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Papers are presented dealing with interdisciplinary research in the fields of geodesy, solid earth and ocean physics. Topics discussed include: solid earth and ocean tides; the rotation of the earth and polar motion; vertical crustal motions; the geoid and ocean surface; earthquake mechanism; sea level changes; and lunar dynamics.
The effect of tidal friction on the inclination of the lunar orbit to the earth's equator for earth-moon distances of less than 10 earth radii is examined. The results obtained bear on a conclusion drawn by Gerstenkorn and others which has been raised as a fatal objection to the fission hypothesis of lunar origin, namely, that the present nonzero inclination of the moon's orbit to the ecliptic implies a steep inclination of the moon's orbit to the earth's equatorial plane in the early history of the earth-moon system. This conclusion is shown to be valid only for particular rheological models of the earth. The earth is assumed to behave like a highly viscous fluid in response to tides raised in it by the moon. The moon is assumed to be tideless and in a circular orbit about the earth. The equations of tidal friction are integrated numerically to give inclination of the lunar orbit as a function of earth-moon distance.
The function of moon position for shoreline orientation by talitrids is investigated. Three major results were found: (1) Observed cases of compensation for changes in the direction of the moon are based on physiological rhythm with a period of about 25 hours which can persist for at least several days under constant conditions. (2) The zeitgeber for physiological rhythm may be either moonlight or some other factor associated with the tides. (3) If talitrids are long removed from environmental entrainment, either artifically or naturally, the internal rhythm no longer exerts an appreciable influence on the angle of lunar orientation; in such cases the system deteriorates into constant angle orientation, with an angle which is determined by the beach orgin, but may be modified by lighting conditions.
Information obtained with the Apollo lunar seismic stations is discussed. The four types of natural seismic sources that have been identified are described, viz., thermal moonquakes, deep moonquakes, meteoroid impacts, and shallow moonquakes. It is suggested that: (1) the thermal quakes represent the slow cracking and movement of surface rocks; (2) the deep quakes are induced by the tide-generating force of the earth's gravity; (3) the meteoroids responsible for most of the observed impacts are in the mass range from 1 to 100 kg and are clustered in groups near the earth's orbit; and (4) the shallow quakes are similar to intraplate earthquakes and indicate that the moon is as seismically active as the interior regions of the earth's tectonic plates. The structure of the lunar interior as inferred from seismic signals due to both the last three natural sources and 'artificial' impacts of used spacecraft is examined in detail.
More than 1400 observations of lunar transient phenomena (LTP), encompassing brightenings, darkenings, and gaseous, reddish, and bluish events, are analyzed in an attempt to determine the possible causes of LTP. Hypotheses considered include effects of earth tides on the moon, low-angle illumination, thermal luminescence, UV heating, solar-particle acceleration by the magnetopause of earth's magnetotail, terrestrial magnetotail bow-shock-front turbulence, cathode luminescence due to magnetotail effects, and solar-flare particle bombardment. Analysis are performed in terms of histograms of the number of observations vs. phase of anomalistic period and of number vs. moon's age, percentage of numbers of observed phenomena and percentage of expected numbers as well as their ratios, and albedo behavior over a lunation period of chosen permanent points in ten specific features. The results indicate that different phenomena may have different causes, strong tidal effects are dubious, correlations with sunrise are most frequent, and the distribution of all LTP sites is distinct from that of deep- and shallow-focus moonquake epicenters.
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The low degree and order terms in the spherical harmonic model of the tidal potential were observed through the perturbations which are induced on near-earth satellite orbital motions. Evaluations of tracking observations from 17 satellites and a GEM-T1 geopotential model were used in the tidal recovery which was made in the presence of over 600 long-wavelength coefficients from 32 major and minor tides. Wahr's earth tidal model was used as a basis for the recovery of the ocean tidal terms. Using this tidal model, the secular change in the moon's mean motion due to tidal dissipation was found to be -25.27 + or - 0.61 arcsec/century-squared. The estimation of lunar acceleration agreed with that observed from lunar laser ranging techniques (-24.9 + or - 1.0 arcsec/century-squared), with the corresponding tidal braking of earth's rotation being -5.98 + or - 0.22 X 10 to the -22 rad/second-squared. If the nontidal braking of the earth due to the observed secular change in the earth's second zonal harmonic is considered, satellite techniques yield a total value of the secular change in the earth's rotation rate of -4.69 + or - 0.36 X 10 to the -22 rad/second-squared.
