Multispectral polarimetry as a tool to investigate texture and chemistry of lunar regolith particles

We report results of telescope polarimetric imaging of the Moon with a CCD LineScan Camera at large phase angles, near 88°. This allows measurements of the polarization degree with an absolute accuracy better than 0.3% and detection of features with polarization contrast as small as 0.1%. The measurements are carried out in two spectral bands centered near 0.65 and 0.42 μm. We suggest characterizing the lunar regolith with the parameter a(Pmax)A, where Pmax,A, and a are the degree of maximum polarization, albedo, and the parameter describing the linear regression of the correlation Pmax-A. The parameter bears significant information on the particle characteristic size and packing density of the lunar regolith. We also suggest characterizing the lunar regolith with color-ratio images obtained with a polarization filter at large phase angles. We here consider the color-ratios C||(0.65/0.42 μm) and C_⊥(0.65/0.42 μm). Using light scattering model calculations we show that the color-ratio images obtained with a polarization filter at large phase angles suggest a new tool to study the lunar surface. In particular, it turns out that the color-ratios C||(0.65/0.42 μm) and C_⊥(0.65/0.42 μm) are sensitive to somewhat different thicknesses of the surfaces of regolith particles. We consider the applicability of the Hubble Space Telescope, the Very Large Telescope (ESO), and a spacecraft on a lunar polar orbit for polarimetric observations of the lunar surface.     

Properties of the Hermean regolith: IV. Photometric parameters of Mercury and the Moon contrasted with Hapke modelling

A comparison of the photometric properties of Mercury and the Moon is performed, based on their integral phase curves and disk-resolved image data of Mercury obtained with the Swedish Vacuum Solar Telescope. Proper absolute calibration of integral V-band magnitude observations reveals that the near-side of the Moon is 10-15% brighter than average Mercury, and 0-5% brighter for the “bolometric” wavelength range 400-1000 nm. As shown, this is supported by recent estimates of their geometric albedos. Hapke photometric parameters of their surfaces are derived from identical approaches, allowing a contrasting study between their surface properties to be performed. Compared to the average near-side Moon, Mercury has a slightly lower single-scattering albedo, an opposition surge with smaller width and of marginally smaller amplitude, and a somewhat smoother surface with similar porosity. The width of the lobes of the single-particle scattering function are smaller for Mercury, and the backward scattering anisotropy is stronger. In terms of the double Henyey-Greenstein b-c parameter plot, the scattering properties of an average particle on Mercury is closer to the properties of lunar maria than highlands, indicating a higher density of internal scatterers than that of lunar particles. The photometric roughness of Mercury is well constrained by the recent study of Mallama et al. (2002, Icarus 155, 253-264) to a value of about 8°, suggesting that the surfaces sampled by the highest phase angle observations (Borealis, Susei, and Sobkou Planitia) are lunar mare-like in their textural properties. However, Mariner 10 disk brightness profiles obtained at intermediate phase angles indicate a surface roughness of about twice this value. The photometric parameters of the Moon are more difficult to constrain due to limited phase angle coverage, but the best Hapke fits are provided by rather small surface roughnesses. Better-calibrated, multiple-wavelength observations of the integral and disk-resolved brightnesses of both bodies, and obtained at higher phase angle values in the case of the Moon, are urgently needed to arrive at a more consistent picture of the contrasting light scattering properties of their surfaces.     

New Earth-based absolute photometry of the Moon

A 2-month series of quasi-simultaneous imaging photometric observations of the Moon and the Sun has been performed at Maidanak Observatory (Uzbekistan). New absolute values of lunar albedo have been obtained. Maps of lunar apparent albedo and equigonal albedo at phase angles 1.7-73° at wavelength 603 nm are presented. The standard deviation of our data from a best-fitted phase curve is 2%. The average ratio of the Clementine albedo to ours is 1.41. While the ratio of ROLO albedo to ours is 0.87, our data are in agreement with independent measurements of absolute albedo by Saiki et al. (Saiki, K., Saito, K., Okuno, H., Suzuki, A., Yamanoi, Y., Hirata N., Nakamura, R. [2008]. Earth Planets Space 60, 417-424) at a phase angle near 7°. A phase ratio imaging near opposition (1.6°/2.7°) shows almost the same ratio for maria and highlands, though bright craters (e.g., Tycho, Copernicus, Aristarchus) clearly reveal smaller slopes of phase function. This is an unexpected result, as the craters are bright and one could anticipate a manifestation of the coherent backscattering effect resulting in the opposition spike increasing at so small phase angles.     

