On the Breadth of Earth’s Shadow Of Lunar Eclipse - A New Approach To Students’ Understanding Of Aristarchus’s “Hypothesis 5”

The Moon’s surface thermal environment is extreme compared to other planetary bodies in the solar system, with temperatures ranging between 400 K at the subsolar point and lower than 40 K in permanently shadowed regions around the poles (Paige et al. 2010). The surface temperature of the Moon also represents a fundamental boundary condition that governs the thermal state of the Moon’s regolith, the interior, and the behaviour of near-surface volatiles. The regolith is the layer of unconsolidated material covering the lunar surface, created by impacts and space weathering. The lunar environment is known to be characterized by interactions between the space plasma and the dusty surface, leading to a complex exosphere. Knowing more about the current state of the lunar regolith can give us insight into the geological history of the moon.In contrast to in-situ measurements or returned samples, remote sensing measurements can be used to constrain surface properties on a global scale. NASA’s Lunar Reconnaissance Orbiter (LRO) was the first spacecraft to create a global 3D map of the lunar surface. During the 15+ years of operation of LRO, the Diviner Lunar Radiometer Experiment (Diviner) has measured the brightness temperature of the lunar surface in 9 wavelength channels ranging from 0.35 µm to 400 µm (Paige et al. 2010) with a spatial resolution of approximately 250 meters per pixel. With the help of thermal models, the Diviner measurements were used to derive global properties of the lunar regolith (Hayne et al. 2017). Based on the latter work, Bürger et al. (2024) developed a thermal model of the lunar regolith using microphysical parameters, such as the regolith grain size and stratification. However, their best-fit results to Diviner nighttime measurements were non-unique.On the contrary to the diurnal cycle which spans roughly 29.5 Earth days, lunar eclipses (solar eclipses as seen from the lunar surface) provide cooling curves of the regolith on a much smaller timescale of roughly 4 Earth hours. As a consequence, eclipse cooling occurs only within a thin layer corresponding to the much shallower thermal skin depth < 1 cm (compared to ~10 cm for the diurnal cycle). Lunar eclipse events lead to a significant cooling of the lunar surface by ΔT ≈ 200 K, due to the lack of a lunar atmosphere. Therefore, eclipse events offer a unique opportunity to constrain the physical properties of the uppermost regolith layer, the interaction zone between the lunar space environment and the lunar surface.We present a refinement of the thermal model of Bürger et al. (2024) by combining Diviner daytime, nighttime, and eclipse measurements to resolve the degeneracy of the solution space and give best-fit estimates for microphysical properties of the lunar regolith such as regolith grain size and stratification on a global scale. To capture the precise timing and geometry of each lunar eclipse we improve the upper boundary condition of the thermal model by using the SPICE toolkit. We filter for locations with a low rock abundance below the average of 0.4% (Bandfield et al. 2011) and small local slopes below 5 degrees, describing default regolith properties and avoiding offsets of the lunar local time. We analyse lunar maria and highlands independently and investigate a latitudinal trend of the derived regolith properties. A comparison with in-situ measurements conducted by the Apollo mission is made to confirm the results.Figure 1: Comparison of the thermal model with the Diviner data for a location in the maria near the equator. The top panel shows the available Diviner measurements for this location between 2009-12-01 and 2024-06-01 on top of their respective simulated diurnal curves. Nighttime data are marked with triangles, daytime data with asterisks. The eclipse event on the morning side is marked with a circle and shown in the cutout in the top right corner. The temperature drops by ~200 K for a short duration and then rises quickly to continue the ascending curve of the morning side. A drop in temperature without a measurement means that the location was not in the field of view of Diviner during the eclipse, instead it is part of the diurnal curve of another data point. The bottom panel shows the difference between model and data with χ2 = 1.6 K.

