scholarly journals Simulation of general relativistic corrections in long term numerical integrations of planetary orbits

1986 ◽  
Vol 114 ◽  
pp. 105-111
Author(s):  
Anna M. Nobili ◽  
Ian W. Roxburgh
Keyword(s):  
General Relativity ◽  
Solar System ◽  
Computer Time ◽  
Substantial Improvement ◽  
Numerical Integrations ◽  
Planetary Orbits ◽  
General Relativistic ◽  
Theory Of Gravitation ◽  
The Stability

Long term numerical integrations of planetary orbits designed to study the stability of the Solar System over timescales comparable to its age have become very promising thanks to the availability of very powerful computers and to a substantial improvement in our methods of investigating the stability of hierarchical dynamical systems. The stability of such numerical integrations relies on the ability to control all possible sources of error. Among the errors caused by the inadequacy of the physical model are those due to the fact that Newton's theory of gravitation is used instead of general relativity. We show that the secular advance of perihelia predicted by general relativity can be simulated exactly by a 1/r2 perturbing potential with almost negligible additional cost in computer time.

scholarly journals CAN GENERAL RELATIVISTIC DESCRIPTION OF GRAVITATION BE CONSIDERED COMPLETE?

1998 ◽  
Vol 13 (17) ◽  
pp. 1393-1400 ◽  
Author(s):  
D. V. AHLUWALIA
Keyword(s):  
Solar System ◽  
Gravitational Potential ◽  
Invariance Properties ◽  
Planetary Orbits ◽  
Galactic Cluster ◽  
General Relativistic ◽  
Relativistic Description ◽  
Flavor Oscillation ◽  
Weak Fields ◽  
Great Attractor

The local galactic cluster, the Great attractor, embeds us in a dimensionless gravitational potential of about -3×10-5. In the solar system, this potential is constant to about 1 part in 1011. Consequently, planetary orbits, which are determined by the gradient in the gravitational potential, remain unaffected. However, this is not so for the recently introduced flavor-oscillation clocks where the new redshift-inducing phases depend on the gravitational potential itself. On these grounds, and by studying the invariance properties of the gravitational phenomenon in the weak fields, we argue that there exists an element of incompleteness in the general relativistic description of gravitation. An incompleteness-establishing inequality is derived and an experiment is outlined to test the thesis presented.

scholarly journals Perihelion advances for the orbits of Mercury, Earth, and Pluto from extended theory of general relativity (ETGR)

2014 ◽  
Vol 92 (12) ◽  
pp. 1709-1713
Author(s):  
Luis Santiago Ridao ◽  
Rodrigo Avalos ◽  
Martín Daniel De Cicco ◽  
Mauricio Bellini
Keyword(s):  
General Relativity ◽  
Solar System ◽  
Flat Manifold ◽  
Force Component ◽  
Extended Theory ◽  
Ricci Flat ◽  
The Earth ◽  
Canonical Metric ◽  
Planetary Orbits ◽  
Good Agreement

We explore the geodesic movement on an effective four-dimensional hypersurface that is embedded in a five-dimensional Ricci-flat manifold described by a canonical metric, to applying to planetary orbits in our solar system. Some important solutions are given, which provide the standard solutions of general relativity without any extra force component. We study the perihelion advances of Mercury, the Earth, and Pluto using the extended theory of general relativity. Our results are in very good agreement with observations and show how the foliation is determinant to the value of the perihelion’s advances. Possible applications are not limited to these kinds of orbits.

scholarly journals MODIFIED JORDAN–BRANS–DICKE THEORY WITH SCALAR CURRENT AND THE EDDINGTON–ROBERTSON γ-PARAMETER

2012 ◽  
Vol 21 (12) ◽  
pp. 1250084 ◽  
Author(s):  
J. W. MOFFAT ◽  
V. T. TOTH
Keyword(s):  
Scalar Field ◽  
Solar System ◽  
Gravitational Constant ◽  
Weak Equivalence Principle ◽  
A Value ◽  
Specific Choice ◽  
Modified Gravity Theory ◽  
General Relativistic ◽  
Theory Of Gravitation ◽  
Scalar Current

The Jordan–Brans–Dicke theory of gravitation, which promotes the gravitational constant to a dynamical scalar field, predicts a value for the Eddington–Robertson post-Newtonian parameter γ that is significantly different from the general relativistic value of unity. This contradicts precision solar system measurements that tightly constrain γ around 1. We consider a modification of the theory, in which the scalar field is sourced explicitly by matter. We find that this leads to a modified expression for the γ-parameter. In particular, a specific choice of the scalar current yields γ = 1, just as in general relativity, while the weak equivalence principle is also satisfied. This result has important implications for theories that mimic Jordan–Brans–Dicke theory in the post-Newtonian limit in the solar system, including our scalar–tensor–vector gravity (STVG) modified gravity theory (MOG).

