Lunar Orientation Research Articles

Advantages of combining Lunar Laser Ranging and Differential Lunar Laser Ranging

Context. Differential Lunar Laser Ranging (DLLR), which is planned to be conducted at Table Mountain Observatory (TMO) of Jet Propulsion Laboratory (JPL) in the future, is a novel technique for tracking to the Moon. This technique has the potential to determine the orientation, rotation, and interior of the Moon much more accurately if the expected high accuracy of about 30 μm can be achieved. Aims. We focus on the benefit for the related parameters when only DLLR data with a short time span are available in the beginning. Methods. A short DLLR time series is not enough to provide an accurate lunar orbit, which has a negative effect on parameter estimation. Fortunately, Lunar Laser Ranging (LLR) has been collecting data for a very long time span, which can be used to compensate this DLLR disadvantage. The combination of LLR data (over more than 50 yr) and simulated DLLR data over a relatively short time span (e.g., 5 or 10 yr) is used in different cases which include changing reflector baselines and extending data time span, along with adding more stations and “new” reflectors. Results. The results show that the estimated accuracies of the parameters related to the lunar orientation, rotation, and interior can be improved by about 5–100 times by simply adding 5-yr DLLR data in the combination. With LLR, further enhancing the parameter determination can be achieved by choosing appropriate reflector baselines. By investigating different scenarios of reflector baselines based on the present five reflectors on the Moon, we find that two crossing baselines with larger lengths offer the greatest advantage. A longer data time span is more helpful, rather than having more stations involved in the measurement within a shorter time span, assuming the amount of data in these two cases is the same. Furthermore, we evaluated the preferred position of an assumed new reflector.

Characteristics of differential lunar laser ranging

Context. To obtain more details about the lunar interior, a station at Table Mountain Observatory of JPL will enable a new measurement of lunar laser ranging (LLR), known as differential lunar laser ranging (DLLR). It will provide a novel type of observable, namely, the lunar range difference, which is the difference of two consecutive ranges obtained via a single station swiftly switching between two or more lunar reflectors. This previously unavailable observation will have a very high level of accuracy (about 30 μm), mainly resulting from a reduction in the Earth’s atmospheric error. In addition to the intended improvements for the lunar part, it is expected to contribute to improved relativity tests, for instance, the equivalence principle (EP). Aims. This paper focuses on the simulation and investigation of the characteristics of DLLR. Methods. Using simulated DLLR data, we analyzed and compared the parameter sensitivity, correlation, and accuracy obtained by DLLR with those attained by LLR. Results. The DLLR measurement maintains almost the same sensitivity to certain parameters (called group A) as that of LLR, such as the lunar orientation parameters. For other parameters (called group B), such as station coordinates, it is shown to be less sensitive. However, owing to its extraordinary measurement accuracy, it not only retains nearly the same level of accuracy of group B as LLR, but it also improves the estimation of group A significantly (with the exception of reflector coordinates, due to the DLLR measuring mode). Also, DLLR increases the correlations among the reflectors and between stations and reflectors caused by its constellation. Additionally, we compared different switching intervals with respect to sensitivity and correlation. Large switching intervals are more beneficial for group B and the decorrelation of stations and reflectors. Furthermore, DLLR enhances the accuracy of EP tests.

The role of the antennae in the compass-based orientation of the equatorial sandhopper Talorchestia martensii Weber (Crustacea Amphipoda)

The equatorial sandhopper Talorchestia martensii uses the sun, the moon and the natural magnetic field as orienting compass references. In some arthropod species, the antennae are important for time compensated solar orientation. Therefore, we evaluated the role of antennae in solar, lunar and magnetic compass orientation in T. martensii. We released intact and antennaeless individuals in a Plexiglas bowl in the dark, and under the sun or moon, with and without the horizontal component of the magnetic field and recorded their orientation. For the tests under the moon, sandhoppers were released in conditions of modest azimuthal speed (10–15°/hr) and high azimuthal speed (≈ 59°/hr) of the moon. No significant difference in the orienting behaviour between antennaeless and intact individuals was observed. Therefore, the antennae do not seem to be involved in the sun or moon compass mechanisms of T. martensii. The photopositive responses showed by individuals released under high azimuthal speed of the moon and with the horizontal component of the magnetic field zeroed, indicate that the moon is probably not used as a chronometric compass reference in this species because of the variations in its azimuthal speed. This suggests a mechanism of photomenotaxis and therefore, a difference from sandhoppers from temperate latitudes that use a moon compass.

