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NASA NTRS2017

Shallow Lunar Seismic Activity and the Current Stress State of the Moon

A vast, global network of more than 3200 lobate thrust fault scarps has been revealed in high resolution Lunar Reconnaissance Orbiter Camera (LROC) images. The fault scarps very young, less than 50 Ma, based on their small scale and crisp appearance, crosscutting relations with small-diameter impact craters, and rates of infilling of associated small, shallow graben and may be actively forming today. The population of young thrust fault scarps provides a window into the recent stress state of the Moon and offers insight into the origin of global lunar stresses. The distribution of orientations of the fault scarps is non-random, inconsistent with isotropic stresses from late-stage global contraction as the sole source of stress Modeling shows that tidal stresses contribute significantly to the current stress state of the lunar crust. Tidal stresses (orbital recession and diurnal tides) superimposed on stresses from global contraction result in non-isotropic compressional stress and thrust faults consistent with lobate scarp orientations. Stresses due to orbital recession do not change with orbital position, thus it is with the addition of diurnal stresses that peak stresses are reached. At apogee, diurnal and recession stresses are most compressive near the tidal axis, while at perigee they are most compressive 90 degrees away from the tidal axis. Coseismic slip events on currently active thrust faults are expected to be triggered when peak stresses are reached. Analysis of the timing of the 28 the shallow moonquakes recorded by the Apollo seismic network shows that 19 indeed occur when the Moon is closer to apogee, while only 9 shallow events occur when the Moon is closer to perigee. Here we show the results of relocating the shallow moonquake using an algorithm designed for sparse networks to better constrain their epicentral locations in order to compare them with stress models. The model for the current stress state of the Moon is refined by investigating the contribution of polar wander.

siesmology↗
NASA NTRS1979

M2 ocean tide parameters and the deceleration of the moon's mean longitude from satellite orbit data

An estimation is made of the principal long-period spherical harmonic parameters in the representation of the M2 ocean tide from the orbital histories of the three satellites 1967-92A, Starlette, and GEOS 3. The data used are primarily the evolution of the orbital inclinations of the satellites in conjunction with the longitude of the ascending node from GEOS 3. Analysis procedure and analytic formulation, as well as ocean tidal parameter estimation and deceleration of the lunar mean longitude are outlined. The credibility of the M2 ocean tide solution is further enhanced by the close accord between the computed value for the deceleration of the lunar mean longitude and other recently reported estimates. It is evident from the results presented that studies of close earth satellite orbits are able to provide important information about the tidal forces acting on the earth.

Felsentreger, T. L.↗
NASA NTRS2004

Lunar and Planetary Science XXXV: Exploration and Observations

The session, "Exploration and Observations" includes the following topics: 1) Charged Particle dose Measurements by the Odyssey/MARIE Instrument in Mars Orbit and Model Calculations; 2) Earth Thermal Field Variations in Dependence from Lunisolar Tides (by Vorotilovo Deep Well Observations); 3) ASTROHAB: A Modular Construction System for Lunar Bases; and 4) Solar Power Satellites for Orbital and Non-Terrestrial Applications.

