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1.
Recently we (Roy and Rana, 1990a) critically examined the self-consistency of the EIH equations of motion. A static spherically symmetric body as was pointed out there may not appear as a point mass with all its mass concentrated at its centre to a particle placed outside the body. An attempt to analyse this aspect further is made here in the context of the Chandrasekhar gauge. A comparison is also made with the general solutions obtained by Schwarzschild in the standard co-ordinates. Certain difficulties still exist. 相似文献
2.
3.
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
4.
Rabindra Nath Das 《Astrophysics and Space Science》1980,71(1):25-35
A finite atmosphere having distribution of intensity at both surfaces with definite form of scattering function and source function is considered here. The basic integro-differential equation for the intensity distribution at any optical depth is subjected to the finite Laplace transform to have linear integral equations for the surface quantities under interest. These linear integral equations are transformed into linear singular integral equations by use of the Plemelj's formulae. The solution of these linear singular integral equations are obtained in terms of theX-Y equations of Chandrasekhar by use of the theory of linear singular operators which is applied in Das (1978a). 相似文献
5.
R. A. Krikorian 《Astrophysics》2003,46(4):496-501
It is shown that the equation of motion Du
j/Ds = (e/mc
2)F
ji
u
i , a natural generalization to the curved spacetime of the Heaviside-Lorentz law of ponderomotive force, is equivalent to the metric independent and covariant Van Dantzig's equations of motion dx
j [jpi] = 0 or L
v
p
i = 0, where p
i is the conjugate momentum 4-vector and v a vector determined by the condition p
i
v
i, only with respect to holonomic coordinates. With respect to an anholonomic system, the Heaviside-Lorentz equation is a particular case of the VD equations valid for a privileged class of anholonomic frames, those consisting of orthogonal unit vectors. 相似文献
6.
The comoving-frame equations of radiative transfer and moment equations to accurate terms of all orders inv/c are derived in the modified Lagrangian form. The equations exactly describe the interaction of radiation with matter in a relativistically moving medium in flat or curved spacetime. Two specialized sets of equations are presented: (1) the equation of radiative transfer and moment equations accurate to terms of second order (v
2/c
2), and (2) the transfer equation and moment equations for a radial flow in curved spacetime with the Schwarzschild-type metric. 相似文献
7.
David Parry Rubincam 《Celestial Mechanics and Dynamical Astronomy》1977,15(1):21-33
The motion of a satellite with negligible mass in the Schwarzschild metric is treated as a problem in Newtonian physics. The relativistic equations of motion are formally identical with those of the Newtonian case of a particle moving in the ordinary inverse-square law field acted upon by a disturbing function which varies asr ?3. Accordingly, the relativistic motion is treated with the methods of celestial mechanics. The disturbing function is expressed in terms of the Keplerian elements of the orbit and substituted into Lagrange's planetary equations. Integration of the equations shows that a typical Earth satellite with small orbital eccentricity is displaced by about 17 cm from its unperturbed position after a single orbit, while the periodic displacement over the orbit reaches a maximum of about 3 cm. Application of the equations to the planet Mercury gives the advance of the perihelion and a total displacement of about 85 km after one orbit, with a maximum periodic displacement of about 13 km. 相似文献
8.
D. Bancelin D. Hestroffer W. Thuillot 《Celestial Mechanics and Dynamical Astronomy》2012,112(2):221-234
The integration of the equations of motion in gravitational dynamical systems—either in our Solar System or for extra-solar
planetary systems—being non integrable in the global case, is usually performed by means of numerical integration. Among the
different numerical techniques available for solving ordinary differential equations, the numerical integration using Lie
series has shown some advantages. In its original form (Hanslmeier and Dvorak, Astron Astrophys 132, 203 1984), it was limited to the N-body problem where only gravitational interactions are taken into account. We present in this paper a generalisation of the
method by deriving an expression of the Lie terms when other major forces are considered. As a matter of fact, previous studies
have been done but only for objects moving under gravitational attraction. If other perturbations are added, the Lie integrator
has to be re-built. In the present work we consider two cases involving position and position-velocity dependent perturbations:
relativistic acceleration in the framework of General Relativity and a simplified force for the Yarkovsky effect. A general
iteration procedure is applied to derive the Lie series to any order and precision. We then give an application to the integration
of the equation of motions for typical Near-Earth objects and planet Mercury. 相似文献
9.