The following summarizes certain previously unpublished inferences regarding the lunar surface that were included in a more extensive oral presentation. Infrared (Shorthill & Saari 1961; Murray & Wildey 1964) and radar (Pettengill & Henry 1962) observations of the Moon acquired in 1960–62 demonstrated that, in some cases at least, conspicuously bright craters like Tycho also are characterized by the presence of more consolidated material at or very near the surface and by considerably rougher terrain on the metre scale. Interpreting the bright craters generally as younger—and less aged—than the less conspicuous craters leads to the conclusion that the process of modification operative on the lunar surface not only gradually reduce the visible reflectivity to the average back­ground level but also smooth and insulate the surface materials. Recent observations of the infrared emission during a lunar eclipse (Saari & Shorthill 1965) and during the lunar night time (Murray, Westphal & Wildey 1967) reveal further an unexpected degree of variability in thermal properties geographically. The infrared anomalies observed during lunar light time and eclipses generally correspond and are distributed quite nonuniformly. For instance, Mare Tranquillitatis exhibits a much higher surface density of anomalies than does Mare Serenitatis. Also, Mare Crisium is characterized by a small, but real, enhancement of night time infrared emission throughout; similar enhancements are also apparent on some portions of other maria surfaces during an eclipse. Both the nonuniform distribution of infrared anomalies and the nonuniform low level enhancements imply processes on the lunar surface which in some areas preferentially produce or expose material of lower than average thermal inertia (more consolidated material) and/or in other areas preferentially remove or cover such material. Specifically, either random impact must be more effective in exposing consolidated rock in Mare Tranquillitatis than in Mare Serenitatis because of intrinsic physical differences in the host rocks of the two maria, or there has been a more rapid covering process operative in Mare Serenitatis. The broad, low level enhancements require similar selective formation or removal processes. These inferences would seem to be most compatible with a terrain characterized by a range of lithologies and, possibly, by periodic extrusion of thin blankets of new materials. It may be of importance to search for any correlation between the distribution of non-thermal visible emission and the distribution of infrared and other anomalies because the same differential surface processes may control the magnitude and distribution of both sets of phenomena.

A new wide‐angle coronagraphic‐type imaging system used for the lunar eclipse of 16 July 2000 resulted in detections of the lunar sodium exosphere out to ∼20 lunar radii, approximately twice the size recorded with narrower fields of view during previous eclipses. These measurements and subsequent modeling provide a unique constraint on the fastest atoms ejected from the lunar surface that form the lunar exosphere, indicative of the most energetic space weathering processes acting on the lunar surface. At most, only a small fraction of the atoms are ejected from the surface with speeds faster than escape speed of 2.4 km s−1, meaning solar photon radiation pressure largely contributes to the escape of sodium atoms which form the comet‐like tail. The total rate of sodium ejection from the surface for speeds >2.0 km s−1 is comparable to estimates from previous lunar eclipse observations and earlier images of the lunar sodium tail.

Early design phases for lunar surface assets such as instruments, rovers, habitats, or landers require reliable predictions of the thermal environment on the Moon. Elaborate, numerical models exist, are correlated against measurements and predict temperatures with a high precision. Yet, modelling the lunar surface appropriately with detailed models, considering temperature dependencies of material properties, mineralogical differences, angle dependence of thermo-optical properties, or accounting for topography, is computationally expensive. Furthermore, these detailed and elaborate thermal models are at odds with the fidelity of the spacecraft design in early design phases. In consequence, there is a need for quick but accurate assessments of the lunar thermal environment at system level at early design stages. Apart from the numerical models there are also numerous analytical heat balance based models for lunar surface temperature predictions in literature. They allow reproducing daytime temperatures but are often inaccurate or not applicable for eclipses. In this paper we compare several existing analytical models with each other and with an implementation of a widely accepted numerical model. The simplified model’s shortcomings are highlighted and a refined analytical model, called ESAMT, is presented that allows a higher accuracy throughout lunar day and eclipses.

Implications of the Nonuniform cooling behavior of the eclipsed Moon

T brightness temperature of the lunar surface has been determined using telescopes on Earth, on balloons, and on aircraft. Observations revealed more than a thousand anomalous regions (hot spots) during an eclipse. It was also discovered that certain of the mare and portions of mare regions show an anomalous thermal behavior. In 1966 and 1968 Surveyors I, III, V, VI, and VII performed in situ thermal measurements. With the two Apollo landings in 1969, we have passed from a remote sensing to a physical sampling era. Apollo 11 and 12 provided samples of the lunar surface from which certain of its thermophysical properties will be determined. In the coming Apollo missions, it can be expected that a landing will be made on or at least near one of the so-called hot spots, and on one of the enhanced mare locations. The purpose of this paper is to describe the infrared measurements that have been made of the lunar surface. The earliest measurement was made one hundred years ago. The first significant work was done between 1924 and 1928 by Pettit and Nicholson of the Mount Wilson Observatory; their work has been reviewed in detail by others. They reported measurements of brightness temperatures under various conditions: distribution of temperature along the lunar diameter at full moon, the subsolar point temperatures as a function of phase, the antisolar point (nighttime) temperature and the transient temperature during a total lunar eclipse for a point near the disk center and at the limb. In the theoretical work that followed, Wesselink and Jaeger and Harper » assumed that the thermophysical properties of the lunar surface were constant with depth and temperature. Even with a two-layer model, it was not possible to match simultaneously the lunation and eclipse measurements with one set of thermal parameters. These early theoretical studies, however, did suggest that the uppermost layer of the moon was of a porous or dustlike nature. Further measurements of eclipse cooling were made by Sinton and Strong in 1953, and in 1958 and 1959 Sinton constructed isothermal contour maps over the lunar surface at nine different phases. The lunar infrared measurements up to 1960, including a description of certain theoretical models, have been discussed by Sinton. During the lunar eclipse of March 13, 1960, Shorthill, Borough, and Conley discovered that several rayed craters cooled less rapidly than their environs, and in particular, that Tycho was about 40° K warmer than its environs an hour into the umbral phase. This surprising observation in the infrared, revealing differential properties over localized regions, provided an impetus to the author as well as several others to make additional measurements. Subsequently, extensive measurements were made during eclipses and during the lunar daytime. Measurements during the lunar night are less extensive. Some results of these measurements will be discussed as well as -a new thermophysical model developed by Winter and Saari which fits both the lunation and eclipse data.

