Motion Of Celestial Bodies Research Articles

Relativistic aspects of rotational motion of celestial bodies

AbstractRelativistic modelling of rotational motion of extended bodies represents one of the most complicated problems of Applied Relativity. The relativistic reference systems of IAU (2000) give a suitable theoretical framework for such a modelling. Recent developments in the post-Newtonian theory of Earth rotation in the limit of rigidly rotating multipoles are reported below. All components of the theory are summarized and the results are demonstrated. The experience with the relativistic Earth rotation theory can be directly applied to model the rotational motion of other celestial bodies. The high-precision theories of rotation of the Moon, Mars and Mercury can be expected to be of interest in the near future.

Zero initial partial derivatives of satellite orbits with respect to force parameters violate the physics of motion of celestial bodies

Satellite orbits have been routinely used to produce models of the Earth’s gravity field. In connection with such productions, the partial derivatives of a satellite orbit with respect to the force parameters to be determined, namely, the unknown harmonic coefficients of the gravitational model, have been first computed by setting the initial values of partial derivatives to zero. In this note, we first design some simple mathematical examples to show that setting the initial values of partial derivatives to zero is generally erroneous mathematically. We then prove that it is prohibited physically. In other words, setting the initial values of partial derivatives to zero violates the physics of motion of celestial bodies.

EPM ephemerides and relativity

AbstractIn the seventies of the last century the EPM ephemerides (Ephemerides of Planets and the Moon) of IAA RAS originated and have been developed since that time. These ephemerides are based upon relativistic equations of motion of celestial bodies and light rays and upon relativistic time scales. The updated model of EPM2008 includes the new values of planet masses and other constants, the improved dynamical model with adding Trans–Neptunian Objects and the expanded database (1913–2008). More than 260 parameters have been determined while improving the planetary part of EPM2008 to 550000 observations. EPM2008 have been oriented to ICRF by including into the total solution the VLBI data of spacecraft near the planets. The real uncertainty of EPM ephemerides has been checked by comparison with the JPL's DE ephemerides. Some estimates of the post–model parameters have been obtained: |1−β| < 0.0002, |1−γ| < 0.0002, /G = (−5.9±4.4) ⋅ 10−14 per year, the statistic zero corrections to the planet perihelion advances.

A Critical Note on the Guide to the Expression of Uncertainty in Measurement (GUM)

In 1809 Carl Friedrich Gauss' masterpiece “Theoria Motus Corporum Coelestium in sectionibus conicis solem ambientium” on the motion of celestial bodies was published. This book contains also a first version of the famous error propagation formula, which is still the basis of modern metrology and of any relevant national and international standard. Gauss' ideas are reflected in the GUM, the “Guide to the Expression of Uncertainty in Measurement”, published in 1993 by ISO, which is a key document for national measurement institutes and industrial calibration laboratories for evaluating uncertainty in the output of a measurement system. Uncertainty constitutes the main problem of any measurement theory. Because uncertainty is investigated in stochastics, any serious measurement theory should necessarily take into account the state of the art in stochastics. Stochastics was initiated by Jakob Bernoulli in his masterpiece “Ars conjectandi”, which appeared posthumously in 1713, i. e., about 100 years before Gauss established the basis of metrology. The difference between Jakob Bernoulli and Carl Friedrich Gauss is the following: Bernoulli aimed at quantifying and measuring uncertainty, while Gauss aimed at quantifying and measuring a measurement error. In this paper a modern measurement theory based on stochastics is briefly outlined. Subsequently, the antiquated concepts and methods as recommended in the GUM, which go back to the early 19th century, are discussed and their weaknesses are listed.

A multidimensional analysis and the chronologic structure of the Earth’s geodynamic activity