On claims that general relativity differs from Newtonian physics for self-gravitating dusts in the low velocity, weak field limit

2015 ◽  
Vol 24 (08) ◽  
pp. 1550065 ◽  
Author(s):  
David R. Rowland
Keyword(s):  
General Relativity ◽  
Solar System ◽  
Relativistic Effects ◽  
Weak Field ◽  
Newtonian Gravity ◽  
Galactic Rotation ◽  
Low Velocity ◽  
Rotation Curves ◽  
Newtonian Physics ◽  
General Relativistic

Galaxy rotation curves are generally analyzed theoretically using Newtonian physics; however, two groups of authors have claimed that for self-gravitating dusts, general relativity (GR) makes significantly different predictions to Newtonian physics, even in the weak field, low velocity limit. One group has even gone so far as to claim that nonlinear general relativistic effects can explain flat galactic rotation curves without the need for cold dark matter. These claims seem to contradict the well-known fact that the weak field, low velocity, low pressure correspondence limit of GR is Newtonian gravity, as evidenced by solar system tests. Both groups of authors claim that their conclusions do not contradict this fact, with Cooperstock and Tieu arguing that the reason is that for the solar system, we have test particles orbiting a central gravitating body, whereas for a galaxy, each star is both an orbiting body and a contributor to the net gravitational field, and this supposedly makes a difference due to nonlinear general relativistic effects. Given the significance of these claims for analyses of the flat galactic rotation curve problem, this article compares the predictions of GR and Newtonian gravity for three cases of self-gravitating dusts for which the exact general relativistic solutions are known. These investigations reveal that GR and Newtonian gravity are in excellent agreement in the appropriate limits, thus supporting the conventional use of Newtonian physics to analyze galactic rotation curves. These analyses also reveal some sources of error in the referred to works.

Simulation model for anomalous precession of the perihelion of mercury's orbit

Open Physics ◽  
2005 ◽  
Vol 3 (1) ◽  
Author(s):  
Abhijit Biswas ◽  
Krishnan Mani
Keyword(s):  
General Relativity ◽  
Simulation Model ◽  
Complete Agreement ◽  
Alternative Theory ◽  
Critical Test ◽  
Perihelion Precession ◽  
General Relativistic ◽  
Controversial Topic ◽  
Theory Of Gravitation ◽  
Relativistic Equations

AbstractThe ‘anomalous perihelion precession’ of Mercury, announced by Le Verrier in 1859, was a highly controversial topic for more than half a century and invoked many alternative theories until 1916, when Einstein presented his theory of general relativity as an alternative theory of gravitation and showed perihelion precession to be one of its potential manifestations. As perihelion precession was a directly derived result of the full General Theory and not just the Equivalence Principle, Einstein viewed it as the most critical test of his theory. This paper presents the computed value of the anomalous perihelion precession of Mercury's orbit using a new relativistic simulation model that employs a simple transformation factor for mass and time, proposed in an earlier paper. This computed value compares well with the prediction of general relativity and is, also, in complete agreement with the observed value within its range of uncertainty. No general relativistic equations have been used for computing the results presented in this paper.

scholarly journals Rotation Sensing Lasers in General Relativity: Some Technical Notes and Current Advances

Universe ◽  
2019 ◽  
Vol 5 (9) ◽  
pp. 190 ◽  
Author(s):  
K. Ulrich Schreiber ◽  
André Gebauer ◽  
Jan Kodet ◽  
Caroline L. Anyi ◽  
Jon-Paul R. Wells
Keyword(s):  
General Relativity ◽  
Rotation Rate ◽  
Ring Laser ◽  
Laser System ◽  
Physical Models ◽  
Current Status ◽  
Rotation Sensing ◽  
General Relativistic ◽  
Laser Gyroscopes

We review the current status of large ring laser gyroscopes having the potential to contributeto terrestrial measurements of general relativistic precessions. At this point in time, although thesedevices possess the raw sensitivity for such a measurement, they remain limited by long-term geometricinstability, detection noise and imperfections in the physical models required to isolate geophysicaleffects. Furthermore, minute non-reciprocal biases provide a null-shift error and therefore no currentlyconstructed laser system meets the requirement of absolute rotation rate sensing. Nevertheless, we are ofthe view that these are surmountable problems and the ability of ring laser gyroscopes to measure lowfrequency to DC signals has vastly increased in the last decade.