Source record↗
NASA NTRS1999

A View of the Lunar Interior Through Lunar Laser Range Analysis

Laser ranges between observatories on the Earth and retroreflectors on the Moon started in 1969 and continue to the present. Recent range accuracies are 2 cm while earliest ranges are an C, order of magnitude less certain. Four retroreflectors are ranged: three located at the Apollo 11, 14, and 15 sites and one on the Lunakhod 2 rover. Accurate analysis of the range data determines a number of lunar science parameters. The lunar interior variables include a fluid core parameter. The Lunar Laser Ranging effort is reviewed elsewhere. Many parameters are detected through their influence on rotation. Also detected are solid-body tides and accurate selenocentric reflector locations. Determined through the rotation are moment-of-inertia differences, gravitational harmonics, potential Love number, and dissipation effects due to tides and molten core. The rotation of the Moon is not at its minimum energy state; some recently active process has caused free librations. The moment differences contributed to the recent improvement of the Moon's moment of inertia from the Lunar Prospector gravity field. The Love numbers provide bulk elastic properties. Future possibilities for measurement include oblateness of the core-mantle boundary and core moment. A study of dissipation signatures in the rotation determines tidal Q vs. frequency and concludes that the Moon has a molten core. At 1 month the tidal Q is 37 and at 1 yr it is 60. The core radius is < or = 352 km for Fe and < or = 374 km for the Fe-FeS eutectic. The core detection exceeds 3x its uncertainty. The spin of the core is not aligned with the spin of the mantle and torque arises from the velocity difference at the boundary. Yoder's turbulent boundary layer theory is used to compute the radii. The present heat generation from tides and core interaction is minor compared to radiogenic heating. The heating for ancient times is more interesting. Peale and Cassen investigated lunar tidal heating while the lunar orbit expanded due to tides on Earth. Their calculations predate the measurement of Q and should be multiplied by 3.45 to match the lunar-laser-determined Love number and monthly Q. Tidal-heating computations depend on how fast the lunar orbit evolved and whether the tidal dissipation is localized. Neither is known, but plausible assumptions lead to early central region temperature increases of several hundred degrees. Most of the energy is deposited early in the Moon's history. The turbulent boundary layer theory allows a prediction of energy dissipated at the core-mantle boundary during orbit evolution. Under the assumption that the properties of the early core are the same as at present, the energy dissipated by core-mantle interaction is about the same as for tidal dissipation, but it is deposited in a smaller volume. This source of energy is capable of promoting convection in an early fluid core and driving a dynamo. This is a transient phase with a duration depending on the rate of orbit evolution. Plausible assumptions lead to a duration of a few hundred million years. Thus, the remnant magnetization of many lunar rocks is compatible with a brief global magnetic field powered by dynamical energy dissipation. Analysis of the lunar laser ranges is providing information on lunar geophysics. Future data will improve accuracies of present solution parameters, and several more interior effects should be detectable.

Williams, J. G.↗
NASA NTRS2005

Spatial Extent of a Deep Moonquake Nest: A Preliminary Report of Reexamination

Deep moonquakes, occurring at depths about halfway to the center of the Moon, were discovered during the Apollo lunar landing missions, 1969-1972. Their near-monthly occurrence with nearly identical waveforms at any given seismic station suggests that they are strongly influenced by tides, caused by the Earth and the Sun, acting on certain limited regions of the deep lunar interior. However, much about them is unknown, why they are restricted to certain depths and to limited source regions (nests), and what they tell us about the nature of the material and dynamics of the interior of the Moon. A piece of information helphl to decipher their true nature is the spatial extent and distribution of their hypocenters. The occurrence of nearly identical waveforms suggests groups of hypocenters appear in close proximity to one another, but can we tell how closely they are located and how they are distributed? Additional information is included in the original extended abstract.

Nakamura, Yosio↗
NASA NTRS2005

Spatial Extent of a Deep Moonquake Nest: A Preliminary Report of Reexamination

Deep moonquakes, occurring at depths about halfway to the center of the Moon, were discovered during the Apollo lunar landing missions, 1969-1972. Their near-monthly occurrence with nearly identical waveforms at any given seismic station suggests that they are strongly influenced by tides, caused by the Earth and the Sun, acting on certain limited regions of the deep lunar interior. However, much about them is unknown, why they are restricted to certain depths and to limited source regions (nests), and what they tell us about the nature of the material and dynamics of the interior of the Moon. A piece of information helpful to decipher their true nature is the spatial extent and distribution of their hypocenters. The occurrence of nearly identical waveforms suggests groups of hypocenters appear in close proximity to one another, but can we tell how closely they are located and how they are distributed? The Apollo PSE (Passive Seismic Experiment) data from all stations of the seismic network were received in real time at a common receiving station on Earth in digital form. This provided extremely high inter-station timing accuracy not achievable for most earthquake data on Earth at that time. We took advantage of this to compute relative locations of waveform-matched events, and concluded that deep moonquake foci in the A1 moonquake nest were concentrated on a nearly horizontal plane of less than 1 km in diameter. This earlier study was based on deep moonquake events visually identified on seismograms. A recent reanalysis of earlier unidentified seismic events fully utilizing the high capability of present-day computers expanded the list of positively identified deep moonquakes by more than a factor of five. The new list contains many events that are not visually matched in waveforms, yet correlated at a significant level when cross-correlated with a computer. Thus it became imperative to reexamine the spatial distribution of deep moonquake hypocenters including the newly identified events. Additional information is included in the original extended abstract.