An attempt has been undertaken to examine time series of volcanic and seismic events in a multidimensional reference system related to the parameters of the Earth’s orbital motion. Volcanic eruptions and strong (M > 5) earthquakes (a sample from the USGS/NEIC seismological database: Significant Worldwide Earthquakes) [18] were analyzed within the fields of the JPL Planetary and Lunar Ephemerides, (DE-406) astronomical indicators [19]: the Earth-Moon distance, Earth-Sun distance, ecliptic latitude of the Moon, and the differences between the geocentric longitudes of the Moon and Sun, Venus and Sun, and Mars and Sun. Distribution spectra were obtained and normalization was performed taking the nonuniform motion of celestial bodies into consideration, and the values of multidimensional diurnal probability were calculated. As a result, the statistically reliable drift in the distribution of geoevents was calculated relative to the duration of the intervals of multidimensional diurnal probability, which indicates distribution regions where more geoevents can take place during shorter intervals (and vice versa). Linear relationships between the multidimensional diurnal probability and diurnal probability of geoevents were found. All these results and the astronomic ephemerides were used as a base for computing the probabilities of volcanic and seismic activity of the Earth for the period of 2005–2007. The spatial structure of volcanic and seismic processes was examined, which allowed the revelation of probabilistic parameters of the spatiotemporal structure of Earth’s geodynamic activity and outlining an approximate algorithm for its monitoring.

THE APPLICATION OF VIRTUAL REALITY IN ASTRONOMY EDUCATION

In this paper, we study the virtual reality technologies for developing a virtual astronomical museum, which can be applied in astronomy education. The museum contains four exhibition areas of the following topics: Astronomy Technologies, the Moon and Earth, the Solar System, and Observing Constellations. We developed the virtual scenes of astronomical museum, including the domed building, exhibition areas, displayed objects, and several models to simulate the motion of celestial bodies. Users can operate the models by setting time, position, and speed to observe the changes of astronomical phenomena. In virtual astronomical museum, we can see a lot of exhibits as if visiting a real astronomical museum. It is accessible through network and highly interactive with 3D visual effects. In addition, learning on the virtual website is not limited by time or space. Therefore, it is a very useful tool to enhance astronomical knowledge.

Gravitational–tidal evolution of planetary subsystems of the Sun

The results of some of our work and new research in which the motion of celestial bodies is considered to be subject to dissipative interactions is generalized in this article. In a number of problems the interaction of celestial bodies according to the law of universal gravitation is supplemented by a dissipative force. In the framework of this model, the evolution processes are studied, stationary configurations of an n-body systems are found, and their stability is investigated. In other problems the model of the axisymmetric celestial body that consists of a solid core and a viscoelastic mantle is considered. In such a model, the dissipation of energy under deformations is taken into account. The tidal evolution of a planet rotational motion is analysed in detail. Also phase portraits are constructed and an qualitative analysis of the global evolution of the dynamic characteristics of the Sun’s planetary subsystems is presented on the basis of averaged evolution equations.

Hysteresis loops predicted by isoenergy density theory for polycrystals. Part II: cyclic heating and cooling effects predicted from non-equilibrium theory for 6061-T6 aluminum, SAE 4340 steel and Ti–8Al–1Mo–1V titanium cylindrical bars

Mathematical tools and physical models should fit like hand and glove. Traditionally, such an understanding has worked surprisingly well in mechanics and physics. Differential calculus enabled the determination of motion of celestial bodies. Heisenberg's use of Hilbert space applied to calculations in quantum mechanics. These foot steps, however, failed to continue in the field of material science when attempting to address the evolution of material damage. On one hand, the mathematical formulation of the Riemann–Hilbert problem achieved great success for solving macrocrack problems but whether the same tool could be used for lower scale defects seems to be of less concern. This is a surprise because it is not obvious by any means whether microcracks can be distinguished from macrocrack by size difference alone, particularly when they are both treated in a single formulation. There are several issues of the fatigue problem that must be addressed. To begin with, local failure initiating near a surface should be distinguished from global failure that correspond to separation of a specimen into two or more pieces. The interim stages of initiation and termination would depend on the ductility and brittleness of the material in addition to the history of cyclic loading. Three different materials 6061-T6 aluminum, SAE 4340 steel and Ti–8Al–1Mo–1V titanium will therefore be analyzed to show how their uniaxial properties would compare with the dissipation energy density functions and oscillation in temperature. Hysteresis loops for the local material points are determined. Their averages for the ASTM standard hour-glass specimen are then found. They give the global hysteresis loops corresponding to measurements from the uniaxial tests. The local dissipative energy density loops represent the irreversible nature of the materials are also taken into consideration. They are calculated for the soft aluminum and the hard titanium with steel being in between. Obtained also are the cyclic cooling and heating characteristics of the material under fatigue; they fluctuate about the ambient temperature. The H -function designating the order and disorder of the fatigue process is also found to be oscillatory in character. Unlike entropy, it is not non-increasing or non-decreasing. It can change sign in a given process. This implies that the order of a system can be enhanced and then impeded or vice versa. Such a behavior is shown to prevail during the initial stage of the fatigue.