The low degree and order terms in the spherical harmonic model of the tidal potential were observed through the perturbations which are induced on near-earth satellite orbital motions. Evaluations of tracking observations from 17 satellites and a GEM-T1 geopotential model were used in the tidal recovery which was made in the presence of over 600 long-wavelength coefficients from 32 major and minor tides. Wahr's earth tidal model was used as a basis for the recovery of the ocean tidal terms. Using this tidal model, the secular change in the moon's mean motion due to tidal dissipation was found to be -25.27 + or - 0.61 arcsec/century squared. The estimation of lunar acceleration agreed with that observed from lunar laser ranging techniques (-24.9 + or - 1.0 arcsec/century squared), with the corresponding tidal braking of earth's rotation being -5.98 + or - 0.22 x 10 to the minus 22 rad/second squared. If the nontidal braking of the earth due to the observed secular change in the earth's second zonal harmonic is considered, satellite techniques yield a total value of the secular change of the earth's rotation rate of -4.69 + or - 0.36 x 10 to the minus 22 rad/second squared.
A pattern in moonquakes, which correlates with the monthly tidal cycle, also correlates with a phase-shifted pattern of a 7-month tidal cycle. The lead of approximately 2 months in moonquake occurrence can be explained if local tidal forces are combined with a moonquake-driving force. This force, assumed to result from the 6-yr physical libration in latitude, would cause N-S sliding of an outer layer across a solid layer within a decoupled core in a lunar model. During 1969-1971, the sliding would be southward with a progression of monthly maxima in the combined forces. Where these forces control moonquakes, the reversal in direction of the 6-year cyclic force in early 1972 should cause a minimum in moonquake activity. Decreases toward such a minimum did occur simultaneously in the similar progressions of monthly moonquakes and maxima in the combined forces at the most active hypocenter. Repetition of the 1966-1971 force pattern in 1975-1977 should produce a corresponding repetition of the moonquake pattern.
Analyses of Lunar Laser ranges Shaw a displacement in direction of the Moon's pole of rotation which indicates that strong dissipation is acting on the rotation.
From the author's collection of more than 900 reports of lunar transient phenomena (LTP) covering the period 1540-1970, 771 positive plus 112 negative observations (several times more than any previously published analyses) with sufficient ancillary data were analyzed for five hypotheses of causes. Treated as two groups they were divided into four categories (gaseous, reddish, bluish, and brightenings) and were analyzed separately and combined with respect to the hypotheses. The five hypotheses involved effects of tides, sunrise, low-angle illumination, earth's magnetic tail, and solar particles.
The European Space Agency's three-satellite constellation Swarm, launched in November 2013, has provided unprecedented monitoring of Earth's magnetic field via a unique set of gradiometric and multi-satellite measurements from low Earth orbit. In order to exploit these measurements, an advanced "Comprehensive Inversion" (CI) algorithm has been developed to optimally separate the various major magnetic field sources in the near-Earth regime. The CI algorithm is used to determine Swarm Level-2 (L2) magnetic field data products that include the core, lithospheric, ionospheric, magnetospheric, and associated induced sources. In addition, it has become apparent that the CI is capable of extracting the magnetic signal associated with the oceanic principal lunar semi-diurnal tidal constituent M(sub 2) to such an extent that it has been added to the L2 data product line. This paper presents the parent model of the Swarm L2 CI products derived with measurements from the first four years of the Swarm mission and from ground observatories, denoted as "CIY4", including the new product describing the magnetic signal of the M(sub 2) oceanic tide.
The analysis of eight years of lunar laser ranging data yields a value for the tidally induced secular acceleration of the lunar orbital longitude of -23.8 + or - 4 arcsec/century per century. For semidiurnal tidal frequencies this corresponds to a terrestrial Q = 12 + or - 2. The error in n is dominated by noise in the data and its modeling. The error is expected to decrease significantly as future data become available and it may become possible to detect an 18.6-yr periodic modulation of the acceleration which would allow the separation of the effects of diurnal and semidiurnal tides. Comparison of the secular acceleration with values published from the analysis of classical astronomical observations does not show a significant difference which can be attributed to a changing gravitational constant.