scholarly journals On the foundations of general relativistic celestial mechanics

2017 ◽  
Vol 32 (26) ◽  
pp. 1730022 ◽  
Author(s):  
Emmanuele Battista ◽  
Giampiero Esposito ◽  
Simone Dell’Agnello
Keyword(s):  
General Relativity ◽  
Solar System ◽  
Celestial Mechanics ◽  
Body Problem ◽  
Equations Of Motion ◽  
Modern Science ◽  
N Body Problem ◽  
General Relativistic ◽  
New Perspective ◽  
Three Body

Towards the end of nineteenth century, Celestial Mechanics provided the most powerful tools to test Newtonian gravity in the solar system and also led to the discovery of chaos in modern science. Nowadays, in light of general relativity, Celestial Mechanics leads to a new perspective on the motion of satellites and planets. The reader is here introduced to the modern formulation of the problem of motion, following what the leaders in the field have been teaching since the nineties, in particular, the use of a global chart for the overall dynamics of N bodies and N local charts describing the internal dynamics of each body. The next logical step studies in detail how to split the N-body problem into two sub-problems concerning the internal and external dynamics, how to achieve the effacement properties that would allow a decoupling of the two sub-problems, how to define external-potential-effacing coordinates and how to generalize the Newtonian multipole and tidal moments. The review paper ends with an assessment of the nonlocal equations of motion obtained within such a framework, a description of the modifications induced by general relativity on the theoretical analysis of the Newtonian three-body problem, and a mention of the potentialities of the analysis of solar-system metric data carried out with the Planetary Ephemeris Program.

scholarly journals RELATIVISTIC EFFECTS IN EXTRASOLAR PLANETARY SYSTEMS

2006 ◽  
Vol 15 (12) ◽  
pp. 2133-2140 ◽  
Author(s):  
FRED C. ADAMS ◽  
GREGORY LAUGHLIN
Keyword(s):  
General Relativity ◽  
Solar System ◽  
Planetary Systems ◽  
Relativistic Effects ◽  
Interaction Theory ◽  
Orbital Elements ◽  
Secular Resonance ◽  
The Future ◽  
General Relativistic ◽  
Temporal Coverage

This paper considers general relativistic (GR) effects in currently observed extrasolar planetary systems. Although GR corrections are small, they can compete with secular interactions in these systems and thereby play an important role. Specifically, some of the observed multiple planet systems are close to secular resonance, where the dynamics is extremely sensitive to GR corrections, and these systems can be used as laboratories to test general relativity. For the three-planet solar system Upsilon Andromedae, secular interaction theory implies an 80% probability of finding the system with its observed orbital elements if GR is correct, compared with only a 2% probability in the absence of GR. In the future, tighter constraints can be obtained with increased temporal coverage.

scholarly journals Probing general relativity with radar astrometry in the inner solar system

2009 ◽  
Vol 5 (S261) ◽  
pp. 183-188 ◽  
Author(s):  
Jean-Luc Margot ◽  
Jon D. Giorgini
Keyword(s):  
General Relativity ◽  
The Sun ◽  
Solar Oblateness ◽  
Wide Range ◽  
Perihelion Shift ◽  
Orbital Drift ◽  
General Relativistic ◽  
Near Earth Objects ◽  
Dynamical Measurement

AbstractWe describe a long-term program designed to obtain and interpret high-precision radar range measurements of a number of near-Earth objects (NEOs) that have trajectories reaching deep inside the gravitational well of the Sun. Objects in our sample have perihelion shift rates 1.5 to 2.5 times that of (1566) Icarus (10″/cy) and span a wide range of inclinations and semi-major axes, allowing for an unambiguous separation of general relativistic and solar oblateness effects. Four objects have been observed at Arecibo on at least two apparitions since 2000, with typical uncertainties of a few hundred meters. Within the next three years, we anticipate securing a total of 15 observations of 5 different NEOs. This program is expected to provide a purely dynamical measurement of the oblateness of the Sun (J2 at the 10−8 level) and to constrain the Eddington parameter β at the 10−4 level. Although our objects are selected to minimize Yarkovsky orbital drift, we also anticipate measuring Yarkovsky drift rates, which are orthogonal to the GR and J2 signatures.

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