Motion and rotation of celestial bodies in the post-Newtonian approximation

Voinov, A. V.

doi:10.1007/bf01232964

Cited by 14 publications

(7 citation statements)

References 5 publications

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“…In Voinov (1988), andXu (1993) it has been shown that the local reference system (GRS) is physically adequate for modelling rotational motion of a body being a member of an N-body system. From now on, we consider the "nonrotating" reference system (t,x % ) used above to coincide with the GRS.…”

Section: The Post-newtonian Torque and The Bd Momentsmentioning

confidence: 99%

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Angular velocity of rotation of extended bodies in general relativity

Klioner

1996

Symp. - Int. Astron. Union

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Abstract. We consider rotational motion of an arbitrarily composed and shaped, deformable weakly self-gravitating body being a member of a system of Ν arbitrarily composed and shaped, deformable weakly selfgravitating bodies in the post-Newtonian approximation of general relativity. Considering importance of the notion of angular velocity of the body (Earth, pulsar) for adequate modelling of modern astronomical observations, we are aimed at introducing a post-Newtonian-accurate definition of angular velocity. Not attempting to introduce a relativistic notion of rigid body (which is well known to be ill-defined even at the first post-Newtonian approximation) we consider bodies to be deformable and introduce the postNewtonian generalizations of the Tisserand axes and the principal axes of inertia.

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Section: The Post-newtonian Torque and The Bd Momentsmentioning

confidence: 99%

“…However, the first and probably the only paper dealing with rotation of non-rigid bodies in general relativity is Voinov (1988). The principal idea is to consider relativistic effects in internal motions within the body as additional deformations which can be treated in analogy to Newtonian deformations.…”

Section: Introductionmentioning

confidence: 99%

Angular velocity of rotation of extended bodies in general relativity

Klioner

1996

Symp. - Int. Astron. Union

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“…The first attempt to use a version of such a local reference system to study the rotational motion of an extended body has been undertaken by Voinov [8]. Major progress to solve the problem in the Einsteinian post-Newtonian theory was achieved by Damour, Soffel and Xu [2] who used their DSX formalism aimed at constructing the local reference systems and derived the rotational equations of motion of each body of an N-body system with full multipole structure.…”

Section: Introductionmentioning

confidence: 99%

Nordtvedt effect in rotational motion

Söffel

1998

Phys. Rev. D

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Rotational motion of extended celestial bodies is discussed in the framework of the Parametrized Post-Newtonian (PPN) formalism with the two parameters γ and β. A local PPN reference system of a massive extended body being a member of a system of N massive extended bodies is constructed. In the local PPN reference system the external gravitational field manifests itself only in the form of tidal potentials. Rotational equations of motion, which are then derived in the local reference system, reveal a special term in the torque analogous to the Nordtvedt effect in the translational equations of motion: it is proportional to 4β − γ − 3, to the acceleration of the body relative to the global PPN reference system and to some quantity characterizing the distribution of inertial gravitational energy within the body. This term is a direct consequence of the violation of the Strong Equivalence Principle in alternative theories of gravitation.

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“…For instance, Martin et al (1985) and Hellings (1986) have tried, in an essentially heuristic manner, to explicitly take into account the main apparent deformations due to the use of an external coordinate representation. More recently a notable progress in the theory of such local relativistic frames (at the post-Newtonian approximation, relevant to systems of N weakly self-gravitating bodies) has been achieved by Brumberg and Kopejkin (1988a,b) (Kopejkin, 1988;Brumberg, 1990) in a series of publications (see also Voinov, 1988). Their approach combines the usual post-Newtonian-type expansions with the multipole expansion formalisms for internally generated (Thome, 1980;Blanchot andDamour, 1986, 1989) and externally generated (Thorne and Hartle, 1985), gravitational fields, and with asymptotic matching techniques (D'Eath, 1975, Damour, 1983.…”

Section: Introductionmentioning

confidence: 99%

Relativistic Celestial Mechanics and Reference Frames

Damour

Söffel

Chun

1991

International Astronomical Union Colloquium

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A new formalism for treating the relativistic celestial mechanics of systems of N, arbitrarily composed and shaped, weakly self-gravitating, rotating, deformabile bodies is presented. This formalism is aimed at yielding a complete description, at the first post-Newtonian approximation level, of (i) the global dynamics of such N-body systems (“external problem”), (ii) the local gravitational structure of each body (“internal problem”), and, (iii) the way the external and the internal problems fit together (“theory of reference systems”).

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Motion and rotation of celestial bodies in the post-Newtonian approximation

Cited by 14 publications

References 5 publications

Angular velocity of rotation of extended bodies in general relativity

Angular velocity of rotation of extended bodies in general relativity

Nordtvedt effect in rotational motion

Relativistic Celestial Mechanics and Reference Frames

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