular, large extracts of the unpublished correspondence between Ernest W. Brown and George H. Darwin are presented.The book is divided in three parts. The first two are devoted to the elaboration of the Hill-Brown theory and to the construction of the Brown-Hedrick Tables. In the first part, after a short description of the preceding works in lunar theory, Wilson presents two papers (1877 and 1878) of George William Hill dealing with the lunar in a simplified case but tackling the major difficulty: the slow convergence of the series representing lunar coordinates with respect to the ratio of the lunar and terrestrial orbital periods. Here appears the famous curve.Ernest William Brown is the hero of the second part. A recent graduate of Cambridge University, he is induced in 1889 to carry on Hill's works by George Howard Darwin. Brown will achieve a complete lunar theory in 1908, after he in 1891 had moved to the USA. From a theoretical point of view, Brown takes Hill's variation curve as a starting approximation and builds a solution of the main problem (threebody of the Moon-Earth-Sun, the heliocentric orbit of the Earth-Moon barycentre being supposedly Keplerian) using methods inherited from Hill and from John Couch Adams. Then Brown uses Jacobi's method to complete his solution by adding the perturbations due to planets and to the Moon's and Earth's figures. From a practical point of view, the elaboration of such a complete solution involves a massive amount of computation, in which Brown is assisted by a computer partially paid by grants from the Royal Society. …

Measuring moonlight: An overview of the spatial properties, lunar coverage, selenolocation, and related Level 1B products of the Moon Mineralogy Mapper

[1] The Moon Mineralogy Mapper (M3), a high-resolution, high-precision imaging spectrometer, flew on board India's Chandrayaan-1 Mission from October 2008 through August 2009. This paper describes some of the spatial sampling aspects of the instrument, the planned mission, and the mission as flown. We also outline the content and context of the resulting Level 1B spatial products that form part of the M3 archive. While designed and planned to operate for 2 years in a 100 km lunar orbit, M3 was able to meet its lunar coverage requirements despite the shortened mission; an increase of the orbit altitude to 200 km; and several relevant problems with spacecraft attitude, timing, and ephemeris. The unexpected spacecraft issues required us to invent a novel two-step approach for selenolocation. Leveraging newly available Lunar Reconnaissance Orbiter-Lunar Orbiter Laser Altimeter (LOLA) topography and an improved spacecraft ephemeris, we have created a method that permits us to bootstrap spacecraft attitude estimates from the image data themselves. This process performs a nonlinear optimization to honor a set of data-derived image-to-image tie points and image-to-LOLA control points. Error analysis of the final results suggests we have converged to a selenolocation result that has image-to-image root-mean-square (RMS) errors less than 200 m and image-to-LOLA RMS errors less than 450 m, despite using data-derived spacecraft attitude results. The Level 1B products include the lunar coordinates resulting from this inversion process and 10 relevant observational geometry parameters that fully characterize the ray tracing geometry on a pixel-by-pixel basis.

Estimation of solar illumination on the Moon: A theoretical model

The solar illumination conditions on the lunar surface represent a key resource with respect to returning to the Moon. As a supplement to mapping the solar illumination by exploring data, lighting simulations using high-resolution topography could produce quantitative illumination maps. In this study, a theoretical model is proposed for estimating the solar illumination conditions. It depends only on the solar altitude and topographical factors. Besides the selenographic longitude and latitude, the former is determined by the selenographic longitude and latitude at the subsolar site, the geocentric ecliptical latitude, and the dimensionless distance of the Sun–Moon relative to 1 AU, which are function of time. The latter is determined by comparing the elevations in solar irradiance direction within 210 km in which the topography might shadow the behind sites to the critical elevations determining whether the behind sites are shadowed or not. Compared to Zuber's model, the model proposed in this study is simpler and easier for computing. It is parameterized with selenographic coordinates, elevations, and time. With high-resolution topography data, the solar illumination conditions at any selenographic coordination could be estimated by this model at any date and time. The lunar surface is illuminated when the solar altitude is non-zero and all the elevations within 210 km in solar irradiance direction are lower than the critical elevations. Otherwise it would be shadowed.

