共查询到20条相似文献，搜索用时 15 毫秒
1.
Victor Brumberg 《Celestial Mechanics and Dynamical Astronomy》2007,99(3):245-252
The half-century old idea of Infeld to use the variational principle of the general relativity field equations is reminded
to show that the commonly employed EIH (Einstein–Infeld–Hoffman) equations of motion may be derived from the linearized (weak-field)
metric alone. Based on it, the linearized metric might be sufficient for post-Newtonian celestial mechanics and astrometry
enabling one to derive the post-Newtonian equations of motion and rotation of celestial bodies as well as the post-Newtonian
equations of light propagation within the general relativity framework. 相似文献
2.
3.
Walter Petry 《Astrophysics and Space Science》1994,211(1):71-91
Starting from a previously studied theory of gravitation in flat space-time the post-Newtonian approximation of the gravitational field of an nonstationary spherically symmetric star is derived. To the post-Newtonian order the equations of motion and the conserved total energy of a collapsing star are given. Birkhoff's theorem holds to this accuracy. 相似文献
4.
Demetrios D. Dionysiou 《Astrophysics and Space Science》1986,125(1):115-125
The average loss of energy over one period of the elliptical motion of the two-body system is given, within the quadrupole approximation, by using the relative motion in the post-Newtonian centre of the mass frame. More explicit formulae are derived for the elliptical orbits and detailed results are presented for the circular orbits assuming small orbital velocities compared to the velocity of light. On the other hand, using the defined Lagrangian we give the integrals of motion. 相似文献
5.
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
6.
《Chinese Astronomy and Astrophysics》2007,31(2):192-204
Under the post-Newtonian approximation, the internal and external metrics of a rigidly rotating oblate spheroid filled by a uniform and incompressible perfect fluid are obtained. And the analytic solutions of post-Newtonian metric components are derived by using the series expansion in an ellipsoidal coordinate system. For this specific problem, there are only finite terms remaining in the series expansion, so the obtained results can be used to study particle motion under these metrics. 相似文献
7.
We discuss in detail the general relativistic effect in the X-ray sourcebased navigation for autonomous position determination program (XNAV). By using the post-Newtonian approximate method of the DSX scheme, we calculate the bending of light and the gravitational time delay under the 1PN metric, as well as the gravitational time delay under the 2PN metric, and finally obtain the high-accuracy time equation of light propagation in XNAV. 相似文献
8.
Toshio Fukushima 《Celestial Mechanics and Dynamical Astronomy》1988,44(1-2):61-75
The Fermi coordinate system (or the non-rotating proper reference frame) is studied within the framework of the post-Newtonian approximation of general relativity. First its general functional form is found to consist of three parts; (1) the motion of the space origin of the Fermi coordinate system relative to the background one, (2) the Fermi-Walker tetrad transported along the world line of the space origin, and (3) the spacelike geodesic starting from the space origin. Next, the post-Newtonian expressions of the latter two are obtained under the condition that the first is given. Then the full coordinate transformation formula connecting the Fermi coordinate system to the background one is derived explicitly. The effectiveness of the Fermi coordinate system is discussed and the effective region is found to be a cylinder with the radius of about 0.5 kpc for the Fermi coordinate system comoving with the Earth. The mathematical way to derive the generalized Fermi coordinate system which Ashby and Bertotti defined is also shown. 相似文献
9.
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
10.
本文给出考虑后牛顿(PN)效应的二体问题解所对应的基本关系式,并仿照开普勒(Kepler)运动,给出星历表计算方法和相应的计算公式以及适用于数值研究中的简单形式。 相似文献
11.
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
12.
本文利用解摄动方程的平均值法求得在PPN框架中二体自转对轨道要素产生的后牛顿效应的长期变化影响．利用这一理论对CWCep和DRVul两颗双星中两子星的自转对轨道近星点和平近点角的长期摄动的后牛顿效应做了计算。结果表明：对于两个质量较大快速自转的子星,由此所产生的后牛顿效应的摄动量是不能忽视的。 相似文献
13.
Joseph O’Leary James M. Hill James C. Bennett 《Celestial Mechanics and Dynamical Astronomy》2018,130(7):44
The post-Newtonian approximation for general relativity is widely adopted by the geodesy and astronomy communities. It has been successfully exploited for the inclusion of relativistic effects in practically all geodetic applications and techniques such as satellite/lunar laser ranging and very long baseline interferometry. Presently, the levels of accuracy required in geodetic techniques require that reference frames, planetary and satellite orbits and signal propagation be treated within the post-Newtonian regime. For arbitrary scalar W and vector gravitational potentials \(W^j (j=1,2,3)\), we present a novel derivation of the energy associated with a test particle in the post-Newtonian regime. The integral so obtained appears not to have been given previously in the literature and is deduced through algebraic manipulation on seeking a Jacobi-like integral associated with the standard post-Newtonian equations of motion. The new integral is independently verified through a variational formulation using the post-Newtonian metric components and is subsequently verified by numerical integration of the post-Newtonian equations of motion. 相似文献
14.
