共查询到20条相似文献，搜索用时 31 毫秒
1.
There is a growing population of relativistically relevant minor bodies in the Solar System and a growing population of massive
extrasolar planets with orbits very close to the central star where relativistic effects should have some signature. Our purpose
is to review how general relativity affects the orbital dynamics of the planetary systems and to define a suitable relativistic
correction for Solar System orbital studies when only point masses are considered. Using relativistic formulae for the N body
problem suited for a planetary system given in the literature we present a series of numerical orbital integrations designed
to test the relevance of the effects due to the general theory of relativity in the case of our Solar System. Comparison between
different algorithms for accounting for the relativistic corrections are performed. Relativistic effects generated by the
Sun or by the central star are the most relevant ones and produce evident modifications in the secular dynamics of the inner
Solar System. The Kozai mechanism, for example, is modified due to the relativistic effects on the argument of the perihelion.
Relativistic effects generated by planets instead are of very low relevance but detectable in numerical simulations. 相似文献
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3.
Vladimír Skalský 《Astrophysics and Space Science》2010,330(2):373-398
Assuming that the relativistic universe is homogeneous and isotropic, we can unambiguously determine its model and physical properties, which correspond with the Einstein general theory of relativity (and with its two special partial solutions: Einstein special theory of relativity and Newton gravitation theory), quantum mechanics, and observations, too. 相似文献
4.
Walter Petry 《Astrophysics and Space Science》1991,175(1):1-14
The study of a previously proposed theory of gravitation in flat space-time (Petry, 1981a) is continued. A conservation law for the angular momentum is derived. Additional to the usual form, there must be added a term coming from the spin of the gravitational field. The equations of motion and of spin angular momentum for a spinning test particle in a gravitational field are given. An approximation of the equations of the spin angular momentum in the rest frame of the test particle is studied. For a gyroscope in an orbit of a rotating massive body (e.g., the Earth) the precession of the spin axis agrees with the result of Einstein's general theory of relativity. 相似文献
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6.
Yu. I. Morozov 《Astrophysics and Space Science》1987,133(1):107-148
This paper deals with the representation of relativistic equations of gas dynamics with due regard to the general relativity theory effects in the form accepted and widely applied in the special relativity theory. With this purpose, a strict formal definition of a non-inertial co-moving reference frame without rotation is carried out on the basis of a tetrad formalism by use of the Fermi—Walker rules of transport of 4-frame. The equations of physical kinetics, relativistic collapse, Einstein's equations, equations of relatiivistic radiation gas dynamics for ideal and dissipative gases, Taub's equations for a shock wave, which allow for radiation and electron-positron pairs, are obtained in this reference frame. On the basis of the local Lorentz transformation and the Ricci rotation coefficients, these equations are written in the laboratory reference frame, in order to illustrate the fact that the general relativity effects can be simply taken into account in the equations having a form accepted in the special relativity theory. 相似文献
7.
The paper presents a detailed review of the smooth particle hydrodynamics (SPH) method with particular focus on its astrophysical applications. We start by introducing the basic ideas and concepts and thereby outline all ingredients that are necessary for a practical implementation of the method in a working SPH code. Much of SPH’s success relies on its excellent conservation properties and therefore the numerical conservation of physical invariants receives much attention throughout this review. The self-consistent derivation of the SPH equations from the Lagrangian of an ideal fluid is the common theme of the remainder of the text. We derive a modern, Newtonian SPH formulation from the Lagrangian of an ideal fluid. It accounts for changes of the local resolution lengths which result in corrective, so-called “grad-h-terms”. We extend this strategy to special relativity for which we derive the corresponding grad-h equation set. The variational approach is further applied to a general-relativistic fluid evolving in a fixed, curved background space-time. Particular care is taken to explicitly derive all relevant equations in a coherent way. 相似文献
8.
Harald H. Soleng 《Astrophysics and Space Science》1987,138(1):19-21
The vacuum field equations of the self-creation theory of gravitation are solved for the Robertson-Walker space-time, by using a correspondence to known solutions of general relativity. 相似文献
9.