Asymptotic theory of the motion of celestial bodies in the atmosphere

At a large entry velocity of celestial bodies into the atmosphere, a mass-loss parameter β=σVe2/2 (σ is the ablation coefficient) is very large. So, for some versions of the 1908 Tunguska event parameters, one has β=5–25. In the case of comet Shoemaker-Levy 9 fragments entry into Jupiter, the parameter β is 75–100. Some stations of European Fireball Network have observed at May, June 1997 two bolides, for which β was estimated as 150 and 40. Therefore, the limiting theory for meteoroid motion in the atmosphere is developed. The solution of meteoric physics equations depends on two (single body) or three parameters (splitting body), and β is among them as argument of some special functions. The asymptotic limit of the solution at β⪢1 looks like changing meteoroid mass from entry value to zero at constant velocity. This limit for a single body was compared with observations in May, June 1997 in Czech Republic, and good agreement was achieved. Ultimate models with fragmentation are necessary to understand some real features of large-scale events. So, results of this work show that for large bodies such as Tunguska space body and comet Shoemaker-Levy 9 fragments, we should discuss a motion of gaseous volume after finishing ablation at almost entry velocity. Probably, the big forest fall in 1908 in Siberia and plumes in 1994 on Jupiter are results of such gas jets.

Stochastic Correlation Models for the Motion of the Pole of the Deformable Earth

In this paper we develop an unconventional approach to investigations of possible stochastic phenomena in the rotational motions of celestial bodies. The approach is based on special equations of the rotational motion, which represent a three-dimensional nonlinear system of differential equations with random parameters.

Essays on the Motion of Celestial Bodies

Essays on the Motion of Celestial Bodies

A religião como fundamento da reflexão filosófica e como meio de ação política nas Leis de Platão

No décimo livro das Leis, Platão inaugura uma nova maneira de falar da divindade, mas o faz a contragosto e endereçando-se a uma minoria de indivíduos, a saber, jovens ateus que não foram convencidos pelos mitos que lhes foram contados desde a infância nem pelas práticas cultuais que testemunharam. Não podendo invocar a religião tradicional, Platão tenta dar uma demonstração da existência dos deuses, bem como de sua providência e incorruptibilidade, tomando por testemunho a regularidade e a permanência do movimento dos corpos celestes. Esse novo tipo de discurso sobre os deuses, que, mesmo se fundando sobre a religião tradicional, procura superá-la através da reflexão filosófica, é destinado a dar uma base ao governo da sociedade em seu conjunto.

Egypt’s Role in the Origins of Science: An Essay in Aligning Conditions, Evidence and Interpretations

The author argues that the evidence of observation in Egyptian third millennium BCE medicine and astronomy should allow ancient Egypt an important place in the history of science. The argument is primarily based on the absence of evidence of scientific observation in Mesopotamia preceding the Egyptian material, which renders the Egyptian observations of the movements of celestial bodies and trauma the earliest signs of science. While assigning “predictions” and “mathematical astronomy” a more important place, Assyriologists also date what they can document to long after the Egyptian observations and predictions, highlighting the chronological precedence of Egypt. Furthermore, the author stresses a complicated discourse involving the exchange of ideas that was ultimately stymied by the growing importance of religion and magic. Yet the development was not as linear as the usual versions suggest.

Osculating and Superosculating Intermediate Orbits and their Applications

A method of construction of intermediate orbits for approximating the real motion of celestial bodies in the initial part of trajectory is proposed. The method is based on introducing a fictitious attracting centre with a time-variable gravitational parameter. The variation of thisparameter is assumed to obey the Eddington–Jeans mass-variationlaw. New classes of orbits having first-, second-, and third-order tangency to the perturbed trajectory at the initial instant of time are constructed. For planar motion, the tangency increases by one or two orders. The constructed intermediate orbits approximate the perturbed motion better than the osculating Keplerian orbit and analogous orbits of otherauthors. The applications of the orbits constructed in Encke's methodfor special perturbations and in the procedure for predicting themotion in which the perturbed trajectory is represented by a sequenceof short arcs of the intermediate orbits are suggested.The use of the constructed orbits is especially advantageous in the investigation of motion under the action of large perturbations.

