Effects on satellite orbits in the gravitational field of an axisymmetric central body with a mass monopole and arbitrary spin multipole moments

Meichsner, Jan; Söffel, M.

doi:10.1007/s10569-015-9626-3

Cited by 11 publications

(13 citation statements)

References 25 publications

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“…The influence of higher spin-multipole moments onto satellite orbits has been discussed in Meichsner and Soffel (2015). Here, it was shown that˙ l=3 LT is less than 0.02 mas/y and hence negligible as are the contributions from other spin multipoles with l ≥ 2.…”

Section: Satellite Motionmentioning

confidence: 88%

On the usefulness of relativistic space-times for the description of the Earth’s gravitational field

Söffel

Frutos

2016

J Geod

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The usefulness of relativistic space-times for the description of the Earth's gravitational field is investigated. A variety of exact vacuum solutions of Einstein's field equations (Schwarzschild, Erez and Rosen, Gutsunayev and Manko, Hernández-Pastora and Martín, Kerr, Quevedo, and Mashhoon) are investigated in that respect. It is argued that because of their multipole structure and influences from external bodies, all these exact solutions are not really useful for the central problem. Then, approximate space-times resulting from an MPM or post-Newtonian approximation are considered. Only in the DSX formalism that is of the first post-Newtonian order, all aspects of the problem can be tackled: a relativistic description (a) of the Earth's gravity field in a well-defined geocentric reference system (GCRS), (b) of the motion of solar system bodies in a barycentric reference system (BCRS), and (c) of inertial and tidal terms in the geocentric metric describing the external gravitational field. A relativistic SLR theory is also discussed with respect to our central problem. Orders of magnitude of many effects related to the Earth's gravitational field and SLR are given. It is argued that a formalism with accuracies better than of the first post-Newtonian order is not yet available.

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Section: Satellite Motionmentioning

confidence: 88%

On the usefulness of relativistic space-times for the description of the Earth’s gravitational field

Söffel

Frutos

2016

J Geod

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“…Let us consider a single isolated extended rotating body at rest as source of the gravitational field. The gravitomagnetic acceleration experienced by a test particle orbiting it is (Damour, Soffel & Xu 1994;Meichsner & Soffel 2015)…”

Section: Introductionmentioning

confidence: 99%

The post-Newtonian gravitomagnetic spin-octupole moment of an oblate rotating body and its effects on an orbiting test particle; are they measurable in the Solar system?

Iorio

2019

Monthly Notices of the Royal Astronomical Society

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We analytically work out the orbital effects induced by the post-Newtonian gravitomagnetic spin-octupole moment of an extended spheroidal rotating body endowed with angular momentum S and quadrupole mass moment J 2 . Our results, proportional to GS J 2 c −2 , hold for an arbitrary orientation of the body's symmetry axisŜ and a generic orbital configuration of the test particle. Such effects may be measurable, in principle, with a dedicated spacecraft-based mission to Jupiter. For a moderately eccentric and fast path, the gravitomagnetic precessions of the node and the pericentre of a dedicated orbiter could be as large as 400 milliarcseconds per year or even 1, 600−4, 000 milliarcseconds per year depending on the orientation of its orbital plane in space. Numerical simulations of the Earth-probe range-rate signal confirm such expectations since its magnitude reaches the 0.03−0.3 millimetre per second level after just 1 day. The precision of the current two-way Ka-band Doppler measurements of the spacecraft Juno, presently orbiting Jupiter, amounts to 0.003 millimetre per second after 1, 000 seconds. Other general relativistic effects might be measurable, including also those proportional to GMJ 2 c −2 , never put to the test so far. Most of the competing Newtonian signals due to the classical multipoles of the planet's gravity field have quite different temporal signatures with respect to the post-Newtonian

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“…Effects from higher spinmoments with l > 4 are even smaller (see e.g. Meichsner & Soffel 2015 for related material).…”

Section: The Influence Of Spin-dipole Momentsmentioning

confidence: 99%

Advanced relativistic VLBI model for geodesy

Söffel

Kopeikin

Han

2016

J Geod

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Abstract:Our present relativistic part of the geodetic VLBI model for Earthbound antennas is a consensus model which is considered as a standard for processing high-precision VLBI observations. It was created as a compromise between a variety of relativistic VLBI models proposed by different authors as documented in the IERS Conventions 2010. The accuracy of the consensus model is in the picosecond range for the group delay but this is not sufficient for current geodetic pur-poses. This paper provides a fully documented derivation of a new relativistic model having an accuracy substantially higher than one picosecond and based upon a well accepted formalism of relativistic celestial mechanics, astrometry and geodesy. Our new model fully confirms the consensus model at the picosecond level and in several respects goes to a great extent beyond it. More specifically, terms related to the acceleration of the geocenter are considered and kept in the model, the gravitational time-delay due to a massive body (planet, Sun, etc.) with arbitrary mass and spin-multipole moments is derived taking into account the motion of the body, and a new formalism for the time-delay problem of radio sources located at finite distance from VLBI stations is presented. Thus, the paper presents a substantially elaborated theoretical justification of the consensus model and its significant extension that allows researchers to make concrete estimates of the magnitude of residual terms of this model for any conceivable configuration of the source of light, massive bodies, and VLBI stations. The largest terms in the relativistic time delay which can affect the current VLBI observations are from the quadrupole and the angular momentum of the gravitating bodies that are known from the literature. These terms should be included in the new geodetic VLBI model for improving its consistency.

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Effects on satellite orbits in the gravitational field of an axisymmetric central body with a mass monopole and arbitrary spin multipole moments

Cited by 11 publications

References 25 publications

On the usefulness of relativistic space-times for the description of the Earth’s gravitational field

On the usefulness of relativistic space-times for the description of the Earth’s gravitational field

The post-Newtonian gravitomagnetic spin-octupole moment of an oblate rotating body and its effects on an orbiting test particle; are they measurable in the Solar system?

Advanced relativistic VLBI model for geodesy

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