First two-way laser ranging to a lunar orbiter: infrared observations from the Grasse station to LRO\u2019s retro-reflector array

We present the results of the first series of successful two-way laser ranging experiments from a ground station, the Lunar Laser Ranging (LLR) station in Grasse, France, to a spacecraft at lunar distance, the Lunar Reconnaissance Orbiter (LRO). A 15 × 18 × 5 cm, 650-g array of twelve 32-mm diameter solid corner cubes is mounted on its anti-nadir deck. Ranging to this small retro-reflector array onboard a lunar orbiter from a ground station was a challenge compared to ranging to larger lunar surface retro-reflectors. Grasse measured 67 returns in two 6-min sessions on September 4, 2018. Clear returns were also recorded during two additional sessions on August 23–24, 2019 for which active slewing by LRO was performed to bring the array in view of the station. The measured echos yielded range residuals less than 3 cm (two-way time-of-flight RMS < 180 ps) relative to the reconstructed LRO trajectory. This experiment provides a new method of verifying theories of dust accumulation over decades on the lunar surface. It also showed that the use of similar arrays onboard future lunar landers and orbiters can support LLR lunar science goals, particularly with landing sites near the lunar limbs and poles, which would have better sensitivity to lunar orientation.

Role of lunar laser ranging in realization of terrestrial, lunar, and ephemeris reference frames

Three possible applications of lunar laser ranging to space geodesy are studied. First, the determination of daily Earth orientation parameters (UT0 and variation of latitude), which is rarely used nowadays in presence of all-year VLBI, SLR, and GNSS data. The second application is the determination of two (out of three) lunar orientation parameters, i.e. daily corrections to the rotational ephemeris of the Moon. It may be of importance for the future lunar satellite-based navigational systems. The third application is the tie of ephemeris frame (BCRF) to the ICRF. It has been studied before, though in this work it is extensively compared to another realization of the same tie, obtained by spacecraft VLBI observations; also, two different EOP series and two different models of tidal variations of geopotential are applied, with different outcomes on the tie. The EPM lunar-planetary ephemeris, along with its underlying dynamical model and software, was used to obtain the presented results. All available observations were processed, since the earliest made at the end of 1969 at the McDonald observatory till the end of July 2019 (Matera, Grasse and also Wettzell observatory which began to provide data in 2018). The results and some open questions are discussed.

Construction of simulation models of lunar observations

The aim of the present paper is to establish optimal parameters for simulation models of the lunar telescope. Modelling of the observations taken from the surface of the Moon is carried out on the basis of dynamic algorithms describing diurnal motion of stars and specifically designed software modules. The first steps in the development of simulation models were made when planning the ILOM (In-Situ Lunar Orientation Measurement) mission which implied the installation of an optical telescope on one of the lunar Poles. The main task of the project was to observe physical libration of the Moon directly from its surface in order to reveal subtle effects related to the characteristics of internal structure of our natural satellite, including the refinement of the Lava elasticity coefficients, tidal dissipation and dissipation at the core-mantle boundary parameters, core’s size, ellipticity, and its chemical composition. The results obtained in this work allow for the development of lunar physical libration and dynamics theory in order to apply them in the future lunar observations taken with the automated optical telescope.

Sun and moon compasses in Tylos europaeus (Crustacea Isopoda)

Experiments conducted in the 1950s provided first evidences that both the sun and the moon constitute astronomical compass cues in the zonal recovery of the supralittoral isopod Tylos europaeus. Whereas the sun-based orientation of this species has been thoroughly confirmed, no other investigation on its ability to orientate according to the moon has been carried out. In our studies we tested adult individuals in a confined environment and demonstrated that: (1) animals can rely on the moon as a compass orienting factor despite the difficulties met in the time-compensated use of this celestial body; (2) the lunar orientation is largely independent of the geomagnetic field; and (3) the moon compass seems to operate throughout the 24-hr period thus even in the absence of the direct vision of the moon. Moreover, our preliminary tests conducted to assess the existence of discrete time-keepers regulating the sun and the moon compasses pointed out a partial separation between the two mechanisms even though further investigations are required to clarify this aspect.

