On the precession constant: Values and constraints on the dynamical ellipticity; link with Oppolzer terms and tilt-over-mode

The luni-solar precession, derived by theoretical considerations from the precession of the equator, is one of the most important parameters for computing not only precession but also nutations, due to its relation to the dynamical flattening. In this paper, we review the numerical values of this parameter, from the geodynamical point of view as well as the astronomical point of view, from the observational point of view as well as from the theoretical point of view. In particular, we point out a difference of about 1 percent between the global Earth dynamical flattening derived from the astronomical observations and the values derived from the different geophysical computations. The nutation amplitudes depend on the Earth dynamical flattening and this dependence is amplified by a resonance at an important normal mode, the Tilt-Over-Mode (TOM). Since the astronomical point of view as well as the geophysical one are confronted, we also take the opportunity to make the link between the TOM and the expressions of the nutations of the different axes which, in turn, are related with one another by the Oppolzer terms. Both, the Oppolzer terms and the TOM originate from a reference frame tilt effect. In writing the link between the nutational motions of the different axes, and so, in writing the Oppolzer terms, we also make the link with the precessional motion.     

Conjectures on the ellipticity of cD galaxies

We give a possible explanation for the peculiar flattening of some cD galaxies, and for their alignment with the cluster's overall rotation.     

The dynamical environment of Dawn at Vesta

Dawn is the first NASA mission to operate in the vicinity of the two most massive asteroids in the main belt, Ceres and Vesta. This double-rendezvous mission is enabled by the use of low-thrust solar electric propulsion. Dawn will arrive at Vesta in 2011 and will operate in its vicinity for approximately one year. Vesta's mass and non-spherical shape, coupled with its rotational period, presents very interesting challenges to a spacecraft that depends principally upon low-thrust propulsion for trajectory-changing maneuvers. The details of Vesta's high-order gravitational terms will not be determined until after Dawn's arrival at Vesta, but it is clear that their effect on Dawn operations creates the most complex operational environment for a NASA mission to date. Gravitational perturbations give rise to oscillations in Dawn's orbital radius, and it is found that trapping of the spacecraft is possible near the 1:1 resonance between Dawn's orbital period and Vesta's rotational period, located approximately between 520 and 580 km orbital radius. This resonant trapping can be escaped by thrusting at the appropriate orbital phase. Having passed through the 1:1 resonance, gravitational perturbations ultimately limit the minimum radius for low-altitude operations to about 400 km, in order to safely prevent surface impact. The lowest practical orbit is desirable in order to maximize signal-to-noise and spatial resolution of the Gamma-Ray and Neutron Detector and to provide the highest spatial resolution observations by Dawn's Framing Camera and Visible InfraRed mapping spectrometer. Dawn dynamical behavior is modeled in the context of a wide range of Vesta gravity models. Many of these models are distinguishable during Dawn's High Altitude Mapping Orbit and the remainder are resolved during Dawn's Low Altitude Mapping Orbit, providing insight into Vesta's interior structure. Ultimately, the dynamics of Dawn at Vesta identifies issues to be explored in the planning of future EP missions operating in close proximity to larger asteroids.     

Micrometeoroid impact crater statistics at the boundary of Earth's gravitational sphere of influence

We surveyed craters on a space-exposed surface from the Genesis solar wind sample return mission to find new constraints on the population of micrometeoroids at the edge of the Earth's gravitational sphere of influence. The target was made of 6061-T6 aluminum, identical to the composition of the space-facing end of the Long Duration Exposure Facility satellite, which recorded micrometeoroid impacts in low Earth orbit. We use data from both locations to compare crater frequency as a function of size, with and without gravitational focussing by the Earth. We find that the cratering flux near the Earth-Sun L1 libration point is indistinguishable, within the ∼40% uncertainty of this study, from that in low Earth orbit. The small degree of gravitational focussing between the two locations indicates that particles with geocentric free-space velocities less than a few kilometers per second comprise no more than a few percent of the interplanetary dust complex.     

The flux of meteorites on the Earth's surface

Abstract— We derive values for the number and size distributions of meteorites landing on Earth from a study of photographic observations of bright fireballs with the Canadian camera network. The observations cover 11 years from 1974 to 1985. This analysis is an extension of a previous study and represents a 30% increase in the data base. The cumulative plot of numbers vs estimated mass of the largest fragment for each event shows a change in slope near 0.6 kg due to a deficiency of small meteorites surviving from the group of slow fireballs. The change can be explained by a mass dependence of the fraction of the incoming object that survives as the largest fragment. For larger falls, the main mass appears to represent a decreasing fraction of the total mass of the surviving meteorites and estimates of these effects are used to derive the final distribution of both main masses and total masses of meteoritic events. For total masses greater than 1 kg the population index is 1.82, close to previous estimates. About 9 events per year drop at least 1 kg of meteorites in an area of a million square km and the same area receives an annual influx of 54 kg from meteorite events with total masses between 0.01 and 100 kg. There is sufficient confidence in these results that they may be used for comparison of the present flux of meteorites with values inferred for other times, in particular the long accumulation times of the Antarctic meteorite collections.     