Photometric properties of lunar terrains derived from Hapke's equation

The photometric parameters of B. W. Hapke's (1986, Icarus 67, 264–280) equation are fit to the lunar disk-integrated visual lightcurve and to disk-resolved data of R. W. Shorthill, J. M. Saari, F. E. Baird, and J. R. LeCompte (1969, Photometric Properties of Selected Lunar Features, NASA Contractor Report CR-1429) for dark, average, and bright lunar terrains. The lunar nearside geometric albedo and phase integral computed from the disk-integrated results are consistent with those of earlier investigators. The single scattering albedos of disk-resolved average and bright lunar terrains are systematically larger than that of lunar mare. Average particles in dark terrain regoliths are more backscattering than those in average and bright lunar terrains. The angular width of the opposition surge is greatest in dark terrains and is found to be best explained by modest differences in regolith particle-size distributions which might accompany the normal regolith maturation process. The total amplitude of the opposition surge for dark terrains is larger than for average and bright terrains. This result appears to be a consequence of the fact that in opaque particles, a larger fraction of singly scattered light at zero phase comes from first-surface reflection. The average subcentimeter macroscopic roughness of dark terrains is significantly lower than that of average and bright terrains. The relative magnitude of this difference is consistent with that obtained from radar measurements at decimeter scales.     

The phase dependence of brightness and color of the lunar surface: a study based on integral photometric data

A procedure of an a posteriori correction of the available data on the integral photometry of the Moon is described. This procedure reduces the regular errors of the integral phase curves caused by variations of the libration parameters; the effect due to libration can reach 4%. A method allowing the integral measurements of the Moon to be compared correctly with the photometric measurements of the lunar areas or laboratory samples imitating the lunar soil has been developed. To approximate the phase curves of integral albedo in the phase-angle range from 6° to 120°, we proposed a simple empirical formula A _eq(α) = m _l e ^?ρα + m ₂ e ^?0.7α, where α is the phase angle, ρ is the factor of effective roughness, and m ₁ + m ₂ is the surface albedo at a zero phase angle. An empirical phase dependence of the slope of the lunar spectrum in the 360–1060 nm range has been obtained. The results may be used to test various theoretical models of the light scattering by the lunar surface and to calibrate the data of ground-based and space-borne spectrophotometric observations.     

Optical polarimetry of planet mercury

Polarimetric measurements were collected at different areas of the surface of Mercury, and for the whole disk in six wavelengths. The curves of polarization are compared with telescopic observations of the Moon and laboratory studies of minerals and returned lunar samples. The negative branch of polarization proves that Mercury's surface is almost everywhere covered by a regolith layer of fines of the lunar type, also made of dark and adsorbing material, and most probably of the same impact generated origin. The polarization maximum of Mercury is reproduced by lunar samples of fines of intermediate albedo corresponding to the lightest regolith found in the Apollo explored maria.The albedo of Mercury at phase angle 5° deduced from telescopic photometry is to be corrected by a factor of 1.20 and the best “polarimetric” values of albedos are 0.130 at λ = 0.585μm, 0.119 at λ = 0.520 μm, 0.093 at λ = 0.379μm and 0.087 at λ = 0.354μm. The contrast between light and dark-lined regions at the surface of Mercury is most probably much fainter than between the maria and continents on the Moon.The molecular atmosphere of Mercury, if any, has a surface pressure probably smaller than 2 × 10^?4 bars.     

Lunar Dust: Properties and Investigation Techniques

Physical conditions in the near-surface layer of the Moon are overviewed. This medium is formed in the course of the permanent micrometeoroid bombardment of the lunar regolith and due to the exposure of the regolith to solar radiation and high-energy charged particles of solar and galactic origin. During a considerable part of a lunar day (more than 20%), the Moon is passing through the Earth’s magnetosphere, where the conditions strongly differ from those in the interplanetary space. The external effects on the lunar regolith form the plasma-dusty medium above the lunar surface, the so-called lunar exosphere, whose characteristic altitude may reach several tens of kilometers. Observations of the near-surface dusty exosphere were carried out with the TV cameras onboard the landers Surveyor 5, 6, and 7 (1967–1968) and with the astrophotometer of Lunokhod-2 (1973). Their results showed that the near-surface layer glows above the sunlit surface of the Moon. This was interpreted as the scattering of solar light by dust particles. Direct detection of particles on the lunar surface was made by the Lunar Ejects and Meteorite (LEAM) instrument deployed by the Apollo 17 astronauts. Recently, the investigations of dust particles were performed by the Lunar Atmosphere and Dust Environment Explorer (LADEE) instrument at an altitude of several tens of kilometers. These observations urged forward the development of theoretical models for the lunar exosphere formation, and these models are being continuously improved. However, to date, many issues related to the dynamics of dust and the near-surface electric fields remain unresolved. Further investigations of the lunar exosphere are planned to be performed onboard the Russian landers Luna-Glob and Luna-Resurs.     

