scholarly journals Palatini f(R) gravity in the solar system: Post-Newtonian equations of motion and complete PPN parameters

2020 ◽  
Vol 101 (6) ◽  
Author(s):  
Júnior D. Toniato ◽  
Davi C. Rodrigues ◽  
Aneta Wojnar
Keyword(s):  
Solar System ◽  
Equations Of Motion ◽  
Ppn Parameters

scholarly journals Relativistic aspects of the JPL planetary ephemeris

2009 ◽  
Vol 5 (S261) ◽  
pp. 155-158 ◽  
Author(s):  
W. M. Folkner
Keyword(s):  
Solar System ◽  
Time Variation ◽  
Gravitational Constant ◽  
Equations Of Motion ◽  
Relativistic Effects ◽  
Radio Tracking ◽  
Data Set ◽  
Inverse Square Law ◽  
Radio Signals ◽  
Ppn Parameters

AbstractThe orbits of the planets as represented by the JPL planetary ephemerides are now primarily determined by radio tracking of spacecraft. Analysis of the data and propagation of the orbits relies on an internally consistent set of equations of motion and propagation of radio signals including relativistic effects at the centimeter level. The planetary ephemeris data set can be used to test some aspects of the underlying theory such as estimates of PPN parameters γ and β, time variation in the gravitational constant G, rotation of the solar system relative to distant objects (Mach's principle), and place stringent limits on the possible violation of the inverse-square law.

scholarly journals CONSTRAINING THE PREFERRED-FRAME α1, α2 PARAMETERS FROM SOLAR SYSTEM PLANETARY PRECESSIONS

2014 ◽  
Vol 23 (01) ◽  
pp. 1450006 ◽  
Author(s):  
L. IORIO
Keyword(s):  
Binary System ◽  
Solar System ◽  
Relative Motion ◽  
A Priori ◽  
The Other ◽  
Preferred Frame ◽  
General Relativistic ◽  
Ppn Parameters ◽  
Invariable Plane ◽  
Analytical Expressions

Analytical expressions for the orbital precessions affecting the relative motion of the components of a local binary system induced by Lorentz-violating Preferred Frame Effects (PFE) are explicitly computed in terms of the Parametrized Post-Newtonian (PPN) parameters α1, α2. Preliminary constraints on α1, α2 are inferred from the latest determinations of the observationally admitted ranges [Formula: see text] for any anomalous Solar System planetary perihelion precessions. Other bounds existing in the literature are critically reviewed, with particular emphasis on the constraint [Formula: see text] based on an interpretation of the current close alignment of the Sun's equator with the invariable plane of the Solar System in terms of the action of a α2-induced torque throughout the entire Solar System's existence. Taken individually, the supplementary precessions [Formula: see text] of Earth and Mercury, recently determined with the INPOP10a ephemerides without modeling PFE, yield α1 = (0.8±4) × 10-6 and α2 = (4±6) × 10-6, respectively. A linear combination of the supplementary perihelion precessions of all the inner planets of the Solar System, able to remove the a priori bias of unmodeled/mismodeled standard effects such as the general relativistic Lense–Thirring precessions and the classical rates due to the Sun's oblateness J2, allows to infer α1 = (-1 ± 6) × 10-6, α2 = (-0.9 ± 3.5) × 10-5. Such figures are obtained by assuming that the ranges of values for the anomalous perihelion precessions are entirely due to the unmodeled effects of α1 and α2. Our bounds should be improved in the near-mid future with the MESSENGER and, especially, BepiColombo spacecrafts. Nonetheless, it is worthwhile noticing that our constraints are close to those predicted for BepiColombo in two independent studies. In further dedicated planetary analyses, PFE may be explicitly modeled to estimate α1, α2 simultaneously with the other PPN parameters as well.

Orbits of Trojan Asteroids

1974 ◽  
Vol 62 ◽  
pp. 63-69 ◽  
Author(s):  
G. A. Chebotarev ◽  
N. A. Belyaev ◽  
R. P. Eremenko
Keyword(s):  
Solar System ◽  
Body Problem ◽  
Equations Of Motion ◽  
Orbital Evolution ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Trojan Asteroids ◽  
Actual Motion ◽  
Three Body

In this paper the orbital evolution of Trojan asteroids are studied by integrating numerically the equations of motion over the interval 1660–2060, perturbations from Venus to Pluto being taken into account. The comparison of the actual motion of Trojans in the solar system with the theory based on the restricted three-body problem are given.

scholarly journals The Quadrantid Meteor Stream: Past, Present and Future

1980 ◽  
Vol 90 ◽  
pp. 153-156
Author(s):  
David W. Hughes ◽  
Iwan P. Williams ◽  
Carl D. Murray
Keyword(s):  
Solar System ◽  
Fourth Order ◽  
Equations Of Motion ◽  
Meteor Stream ◽  
Eccentric Anomaly ◽  
Test Particles ◽  
The Future ◽  
Runge Kutta

At the present time the orbit of the Quadrantid meteor stream not only intersects the orbit of Earth but also passes very close to the orbit of the planet Jupiter. This causes considerable perturbations. In a series of three papers (1,2,3) the authors replaced the myriad of meteoroids in the stream by ten test particles set at equal intervals of eccentric anomaly around the orbit. The equations of motion of these particles in the solar system were solved using a standard fourth order Runge–Kutta technique with self–adjusting step lengths. The orbits of the test particles were output at ten year intervals going back from the present to the year 300 B.C. and forward into the future to the year A.D. 3780.