Long-term harmonic development of lunar ephemeris

Aims. The aim of this study is to develop new analytical series representing lunar coordinates to accuracy compatible with the accuracy of the modern numerical ephemeris of the Moon. Methods. An improved method of spectral analysis of tabulated function is used to make harmonic development of the latest long-term numerical ephemeris of the Moon LE-406 which covers a six thousand-year interval. A feature of the method is that the development is made directly to Poisson series where both amplitudes and arguments of the series’ terms are high-degree polynomials of time. Results. The new analytical development includes 42 270 Poisson series’ terms of minimal amplitude equivalent to 1 cm and is valid over 1500–2500. A simplified version of the development includes 7952 series’ terms of minimal amplitude equivalent to 1 m and is valid over 3000BC–3000AD. Over 1500–2500 the maximum difference between lunar coordinates calculated by means of the new analytical series and numerical ephemeris LE-406 is 3.2 m in geocentric distance, 0. �� 0056 in ecliptic longitude, and 0. �� 0018 in ecliptic latitude. This is 9–70 times better than the accuracy of the latest analytical theory of lunar motion ELP/MPP02, and the number of terms in the new development is less than that in ELP/MPP02.

The Standard Scheme of the Moon and Its Mean Quantities

The Papyrus Rylands 27, of the John Rylands Library, Manchester, is a portion of a Greek treatise or tract of the third century A.D., providing rules for the longitude and node of the Moon. Apart from the illuminating analysis provided by Hunt, it has been the subject of a number of profound studies by Neugebauer, van der Waerden and Jones.1 These have culminated in the presentation by Jones of what he calls the Standard Scheme of lunar motion, illustrated by its application in various parts of the Oxyrhynchus Papyri, and elsewhere.2 It is clear from all this that we have here a scheme for the computation of the true longitude and node of the Moon based on a Babylonian type of 'zigzag' model. Jones has provided all that one needs for the practical derivation of the lunar coordinates, including lengthy tables to facilitate the computation of the summation of values from the zigzag functions that determine the coordinates. That much completes the subject as a self-contained model within the context of 'arithmetical' schemes, but leaves untouched the question of the relation between the Standard Scheme and the trigonometrical models, that is, those based on the use of one or more epicycles, etc. The purpose of this article is to develop this relation, one that situates the model in the interface between Babylonian and Greek astronomy.

Lunar domes in the Doppelmayer region: Spectrophotometry, morphometry, rheology, and eruption conditions

In this study we examine a lunar volcanic region near Doppelmayer, composed of two domical structures previously not studied in detail and a well-known lunar pyroclastic deposit. Dome 1 is situated at selenographic coordinates 41 . 92 ∘ W and 30 . 08 ∘ S , dome 2 at 43 . 42 ∘ W and 30 . 66 ∘ S . We perform a spectrophotometric study of representative locations of the volcanic region based on Clementine UVVIS data. Relying on ground-based high-resolution CCD imagery, we furthermore examine the morphometric characteristics of the two domes, making use of a combined photoclinometry and shape from shading technique. Based on a rheologic model, we examine the physical conditions under which the domes were formed. Dome 1 is spectrally atypically red for mare domes and shows a very weak mafic absorption, implying a low TiO 2 and FeO content. The overall spectral signature corresponds to that of a mixture between mare and highland soils. Dome 1 was formed of lava with a relatively high viscosity value of ∼ 10 7 Pa s , situated between the ranges of values typically observed for mare domes and for the Gruithuisen and Mairan highland domes, respectively, erupting at moderate rates over a long period of time. Dome 1 is larger, steeper, and more voluminous than typical mare domes but has a much lower flank slope than the Gruithuisen and Mairan highland domes. It is an exemplar of a rare type of unusually steep and voluminous mare domes, similar to the well-known mare domes Hortensius 5 and 6 and Herodotus ω . We discuss the relevance of vertical (assimilation of crustal material) vs. lateral (distribution of material across mare-highland boundaries by random impacts) mixing mechanisms as being responsible for the observed spectral appearance of dome 1. The thermal conditions in the lunar interior did not favour the assimilation of crustal wallrock into the ascending magma. Due to the fact that dome 1 is located right on the boundary between hummocky terrain and a mare pond, lateral mixing of mare and highland soils is a much more natural explanation for the observed spectral signature. For dome 2, we find that it is a typical effusive mare dome, given its spectral and morphometric properties and inferred rheologic parameters. An estimation of the dimensions of the feeder dikes of the two domes reveals that the dike which formed dome 1 was five times as broad as the one which formed dome 2, while the dike lengths only differ by about one third. The dike dimensions suggest that their source regions were located below the lunar crust.