Optical scattering processes observed at the Moon: Predictions for the LADEE Ultraviolet Spectrometer

The Lunar Atmosphere and Dust Environment Explorer (LADEE) spacecraft will orbit the Moon at an altitude of ≈50 km with a payload that includes the Ultraviolet Spectrometer (UVS) instrument, which will obtain high spectral resolution measurements at near-ultraviolet and visible wavelengths (≈231-826 nm). When LADEE/UVS observes the lunar limb from within the shadow of the Moon it is anticipated that it will detect a lunar horizon glow (LHG) due to sunlight scattered from submicron exospheric dust, as well as emission lines from exospheric gases (particularly sodium), in the presence of the bright coronal and zodiacal light (CZL) background. A modularized code has been developed at NMSU for simulations of scattered light sources as observed by orbiting instruments in lunar shadow. Predictions for the LADEE UVS and star tracker cameras indicate that LHG, sodium (Na) emission lines, and CZL can be distinguished based on spatial morphology and spectral characteristics, with LHG dominant at blue wavelengths (∼250-450 nm) and small tangent heights. If present, LHG should be readily detected by LADEE/UVS and distinguishable from other sources of optical scattering. Observations from UVS and the other instruments aboard LADEE will significantly advance our understanding of how the Moon interacts with the surrounding space environment; these new insights will be applicable to the many other airless bodies in the solar system.     

A motivating exploration on lunar craters and low-energy dynamics in the Earth–Moon system

It is known that most of the craters on the surface of the Moon were created by the collision of minor bodies of the Solar System. Main Belt Asteroids, which can approach the terrestrial planets as a consequence of different types of resonance, are actually the main responsible for this phenomenon. Our aim is to investigate the impact distributions on the lunar surface that low-energy dynamics can provide. As a first approximation, we exploit the hyberbolic invariant manifolds associated with the central invariant manifold around the equilibrium point L ₂ of the Earth–Moon system within the framework of the Circular Restricted Three-Body Problem. Taking transit trajectories at several energy levels, we look for orbits intersecting the surface of the Moon and we attempt to define a relationship between longitude and latitude of arrival and lunar craters density. Then, we add the gravitational effect of the Sun by considering the Bicircular Restricted Four-Body Problem. In the former case, as main outcome, we observe a more relevant bombardment at the apex of the lunar surface, and a percentage of impact which is almost constant and whose value depends on the assumed Earth–Moon distance d_EM. In the latter, it seems that the Earth–Moon and Earth–Moon–Sun relative distances and the initial phase of the Sun θ ₀ play a crucial role on the impact distribution. The leading side focusing becomes more and more evident as d_EM decreases and there seems to exist values of θ ₀ more favorable to produce impacts with the Moon. Moreover, the presence of the Sun makes some trajectories to collide with the Earth. The corresponding quantity floats between 1 and 5 percent. As further exploration, we assume an uniform density of impact on the lunar surface, looking for the regions in the Earth–Moon neighbourhood these colliding trajectories have to come from. It turns out that low-energy ejecta originated from high-energy impacts are also responsible of the phenomenon we are considering.     

A theoretical evaluation of the lunar tidal variations in the ionospheric F2-layer

