The improvement of the lunar ephemeris

At present the fundamental lunar ephemeris is based on Brown's theory of the motion of the Moon with improvements based on the bypassing of Brown's Tables, the removal of the great empirical term, the substitution of the relevant constants of the IAU system of astronomical constants and the retransformation of Brown's series in rectangular coordinates to spherical coordinates. Even so this ephemeris does not represent adequately the recent range and range-rate radio observations, and it will be inadequate for use in the analysis of laser observations of corner reflectors on the Moon. Numerical integrations for these purposes have already been made at the Jet Propulsion Laboratory, but improved theoretical developments are also required; new solutions of the main problem are in hand elsewhere. Work at H.M. Nautical Almanac Office is aimed at obtaining improved values of the constants of the lunar orbit by a rediscussion of occultation observations made since 1943 and at the redevelopment of the series for the planetary perturbations using more precise theories of the motion of the Sun and planets. The techniques and preliminary results of exploratory numerical integrations were briefly described.Presented at the Conference on Celestial Mechanics, Oberwolfach, Germany, 17–23 August, 1969.     

The main problem of lunar theory solved by the method of Brown

Brown's method for solving the main problem of lunar theory has been adapted for the computation by machine with the help of an algebraic processor. Brown's results are first recovered and refined. The solution is then expanded to include most terms of order nine. The terms in the series for the longitude and latitude are listed with an accuracy of 0.000 01 and of 0.000 001 for the parallax.This research was supported in parts by the National Science Foundation grant MCS 78-01425.     

Literal solution for Hill's lunar problem

A computer program for the manipulation of power series in several variables is used to find the first order solution to Hill's lunar problem. The ratiom of the mean motion of the Sun to that of the Moon is kept as a formal parameter. The series inm are known to converge very poorly. It is shown how efficient algorithms among them the Lie transformation allow us to compute the series inm as far as they are needed. When the series are evaluated at Brown's numerical value form the results achieve or exceed his accuracy.     

Some differentials in Brown's lunar theory

Differences between expressions derived by Brown and Griffith are shown to be a consequence of the different methods of derivation. Other differentials used in Brown's method are derived.     

The main problem of lunar theory solved by the method of Brown

Brown's method for solving the main problem of lunar theory has been adapted for the computation by machine. The computations are carried out with the help of an algebraic processor called POLYPAK, which can manipulate power series in several real or complex variables. Brown's result have been recovered and refined first and the solution, in Cartesian coordinates to the sixth order, has been compared to the work of Eckert (see Gutzwiller, 1979). The solution has then been expanded to include most terms through order nine. This order is necessary to get an accuracy of 0.00001 for the terms in longitude and latitude and of 0.000001 for the terms in the sine parallax. A preliminary comparison with the theories of Chapront and Henrard (1980) indicates that the solution has an accuracy which is close to the one desired. For details see Schmidt (1980).The next step in developing a complete lunar theory requires the computation of the partial derivatives of the solution with respect to the primary parameters. Since Brown's method gives a semianalytical solution only the derivative with respect ton, the mean motion of the Moon, is difficult to compute. It is possible to find this derivative with one quadrature from the other derivatives if one takes into account that the Jacobian has to be a symplectic matrix when a canonical set of primary parameters is used.The mean motions of the perigee and node often exhibit the largest discrepancies among the different theories. Therefore it is not too surprising that also their derivatives show significant differences. It is hoped by providing another independent computation of the derivatives by a different method their accuracy can be improved.Proceedings of the Conference on Analytical Methods and Ephemerides: Theory and Observations of the Moon and Planets. Facultés universitaires Notre Dame de la Paix, Namur, Belgium, 28–31 July, 1980.     

An analysis of lunar occultations in the years 1955–1980 using the new lunar ephemeris ELP2000

About 60,000 observations of lunar occultations made during 1955–1980 are analysed using recently-developed semi-analytical solution ELP2000-82 for the Moon's position in order to determine the constants in the lunar theory and to investigate the tidal term in the Moon's mean longitude and the motions of the perigee and node of the lunar orbit. The equinox correction and systematic correction to the fundamental star catalogue and the correction to the datum of the lunar-profile in Watts' charts are also investigated. It is confirmed that the occultation observations do not have inconsistent tidal term with the modern observations and the observed mean motions of the perigee and node coincide with the theoretical ones within the error of observations. Some of the values of the constants in the lunar theory and the equinox correction to the fundamental catalogue FK5 obtained in this paper are significantly different from the values obtained using the Brown's theory. The reason of the difference is almost attributed to the deficiencies in the Brown's theory. The obtained correction to the datum of the lunar-profile in Watts' charts is almost consistent with the results by earlier investigators.     