New Numerical/Analytical Methods for Solving Equations of Orbital Motion

New methods are proposed for solving equations of motion of celestial bodies. The methods are based on the use of superosculating orbits with second- and third-order tangency to the trajectory of the real motion of a body. The construction of these orbits is related to the concept of a fictitious attracting center, whose mass varies in accordance with the first Meshchersky law. In the original reference methods, the perturbed trajectory is represented by a sequence of small arcs of superosculating orbits. The order of accuracy of the reference methods coincides with the order of tangency of the superosculating orbit used in calculations. Using Runge's rule and Richardson's extrapolation scheme leads to the methods of higher order. The efficiency of the new methods in comparison with the numerical integration of equations of motion based on the well-known fourth- and seventh-order Runge–Kutta–Fehlberg methods is illustrated by examples of the calculation of perturbed orbits of some asteroids.

Stability of the relative equilibria in the generalized J2 problem

For a large class of concrete astronomical situations, the motion of celestial bodies is modelled by dynamical systems associated to a potential function ?/r + ?U (r = distance between particles, ? = real constant, ? = real small parameter, U = perturbing potential). In this paper the nonlinear stability of the relative equilibrium orbits corresponding to such a potential is being investigated using a less usual method, which combines a block diagonalization technique with the reduction procedure. The test points out certain nonlinearly stable orbits, and is inconclusive for the remaining equilibria. The latter ones are treated via linearization; all of them prove instability. The nonlinearly stable orbits remain stable under any perturbation that preserves the conserved momentum.

Regularization of Equations of Motion of Celestial Bodies. 2. Correction of the KS-Coordinate System in Numerical Integration

The idea of using various L-matrices in numerical integration of the regular equations, which describe the motion of small bodies of the Solar System, is developed. The problem of the optimal position of the radius vector and velocity at numerical integration in the KS-coordinate system is posed. The solution of this problem, which reduces the number of calculations of the vector of perturbing accelerations, is given. The transformation providing this optimal solution is suggested, and the results of numerical integration are given.

Rotational Motion of Celestial Bodies in the Relativistic Framework

There are several important reasons to consider relativistic effects in rotational motion of celestial bodies. General Relativity is now recommended by the International Astronomical Union and International Union of Geodesy and Geophysics as a theoretical framework for modeling of high-precision observational data. On the other hand, various geodynamical observations provide data which are widely used for testing General Relativity itself.In Newtonian mechanics it is well known how to describe rotational motion of an extended body. In General Relativity this is a rather subtle issue. The concept of a precessing extended rigid body in general relativity encounters fundamental difficulties and cannot be introduced even in the first post-Newtonian approximation. From a practical point of view, however, the rotational motion of the Earth even at the Newtonian level is defined operationally through the time-dependence of geocentric quasi-inertial coordinates of observing sites. An analogous operational definition can be applied in general relativity. To this end, we need a set of physically adequate reference systems.

Symmetric Multistep Methods Revisited: II. Numerical Experiments

AbstractBy using the stability condition and general formulas developed by Fukushima (1998 = Paper I) we discovered that, just as in the case of the explicit symmetric multistep methods (Quinlan and Tremaine, 1990), when integrating orbital motions of celestial bodies, the implicit symmetric multistep methods used in the predictor-corrector manner lead to integration errors in position which grow linearly with the integration time if the stepsizes adopted are sufficiently small and if the number of corrections is sufficiently large, say two or three. We confirmed also that the symmetric methods (explicit or implicit) would produce the stepsize-dependent instabilities/resonances, which was discovered by A. Toomre in 1991 and confirmed by G.D. Quinlan for some high order explicit methods. Although the implicit methods require twice or more computational time for the same stepsize than the explicit symmetric ones do, they seem to be preferable since they reduce these undesirable features significantly.

Newcomb's Paradox Realized with Backward Causation

In order to refute the widely held belief that the game known as 'Newcomb's paradox' is physically nonsensical and impossible to imagine (e.g. because it involves backward causation), I tell a story in which the game is realized in a classical, deterministic universe in a physically plausible way. The predictor is a collection of beings which are by many orders of magnitude smaller than the player and which can, with their exquisite measurement techniques, observe the particles in the player's body so accurately that they can predict his choice (in much the same way as we can predict the motion of celestial bodies). I argue that the player, by choosing whether to take only one box or both boxes, influences whether or not, in the past, the predictor put a million pounds into the second box. Yet, I establish that no causal paradox can arise in this set-up.