The first confirmed Perseid lunar impact flash

The first confirmed lunar impact flash due to a non-Leonid meteoroid is reported. The observed Perseid meteoroid impact occurred at 18 h28 m27 s on August 11, 2004 (UT). The selenographic coordinates of the lunar impact flash are 48 ± 1 ° N and 72 ± 2 ° E , and the flash had a visual magnitude of ca. 9.5 with duration of about 1/30 s. The mass of the impactor is estimated to have been 12 g based on a nominal model with conversion efficiency from kinetic to optical energy of 2 × 10 −3 . Extrapolation of a power law size-frequency distribution fitting the sub-centimeter Perseid meteoric particles to large meteoroids suggests that several flashes should have been observed at this optical efficiency. The detection of only one flash may indicate that the optical efficiency for Perseid lunar impact is much lower, or that the slope of the size distribution differs between large meteoroids and typical sub-centimeter meteoric particles.

Lunar coordinates in the regions of the Apollo landers

Laser retroreflectors were placed on the Moon by Apollo 11, Apollo 14, Apollo 15, and Lunakhod 2. Since then, lunar laser ranging retroreflector measurements of the true distances between retroreflectors and Earth‐based laser telescopes have been made by recording transit times. The accuracy of these measurements has evolved from 10 cm in the 1970s to 3 cm in the 1990s. Accurate lunar coordinates of the retroreflectors were determined from these measurements [Williams et al., 1996]. Apollo lunar surface experiment packages (ALSEP) were delivered to the lunar surface on missions 12, 14, 15, 16, and 17. Coordinates of these stations were determined from very long baseline interferometry (VLBI) measurements of their transmissions. The VLBI measurements were combined with the laser‐ranging coordinates available at that time [King et al., 1976]. These solutions for the ALSEP locations have been modified to be compatible with the current retroreflector solutions. Coordinates of lunar module locations and nearby craters are given.

Morphological characteristics of lunar craters with moderate depth/diameter ratio. II (0.12<d/D<0.15)

The morphological characteristics of craters, the depth/diameter ratio of which is between 0.12 and 0.15, are discussed. Many small secondary craters belong to that class—results of low velocity impacts—as well as young craters created by low angle impacts. Revised values for the craters' selenographic coordinates are also presented.

Astronomical supplement to the 1:5 000 000 albedo map of the moon and the establishment of a 1:2 500 000 auxiliary mosaic

