scholarly journals A GRAVITOMAGNETIC EFFECT ON THE ORBIT OF A TEST BODY DUE TO THE EARTH'S VARIABLE ANGULAR MOMENTUM

2002 ◽  
Vol 11 (05) ◽  
pp. 781-787 ◽  
Author(s):  
LORENZO IORIO
Keyword(s):  
Angular Momentum ◽  
Test Particle ◽  
Equations Of Motion ◽  
Time Derivative ◽  
Slow Motion ◽  
Weak Field ◽  
Test Body ◽  
Angular Velocity Vector ◽  
Motion Approximation ◽  
General Relativistic

The well known general relativistic Lense–Thirring drag of the orbit of a test particle in the stationary field of a central slowly rotating body is generated, in the weak-field and slow-motion approximation of General Relativity, by a gravitomagnetic Lorentz-like acceleration in the equations of motion of the test particle. In it the gravitomagnetic field is due to the central body's angular momentum supposed to be constant. In the context of the gravitational analogue of the Larmor theorem, such acceleration looks like a Coriolis inertial term in an accelerated frame. In this paper the effect of the variation in time of the central body's angular momentum on the orbit of a test mass is considered. It can be shown that it is analogue to the inertial acceleration due to the time derivative of the angular velocity vector of an accelerated frame. The possibility of detecting such effect in the gravitational field of the Earth with LAGEOS-like satellites is investigated. It turns out that the orbital effects are far too small to be measured.

scholarly journals A Post-Newtonian Gravitomagnetic Effect on the Orbital Motion of a Test Particle around Its Primary Induced by the Spin of a Distant Third Body

Universe ◽  
2019 ◽  
Vol 5 (4) ◽  
pp. 87
Author(s):  
Lorenzo Iorio
Keyword(s):  
Angular Momentum ◽  
Test Particle ◽  
Equations Of Motion ◽  
Body System ◽  
Long Term Effects ◽  
Body Effect ◽  
Angular Momenta ◽  
General Relativistic ◽  
Range Rate

We study a general relativistic gravitomagnetic 3-body effect induced by the spin angular momentum S X of a rotating mass M X orbited at distance r X by a local gravitationally bound restricted two-body system S of size r ≪ r X consisting of a test particle revolving around a massive body M. At the lowest post-Newtonian order, we analytically work out the doubly averaged rates of change of the Keplerian orbital elements of the test particle by finding non-vanishing long-term effects for the inclination I, the node Ω and the pericenter ω . Such theoretical results are confirmed by a numerical integration of the equations of motion for a fictitious 3-body system. We numerically calculate the magnitudes of the post-Newtonian gravitomagnetic 3-body precessions for some astronomical scenarios in our solar system. For putative man-made orbiters of the natural moons Enceladus and Europa in the external fields of Saturn and Jupiter, the relativistic precessions due to the angular momenta of the gaseous giant planets can be as large as ≃10 − 50 milliarcseconds per year (mas year−1). A preliminary numerical simulation shows that, for certain orbital configurations of a hypothetical Europa orbiter, its range-rate signal Δ ρ ˙ can become larger than the current Doppler accuracy of the existing spacecraft Juno at Jupiter, i.e., σ ρ ˙ = 0.015 mm s−1, after 1 d. The effects induced by the Sun’s angular momentum on artificial probes of Mercury and the Earth are at the level of ≃ 1 − 0.1 microarcseconds per year (μas year −1).

scholarly journals Analytic approximations in GR and gravitational waves

2019 ◽  
Vol 28 (06) ◽  
pp. 1930011 ◽  
Author(s):  
Luc Blanchet
Keyword(s):  
Binary Systems ◽  
State Of The Art ◽  
Equations Of Motion ◽  
Slow Motion ◽  
Weak Field ◽  
Analytic Approximation ◽  
Compact Binary ◽  
Recent Developments ◽  
Motion Approximation ◽  
Self Force

Analytic approximation methods in general relativity play a very important role when analyzing the gravitational wave signals recently discovered by the LIGO and Virgo detectors. In this contribution, we present the state of the art and some recent developments in the famous post-Newtonian (PN) or slow-motion approximation, which has successfully computed the equations of motion and the early inspiral phase of compact binary systems. We discuss also some interesting interfaces between the PN and the gravitational self-force (GSF) approach based on black-hole perturbation theory, and between PN and the post-Minkowskian (PM) approximation, namely a nonlinearity expansion valid for weak field and possibly fast-moving sources.

scholarly journals PHENOMENOLOGICAL CONSTRAINTS ON THE KEHAGIAS–SFETSOS SOLUTION IN THE HOŘAVA–LIFSHITZ GRAVITY FROM SOLAR SYSTEM ORBITAL MOTIONS

2010 ◽  
Vol 25 (29) ◽  
pp. 5399-5408 ◽  
Author(s):  
L. IORIO ◽  
M. L. RUGGIERO
Keyword(s):  
General Relativity ◽  
Black Hole ◽  
Solar System ◽  
Slow Motion ◽  
Analytical Form ◽  
Weak Field ◽  
Schwarzschild Black Hole ◽  
Anomalous Acceleration ◽  
Motion Approximation ◽  
General Relativistic