Time-varying solutions of the full continuity equation for electrons in the F2-region are obtained. The effects of production, loss, diffusion and electrodynamic ‘E × B’ drift are taken into account. The ‘E × B’ drift term consists of a solar and a lunar component. The solar component of drift is assumed diurnal with 14.6m/sec maximum upward speed at mid-day. The lunar component is assumed sinusoidal with period of half lunar day and amplitude one tenth of the solar drift; the phase is assumed to remain constant in lunar time, in accordance with Chapman's phase law.The results show that the lunar variations in the F2-region are markedly dependent on solar time and latitude. It is also shown that the average semi-diurnal lunar variations in N_mF2 and h_mF2 at any particular lunar time are almost opposite in phase to each other (i.e. out of phase by 6 hr) in the magnetic equatorial zone, and out of phase by 2 hr at moderate latitudes. The phase of δh_mF2 is 10 hr at low latitudes and 9 hr at moderate latitudes. The phase of δN_mF2 is 4 hr at low latitudes and 11 lunar hr at moderate latitudes.The results also show that the phase of the lunar semi-monthly oscillations in N_mF2 undergoes a rapid shift of about 5 lunar hr in going from 8 to 12° and the so called phase reversal occurs at about 10° lat at which the amplitude of N_mF2. becomes extremely small.These and other results are in good agreement with observations. Thus it is shown that the main features of the observed lunar tidal variations of the F2-region within 20° of the magnetic equator can be explained satisfactorily by the superposition of a small lunar drift on a large solar drift.     

‘Direct’ evidence for water (H2O) in the sunlit lunar ambience from CHACE on MIP of Chandrayaan I

Direct detection of water in its vapour phase in the tenuous lunar environment through in situ measurements carried out by the Chandra’s Altitudinal Composition Explorer (CHACE) payload, onboard the Moon Impact Probe (MIP) of Chandrayaan I mission vindicates the presence of water on the surface of the moon in form of ice at higher lunar latitudes inferred from IR absorption spectroscopy, (especially that of OH), by the Moon Mineralogy Mapper (M³) of Chandrayaan I. The quadrupole mass spectrometer based payload, CHACE, sampled the lunar neutral atmosphere every 4 s with a broad latitudinal (∼40°N to 90°S, with a resolution of ∼0.1°) and altitudinal (from 98 km up to impact on the lunar surface with a resolution of ∼0.25 km) coverage in the sunlit side of the moon for the first time. These two (CHACE and M³) complementary experiments are shown to collectively provide unambiguous signatures for the distribution of water in solid and gaseous phases in Earth’s moon.     

Contribution of tidal dissipation to lunar thermal history

The possible contributions of tidal heating to lunar thermal history are investigated. Analytic determinations of tidal dissipation in a homogeneous, incompressible Moon and in a two-layer Moon with a soft core and rigid mantle are given as a function of position in the Moon and as a function of Earth-Moon separation. The most recent information on the historical values of the lunar obliquity is employed, and we present results for the constant values of orbital eccentricity of e = 0.0 and e = 0.055. For a simplified orbital evolution and a dissipation factor Q = 100, the total increase in the mean lunar temperature for the homogeneous case does not exceed several tens of degrees. For the two-layer models the local dissipation may be enhanced over that of the homogeneous Moon by a factor of 5 for a core radius of 0.5 lunar radii and by a factor of 100 for a core radius of 0.95 lunar radii. The corresponding factors for the total dissipation are 3 and 15 for the two values of core radii, respectively. We conclude that tidal contributions to lunar thermal history are probably not important. But under special circumstances the enhanced dissipation in a two-layer Moon could have led to a spectacular thermal event.     

The lunar dust environment

Each year the Moon is bombarded by about 10⁶ kg of interplanetary micrometeoroids of cometary and asteroidal origin. Most of these projectiles range from 10 nm to about 1 mm in size and impact the Moon at 10–72 km/s speed. They excavate lunar soil about 1000 times their own mass. These impacts leave a crater record on the surface from which the micrometeoroid size distribution has been deciphered. Much of the excavated mass returns to the lunar surface and blankets the lunar crust with a highly pulverized and “impact gardened” regolith of about 10 m thickness. Micron and sub-micron sized secondary particles that are ejected at speeds up to the escape speed of 2300 m/s form a perpetual dust cloud around the Moon and, upon re-impact, leave a record in the microcrater distribution. Such tenuous clouds have been observed by the Galileo spacecraft around all lunar-sized Galilean satellites at Jupiter. The highly sensitive Lunar Dust Experiment (LDEX) onboard the LADEE mission will shed new light on the lunar dust environment. LADEE is expected to be launched in early 2013.Another dust related phenomenon is the possible electrostatic mobilization of lunar dust. Images taken by the television cameras on Surveyors 5, 6, and 7 showed a distinct glow just above the lunar horizon referred to as horizon glow (HG). This light was interpreted to be forward-scattered sunlight from a cloud of dust particles above the surface near the terminator. A photometer onboard the Lunokhod-2 rover also reported excess brightness, most likely due to HG. From the lunar orbit during sunrise the Apollo astronauts reported bright streamers high above the lunar surface, which were interpreted as dust phenomena. The Lunar Ejecta and Meteorites (LEAM) Experiment was deployed on the lunar surface by the Apollo 17 astronauts in order to characterize the lunar dust environment. Instead of the expected low impact rate from interplanetary and interstellar dust, LEAM registered hundreds of signals associated with the passage of the terminator, which swamped any signature of primary impactors of interplanetary origin. It was suggested that the LEAM events are consistent with the sunrise/sunset-triggered levitation and transport of charged lunar dust particles. Currently no theoretical model explains the formation of a dust cloud above the lunar surface but recent laboratory experiments indicate that the interaction of dust on the lunar surface with solar UV and plasma is more complex than previously thought.     