scholarly journals Solar system tests of a new class of f(z) theory

2020 ◽  
Vol 29 (08) ◽  
pp. 2050060
Author(s):  
Ji-Yao Wang ◽  
Chao-Jun Feng ◽  
Xiang-Hua Zhai ◽  
Xin-Zhou Li
Keyword(s):  
Solar System ◽  
Observational Data ◽  
Ricci Scalar ◽  
Parametric Models ◽  
Alternative Models ◽  
New Class ◽  
Cosmological Data ◽  
Ppn Parameters ◽  
Models Of Gravity

Recently, a new kind of [Formula: see text] theory is proposed to provide a different perspective for the development of reliable alternative models of gravity in which the [Formula: see text] Lagrangian terms are reformulated as polynomial parametrizations [Formula: see text]. In the previous study, the parameters in the [Formula: see text] models have been constrained by using cosmological data. In this paper, these models will be tested by the observations in the solar system. After solving the Ricci scalar as a function of the redshift, one could obtain [Formula: see text] that could be used to calculate the standard Parametrized-Post-Newtonian (PPN) parameters. First, we fit the parametric models with the latest cosmological observational data. Then, the tests are performed by solar system observations. And last we combine the constraints of solar system and cosmology together and reconstruct the [Formula: see text] actions of the [Formula: see text] parametric models.

scholarly journals Orbital stability of high inclination asteroids

1996 ◽  
Vol 172 ◽  
pp. 187-192
Author(s):  
N. A. Solovaya ◽  
E. M. Pittich
Keyword(s):  
Solar System ◽  
Body Problem ◽  
Equations Of Motion ◽  
Orbital Stability ◽  
Dynamical Model ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Three Body

The orbital evolutions of fictitious asteroids with high inclinations have been investigated. The selected initial orbits represent asteroids with movement, which corresponds to the conditions of the Tisserand invariant for C = C (L1) in the restricted three body problem. Initial eccentricities of the orbits cover the interval 0.0–0.4, inclinations the interval 40–80°, and arguments of perihelion the interval 0–360°. The equations of motion of the asteroids were numerically integrated from the epoch March 25, 1991 forward within the interval of 20,000 years, using a dynamical model of the solar system consisting of all planets. The orbits of the model asteroids are stable at least during the investigated period.

scholarly journals Fab Four: When John and George Play Gravitation and Cosmology

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
J.-P. Bruneton ◽  
M. Rinaldi ◽  
A. Kanfon ◽  
A. Hees ◽  
S. Schlögel ◽  
...  
Keyword(s):  
Scalar Field ◽  
Solar System ◽  
Parameter Space ◽  
Ad Hoc ◽  
Initial Conditions ◽  
Equations Of Motion ◽  
Inflationary Model ◽  
Einstein Tensor ◽  
Chameleon Mechanism ◽  
Derivatives Of

Scalar-tensor theories of gravitation attract again a great interest since the discovery of the Chameleon mechanism and of the Galileon models. The former allows reconciling the presence of a scalar field with the constraints from Solar System experiments. The latter leads to inflationary models that do not need ad hoc potentials. Further generalizations lead to a tensor-scalar theory, dubbed the “Fab Four,” with only first and second order derivatives of the fields in the equations of motion that self-tune to a vanishing cosmological constant. This model needs to be confronted with experimental data in order to constrain its large parameter space. We present some results regarding a subset of this theory named “John,” which corresponds to a nonminimal derivative coupling between the scalar field and the Einstein tensor in the action. We show that this coupling gives rise to an inflationary model with very unnatural initial conditions. Thus, we include the term named “George,” namely, a nonminimal, but nonderivative, coupling between the scalar field and Ricci scalar. We find a more natural inflationary model, and, by performing a post-Newtonian analysis, we derive the set of equations that constrain the parameter space with data from experiments in the Solar System.

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 New accuracy levels for solar system ephemerides

1996 ◽  
Vol 172 ◽  
pp. 29-36 ◽  
Author(s):  
E. M. Standish ◽  
X X Newhall
Keyword(s):  
Solar System ◽  
Reference Frame ◽  
Data Reduction ◽  
Equations Of Motion ◽  
Adjustment Process ◽  
Dynamical Modeling ◽  
Reduction Techniques ◽  
Condensed Representation ◽  
Lunar Ephemeris ◽  
Hipparcos Catalogue

DE403/LE403 is the latest JPL Planetary and Lunar Ephemeris. It represents a number of changes and improvements to previous JPL ephemerides: the reference frame is now that of the IERS, newer and more accurate observations are used in the adjustment process, some of the data reduction techniques have been refined, and improved dynamical modeling has been incorporated into the equations of motion. As a result, the internal accuracy of the inner four planets has been improved. Further, various measurements accurately tie Jupiter onto the IERS Reference Frame. In the future, use of CCD measurements and the Hipparcos Catalogue should improve the ephemerides of the outermost four planets.DE403/LE403 has been integrated over 6000 years, from 3000 BC to 3000 AD. A more condensed representation has been made from this, named DE404/LE404. It replaces DE102 as the new JPL “Long Ephemeris”.

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