Precision mean element (PME) satellite theories play a key role in orbit dynamics analyses. These theories employ: nonsingular orbital elements comprehensive force models Generalized Method of Averaging Numerical interpolation concepts The Draper Semianalytical Satellite Theory (DSST) (Refs. 1 - 6), whose development was led by the author, and the independently-developed Universal Semianalytical Method (USM) (Ref. 7) are examples of such theories. These theories provide the capability to tailor the force modeling to meet the desired computational speed vs. accuracy trade-off. The flexibility of such theories is demonstrated by their ability to include complicated atmosphere density models and spacecraft models in the perturbation theory context. The value of high speed satellite theories, in this era of computational plenty, is that they allow new ways of looking at astrodynamical problems such as orbit design (Refs. 8, 9) and atmosphere density updating (Refs. 10, 11). In the mid to late-1980 s, the geodynamics community led the development of very precise geopotential models such as GEM T2 and GEM T3 (Ref. 12), and with the subsequent analysis of the TOPEX flight data, JGM-2 and JGM-3 (Ref. 13). These were high degree and order geopotentials, at least 50 x 50. In 1993, the DSST implementation in the GTDS program was extended to include the 50 x 50 geopotential models (Ref. 14). The 50 x 50 geopotential, J2000 integration coordinate system, and solid Earth tide capabilities were integrated in GTDS by Scott Carter (Ref. 15). This capability demonstrated 1 m accuracy versus the TOPEX Precise Orbit Ephemerides. Subsequently the DSST Standalone program was also extended to include high degree and order geopotential models (Ref. 5). More recently GTDS has been hosted in the Linux PC environment. However, all of these efforts have been limited to modeling the motion of an artificial Earth satellite. They did not consider the additional complexities associated with lunar, planetary, or other natural satellite orbiters. Such complexities include: additional coordinate systems (associated with the direction of the north pole of rotation and the prime meridian of the new central bodies) (Ref. 16) normalized gravity model coefficients (desirable for high degree and order fields) (Ref. 17) indirect oblateness
From the launch of the Oersted satellite in 1999, through the CHAMP mission from 2000 to 2010, and now with the Swarm constellation mission starting in 2013, satellite magnetometry has provided excellent monitoring of the near-Earth magnetic field regime. The advanced Comprehensive Inversion scheme has been applied to data before Swarm and to the Swarm data itself, but now for the first time to all the satellite data in this new era, culminating in the CM6 model. The highlights of this model include not only a continuous core magnetic field description over the entire time period 1999 to 2019.5 in good agreement with the CHAOS model series, but the addition of two new oceanic tidal magnetic sources: the larger lunar elliptic semi-diurnal constituent N2 and the lunar diurnal constituent O1. CM6 is also the parent model of the NASA/GSFC candidates for the DGRF2015 and IGRF2020 in response to the IGRF-13 call. This paper provides a full report on the development of CM6.
Phobos, the innermost satellite of Mars, displays an extensive system of grooves that are mostly symmetric about its sub-Mars point. Phobos is steadily spiraling inward due to the tides it raises on Mars lagging behind Phobos' orbital position and will suffer tidal disruption before colliding with Mars in a few tens of millions of years. We calculate the surface stress field of the deorbiting satellite and show that the first signs of tidal disruption are already present on its surface. Most of Phobos' prominent grooves have an excellent correlation with computed stress orientations. The model requires a weak interior that has very low rigidity on the tidal evolution time scale, overlain by an approximately 10-100 m exterior shell that has elastic properties similar to lunar regolith as described by Horvath et al. (1980).
Two methods are considered to 'tap' the earth's rotational energy. This ancient 'collapsed gravitational energy' exceeds the earth-lunar binding energy. One involves an orbiting 'electromagnetic-gravitational' coupling system whereby the earth's rotation, with its nonuniform mass distribution, first uses gravity to add orbital energy to a satellite, similar to a planetary 'flyby'. The second stage involves enhanced satellite 'drag' as current-carrying coils withdraw the added orbital energy as they pass through the earth's nonuniform magnetic field. A second more direct method couples the earth's rotational motion using conducting wires moving through the noncorotating part (ionospheric current systems) of the geomagnetic field. These methods, although not immediately feasible, are considerably more efficient than using pure gravitational coupling to earth-moon tides.
The Moon's center of mass is displaced from its center of figure about 2 km in a roughly earthward direction. Most maria are on the side of the Moon which faces the Earth. It is assumed that the Moon was initially spherically symmetric. The emplacement of mare basalts transfers mass which produces most of the observed center of mass displacement toward the Earth. The cause of the asymmetric distribution of lunar maria was examined. The Moon is in a spin orbit coupled relationship with the Earth and the effect of the Earth's gravity on the Moon is asymmetric. The earth-facing side of the Moon is a gravitational favored location for the extrusion of mare basalt magma in the same way that the topographically lower floor of a large impact basin is a gravitationally favored location. This asymmetric effect increases inversely with the fourth power of the Earth Moon distance. The history of the Earth-Moon system includes: formation of the Moon by accretion processes in a heliocentric orbit ner that of the Earth; a gravitational encounter with the Earth about 4 billion years ago resulting in capture of the Moon into a geocentric orbit and heating of the Moon through dissipation of energy related to tides raised during close approaches to the Earth(5) to produce mare basalt magma; and evolution of the Moon's orbit to its present position, slowly at first to accommodate more than 500 million years during which magmas were extruded.