Astronomical Orientations of the Great Enclosure of Musawwarat Es Sufra

Here we propose the use of Stellarium and Photographer’s Ephemeris software to test a possible astronomical orientation of the Great Enclosure of Musawwarat es Sufra, in the heartland of the Kingdom of Kush. Using the Photographer’s Ephemeris, we can see that the central part of the enclosure is aligned perfectly along the southern direction of the moonrise on a major lunar standstill, whereas the norther part of the enclosure has an orientation along the sunrise on the winter solstice. Besides the simulations, a discussion is also given about the plausibility of solar and lunar orientations.

Tides on the Moon: Theory and determination of dissipation

AbstractSolid body tides on the Moon vary by about ±0.1 m each month. In addition to changes in shape, the Moon's gravity field and orientation in space are affected by tides. The tidal expressions for an elastic sphere are compact, but dissipation introduces modifications that depend on the forcing period. Consequently, a Fourier representation of the tide‐raising potential is needed. A mathematical model for the distortion‐caused tidal potential may be used for the analysis of precise spacecraft tracking data. Since tides affect gravitational torques on the Moon from the Earth's attraction, the lunar orientation is also affected. Expressions for five periodic perturbations of orientation are presented. The rheological properties of lunar materials determine how the Moon responds to different tidal periods. New lunar laser ranging solutions for the tidal orientation terms are presented. The quality factor Q is 38 ± 4 at 1 month, 41 ± 9 at 1 year, ≥74 at 3 years, and ≥58 at 6 years. The ranging results can be matched with absorption band models that peak at ~120 days and single relaxation time models that peak at ~100 days. Combined models are possibilities. Dissipation can modify laser ranging solutions; previously reported core flattening is too uncertain to be useful. Strong lunar tidal dissipation, modeled to arise in the deep hot mantle, appears to be from a region with radius ≥535 km. Classical Maxwell‐type dissipation is too weak to detect at 3 and 6 year periods.

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:

Dung Beetles Use the Milky Way for Orientation

When the moon is absent from the night sky, stars remain as celestial visual cues. Nonetheless, only birds, seals, and humans are known to use stars for orientation. African ball-rolling dung beetles exploit the sun, the moon, and the celestial polarization pattern to move along straight paths, away from the intense competition at the dung pile. Even on clear moonless nights, many beetles still manage to orientate along straight paths. This led us to hypothesize that dung beetles exploit the starry sky for orientation, a feat that has, to our knowledge, never been demonstrated in an insect. Here, we show that dung beetles transport their dung balls along straight paths under a starlit sky but lose this ability under overcast conditions. In a planetarium, the beetles orientate equally well when rolling under a full starlit sky as when only the Milky Way is present. The use of this bidirectional celestial cue for orientation has been proposed for vertebrates, spiders, and insects, but never proven. This finding represents the first convincing demonstration for the use of the starry sky for orientation in insects and provides the first documented use of the Milky Way for orientation in the animal kingdom.

Same beam interferometry as a tool for the investigation of the lunar interior

Lunar Laser Ranging (LLR), by providing routine measurements of the distance to retro-reflector arrays on the lunar surface with centimeter accuracy, has allowed very accurate investigations of the Moon's orbital dynamics, including relativistic corrections. The lunar rotation, physical librations, and tidal deformation have also been investigated, providing new insight on the fluid core and the physical properties of the interior (Williams et al., 2006). A new laser ranging station is now operating with a precision of a few millimeters (Murphy et al., 2008). However, even with this improved accuracy, important details of the Moon's internal structure and physical properties may be missed.There are strong indications that significant dissipative processes are at play in the lunar interior; they could be due, in particular, to tides and to the presence of a fluid core, which rotates about a different axis than the mantle (Williams et al., 2006). Accurate measurements of the lunar orientation, together with radio science determinations of the gravity field, may reveal also interesting details about the Moon's geological past. The angular accuracy required to unravel the different effects is about 10−10rad, corresponding, for a baseline of 1000km, to accuracy in differential distance of 0.1mm.The present work is a follow-up of an earlier proposal (Bender, 1994) of a microwave interferometer: a network of three widely separated landers coherently and simultaneously tracked at Ka-band by a single antenna on the ground. The uplink signal will be separately sent back to the Earth by phase-stable transponders hosted by each lander; measurements of the differential phases will provide the differences between the three distances and will determine changes in the attitude and the tides of the Moon, with little sensitivity to the atmospheric delays. We present a technological assessment of this experimental configuration, known as Same Beam Interferometry (SBI), with emphasis on the technological challenges, weighted against the science benefits. Among the critical points of SBI operations with lunar landers, we mention the energy sources, and the issues related to the permanence of the transponders in the harsh lunar environment. Some operational scenarios are also analyzed.The recent advancement in the design of Ka-band transponders (e.g., in the BepiColombo mission) enables very accurate and stable phase measurements. The error budget presented in this paper shows that a single measurement provides an accuracy in the order of λ/100=0.1mm in the differential range of any lander pair with just 60s integration time.