On the basis of the results by Huang et al. (1990), this paper further discusses and analyses the four post-Newtonian effects in a near-Earth satellite orbit: the Schwarzschild solution, the post-Newtonian effects of the geodesic precession, the Lense-Thirring precession and the oblateness of the Earth. A full analytical solution to the effects including their direct perturbations and mixed perturbations due to the Newtonian oblateness (J
2) perturbation and the Schwarzschild solution is obtained using the quasi-mean orbital element method analogous to the Kozai's mean orbital element one. Some perturbation properties of the post-Newtonian effects are revealed. The results obtained not only can provide a sound scientific basis for the precise determination of a man-made satellite orbit but also is suitable for similar mechanics systems, such as the motions of planets, asteroids and natural satellites. 相似文献
15.
Relativistic effects and solar oblateness from radar observations of planets and spacecraft 总被引：1，自引：0，他引：1
E. V. Pitjeva 《Astronomy Letters》2005,31(5):340-349
We used more than 250 000 high-precision American and Russian radar observations of the inner planets and spacecraft obtained in the period 1961–2003 to test the relativistic parameters and to estimate the solar oblateness. Our analysis of the observations was based on the EPM ephemerides of the Institute of Applied Astronomy, Russian Academy of Sciences, constructed by the simultaneous numerical integration of the equations of motion for the nine major planets, the Sun, and the Moon in the post-Newtonian approximation. The gravitational noise introduced by asteroids into the orbits of the inner planets was reduced significantly by including 301 large asteroids and the perturbations from the massive ring of small asteroids in the simultaneous integration of the equations of motion. Since the post-Newtonian parameters and the solar oblateness produce various secular and periodic effects in the orbital elements of all planets, these were estimated from the simultaneous solution: the post-Newtonian parameters are β = 1.0000 ± 0.0001 and γ = 0.9999 ± 0.0002, the gravitational quadrupole moment of the Sun is J2 = (1.9 ± 0.3) × 10?7, and the variation of the gravitational constant is ?/G = (?2 ± 5) × 10?14 yr?1. The results obtained show a remarkable correspondence of the planetary motions and the propagation of light to General Relativity and narrow significantly the range of possible values for alternative theories of gravitation. 相似文献
16.
Lin-Sen Li 《Astrophysics and Space Science》2012,340(2):323-330
Perturbative post-Newtonian variations of the standard osculating orbital elements are obtained by using the two-body equations of motion in the parameterized post-Newtonian theoretical framework. The results obtained are applied to the Einstein and Brans–Dicke theories. As a results, the semi-major axis and eccentricity exhibit periodic variation, but no secular changes. The longitude of periastron and mean longitude at epoch experience both secular and periodic shifts. The post-Newtonian effects are calculated and discussed for six extrasolar planets. 相似文献
17.
In this paper we present a second order post-Newtonian approximation to the Hamiltonian of theN-body system. Subsequently we improve the well-known Robertson's formula for the perihelion advancement by a correction term of orderc, wherec
–4 is the velocity of light. 相似文献
18.
从球对称引力场中光子在赤道面上的运动微分方程出发,采用后牛顿近似方法,讨论了Reissner-Nordstr(o|¨)m度规场中雷达回波延迟实验的后后牛顿修正.通过计算给出了后牛顿以及后后牛顿的修正结果,当荷电量Q为零时,该结果适用于电中性天体,其后牛顿部分的修正与经典文献一致.文中采用的近似展开方法同样适用于讨论更高阶的修正.雷达回波的高阶修正对目前展开的高精度空间引力试验有着重要的参考价值. 相似文献
19.
A complement to the the analytical solution given by Damour and Deruelle (D&D) in order to solve the differential equations
that describe the conic-like and rectilinear post-Newtonian two-body problem is presented. We show the geometric relation
between the eccentric and true anomalies for the elliptic-like and hyperbolic-like cases and expressions for their velocities
are obtained. A post-Newtonian version of the Lambert's theorem is shown.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
20.
Yi Xie 《中国天文和天体物理学报》2014,(9)
With the rapid development of techniques for astronomical observations,the precision of measurements has been significantly increasing. Theories describing astronomical relativistic reference systems, which are the foundation for processing and interpreting these data now and in the future, may require extensions to satisfy the needs of these trends. Besides building a framework compatible with alternative theories of gravity and the pursuit of higher order post-Newtonian approximation, it will also be necessary to make the first order post-Newtonian multipole moments of celestial bodies be explicitly expressed in the astronomical relativistic reference systems.This will bring some convenience into modeling the observations and experiments and make it easier to distinguish different contributions in measurements. As a first step,the global solar system reference system is expressed as a multipolar expansion and the post-Newtonian mass and spin moments are shown explicitly in the metric which describes the coordinates of the system. The full expression of the global metric is given. 相似文献