Photometry of the lunar surface

The photometry of the Moon gives us some information about the properties of the lunar surface. The photometric uniformity of the lunar surface as a scattering screen is determined by the shadow phenomena on small irregularities due to the dust layer covering the whole surface. A small component of light (< 10 %) exhibits the features of the luminescence excited by solar radiations.Paper presented to the NATO Advanced Study Institute on Lunar Studies, Patras, Greece, September 1971.     

Seismic effects from major basin formations on the moon and mercury

Grooved and hilly terrains occur at the antipode of major basins on the Moon (Imbrium, Orientale) and Mercury (Caloris). Such terrains may represent extensive landslides and surface disruption produced by impact-generatedP-waves and antipodal convergence of surface waves. Order-of-magnitude calculations for an Imbrium-size impact (10³⁴ erg) on the Moon indicateP-wave-induced surface displacements of 10 m at the basin antipode that would arrive prior to secondary ejecta. Comparable surface waves would arrive subsequent to secondary ejecta impacts beyond 10³ km and would increase in magnitude as they converge at the antipode. Other seismically induced surface features include: subdued, furrowed crater walls produced by landslides and concomitant secondary impacts; emplacement and leveling of light plains units owing to seismically induced ‘fluidization’ of slide material; knobby, pitted terrain around old basins from enhancement of seismic waves in ancient ejecta blankets; and perhaps the production and enhancement of deep-seated fractures that led to the concentration of farside lunar maria in the Apollo-Ingenii region.     

Height-to-diameter ratios of moon rocks from analysis of Lunokhod-1 and -2 and Apollo 11–17 panoramas and LROC NAC images

An analysis is performed of 91 panoramic photographs taken by Lunokhod-1 and -2, 17 panoramic images composed of photographs taken by Apollo 11–15 astronauts, and six LROC NAC photographs. The results are used to measure the height-to-visible-diameter (h/d) and height-to-maximum-diameter (h/D) ratios for lunar rocks at three highland and three mare sites on the Moon. The average h/d and h/D for the six sites are found to be indistinguishable at a significance level of 95%. Therefore, our estimates for the average h/d = 0.6 ± 0.03 and h/D = 0.54 ± 0.03 on the basis of 445 rocks are applicable for the entire Moon’s surface. Rounding off, an h/D ratio of ≈0.5 is suggested for engineering models of the lunar surface. The ratios between the long, medium, and short axes of the lunar rocks are found to be similar to those obtained in high-velocity impact experiments for different materials. It is concluded, therefore, that the degree of penetration of the studied lunar rocks into the regolith is negligible, and micrometeorite abrasion and other factors do not dominate in the evolution of the shape of lunar rocks.     

Does the Moon Have a Metallic Core?: Constraints from Giant Impact Modeling and Siderophile Elements

The issue of whether the Moon has a small metallic core is reexamined in light of new information: improved dynamical modeling, new constraints on core size, and high temperature and pressure metal-silicate partition coefficients. Addressed specifically is the question of whether the Moon's siderophile element budget can be explained by derivation of the Moon from a differentiated impactor or proto-Earth (stage 1), followed by formation of a small metallic core within the Moon (stage 2). If the Moon is made of mantle material from either a “hot” impactor or a “warm” impactor or proto-Earth, a small metallic core (0.7 to 2 mass%) is predicted. If the Moon is made from mantle material from a “hot” proto-Earth, the lunar mantle would be more depleted in W or Re than is observed. Scenarios in which the Moon is made from impactor or proto-Earth mantle material that has equilibrated with metal at low pressures and temperatures (“cold” scenarios) would yield a much larger metallic core than observed. Finally, the greater depletions of Ni, Mo, and Re in the Moon (relative to the Earth) can be explained by low PT and reduced metal-silicate equilibrium in an impactor without later core formation in the Moon (i.e., no stage 2), but depletions of Co, Ga, and W cannot. Altogether, geochemically unlikely or geophysically inadequate non-metallic core alternatives, substantial geophysical evidence for a metallic core, and the successful models presented here for siderophile element depletions all favor the presence of a small lunar metallic core. Previous geochemical objections to an impactor origin of the Moon are eliminated because siderophile element concentrations in the lunar mantle are consistent with separation of a small core from a bulk Moon derived from impactor mantle material.     