On the perturbations of a close-Earth satellite due to lunar inequalities

The lunar disturbing function for a close-Earth satellite is expressed as a sum of products of harmonics of the satellite's position and harmonics of the Moon's position, and the latter are expanded about a rotating and precessing elliptic orbit inclined to the ecliptic. The deviations of the Moon from this approximate orbit are computed from Brown's lunar theory andthe perturbations in satellite orbital elements due to these inequalities are derived. Numerical calculations indicate that several perturbations in the position of the satellite's node and perigee have magnitudes on the order of one meter.The author is supported in part by a National Science Foundation Graduate Fellowship.     

The supernova fragmentation model of solar system formation

We have further developed Brown's model of solar system formation. In this model, each fragment of an ejected supernova shell evolves into a separate solar system. Specifically, we have formulated the reverse-flow hypothesis that may be responsible for the inner, earthlike planets. We have written a computer program with which it is possible to calculate mass distributions within a solar nebula. We have found mass distributions similar to our solar system over a wide range of the model parameters.Los Alamos National Laboratory is operated by the University of California for the U.S. Dept. of Energy under contract W-7405-ENG-36.     

Luni-solar perturbations of an Earth satellite

Luni-solar perturbations of the orbit of an artificial Earth satellite are given by modifying the analytical theory of an artificial lunar satellite derived by the author in recent papers. Expressions for the first-order changes, both secular and periodic, in the elements of the geocentric Keplerian orbit of the earth satellite are given, the moon's geocentric orbit, including solar perturbations in it, being found by using Brown's lunar theory.The effects of Sun and Moon on the satellite orbit are described to a high order of accuracy so that the theory may be used for distant earth satellites.     

Modelling the dynamics of superfluid neutron stars

In this brief summary I describe our recent work on superfluid neutron star dynamics. I review results on shear viscosity, hyperon bulk viscosity, vortex mediated mutual friction and the modelling of multifluid systems in general. For each problem I provide a set of questions that need to be addressed by future work.     

The solar neutrino problem

The observed capture rate for solar neutrinos in the ³⁷Cl detector is lower than the predicted capture rate. This discrepancy between theory and observation is known as the ‘solar neutrino problem’. I review the basic elements in this problem: the detector efficiency, the theory of stellar (solar) evolution, the nuclear physics of energy generation, and the uncertainties in the predictions. I also answer the questions of: So What? and What Next?

     

太阳风离子尺度湍流与太阳风加热

太阳风源自太阳大气,在行星际空间传播过程中被持续加热,然而究竟是何种能量加热了太阳风至今未研究清楚.太阳风普遍处于湍动状态,其湍动能量被认为是加热太阳风的重要能源.然而,太阳风湍流通过何种载体、基于何种微观物理机制加热了太阳风尚不明确,这是相关研究的关键问题.将回顾人类对太阳风加热问题的研究历史,着重介绍近年来我国学者在太阳风离子尺度湍流与加热方面取得的研究进展,展望未来在太阳风加热研究中有待解决的科学问题和可能的研究方向.     

Early applications of computer technology to dynamical astronomy

The review traces the progress from the early application of the Hollerith Tabulating Machine to the construction of astronomical tables by interpolation and to the evaluation of Brown's Tables of the Moon by L. J. Comrie in the late 1920's and early 1930's to the introduction of large programmable electronic calculators in the post World War II era. The early application of electromechanical punched-card machines to astronomical problems stemmed from the needs of the national ephemeris offices to evaluate theories of the Sun, Moon and planets and to subtabulate these positions to form the tables of daily values given in the national almanacs. These techniques were quickly applied to other astronomical problems such as the construction of star catalogs, the reduction of astrometric observations and the numerical integration of the equations of motion of objects in the solar system.     

Cosmic dust,planets and related problems

The study of micrometeorites which reach the Earth and of cosmic dust in general in inter-planetary space and in a planet's atmosphere may contribute significantly to the resolution of important astrophysical and geophysical problems, such as the origin and evolution of our solar system and the universe, and the problem of medium range weather forecasting (for about one month), in addition to the practical problem of NASA's “Man in Space” Programme. In this paper, the questions related to the fall of matter of cosmic origin on Earth, a possible mechanism for the capture of micrometeoric particles by the Earth and other planets of the solar system, indicated by the author, will be dealt with.     