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.

Lunar project ILOM: application of the analytical theory of Lunar physical libration for the simulation of star observations

This study briefly describes the targets and problems of the future Japanese project In situ Lunar Orientation Measurement (ILOM), which is planned for the year 2017. One of the important parts of the project is to place a small optical telescope on the Lunar surface with the purpose to detect the Lunar physical libration with unprecedented accuracy 0.001 arcsec. At the present stage of research the computer simulation of future observations is going on, aiming to determine the moments of transition of a star through the first meridian and the polar distance of the star. Rotation of the Moon is being calculated under the analytical theory developed in the frame of a theme of the grant. A list of stars brighter than 12 m, whose coordinates are close to the Lunar precession pole motion, was constructed on the basis of several star catalogues. On average, for each moment of observation in the field of view of the telescope (1A degrees) there are approximately 20-25 stars. Analyses of simulated stellar tracks observable from the Lunar surface (in a polar zone) reveal the significant difference from daily parallels of stars in comparison with the Earth. During one Lunar "day" equal 237 terrestrial days, a star moves on a spiral. However, depending on a longitude of a star, these spirals can be untwisted or twisted. In the latter case a star can describe a loop in the sky of the Moon during the period of supervision. Such an unusual astrometric phenomenon combined with the slow rotation of the Moon is compared with the Earth and the fast precession motion of the Lunar pole (in comparison with the precession motion of a terrestrial pole).

Development of a digital zenith telescope for advanced astrometry

Like other optical astrometric techniques, the Photographic Zenith Tube (PZT) has played a key role in the past observations of the Earth rotation, and it also has a potential to be applied to several other observations by taking advantage of automatic observations with self compensation of tilt of the tube. We here propose In-situ Lunar Orientation Measurement (ILOM) to study lunar rotational dynamics by direct observations of the lunar rotation from the lunar surface by using a small telescope like PZT with an accuracy of 1 milli-seconds of arc (1 mas) in the post-SELENE mission. Our second application is to obtain local gravity field on the Earth by combining deflection of the vertical measured by PZT and the position measured by Global Positioning System (GPS) or Global Navigation Satellite System (GNSS). The accuracy required for this purpose is not as strict as ILOM. We have already developed a Bread Board Model (BBM) of the telescope for ILOM and made some experiments in order to know the performance of the driving mechanism under a similar condition to the lunar environment showing high vacuum, large temperature change and dusty condition. We have also shown that it is possible to correct the effects of uniform temperature change upon the optical system by using a simple model with an accuracy of better than 1 mas. This model has the potential to attain the accuracy of 1 mas, based on the results of the experiments and the simulations.

Lunar Gravity and Rotation Measurements by Japanese Lunar Landing Missions

Measurements of lunar gravity and rotation are important because they provide information of the physical state of the lunar interior. Previously only passive LLR (Lunar Laser Ranging) using CCR (corner cube reflectors) has been applied for the detailed study of lunar librations, rotation variability. As for candidate instruments for SELENE-2 (forthcoming lunar landing mission by JAXA) and future lunar missions, we propose VLBI (inverse-VLBI and differential VLBI) for gravity measurement to constrain tidal Love number, LLR (Lunar Laser Ranging) and ILOM (In-situ Lunar Orientation Measurement) for libration measurements.