Nakamura, Yosio↗
NASA NTRS2004

Lunar Laser Ranging Science: Gravitational Physics and Lunar Interior and Geodesy

Laser pulses fired at retroreflectors on the Moon provide very accurate ranges. Analysis yields information on Earth, Moon, and orbit. The highly accurate retroreflector positions have uncertainties less than a meter. Tides on the Moon show strong dissipation, with Q=33+/-4 at a month and a weak dependence on period. Lunar rotation depends on interior properties; a fluid core is indicated with radius approx.20% that of the Moon. Tests of relativistic gravity verify the equivalence principle to +/-1.4x10(exp -13), limit deviations from Einstein's general relativity, and show no rate for the gravitational constant G/G with uncertainty 9x10(exp -13)/yr.

relativity↗
NASA NTRS1973

Some effects of elasticity on lunar rotation

A general Hamiltonian for a rotating moon in the field of the earth is expanded in terms of parameters orienting the spin angular momentum relative to the principal axes of the moon and relative to coordinate axes fixed in the orbital plane. The effects of elastic distortion are included as modifications of the moment of inertia tensor, where the magnitude of the distortion is parameterized by the Love number k2. The amplitudes of the principal periodic terms in the longitude of a point on the moon due to variations of the tide caused by the earth are discussed. A detailed derivation of the free wobble of the lunar spin axis about the axis of maximum moment of inertia is given. If the moon's rigidity is close to that of the earth there is no effect of elasticity on the rotation which can be measured with the laser ranging and, therefore, no elastic properties of the moon can be determined from variations in the rotation.

Peale, S. J.↗
NASA NTRS2013

Lunar Science from Lunar Laser Ranging

Variations in rotation and orientation of the Moon are sensitive to solid-body tidal dissipation, dissipation due to relative motion at the fluid-core/solid-mantle boundary, tidal Love number k2, and moment of inertia differences. There is weaker sensitivity to flattening of the core/mantle boundary (CMB) and fluid core moment of inertia. Accurate Lunar Laser Ranging (LLR) measurements of the distance from observatories on the Earth to four retroreflector arrays on the Moon are sensitive to variations in lunar rotation, orientation and tidal displacements. Past solutions using the LLR data have given results for Love numbers plus dissipation due to solid-body tides and fluid core. Detection of the fluid core polar minus equatorial moment of inertia difference due to CMB flattening is weakly significant. This strengthens the case for a fluid lunar core. Future approaches are considered to detect a solid inner core.

Love numbers↗
NASA NTRS2003

Lunar Rotation and the Lunar Interior

Variations in rotation and orientation of the Moon are sensitive to solid-body tidal dissipation, dissipation due to relative motion at the fluid-core/ solid-mantle boundary, and tidal Love number k2. There is weaker sensitivity to flattening of the core-mantle boundary (CMB) and fluid core moment of inertia. Accurate Lunar Laser Ranging (LLR) measurements of the distance from observatories on the Earth to four retroreflector arrays on the Moon are sensitive to lunar rotation and orientation variations and tidal displacements. Past solutions using the LLR data have given results for dissipation due to solid-body tides and fluid core plus Love number. Past detection of CMB flattening has been marginal but is improving, while direct detection of the core moment has not yet been achieved. Three decades of Lunar Laser Ranging (LLR) data are analyzed using a weighted least-squares approach. The lunar solution parameters include dissipation at the fluid-core/solid-mantle boundary, tidal dissipation, dissipation-related coefficients for rotation and orientation terms, potential Love number k2, a correction to the constant term in the tilt of the equator to the ecliptic which is meant to approximate the influence of core-mantle boundary flattening, and displacement Love numbers h2 and l2. Several solutions, with different combinations of solution parameters and constraints, are considered.

Williams, J. G.↗
NASA NTRS1971

The lunar laser ranging experiment

With data from two or more well-located observing stations, the lunar range can be corrected accurately for the effects of polar motion and fluctuations in the earth's rotation rate. Very accurate corrections can be made for the earth tides at each station. It appears that the use of lasers giving roughly 0.1-msec pulse lengths is highly desirable. With them, single-shot ranging accuracies of about 3 cm are expected. The actual lunar range results will be analyzed by fitting a numerical integration for the lunar motion to the data. A mathematical model for lunar range is given. Tests of the theory of gravitation are considered.