Walter Petry 《Astrophysics and Space Science》1992,189(1):63-77
The post-Newtonian approximation of the gravitational field of a perfect fluid for a previously stated theory of gravitation in flat space-time is studied. The conservation laws of energy-momentum and angular-momentum are derived and the equivalence of the conservation law of energy-momentum and the equations of motion is shown to the studied accuracy. The equations of motion are stated. All the results of the post-Newtonian approximation of the gravitation theory in flat space-time and of the general theory of relativity, as considered by Will in his famous book, agree to the studied accuracy. 相似文献
10.
Giulia Schettino Daniele Serra Giacomo Tommei Andrea Milani 《Celestial Mechanics and Dynamical Astronomy》2018,130(11):72
The Mercury Orbiter Radio science Experiment (MORE) is one of the experiments on-board the ESA/JAXA BepiColombo mission to Mercury, to be launched in October 2018. Thanks to full on-board and on-ground instrumentation performing very precise tracking from the Earth, MORE will have the chance to determine with very high accuracy the Mercury-centric orbit of the spacecraft and the heliocentric orbit of Mercury. This will allow to undertake an accurate test of relativistic theories of gravitation (relativity experiment), which consists in improving the knowledge of some post-Newtonian and related parameters, whose value is predicted by General Relativity. This paper focuses on two critical aspects of the BepiColombo relativity experiment. First of all, we address the delicate issue of determining the orbits of Mercury and the Earth–Moon barycenter at the level of accuracy required by the purposes of the experiment and we discuss a strategy to cure the rank deficiencies that appear in the problem. Secondly, we introduce and discuss the role of the Solar Lense–Thirring effect in the Mercury orbit determination problem and in the relativistic parameters estimation. 相似文献
11.
K. Shanthi 《Astrophysics and Space Science》1989,162(1):163-165
Explicit vacuum field equations in the general scalar-tensor theory of gravitation proposed by Nordtvedt are obtained with the aid of the most general conformally flat spherically-symmetric static space-time. It is shown that the most general conformally flat spherically-symmetric static solution of Nordtvedt-Barker vacuum field equations is simply the empty flat space-time of general relativity. 相似文献
12.
Walter Petry 《Astrophysics and Space Science》1993,203(1):147-160
For a previously studied theory of gravitation in flat space-time a general formula of the gravitational radiation at large distances from a system of bodies is derived. The calculations are carried out through post-Newtonian order within this theory of gravitation. A more explicit formula is given for a binary system. It agrees with the result of general relativity. 相似文献
13.
Recently Lau & Prokhovnik (1986) have formulated a new scalar-tensor theory of gravitation which reconciles Dirac’s large
numbers hypothesis with Einstein’s theory of general relativity. The present work points out an error in the time-dependent
cosmological term and the scalar potential given by Lau and Prokhovnik. The correct forms for these quantities are derived.
Further, a vacuum Robertson-Walker solution to the generalized field equations is obtained, under an anasatz that we propose,
which illustrates that the theory is, in some sense, incomplete. 相似文献
14.
R. Illge 《Astronomische Nachrichten》1988,309(4):253-257
15.
David F. Roscoe 《Astrophysics and Space Science》1995,227(1-2):119-132
It is shown that global four-momentum conservation provides all the necessary structure toderive a metric gravity theory which conforms to the requirements of the Strong Equivalence Principle (Will, 1981), and which satisfies all empirical tests up to, and including, those derived from the binary pulsar measurements. Significant consequences arising from this theory are: concepts of curved spacetimes become strictly superfluous to the function of describing gravitational physics; gravitational processes become direct particle/particle interactions; these interactions are arbitrated by wave processes of a kind familiar in electromagnetism; gravitational waves carry energy-momentum in the direction of their propogation vector; the essential singularities at gravitational origins, which are features of both Newtonian gravitation and General Relativity, do not exist. 相似文献
16.