Space-based observations of the total lunar eclipse on 21 January 2019 were conducted using the geostationary Earth-orbiting satellite Gaofen-4 (GF-4). This study represents a pioneering effort to address the observational gap in full-disk lunar eclipse photometry from space. With its high resolution and ability to capture the entire lunar disk, GF-4 enabled both quantitative and qualitative analyses of the variations in lunar brightness, as well as spectra and color changes, across two spatial dimensions, from the whole lunar disk to resolved regions. Our results indicate that before the totality phase of the lunar eclipse, the irradiance of the Moon diminishes to below approximately 0.19% of that of the uneclipsed Moon. Additionally, we observed an increase in lunar brightness at the initial entry into the penumbra. This phenomenon is attributed to the opposition effect, providing scientific evidence for this unexpected behavior. To investigate detailed spectral variations, specific calibration sites, including the Chang’E-3 landing site, MS-2 in Mare Serenitatis, and the Apollo 16 highlands, were analyzed. Notably, the red-to-blue ratio dropped below 1 near the umbra, contradicting the common perception that the Moon appears red during lunar eclipses. The red/blue ratio images reveal that as the Moon enters Earth’s umbra, it does not simply turn red; instead, a blue-banded ring appears at the boundary due to ozone absorption and the lunar surface composition. These findings significantly enhance our understanding of atmospheric effects on lunar eclipses and provide crucial reference information for the future modeling of lunar eclipse radiation, promoting the integration of remote sensing science with astronomy.

Abstract. This paper shows how the exposure of the Moon to the Earth's plasmasheet is subject to decadal variations due to lunar precession. The latter is a key property of the Moon's apparent orbit around the Earth – the nodes of that orbit precess around the ecliptic, completing one revolution every 18.6 years. This precession is responsible for a number of astronomical phenomena, e.g. the year to year drift of solar and lunar eclipse periods. It also controls the ecliptic latitude at which the Moon crosses the magnetotail and thus the number and duration of lunar encounters with the plasmasheet. This paper presents a detailed model of those encounters and applies it to the period 1960 to 2030. This shows that the total lunar exposure to the plasmasheet will vary from 10 h per month at a minimum of the eighteen-year cycle rising to 40 h per month at the maximum. These variations could have a profound impact on the accumulation of charge due plasmasheet electrons impacting the lunar surface. Thus we should expect the level of lunar surface charging to vary over the eighteen-year cycle. The literature contains reports that support this: several observations made during the cycle maximum of 1994–2000 are attributed to bombardment and charging of the lunar surface by plasmasheet electrons. Thus we conclude that lunar surface charging will vary markedly over an eighteen-year cycle driven by lunar precession. It is important to interpret lunar environment measurements in the context of this cycle and to allow for the cycle when designing equipment for deployment on the lunar surface. This is particularly important in respect of developing plans for robotic exploration on the lunar surface during the next cycle maximum of 2012–2019.

This paper provides an overview of the computational techniques used to characterize the viability of different lunar architectures and their ability to provide communication services to the Lunar surface. This analysis was done with ray-tracing techniques that allow for computations on Graphics Processing Unit (GPU) clusters for a high level of parallelism and severe reduction in computation time. The ray-tracing computations were done with the GPU platform Compute Unified Device Architecture (CUDA) provided by NVIDIA, which utilizes General-Purpose computing on Graphics Processing Units (GPGPU). This new method offers the advantage of being able to characterize a significantly larger portion of the Lunar surface due to its computational efficiency and providing a more accurate representation of communication limits instead of the typical and often inaccurate elevation angle mask. The Lunar surface can now be characterized by contact time, outage time, and distance metrics. With these metrics, different proposed Lunar architectures can be evaluated. This reduction in computation time leads to more accurate results and allows these results to be obtained in a time frame that allows for the complete characterization of the trade space. It is then shown that the architecture that provides the highest overall performance will be the dual twelve-hour pathfinder configuration. In addition, this computation method can recreate network parameter figures generated by previous methods but with an increased level of accuracy.