Minimum energy configurations in the N-body problem and the celestial mechanics of granular systems

Minimum energy configurations in Celestial Mechanics are investigated. It is shown that this is not a well defined problem for point-mass celestial mechanics but well-posed for finite density distributions. This naturally leads to a granular mechanics extension of usual Celestial Mechanics questions such as relative equilibria and stability. This paper specifically studies and finds all relative equilibria and minimum energy configurations for N?=?1, 2, 3 and develops hypotheses on the relative equilibria and minimum energy configurations for N ? 1 bodies.     

Theorie generale planetaire etendue au cas de la resonance et application au systeme des satellites galileens de Jupiter

We consider a system of planets defined by a given distribution of mean mean motions and masses: we represent the osculating elliptic elements of their heliocentric orbits by quasi-periodic functions of time, through a method adapted to the commensurability case; these functions are the sum of the general solution of a critical system, expressed in long-period terms, and of a particular solution. As in the B. Brown's method (applied to the galilean satellites), the critical system contains the secular terms, the longperiod terms (great inequalities), and the resonant terms; the particular solution consists of short-period terms only, whose amplitude is an explicit function of the solution of the critical system.If all the long-period terms in the critical system are harmonic of one fundamental term, we can perform a simple change of variables which transforms the critical system in an autonomous one, and thus we reduce the resolution to an eigenvalue problem. Applying that to the galilean satellites of Jupiter and neglecting the solar perturbations, we obtain a differential system with constant coefficients, whose linear part concerns all the variables (including the major-axes and the mean longitudes) and gives, as a first approximation, the great inequalities, the free oscillations and the libration; nevertheless this solution agrees already with known results, but should be improved by taking into account the non-linear parts and the solar terms in a new approximation.

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Proceedings of the Conference on Analytical Methods and Ephemerides: Theory and Observations of the Moon and Planets. Facultés universitaires Notre Dame de la Paix, Namur, Belgium, 28–31 July, 1980     

Cosmological magnetic fields: their generation,evolution and observation

We review the possible mechanisms for the generation of cosmological magnetic fields, discuss their evolution in an expanding Universe filled with the cosmic plasma and provide a critical review of the literature on the subject. We put special emphasis on the prospects for observational tests of the proposed cosmological magnetogenesis scenarios using radio and gamma-ray astronomy and ultra-high-energy cosmic rays. We argue that primordial magnetic fields are observationally testable. They lead to magnetic fields in the intergalactic medium with magnetic field strength and correlation length in a well defined range.We also state the unsolved questions in this fascinating open problem of cosmology and propose future observations to address them.     

Hα profiles from electron-heated solar flares

We briefly review the status of models of optical flare heating by electron bombardment. We recompute Brown's (1973a) flare model atmospheres using considerably revised radiative loss rates, based on Canfield's (1974b) method applied to , L, and H^–. Profiles of are computed and compared with observation. The computed profiles agree satisfactorily with those observed during the large 1972 August 7 flare, if spatial and velocity inhomogeneities are assumed. The electron injection rate inferred from is one order of magnitude less than that inferred from hard X-rays, for this event. This may be due to either (1) the neglect of a mechanism that reduces the thick-target electron injection rate or (2) failure to incorporate important radiative loss terms.     

Current state of the problem of solar flares: New observations and new models

A review of current questions related to the problem of large solar flares is given. The basic physical principles applied in numerical simulation of flares are presented and illustrated. The main attention is given to the phenomenon of magnetic reconnection in large-scale current layers at separators of magnetic field in the corona. This phenomenon is demonstrated within the framework of the Rainbow topological model. The model provides the possibility of explaining specific features of large-scale reconnection as a physical process that makes it possible to accumulate large energy in the form of the magnetic energy of current layers before a flare and to quickly transform this energy to the kinetic energy of particles during a flare. The secondary effects in the solar atmosphere caused by energy fluxes from reconnecting current layers are also discussed. These consequences of the primary energy release are responsible for the flare pattern observed in X-ray, optical, UV, and other spectral ranges.     

Spectral theory and stability in astrophysics

This paper is part II of a limited review of the applications of the spectral theory of linear operators in an astrophysical context. A major part of the paper is devoted to describing the results obtained by Dyson and Schutz (1979) for differentially rotating perfect fluid stars. The functional-analytic techniques used and the results so obtained are compared with those in Paper I. As in the case of ideal magnetohydrodynamics, the mathematical structure of the rotating star problem is very rich indeed. Many questions remain unanswered in both areas.