The first post-Newtonian approximation of general relativity is used to account for the motion of solar system bodies and near-Earth objects which are slow moving and produce weak gravitational fields. The \(n\)-body relativistic equations of motion are given by the Einstein-Infeld-Hoffmann equations. For \(n=2\), we investigate the associated dynamics of two-body systems in the first post-Newtonian approximation. By direct integration of the associated planar equations of motion, we deduce a new expression that characterises the orbit of test particles in the first post-Newtonian regime generalising the well-known Binet equation for Newtonian mechanics. The expression so obtained does not appear to have been given in the literature and is consistent with classical orbiting theory in the Newtonian limit. Further, the accuracy of the post-Newtonian Binet equation is numerically verified by comparing secular variations of known expression with the full general relativistic orbit equation. 相似文献
17.
Myeong-Gu Park 《Monthly notices of the Royal Astronomical Society》2006,367(4):1739-1745
Radiation interacts with matter via exchange of energy and momentum. When matter is moving with a relativistic velocity or when the background space–time is strongly curved, rigorous relativistic treatment of hydrodynamics and radiative transfer is required. Here, we derive fully general relativistic radiation hydrodynamic equations from a covariant tensor formalism. The equations can be applied to any three-dimensional problems and are rather straightforward to understand compared to the comoving frame-based equations. The current approach is applicable to any space–time or coordinates, but in this work we specifically choose the Schwarzschild space–time to show explicitly how the hydrodynamic and the radiation moment equations are derived. Some important aspects of relativistic radiation hydrodynamics and the difficulty with the radiation moment formalism are discussed as well. 相似文献
18.
Static and spherically-symmetric solutions of the field equations in the bimetric theory of gravitation are obtained for isotropic and anisotropic distributions of matter when the physical metric admits a one-parameter group of conformal motions. The solutions agree with Einstein's general relativity for physical systems comparable to the size of the Universe, such as the solar system. 相似文献
19.
H.-J. Treder 《Astronomische Nachrichten》1974,295(1):1-8
According to the principle of correspondence (in HEISENBERG 's formulation) each general relativistic theory of gravitation must give a NEWTON ian representation for an isotropic cosmos with the ROBERTSON -WALKER metric. Indeed, the FRIEDMANN equations can be interpreted as the expression for the HAMILTON ian H of a closed NEWTON ian system of the cosmic fundamental particles, written in the rest-system of the center of gravity. In this HAMILTON ian H only the relative-coordinates and the relative-velocities of the particles are present and one can write H without absolute quantities but only with MILNE 's relative-quantities. The time-independence of the HAMILTON ian H = 0 is the FRIEDMANN equation. – This NEWTON ian deduction of the FRIEDMANN equation is more general than the relativistic deduction and than MILNE 's deduction for a NEWTON ian fluid, too. In the general NEWTON ian form H the parameter f M of the active mass can be an arbitrary function of the cosmic time t. The choice f = f(t), M = M(t) defines the divers modifications of relativistic cosmology. – In general relativity fM = const and M = const are resulting from EINSTEIN 's equations and from EINSTEIN 's principle of equivalence. 相似文献
20.
V. A. Brumberg 《Celestial Mechanics and Dynamical Astronomy》2004,88(2):209-225
For numerical integration of the geocentric equations of motion of Earth satellites in the general relativity framework one may choose now between rather simple equations involving in their relativistic dynamical part only the Earth-induced terms and very complicated equations taking into account the relativistic third-body action. However, it is possible quite easily to take into account the relativistic indirect third-body perturbations and to neglect much lesser direct third-body perturbations. Such approach is based on the use of the Newtonian third-body perturbations in geocentric variables with expressing them in the relativistic manner in terms of the barycentric arguments. Together with it, to extend the known results for the spheroid model of the Earth, the Earth-induced terms are treated in great detail by including the non-spin part of the Earth vector-potential and the Earth triaxial non-sphericity.This revised version was published online in October 2005 with corrections to the Cover Date. 相似文献