Computer simulating of stellar tracks for observations with the lunar polar telescope

A brief description of targets and problems of the future Japanese project ILOM (In situ Lunar Orientation Measurement), which is planned to be realized as one of kinds of observations of lunar rotation at the second stage of SELENE-2 mission, is given in the article. One of the important elements of the project is placing of a small optical telescope on the lunar surface with the purpose to detect the lunar physical libration with high accuracy of 0.001arcsec. Computer simulation of the future observations is being done with the purpose of their optimisation: effective placement of measuring system on the lunar surface and formation of scheduling of observations for monitoring the physical libration of the Moon. The results of the first stage of the simulation are presented in the paper. At this stage the software for the selection of stars and reduction of their coordinates onto the period of observations is developed, the tracks for the selected stars are constructed and analysed, their sensitivity to the internal characteristics of the lunar body, in the first place, to the selenopotential coefficients, is tested.Analyses of simulated stellar tracks observable from the lunar surface (in a polar zone) revealed a difference from daily parallels of stars in comparison with ground based observations. During one “lunar day” equal to 27.3 terrestrial days, a star moves along a spiral. In dependence on the longitude of the star, these spirals can be untwisted or twisted. In the latter case a star can describe a loop in the sky of the Moon during the observation period. The reason of such unusual astrometry phenomenon is the combination of the slow rotation of the Moon as compared with the Earth and the fast precession motion of the lunar pole (in comparison with precession motion of a terrestrial pole). Due to the physical libration the shifts of all tracks will be observed towards direction opposite the Earth. The tracks are sensitive to gravity model of the Moon and are different even for the most accurate modern gravity field models—LP150Q (Konopliv, 2000) and SGM100h (Matsumoto et al., 2010).

In Situ Measurements of Lunar Rotation for the Study of the Interior of the Moon

Measurements of physical and free librations of lunar rotation are important because they provide information of the physical state of the lunar interior. For example, we can discuss if the lunar core is molten from the amplitudes of libration terms. Previously only passive LLR (Lunar Laser Ranging) using CCR (corner cube reflectors) has been applied for the detailed study of lunar librations. As for candidate instruments for SELENE-II (forthcoming lunar landing mission by JAXA), we propose detailed measurements of lunar rotation by ILOM (In-situ Lunar Orientation Measurement) and IVLBI (Inverse-VLBI) in addition to LLR.

Synthetic Vision Displays for Planetary and Lunar Lander Vehicles

Aviation research has demonstrated that Synthetic Vision (SV) technology can substantially enhance situation awareness, reduce pilot workload, improve aviation safety, and promote flight path control precision. SV, and related flight deck technologies are currently being extended for application in planetary exploration vehicles. SV, in particular, holds significant potential for many planetary missions since the SV presentation provides a computer-generated view for the flight crew of the terrain and other significant environmental characteristics independent of the outside visibility conditions, window locations, or vehicle attributes. SV allows unconstrained control of the computer-generated scene lighting, terrain coloring, and virtual camera angles which may provide invaluable visual cues to pilots/astronauts, not available from other vision technologies. In addition, important vehicle state information may be conformally displayed on the view such as forward and down velocities, altitude, and fuel remaining to enhance trajectory control and vehicle system status. The paper accompanies a conference demonstration that introduced a prototype NASA Synthetic Vision system for lunar lander spacecraft. The paper will describe technical challenges and potential solutions to SV applications for the lunar landing mission, including the requirements for high-resolution lunar terrain maps, accurate positioning and orientation, and lunar cockpit display concepts to support projected mission challenges.

Lunar orientation in sandhoppers is affected by shifting both the moon phase and the daily clock

The use of a moon compass in the sandhopper, Talitrus saltator, is well known, but the mechanism that allows compensation for the changes in moon position during single nights and from night to night is still poorly understood. In a moon phase shift experiment, we exposed sandhoppers to a dim nocturnal light simulating the moon. The false moon was kept in phase with the true moon for controls and gradually shifted for experimental animals so that, at the time of the test, the false moon calendar was set up to coincide with the first quarter for one experimental group and with the last quarter for the other. During the test under the full moon, the experimental groups behaved as expected on the basis of the moon phase shift, whereas controls showed an intermediate orientation. In a daily clock shift experiment, the sandhoppers were subjected to an artificial light:dark treatment, which was coincident with the natural 24 h light:dark cycle for controls, but was slow or fast shifted by 3 h for the experimental groups. When tested under the full moon, the slow- and fast-shifted experimental groups oriented in a direction that was appropriate to the position of the moon some hours later and before the test, respectively. We conclude that the sun and moon compasses are not ruled by independent rhythms and propose that three interacting rhythms (a circadian, a circalunidian and a circalunar one) are involved in the functioning of the moon compass.