The solution of the Einstein field equations in the case of an infinite, static, uniform distribution of matter lying parallel to thex–y plane is obtained. This metric is equivalent to the uniformly accelerated metric which causes the particles to move with uniform acceleration parallel to thez-axis. 相似文献
10.
Celestial coordinate reference systems in curved space-time 总被引：1，自引：1，他引：0
S. M. Kopejkin 《Celestial Mechanics and Dynamical Astronomy》1988,44(1-2):87-115
11.
G. Ter-Kazarian 《Astrophysics and Space Science》2010,327(1):91-109
We address gravitation and inertia in the framework of a general gauge principle (GGP) which accounts for the gravitation gauge group
G
R
generated by a hidden local internal symmetry implemented on the flat space. Following the method of phenomenological Lagrangians,
we connect the group G
R
to a non-linear realization of the Lie group of the distortion
G
D
of the local internal properties of six-dimensional flat space, M
6, which is assumed as a toy model underlying four-dimensional Minkowski space. We study the geometrical structure of the space
of parameters and derive the Maurer–Cartan’s structure equations. We treat distortion fields as Goldstone fields, to which
the metric and connection are related, and we infer the group invariants and calculate the conserved currents. The agreement
between the proposed gravitational theory and available observational verifications is satisfactory. Unlike the GR, this theory
is free of fictitious forces, which prompts us to address separately the inertia from a novel view point. We construct a relativistic
field theory of inertia, which treats inertia as a distortion of local internal properties of flat space M
2 conducted under the distortion inertial fields. We derive the relativistic law of inertia (RLI) and calculate the inertial force acting on the photon in a gravitating system. In spite of the totally different and
independent physical sources of gravitation and inertia, the RLI furnishes a justification for the introduction of the Principle
of Equivalence. Particular attention is given to the realization of the group G
R
by the hidden local internal symmetry of the abelian group U
loc=U(1)
Y
×diag[SU(2)], implemented on the space M
6. This group has two generators, the third component T
3 of isospin and the hypercharge Y, implying Q
d
=T
3+Y/2, where Q
d
is the distortion charge operator assigning the number −1 to particles, but +1 to anti-particles. This entails two neutral gauge bosons that coupled
to T
3 and Y. We address the rearrangement of the vacuum state in gravity resulting from these ideas. The neutral complex Higgs scalar
breaks the vacuum symmetry leaving the gravitation subgroup intact. The resulting massive distortion field component may cause
an additional change of properties of the spacetime continuum at huge energies above the threshold value. 相似文献
12.
J. A. De Freitas Pacheco 《Astrophysics and Space Science》1984,105(2):393-400
The analysis of a homogeneous sample of 108 Abell clusters has led to an average peculiar velocity for the center of mass motion of these clusters of 610±750 km s–1. From this result, an upper limit for the average mass of the Abell clusters of (1.6±2.4)×1015
M
was obtained under the assumption that the peculiar motion is due to the excess of neighbours with respect to an uniform background. A lower limit of (2.42.9) x 1014
h
-10.4
M
was derived if one assumes that the peculiar velocity results from the mutual acceleration with the nearest neighbour. 相似文献
13.