We observed the 2019 January total lunar eclipse with the Hubble Space Telescope’s STIS spectrograph to obtain the first near-UV (1700–3200 Å) observation of Earth as a transiting exoplanet. The observatories and instruments that will be able to perform transmission spectroscopy of exo-Earths are beginning to be planned, and characterizing the transmission spectrum of Earth is vital to ensuring that key spectral features (e.g., ozone, or O3) are appropriately captured in mission concept studies. O3 is photochemically produced from O2, a product of the dominant metabolism on Earth today, and it will be sought in future observations as critical evidence for life on exoplanets. Ground-based observations of lunar eclipses have provided the Earth’s transmission spectrum at optical and near-IR wavelengths, but the strongest O3 signatures are in the near-UV. We describe the observations and methods used to extract a transmission spectrum from Hubble lunar eclipse spectra, and identify spectral features of O3 and Rayleigh scattering in the 3000–5500 Å region in Earth’s transmission spectrum by comparing to Earth models that include refraction effects in the terrestrial atmosphere during a lunar eclipse. Our near-UV spectra are featureless, a consequence of missing the narrow time span during the eclipse when near-UV sunlight is not completely attenuated through Earth’s atmosphere due to extremely strong O3 absorption and when sunlight is transmitted to the lunar surface at altitudes where it passes through the O3 layer rather than above it.

We report on the first documented observations, to the best of our knowledge, of the amethyst (super wolf) Moon recorded in the region just south of the northern Tropic of Cancer (latitude ${21}^\circ {7.745^\prime}\;{\rm N}$21∘7.745'N), at about 2000 m height above the sea level during the lunar eclipse on 20 January 2019. During the color transition from the brownish red to amethyst blue (a mixture of dark blue and some red), the moon in the center of the Earth shadow (mid-eclipse) was nearly in zenith in Leon, Mexico. We interpret the amethyst color as arising from the inability of red rays to curve into the axial regions of the lunar spherical surface, while the scarce, randomly distributed blue rays are still incident there.

<p>Recent sample-return missions to asteroids (101955) Bennu and (162173) Ryugu have revealed their rough surfaces are strewn with regolith particles ranging from millimeters to tens of meters in diameter with a broad spectrum of shapes. Numerical modelers often simulate these kinds of bodies as rubble piles composed of discrete particles with rock-like material properties. The particles in most models for the past few decades have been independent spheres meant to represent the individual grains that make up the surface and interior of a rubble pile. It has been shown, however, that grain shape has a significant effect on the flow and equilibrium states of particles in granular media. Simulating irregular grain shape is thus imperative for accurately modeling the surfaces and interiors of rubble-pile asteroids.</p> <p>One of the most challenging aspects of simulations using spherical particles is creating high-porosity media. The densest packing distribution of monodisperse spheres has ~26% porosity; porosities of polydisperse spheres in a randomly packed orientation approach 35-45%. Bennu and Ryugu were each found to have bulk densities on the order of 1.1 g/cc, indicating bulk macroporosities of 50% or larger. Furthermore, the depth to which the arm of the OSIRIS-REx TAGSAM spacecraft penetrated Nightingale crater showed that it met little resistance from the regolith surface of Bennu, which may indicate that the finer-grained parts of regolith surfaces could have porosities larger than the bulk macroporosity. The low bulk densities and high macroporosities of rubble piles that have been visited by spacecraft seem to indicate subsurface structure mainly supported by contact networks between regolith grains strengthened by grain shape and interparticle cohesion from electrostatic and van der Waals forces. These recent results, in combination with historical measurements on the lunar surface, show a need to be more methodical in preparing “fluffy” granular beds to accurately reproduce surface structure on low-gravity, airless bodies.</p> <p>For our experiments, we use the parallel<em> N</em>-body gravity tree code PKDGRAV.<em> </em>PKDGRAV uses a soft-sphere discrete element method to model surface grains as individual spheres that feel interparticle and uniform gravity, cohesion, and contact forces. The contact forces from the soft-sphere method allow particles to slightly interpenetrate at the point of contact, using a restoring spring force to model the stiffness (akin to the Young’s modulus) of the material and applying normal and tangential damping and forces like interparticle friction. More recently, we have made improvements to routines handling irregularly shaped “aggregate” particles, made by “gluing” together two or more spheres.</p> <p>Aggregates allow PKDGRAV users to capture geometric effects like bulking, where low-sphericity polyhedra generally occupy larger volumes than spheres when packing, accounting for increased porosity and resistance to flow in granular media. With this in mind, we model the gentle deposition of aggregates under microgravity and lunar gravity to create highly porous (>50% porosity) granular assemblies both with and without cohesion. We use aggregates composed of centimeter-scale spheres and model both symmetric and asymmetric shapes, as well as systems with both aggregates and single spheres. We calculate the porosity of these systems by generating a concave hull around the settled system and calculating the ratio of the total volume in particles interior to the hull to the total hull volume, with interior particle volume modified to account for particle-particle overlaps and particle fractions partially exterior to the hull.</p>