Bender, P. L.↗
NASA NTRS2017

Manuel Johnson's Tide Record at St. Helena

The astronomer Manuel Johnson, a future President of the Royal Astronomical Society, recorded the ocean tides with his own instrument at St. Helena in 1826-1827, while waiting for an observatory to be built. It is an important record in the history of tidal science, as the only previous measurements at St. Helena had been those made by Nevil Maskelyne in 1761, and there were to be no other systematic measurements until the late 20th century. Johnsons tide gauge, of a curious but unique design, recorded efficiently the height of every tidal high and low water for at least 13 months, in spite of requiring frequent re-setting. These heights compare very reasonably with a modern tidal synthesis based on present-day tide gauge measurements from the same site.Johnsons method of timing is unknown, but his calculations of lunar phases suggest that his tidal measurements were recorded in Local Apparent Time. Unfortunately, the recorded times are found to be seriously and variably lagged by many minutes. Johnsons data have never been fully published, but his manuscripts have been safely archived and are available for inspection at Cambridge University. His data have been converted to computerfiles as part of this study for the benefit of future researchers.

Cartwright, David E.↗
NASA NTRS1965

A rising tide of structural problems.

Structural problems for advanced launch vehicle and spacecraft, discussing size, environment, material, human attitude, propellant tank, bulkhead and lunar-vehicle landing-gear designs

PROPELLANT TANK↗
NASA NTRS1992

Tidal deceleration of the moon's mean motion

The secular change in the mean motion of the moon, n, caused by the tidal dissipation in the ocean and solid earth is due primarily to the effect of the diurnal and semidiurnal tides. The long-period ocean tides produce an increase in n, but the effects are only 1 percent of the diurnal and semidiurnal ocean tides. In this investigation, expressions for these effects are obtained by developing the tidal potential in the ecliptic reference system. The computation of the amplitude of equilibrium tide and the phase corrections is also discussed. The averaged tidal deceleration of the moon's mean motion, n, from the most recent satellite ocean tide solutions is -25.25 +/- 0.4 arcseconds/sq century. The value for n inferred from the satellite-determined ocean-tide solution is in good agreement with the value obtained from the analysis of 20 years of lunar laser-ranging observations.

Cheng, M. K.↗
NASA NTRS1984

Constraints on the origin of viscoelastic bodies

While the oceans undoubtly contribute to energy dissipation, it seems implausible that such a small amount (0.02%) of the Earth's mass could play such a dominant role in lunar orbital evolution. An alternate hypothesis assumes that most of the dissipation is associated with solid-body tides. This mechanism is also capable of varying significantly over time for viscoelastic bodies. In such an analysis of orbital evolution, the bodies are modeled as incompressible, Kelvin-Voight solids. While this material is simplistic, it does provide an analytical characterization of solid-body dissipation and the resulting tidal moment. The orbital history of a two body system is traced back in time to develop constraints on the satellite's origin. These constraints suggest the Moon appeared in a significantly inclined orbit at a distance greater than ten Earth radii. This distance is outside of the Roche limit and would appear to alleviate some difficulties associated with capture hypotheses. Small eccentricity at close approach suggests an origin by accretion.

Vanarsdale, W. E.↗
NASA NTRS1999

A Global Ocean Tide Model From TOPEX/POSEIDON Altimetry: GOT99.2

Goddard Ocean Tide model GOT99.2 is a new solution for the amplitudes and phases of the global oceanic tides, based on over six years of sea-surface height measurements by the TOPEX/POSEIDON satellite altimeter. Comparison with deep-ocean tide-gauge measurements show that this new tidal solution is an improvement over previous global models, with accuracies for the main semidiurnal lunar constituent M2 now below 1.5 cm (deep water only). The new solution benefits from use of prior hydrodynamic models, several in shallow and inland seas as well as the global finite-element model FES94.1. This report describes some of the data processing details involved in handling the altimetry, and it provides a comprehensive set of global cotidal charts of the resulting solutions. Various derived tidal charts are also provided, including tidal loading deformation charts, tidal gravimetric charts, and tidal current velocity (or transport) charts. Finally, low-degree spherical harmonic coefficients are computed by numerical quadrature and are tabulated for the major short-period tides; these are useful for a variety of geodetic and geophysical purposes, especially in combination with similar estimates from satellite laser ranging.

Ray, Richard D.↗