We focus on Hořava–Lifshitz (HL) theory of gravity, and, in particular, on the Kehagias and Sfetsos's solution that is the analog of Schwarzschild black hole of General Relativity. In the weak-field and slow-motion approximation, we analytically work out the secular precession of the longitude of the pericentre ϖ of a test particle induced by this solution. Its analytical form is different from that of the general relativistic Einstein's pericentre precession. Then, we compare it to the latest determinations of the corrections [Formula: see text] to the standard Newtonian/Einsteinian planetary perihelion precessions recently estimated by E. V. Pitjeva with the EPM2008 ephemerides. It turns out that the planets of the solar system, taken singularly one at a time, allow one to put lower bounds on the adimensional HL parameter ψ0 of the order of 10-12(Mercury)-10-24 (Pluto). They are not able to account for the Pioneer anomalous acceleration for r > 20 AU.

scholarly journals The Gravitomagnetism in the Solar System

2017 ◽  
Vol 45 ◽  
pp. 1760052
Author(s):  
Flavia Rocha ◽  
Manuel Malheiro ◽  
Rubens Marinho
Keyword(s):  
Mass Density ◽  
Slow Motion ◽  
Weak Field ◽  
Einstein Equations ◽  
Dipole Potential ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Perihelion Advance ◽  
Motion Approximation

In 1918, Joseph Lense and Hans Thirring discovered the gravitomagnetic (GM) effect of Einstein field equations in weak field and slow motion approximation. They showed that Einstein equations in this approximation can be written as in the same form as Maxwell’s equation for electromagnetism. In these equations the charge and electric current are replaced by the mass density and the mass current. Thus, the gravitomagnetism formalism in astrophysical system is used with the mass assuming the role of the charge. In this work, we present the deduction of gravitoelectromagnetic equations and the analogue of the Lorentz force in the gravitomagnetism. We also discuss the problem of Mercury’s perihelion advance orbit, we propose solutions using GM formalism using a dipole-dipole potential for the Sun-Planet interaction.

scholarly journals A Note on the Gravitoelectromagnetic Analogy

Universe ◽  
2021 ◽  
Vol 7 (11) ◽  
pp. 451
Author(s):  
Matteo Luca Ruggiero
Keyword(s):  
Slow Motion ◽  
Weak Field ◽  
Einstein’S Equations ◽  
Einstein's Equations ◽  
Gravitational Effects ◽  
Force Equation ◽  
Test Particles ◽  
Motion Approximation ◽  
Stationary Conditions ◽  
Definition Of

We discuss the linear gravitoelectromagnetic approach used to solve Einstein’s equations in the weak-field and slow-motion approximation, which is a powerful tool to explain, by analogy with electromagnetism, several gravitational effects in the solar system, where the approximation holds true. In particular, we discuss the analogy, according to which Einstein’s equations can be written as Maxwell-like equations, and focus on the definition of the gravitoelectromagnetic fields in non-stationary conditions. Furthermore, we examine to what extent, starting from a given solution of Einstein’s equations, gravitoelectromagnetic fields can be used to describe the motion of test particles using a Lorentz-like force equation.

scholarly journals Nonlocal Gravitomagnetism

Universe ◽  
2019 ◽  
Vol 5 (9) ◽  
pp. 195 ◽  
Author(s):  
Mashhoon ◽  
Hehl
Keyword(s):  
Slow Motion ◽  
Weak Field ◽  
Relativity Theory ◽  
Current Status ◽  
General Relativity Theory ◽  
Differential Field ◽  
Gravitomagnetic Field ◽  
Motion Approximation ◽  
Theory Of Gravitation ◽  
Stationary Gravitational Field

We briefly review the current status of nonlocal gravity (NLG), which is a classical nonlocalgeneralization of Einstein’s theory of gravitation based on a certain analogy with the nonlocalelectrodynamics of media. Nonlocal gravity thus involves integro-differential field equationsand a causal constitutive kernel that should ultimately be determined from observational data.We consider the stationary gravitational field of an isolated rotating astronomical source in the linearapproximation of nonlocal gravity. In this weak-field and slow-motion approximation of NLG,we describe the gravitomagnetic field associated with the rotating source and compare our resultswith gravitoelectromagnetism (GEM) of the standard general relativity theory. Moreover, we brieflystudy the energy-momentum content of the GEM field in nonlocal gravity.

Relation between mass and angular momentum for a covariant charge distribution

2019 ◽  
Vol 32 (4) ◽  
pp. 477-479
Author(s):  
John French
Keyword(s):  
Angular Momentum ◽  
Charge Distribution ◽  
Rest Frame ◽  
Proper Time ◽  
Equations Of Motion ◽  
Time Derivative

A relation is found between the proper time derivative of mass and angular momentum for a covariant charge distribution. This is based on the rest frame equations of motion of a relativistic rotating charge distribution.

Beyond the Schwarzschild Metric

2018 ◽  
Author(s):  
David M. Wittman
Keyword(s):  
Black Holes ◽  
General Relativity ◽  
Gravitational Waves ◽  
Test Particle ◽  
Direct Detection ◽  
Relativistic Effects ◽  
Big Bang ◽  
Clusters Of Galaxies ◽  
General Relativistic ◽  
The Universe

General relativity explains much more than the spacetime around static spherical masses.We briefly assess general relativity in the larger context of physical theories, then explore various general relativistic effects that have no Newtonian analog. First, source massmotion gives rise to gravitomagnetic effects on test particles.These effects also depend on the velocity of the test particle, which has substantial implications for orbits around black holes to be further explored in Chapter 20. Second, any changes in the sourcemass ripple outward as gravitational waves, and we tell the century‐long story from the prediction of gravitational waves to their first direct detection in 2015. Third, the deflection of light by galaxies and clusters of galaxies allows us to map the amount and distribution of mass in the universe in astonishing detail. Finally, general relativity enables modeling the universe as a whole, and we explore the resulting Big Bang cosmology.

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