The demonstration of soft landing on lunar surface is a critical aspect for ISRO’s future inter-planetary missions. The second Indian mission to Moon, Chandrayaan-2 could not demonstrate soft landing in the final phases of its descent. Keeping this in mind, subsequently, as a follow on mission, Chandrayaan-3 was planned to achieve safe and soft landing on lunar surface. The spacecraft was configured as a two-module concept with a Lander Module (Rover inside) and a Propulsion Module. The Rover Pragyan (meaning "wisdom" in Sanskrit) is a 6-wheeled Rover that was accommodated inside the Lander and carried to the Lunar surface with an aim to traverse the lunar surface and analyse the geological and chemical composition of the Moon. On 23rd August, 2023 Chandrayaan-3 Vikram Lander along with the Pragyan Rover executed a flawless landing on Moon marking a significant milestone in India’s iconic space journey. Following this, Rover performed mobility in low gravity and vacuum environment of Moon and traversed a distance of 103.05 m in one lunar day and also conducted first of its kind in-situ science experiments on lunar surface. This paper brings out the overview of Rover along with the details pertaining to its configuration, brief specifications, tests conducted, mission operations and mission accomplishments w.r.to mobility as well as in-situ science experiments.

A new era of exploration of the low radio frequency universe from the Moon will soon be underway with landed payload missions facilitated by NASA's Commercial Lunar Payload Services (CLPS) program. CLPS landers are scheduled to deliver two radio science experiments, Radio wave Observations at the Lunar Surface of the photoElectron Sheath (ROLSES) to the nearside and Lunar Surface Electromagnetics Experiment (LuSEE) to the farside, beginning in 2021. These instruments will be pathfinders for a 10 km diameter interferometric array, Farside Array for Radio Science Investigations of the Dark ages and Exoplanets (FARSIDE), composed of 128 pairs of dipole antennas proposed to be delivered to the lunar surface later in the decade. ROLSES and LuSEE, operating at frequencies from ≈100 kHz to a few tens of megahertz, will investigate the plasma environment above the lunar surface and measure the fidelity of radio spectra on the surface. Both use electrically short, spiral-tube deployable antennas and radio spectrometers based upon previous flight models. ROLSES will measure the photoelectron sheath density to better understand the charging of the lunar surface via photoionization and impacts from the solar wind, charged dust, and current anthropogenic radio frequency interference. LuSEE will measure the local magnetic field and exo-ionospheric density, interplanetary radio bursts, Jovian and terrestrial natural radio emission, and the galactic synchrotron spectrum. FARSIDE, and its precursor risk-reduction six antenna-node array PRIME, would be the first radio interferometers on the Moon. FARSIDE would break new ground by imaging radio emission from coronal mass ejections (CME) beyond 2R ⊙, monitor auroral radiation from the B-fields of Uranus and Neptune (not observed since Voyager), and detect radio emission from stellar CMEs and the magnetic fields of nearby potentially habitable exoplanets.

New techniques and instrumentation have been developed for the measurement of lunar surface temperatures. The infrared pyrometer has a resolution of about 10 seconds of arc. Special computing methods permit precise determination of the spots being measured on the lunar surface. A theoretical study has enabled the lunar surface temperature and its variation to be predicted during a lunation and during total eclipses of the Moon for a number of models. These include surfaces of solid rock, porous rock, dust, rubble, and various surfaces overlaid with different depths of dust. Certain areas, like the crater Tycho, appear to have no appreciable insulating layer of dust, although the environs may have some dust cover of indefinite thickness. Looking further to the future, we have calculated the temperature of the lunar surface during and immediately after the landing of the manned vehicle known as the Lunar Excursion Module, or lem. High temperatures will result from the exhaust flame of the retro-rocket, of some 1500 to 1600 °K immediately below the LEM. However, the cooling will be rapid and the astronauts could safely leave the craft 5 or 10 min after set-down.