Remarks on the nomenclature of mercury

Longitudes of surface marking observed on Mercury by E.M. Antoniadi are determined. The most frequent of the locations are used to determine the most probable positions on Mercury's surface for the names defined on Antoniadi's 88-day planisphere. It is suggested that these locations can serve as a valid and accurate basis for Mercurian nomenclature.     

The warping of the galactic plane and changes of ellipticity

Observational evidence on the widespread occurrence of warping of the outer part of the galactic plane in many galaxies is presented and various hypotheses for its explanation are reviewed. None is found to be able to account for all the cases reported. Other phenomena considered are: (1) deviations from the galactic plane in the innermost nuclear region; (2) differences in orientation of the nucleus and disk in spiral galaxies; (3) changing ellipticity with distance from the center.After discussing the observations available, a theory has been developed which explains the phenomena mentioned as natural consequences of the non-steady nature of galactic systems due to time-dependent metric. This manifests itself in the appearance of tangential acceleration which leads necessarily to variability of the orbital plane and orbital eccentricity in dependence on the radius vector of the orbits.     

Charged dust in the Earth's magnetosphere

We have considered the electrodynamic effects on small Al₂O₃ spherules dumped into the Earth's magnetosphere in large quantities during solid rocket propellant burns. The charges acquired by these grains in all regions of the terrestrial environment (plasmasphere, magnetosphere, and solar wind) are modest. Consequently electrodynamic effects are significant only at the lower end of the dust size spectrum (R _g0.1 m). In that case, the electrodynamic forces conspire with solar radiation pressure to eliminate the grains from the magnetosphere in a comparatively short time. Although not studied here in detail, we anticipate a similar fate for fine micrometeoroids entering the Earth's magnetosphere, with the electro-dynamic effects playing an even more important role.Paper dedicated to Professor Hannes Alfvén on the occasion of his 80th birthday, 30 May 1988.     

Birkeland currents in the Earth's magnetosphere

As a result of his polar expeditions at the beginning of this century, Kristian Birkeland determined that intense ionospheric currents were associated with the aurora. Birkeland suggested that these currents originated far from the Earth and that they flowed ointo and away from the polar atmosphere along the geomagnetic field lines. The existence of such field-aligned or Birkeland currents was disputed because it was not possible to unambiguously identify current systems that are field-aligned (as suggested by Alfvén, 1939, 1940) and those which are completely contained in the ionosphere (as developed by Vestine and Chapman, 1938) with surface magnetic field observations. The presence of Birkeland currents has been absolutely confirmed with satellite-borne particle and magnetic field experiments conducted over the past two decades. These satellite observations have determined the large-scale patterns, flow directions, and intensities of Birkeland currents in the auroral and polar regions, and their relationship to the orientation and magnitude of the interplanetary magnetic field. The Birkeland currents are directly associated with visible and UV auroral forms observed with satellites. The results obtained from a variety of recently launched satellites are discussed here. These include Sweden's first satellite, VIKING, which has provided evidence for resonant Alfvén waves on the same geomagnetic field lines that guide stationary Birkeland currents. These observations demonstrate the important role that these currents play in the coupling of energy between the interplanetary medium and the lower ionosphere and atmosphere.Paper dedicated to Professor Hannes Alfvén on the occasion of his 80th birthday, 30 May 1988.     

Dimension of the Earth's General Ellipsoid

The problem of specifying the Earth's mean (general)ellipsoid is discussed. This problem has been greatly simplified in the era of satellite altimetry, especially thanks to the adopted geoidal geopotential value, W₀ = (62 636 856.0 ± 0.5) m² s^-2.Consequently, the semimajor axis a of the Earth's mean ellipsoid can be easily derived. However, an a priori condition must be posed first. Two such a priori conditions have been examined, namely an ellipsoid with the corresponding geopotential that fits best W₀ in the least squares sense and an ellipsoid that has the global geopotential average equal to W₀. It has been demonstrated that both a priori conditions yield ellipsoids of the same dimension, with a–values that are practically identical to the value corresponding to the Pizzetti theory of the level ellipsoid: a = (6 378 136.68 ± 0.06) m.     

Representation of the Earth's gravitational potential

The paper represents the Earth's gravitational potentialV, outside a sphere bounding the Earth, by means of its difference V from the author's spheroidal potential. The difference V is in turn represented as arising from a surface density on the sphere bounding the Earth. Because of the slow decrease with ordern of the normalized coefficients in the spherical harmonic expansion ofV, the density anomalies from which the higher coefficients arise must occur in regions close to the Earth's surface. The surface density is thus an idealization of the product of the density anomaly and the crustal thicknessb. Values of are computed from potential coefficients obtained from two sources, Rapp and the Smithsonian Astrophysical Observatory. The two sources give qualitative agreement for the values of and for its contour map. The numerical values obtained for are compatible with the idea that the responsible density anomalies are reasonably small, i.e., less than 0.05 g/cm³, and occur in the crust alone.This paper was prepared under the sponsorship of the Electronics Research Center of the National Aeronautics and Space Administration through NASA Grant NGR 22-009-311.     