Laboratory studies on seismic and electrical properties of the moon

Laboratory measurements of seismic wave velocities and electrical properties of Apollo lunar samples and similar material of terrestrial origin are discussed in this paper. Measurements of the electrical properties show that in the frequency range above a few hundred Hz the outer region of the Moon may be considered as a low loss dielectric. This observation supports a longstanding speculation that dry, powdered rocks in which the dielectric loss tangent is frequency-independent over a wide range of frequency are present in the uppermost lunar surface layers. The surface layers of the Moon are likely to have an extremely low electrical conductivity. Thus future electromagnetic probing of the Moon to a few hundred kilometer depth is possible in the few kHz frequency range. Based on ultrasonic experiments with pressure as a variable, we next present the elastic constants and equations of state of lunar materials and characteristic dispersion of seismic wave velocities of the Moon. We find thatP andS wave velocities increase sharply within the first 30 km depth and then level off gradually. Combining this observation with lunar seismic and geophone data, we believe that the first 30 km of the Moon may be interpreted as a scattering region. If H₂O exists on the Moon, H₂O may occur at some shallow depth beneath the outermost surface layer in solid ice interlocking cracks and pores and mineral grains. The rocks in this permafrost state have relatively low seismic velocity and highQ. If permafrost does exist, we would expect a wide range of electrical conductivity and dielectric constant. Future electromagnetic probing of the Moon should yield very usefull information on the physical state of the lunar interior; when this electrical information is combined with the seismic information, we should learn much more about the internal constitution and the state of the Moon than is known today.     

Numerical simulation of high-velocity impact ejecta following falls of comets and asteroids onto the Moon

High-velocity comet and asteroid impacts onto the Moon are considered and the material masses ejected after such impacts at velocities above the second-cosmic velocity for the Moon (2.4 km/s) are calculated. Although the results depend on a projectile type and the velocity and angle of an impact, it has been demonstrated that, on average, the lunar mass decreases with time. The Moon has lost about 5 × 10¹⁸ kg, that is, about one-hundredth of a percent of its mass, over the last 3.8–3.9 billion years. The ejection of lunar meteorites and lunar dust, rich in ³He, is considered as well. The results of the study are compared to the results of earlier computations and data on lunar meteorites.     

Computer simulation of observations of stars from the moon using the polar zenith telescope of the Japanese project ILOM

The paper briefly describes the purpose and features of the Japanese project ILOM (In-situ Lunar Orientation Measurement) in which it is planned to install the zenith telescope with a CCD lens on one of the poles of the Moon for the observation of stars in order to determine the physical libration of the Moon (PhLM). The studies presented in this paper are the result of the first stage of the theoretical support of the project:

1. The compilation of the list of stars within the field of view of the telescope during the precessional motion of the lunar pole.
2. Modeling and analysis of the behavior of stellar tracks during the observation period.
3. Simulation and testing of the sensitivity of the measured selenographic star coordinates to changes in the parameters of the dynamic model of the Moon and the elastic parameters of the lunar body.

Direct and inverse PhLM problems are discussed. Within the scope of the direct problem visible “daily parallels” and one-year star tracks are calculated. Their behavioral features when observed from the lunar surface are shown. At this stage of the simulation selenographic star coordinates for the four models of the gravitational field of the Moon have been compared, i.e., the model constructed on the basis of the lunar laser ranging (LLR), GLGM-2, LP150Q, and SGM100h. It is shown that even when comparing modern models LP150Q and SGM100h stellar tracks differ from the arc by more than 10 ms of arc. At the stage of the inverse problem, the manifestation of viscoelastic properties of the Moon in selenographic coordinates has been studied. In the spectrum of the simulated residual differences harmonics have been identified which can serve as indicators to refine parameters, Love number k ₂ and the delay time characterizing the viscous properties of the lunar body.