The analysis of relative motion of two spacecraft in Earth-bound orbits is usually carried out on the basis of simplifying assumptions. In particular, the reference spacecraft is assumed to follow a circular orbit, in which case the equations of relative motion are governed by the well-known Hill–Clohessy–Wiltshire equations. Circular motion is not, however, a solution when the Earth’s flattening is accounted for, except for equatorial orbits, where in any case the acceleration term is not Newtonian. Several attempts have been made to account for the \(J_2\) effects, either by ingeniously taking advantage of their differential effects, or by cleverly introducing ad-hoc terms in the equations of motion on the basis of geometrical analysis of the \(J_2\) perturbing effects. Analysis of relative motion about an unperturbed elliptical orbit is the next step in complexity. Relative motion about a \(J_2\)-perturbed elliptic reference trajectory is clearly a challenging problem, which has received little attention. All these problems are based on either the Hill–Clohessy–Wiltshire equations for circular reference motion, or the de Vries/Tschauner–Hempel equations for elliptical reference motion, which are both approximate versions of the exact equations of relative motion. The main difference between the exact and approximate forms of these equations consists in the expression for the angular velocity and the angular acceleration of the rotating reference frame with respect to an inertial reference frame. The rotating reference frame is invariably taken as the local orbital frame, i.e., the RTN frame generated by the radial, the transverse, and the normal directions along the primary spacecraft orbit. Some authors have tried to account for the non-constant nature of the angular velocity vector, but have limited their correction to a mean motion value consistent with the \(J_2\) perturbation terms. However, the angular velocity vector is also affected in direction, which causes precession of the node and the argument of perigee, i.e., of the entire orbital plane. Here we provide a derivation of the exact equations of relative motion by expressing the angular velocity of the RTN frame in terms of the state vector of the reference spacecraft. As such, these equations are completely general, in the sense that the orbit of the reference spacecraft need only be known through its ephemeris, and therefore subject to any force field whatever. It is also shown that these equations reduce to either the Hill–Clohessy–Wiltshire, or the Tschauner–Hempel equations, depending on the level of approximation. The explicit form of the equations of relative motion with respect to a \(J_2\)-perturbed reference orbit is also introduced. 相似文献
14.
Noether gauge symmetry for F(R) theory of gravity has been explored recently. The fallacy is that, even after setting gauge to vanish, the form of F(R)∝R n (where n≠1 is arbitrary) obtained in the process, has been claimed to be an outcome of gauge Noether symmetry. On the contrary, earlier works proved that any nonlinear form other than $F(R) \propto R^{\frac{3}{2}}$ is obscure. Here, we show that, setting gauge term zero, Noether equations are satisfied only for n=2, which again does not satisfy the field equations. Thus, as noticed earlier, the only form that Noether symmetry admits is $F(R) \propto R^{\frac{3}{2}}$ . Noether symmetry with non-zero gauge has also been studied explicitly here, to show that it does not produce anything new. 相似文献
15.
M. Farasat Shamir 《Astrophysics and Space Science》2010,330(1):183-189
The modified theories of gravity, especially the f(R) gravity, have attracted much attention in the last decade. In this context, we study the exact vacuum solutions of Bianchi
type I, III and Kantowski-Sachs spacetimes in the metric version of f(R) gravity. The field equations are solved by taking expansion scalar θ proportional to shear scalar σ which gives A=B
n
, where A and B are the metric coefficients. The physical behavior of the solutions has been discussed using some physical quantities. Also,
the function of the Ricci scalar is evaluated in each case. 相似文献
16.
Numerical integration of particle trajectories is performed to evaluate the statistical acceleration coefficients D
TT for 1 to 100 MeV protons in a solar wind corotating interaction region (CIR) seen at 2.5 and 5.0 AU. Acceleration is followed in the solar wind reference frame and is due to random wave-particle interactions and to random drift motion in moderate scale field gradients. D
TT due to the first effect reaches a peak value of 4 × 10 –7 MeV2 s–1 post shock at 10 MeV at 2.5 AU consistent with estimates based both upon cyclotron resonance and transit time damping theory. D
TT from the second effect is less well established but is of the order of 10–7 MeV2 s–1 at 10 MeV, 5 AU. A comparison is made between the time constant for statistical acceleration within this CIR and estimates for diffuse shock acceleration and adiabatic deceleration. All three time constants are of the same order, but deceleration is faster than shock acceleration which in turn is faster than statistical acceleration. 相似文献
17.