Remarks on the photogravitational restricted three-body problem

The effects of the radiation pressure in the restricted three-body problem are considered and the existence of the out-of-plane equilibrium points is analyzed. It is found that within the framework of the stellar stability, the five Lagrangian points are the only equilibrium points, at least as far as the force of the radiation pressure is taken into account.     

Imprint of Galactic dynamics on Earth's climate

A connection between climate and the Solar system's motion perpendicular to the Galactic plane during the last 200 Myr years is studied. An imprint of galactic dynamics is found in a long‐term record of the Earth's climate that is consistent with variations in the Solar system oscillation around the Galactic midplane. From small modulations in the oscillation frequency of Earth's climate the following features of the Galaxy along the Solar circle can be determined: 1) the mass distribution, 2) the timing of two spiral arm crossings (31 Myr and 142 Myr) 3) Spiral arm/interarm density ratio (ρ _arm/ρ _interarm ≈ 1.5–1.8), and finally, using current knowledge of spiral arm positions, a pattern speed of Ω_P = 13.6 ± 1.4 km s^–1 kpc^–1 is determined. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Analytical study of the Earth's shadowing effects on satellite orbits

In this paper a new mathematical model is proposed for the study of the effects of the direct solar radiation pressure on the orbit of an artificial Earth satellite. The equations for the first order effects become canonical when a different definition for the orders of magnitude is adopted. This enables us the utilization of the method of Von Zeipel to eliminate all periodic terms. The model leads to the non-existence of pure secular perturbations owing to the direct solar radiation pressure on the metric elements: semi-major axis, eccentricity and inclination. Numerical examples built with an approximation for the shadow function show that the secular inequalities on the angle variables—longitude, perigee and node—are very small.     

Momentum of meteoroids and its effect on the Earth's atmosphere

Recent studies have attributed certain properties of the Earth's atmosphere to excess orbita angular momentum of impinging meteoroids. A realistic analysis of meteor observations does not support the existence of this excess.     

Paleontological evidence on the Earth's rotational history since early precambrian

The daily growth layers arranged into seasonal and tidal patterns, present in calcified structures of many modern as well as fossil organisms, provide evidence on the length of lunar month and year in the geological past.The data presented are mainly from molluscan shells and indicate that the number of days per lunar month and per year has decreased significantly since Ordovician time. The change possibly has not taken place at a uniform rate.Banding and periodical patterns in stromatolites reflect cycles of daily, tidal, and seasonal nature, but rarely, if ever, represent a complete growth record. Such lack of completeness is a function of many parameters like water depth, energy of the environment, biological and physical disruptions, which are not always determinable in fossils. Phanerozoic stromatolites show a higher degree of incompleteness than precambrian ones. Figures obtained from stromatolites counts cannot be compared to those from molluscs. Preliminary data indicate that the length of the synodic month during Gunflint time (1750 m.y. ago) was between 36 and 39 days. The oldest known stromatolites ( 2800 m.y.) show patterns that are interpreted as due to tidal influence and have a periodicity of 10, 20 and 40 laminae. The obvious conclusions are that the Moon has been associated with Earth since at least Early Precambrian times, that all theories implying a late capture of the Moon should be revised and that the calculated secular changes in the Earth's rotation rate cannot be accepted as representative for the all geological history.Paper presented at the AAAS Symposium on the Early History of the Earth and Moon in Philadelphia on 28 December 1971.     

Neutrino Water Detector on the Earth's Surface (NEVOD)

A Cherenkov water detector with volume 9× 9 × 26 cubic meters is described.The spatial lattice of the detector is formed by quasispherical measuring modules which allow to detect Cherenkov light from any direction with practically equal efficiency. Each of the modules consists of six PMTs directed along rectangular coordinate axes. The possibility of neutrino-induced muon detection under conditions of high background on the Earth's surface is discussed. Experimental data obtained during Spring 1996 are analysed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Time variation of ellipticity of globular clusters in the Large Magellanic Cloud

Dynamical evolution of globular clusters in the Large Magellanic Cloud (LMC) is investigated by means of N-body simulations; particular attention is paid to time evolution in the ellipticitical figure of globular clusters. The simulations were started with a binary globular cluster. It merged into a single cluster with ellipticity of about 0.3. The simulations were continued until the cluster became rounder due to the effects of two body relaxation and of tidal field of LMC. It is found that the outward angular momentum transport due to the gravothermal contraction makes the inner region rounder; the ellipticity at about the initial half-mass radius (r _h) decreases with the e-folding time of 20 relaxation times. On the other hand, the outer region becomes rounder due to the stripping of stars by the tidal field; the ellipticity at about 3r _h decreases with the e-folding time of 80 crossing times therein, though the time scale depends on the direction of the tidal field relative to the spin of the cluster. These two effects are comparable at about the half-mass radius. Taking account of such theoretical results we reanalyzed observed data for the ellipticity at about the half-mass radius of LMC clusters. We estimated the relaxation time and crossing time for each of the observed clusters, from which we calculated the effective time of getting round of the cluster. We plotted the observed ellipticity of the clusters against their non-dimensional age — i.e., the age normalized by the effective time. We found that observed ellipticity distribution is consistent with our picture.