view Abstract Citations (2) References (10) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Astronomical supplement to the 1:5000000 albedo map of the moon and the establishment of a 1:2500000 auxiliary mosaic. Wildey, R. L. Abstract A photoelectrically calibrated isodensity mosaic of the full Moon has been produced at a scale of 1:2 300 000. A control grid was produced for guiding the mosaicking of the isodensitracing as an ortho- graphic projection of the system of selenographic coordinates in the direction of the observing station ac- cording to the deduced topocentric libration of the epoch. The source of photometric error due to the spectral mismatch between photoelectric and photographic photometry is fully investigated and found to be negligible. This conclusion also applies to the U.S. Geological Survey 1:5 000000 albedo map. Since recent results indicate that correction to a true phase angle of zero is often too large to be a blanket correc- tlo over the whole lunar face and is also variable according to the geologic nature of the terrain, a graphi- cal device has been produced that allows one to read the true phase angle applicable at any selenographic coordinate for either the 1:5000000 albedo map or the 1:2500000 iso den sity mosaic. The new calibration has been rendered in terms of "infranormal" albedo, an observational lower bound to the true normal al- bedo, which can easily be normalized at the investigator's discretion. An alternative absolute calibration method was employed, which produced agreement with the previous scale provided an effective wavelength of 5390 A is assumed. Analysis of the dependence on data scatter of the least-square relationship between photoelectric albedo and photographic density shows that an accurate curve has been obtained. The present document provides all necessary information for using and assessing the reliability of the 1:2 500000 iso- density mosaic, which is in five colors, now housed at the U.S. Geological Survey, Flagstaff, Arizona. Publication: The Astronomical Journal Pub Date: December 1974 DOI: 10.1086/111703 Bibcode: 1974AJ.....79.1471W Keywords: Albedo; Astronomical Photometry; Lunar Maps; Lunar Photography; Ubv Spectra; Black Body Radiation; Electrophotometry; Light Curve; Luminance; Mosaics; Optical Density; Spectral Energy Distribution; Lunar and Planetary Exploration full text sources ADS |

Orbital mapping of the lunar magnetic field

Magnetometer data obtained during the first four lunations after the deployment of the Apollo 15 subsatellite have been used to construct contour maps of the lunar magnetic field referred to 100 km altitude. These contour maps cover a relatively small band on the lunar surface. Within the region covered there is a marked near side-far side asymmetry. The near-side field is generally weaker and less structured than the far-side field. The strongest intrinsic lunar magnetic field detected is between the craters Van de Graaff and Aitken, centered at 20°S and 172°E. The variation in field strength with altitude for this feature suggests that its scale size is on the order of 80 km. A magnetization contrast between this region and its surroundings of the order of 6 × 10−5 emu-cm−3 is obtained assuming a 10-km thick slab. Preliminary Apollo 16 magnetometer data at extremely low altitude (0 to 10 km) show a very structured magnetic field with field strengths up to 56γ. Large compressions in the magnetic field magnitude, just above the lunar limb regions, are occasionally detected when the Moon is in the solar wind. The occurrence of limb compressions is strongly dependent on the selenographic coordinates of the lunar region on the solar wind terminator beneath the orbit of the sub-satellite. The discovery of remanent magnetization of varying strength over much of the lunar surface and its correlation with limb compression source regions supports the hypothesis that limb compressions are due to the deflection of the solar wind by regions of strong magnetization at the lunar limbs. If this hypothesis is correct, then the map of lunar regions associated with compressions indicates that the northerly equatorial region on the far side is less strongly magnetized than the southerly equatorial region on the far side.

Rotation of the moon and lunar coordinate systems

The need for precise definition of lunar reference systems is stressed and the principles on which systems of lunar coordinates could be based are established. Differences between coordinate systems defined by the dynamical properties of the lunar configuration and the rotational motion of the lunar globe about its centre of gravity are outlined, and rigorous mathematical formulae relating those systems have been developed. The principles of reduction of measurements are outlined and in the Appendix the absolute coordinates obtained for 700 lunar features are presented.

On the systems of selenographic coordinates, their determination and terminology

Attention is drawn to the absence in literature of the precise definitions of selenographic and celestial selenocentric coordinate systems. In certain cases inaccuracies in the formulation of the first Cassini law occur. This is due to the fact that the principal directions dealt with in the theory of lunar rotation are being constantly confused. A clear-cut definition of the principal coordinate systems concerned with the lunar rotation is given. It is indicated that there is no necessity in a special astronomical time service on the Moon. Since the future expeditions to the Moon will be able to keep terrestrial time, the problem of the hour angle is simply solved by the Formula (11).