V. A. Shor Yu. A. Chernetenko O. M. Kochetova N. B. Zheleznov 《Solar System Research》2012,46(2):119-129
In October 2009, a new set of optical observations of Apophis, a potentially hazardous asteroid, was published. These data
have significantly expanded the interval of observations and their total number. In the article we compare the results of
refinement of Apophis’ orbit made at the Jet Propulsion Laboratory (JPL, United States), the University of Pisa (Italy), and
the Institute of Applied Astronomy (IAA) of the Russian Academy of Sciences with consideration for new observations. New orbits
lead to a significant decrease in the probability of Apophis’ collision with the Earth in 2036. As a result of processing
a large number of observations of asteroids approaching the Earth and main belt asteroids less than 40 km in size, with a
large number of optical and, in many cases, radar observations in different oppositions, one of the authors revealed that
additional acceleration affects their motion. This acceleration can be represented by the transversal component A
2 in the orbital coordinate system. The presence of this acceleration can be interpreted as the Yarkovsky effect. The statistical
properties of distribution of A
2 for asteroids, for which it is determined quite reliably, evidence in favor of this interpretation. The value of additional
acceleration for bodies the size of Apophis falls in the range ±10−13 AU/day2. In this paper we have calculated the probability of Apophis colliding with the Earth in 2036 at different values of the
transversal component of additional acceleration A
2. For the resulting points, a plot of the probability of the collision against the A
2 value has been constructed. At A
2 = −8.748 × 10−14 AU/day2 (and zero values of the radial A
1 and normal A
3 components) the nominal solution for Apophis’ orbit on April 13, 2029, is only 90 m from the middle of a “keyhole” 600 m
in width, which leads to a collision of Apophis with the Earth in 2036. Since the scattering ellipse in the target plane in
2029 significantly overlaps the keyhole, the probability of collision at the given additional acceleration value is 0.0022.
This result has been verified by the Monte Carlo method. Tests of 10000 random sets of orbital elements, which were found
taking into account their correlation, have shown that 22 cases have resulted in virtual asteroids colliding with Earth in
2036. A plot of the probability of the collision against the value of A
2 has been constructed. 相似文献
18.
Rabindra Nath Das 《Astrophysics and Space Science》1981,76(2):441-463
In this paper we develop a new exact method combined with finite Laplace transform and theory of linear singular operators to obtain a solution of transport equation in finite plane-parallel steady-state scattering atmosphere both for angular distribution of radiation from the bounding faces of the atmosphere and for intensity of radiation at any depth of the atmosphere. The emergent intensity of radiation from the bounding faces are determined from simultaneous linear integral equations of the emergent intensity of radiation in terms ofX andY equations of Chandrasekhar. The intensity of radiation at any optical depth for a positive and negative direction parameter is derived by inversion of the Laplace transform in terms of intergrals of the emergent intensity of radiation. A new expression of theX andY equation is also derived for easy numerical computation. This is a new and exact method applicable to all problems in finite plane parallel steady scattering atmosphere. 相似文献
19.
Srinivas N. Mohan Ph.D. Candidate Dept. of Aeronautics Astronautics John V. Lange Benjamin O. Lange 《Celestial Mechanics and Dynamical Astronomy》1972,5(2):157-173
Interaction between orbital motion and attitude libration dynamics of an arbitrary rigid body moving in a central Newtonian field is considered to second order. Advantage is taken of the decoupling between inplane-pitch and roll-yaw out-of-plane motion to restrict the motion to the orbital plane by an appropriate choice ofinitial conditions. An averaged solution to the nonlinear inplane-pitch equations whose accuracy is determined by ignoring terms of order {·G32/a
2, 2,2,G32/a
2} and higher is presented. The results show that the near-resonant motion is characterized by a periodic interchange of energy between the attitude and orbital motion.Associate Professor, Department of Aeronautics and Astronautics. 相似文献
20.
Lars Wåhlin 《Astrophysics and Space Science》1981,74(1):157-167
In a closed expanding-contracting Universe, matter will be subject to an inward acceleration large enough to prevent perpetual expansion. A closed Universe must also perform a simple harmonic motion, which might consist either of one single cycle or of an infinite series of oscillations about a central point. It is the purpose of this study to find the rate ofa
0, the cosmic acceleration, from which the gravitational constantG can be determined. It will be shown from Ampère's equation and Planck's radiation law that it is possible to derivea
0=7.623×10–12 ms–2, a value which also conforms with the uncertainty principle. The relationship betweena
0 and electromagnetic radiation is based on the concept that charges (such as electrons) must emit radiation while accelerating. The rate ofa
0 yields a universal gravitational constant ofG=6.645×10–11 N m2 kg–2. 相似文献