70 research outputs found

### Field Equations and Equations of Motion in Post-Newtonian Approximation of the Projective Unified Field Theory

The equations of motion of $N$ gravitationally bound bodies are derived from
the field equations of Projective Unified Field Theory. The Newtonian and the
post-Newtonian approximations of the field equations and of the equations of
motion of this system of bodies are studied in detail. In analyzing some
experimental data we performed some numeric estimates of the ratio of the
inertial mass to the scalaric mass of matter.Comment: 17 page

### Estimations of changes of the Sun's mass and the gravitation constant from the modern observations of planets and spacecraft

More than 635 000 positional observations (mostly radiotechnical) of planets
and spacecraft (1961-2010), have been used for estimating possible changes of
the gravitation constant, the solar mass, and semi-major axes of planets, as
well as the value of the astronomical unit, related to them. The analysis of
the observations has been performed on the basis of the EPM2010 ephemerides of
IAA RAS in post-newtonian approximation. The obtained results indicate on
decrease in the heliocentric gravitation constant per year at the level $\dot
{GM_{Sun}}/GM_{Sun} = (-5.0 \pm 4.1) 10^{-14} (3\sigma).$ The positive secular
changes of semi-major axes $\dot a_i/a_i$ have been obtained simultaneously
for the planets Mercury, Venus, Mars, Jupiter, Saturn, as expected if the
geliocentric gravitation constant is decreasing in century wise. The change of
the mass of the Sun $M_{Sun}$ due to the solar radiation and the solar wind and
the matter dropping on the Sun (comets, meteors, asteroids and dust) was
estimated. Taking into account the maximal limits of the possible $M_{Sun}$
change, the value $\dot G/G$ falls within the interval $-4.2\cdot10^{-14} <
\dot G/G < +7.5\cdot10^{-14}$ in year with the 95% probability. The
astronomical unit (au) is only connected with the geliocentric gravitation
constant by its definition. In the future, the connection between $GM_{Sun}$
and au should be fixed at the certain time moment, as it is inconvenient highly
to have the changing value of the astronomical unit.Comment: 20 pages, 4 tables, accepted for publication in Solar System
Research, 2011 (Astronomicheskii vestnik

### On the perspectives of testing the Dvali-Gabadadze-Porrati gravity model with the outer planets of the Solar System

The multidimensional braneworld gravity model by Dvali, Gabadadze and Porrati
was primarily put forth to explain the observed acceleration of the expansion
of the Universe without resorting to dark energy. One of the most intriguing
features of such a model is that it also predicts small effects on the orbital
motion of test particles which could be tested in such a way that local
measurements at Solar System scales would allow to get information on the
global properties of the Universe. Lue and Starkman derived a secular
extra-perihelion \omega precession of 5\times 10^-4 arcseconds per century,
while Iorio showed that the mean longitude \lambda is affected by a secular
precession of about 10^-3 arcseconds per century. Such effects depend only on
the eccentricities e of the orbits via second-order terms: they are, instead,
independent of their semimajor axes a. Up to now, the observational efforts
focused on the dynamics of the inner planets of the Solar System whose orbits
are the best known via radar ranging. Since the competing Newtonian and
Einsteinian effects like the precessions due to the solar quadrupole mass
moment J2, the gravitoelectric and gravitomagnetic part of the equations of
motion reduce with increasing distances, it would be possible to argue that an
analysis of the orbital dynamics of the outer planets of the Solar System, with
particular emphasis on Saturn because of the ongoing Cassini mission with its
precision ranging instrumentation, could be helpful in evidencing the predicted
new features of motion. In this note we investigate this possibility in view of
the latest results in the planetary ephemeris field. Unfortunately, the current
level of accuracy rules out this appealing possibility and it appears unlikely
that Cassini and GAIA will ameliorate the situation.Comment: LaTex, 22 pages, 2 tables, 10 figures, 27 references. Reference [17]
added, reference [26] updated, caption of figures changed, small change in
section 1.

### Quantum effects on Lagrangian points and displaced periodic orbits in the Earth-Moon system

Recent work in the literature has shown that the one-loop long distance quantum corrections to the Newtonian potential imply tiny but observable effects in the restricted three-body problem of celestial mechanics, i.e., at the Lagrangian libration points of stable equilibrium the planetoid is not exactly at equal distance from the two bodies of large mass, but the Newtonian values of its coordinates are changed by a few millimeters in the Earth-Moon system. First, we assess such a theoretical calculation by exploiting the full theory of the quintic equation, i.e., its reduction to Bring-Jerrard form and the resulting expression of roots in terms of generalized hypergeometric functions. By performing the numerical analysis of the exact formulas for the roots, we confirm and slightly improve the theoretical evaluation of quantum corrected coordinates of Lagrangian libration points of stable equilibrium. Second, we prove in detail that also for collinear Lagrangian points the quantum corrections are of the same order of magnitude in the Earth-Moon system. Third, we discuss the prospects to measure, with the help of laser ranging, the above departure from the equilateral triangle picture, which is a challenging task. On the other hand, a modern version of the planetoid is the solar sail, and much progress has been made, in recent years, on the displaced periodic orbits of solar sails at all libration points, both stable and unstable. The present paper investigates therefore, eventually, a restricted three-body problem involving Earth, Moon and a solar sail. By taking into account the one-loop quantum corrections to the Newtonian potential, displaced periodic orbits of the solar sail at libration points are again found to exist

### Stochastic motion of test particle implies that G varies with time

The aim of this letter is to propose a new description to the time varying
gravitational constant problem, which naturally implements the Dirac's large
numbers hypothesis in a new proposed holographic scenario for the origin of
gravity as an entropic force. We survey the effect of the Stochastic motion of
the test particle in Verlinde's scenario for gravity\cite{Verlinde}. Firstly we
show that we must get the equipartition values for $t\rightarrow\infty$ which
leads to the usual Newtonian gravitational constant. Secondly,the stochastic
(Brownian) essence of the motion of the test particle, modifies the Newton's
2'nd law. The direct result is that the Newtonian constant has been time
dependence in resemblance as \cite{Running}.Comment: Accepted in International Journal of Theoretical Physic

### Linearized f(R) Gravity: Gravitational Radiation & Solar System Tests

We investigate the linearized form of metric f(R)-gravity, assuming that f(R)
is analytic about R = 0 so it may be expanded as f(R) = R + a_2 R^2/2 + ... .
Gravitational radiation is modified, admitting an extra mode of oscillation,
that of the Ricci scalar. We derive an effective energy-momentum tensor for the
radiation. We also present weak-field metrics for simple sources. These are
distinct from the equivalent Kerr (or Schwarzschild) forms. We apply the
metrics to tests that could constrain f(R). We show that light deflection
experiments cannot distinguish f(R)-gravity from general relativity as both
have an effective post-Newtonian parameter \gamma = 1. We find that planetary
precession rates are enhanced relative to general relativity; from the orbit of
Mercury we derive the bound |a_2| < 1.2 \times 10^18 m^2. Gravitational wave
astronomy may be more useful: considering the phase of a gravitational waveform
we estimate deviations from general relativity could be measurable for an
extreme-mass-ratio inspiral about a 10^6 M_sol black hole if |a_2| > 10^17 m^2,
assuming that the weak-field metric of the black hole coincides with that of a
point mass. However Eot-Wash experiments provide the strictest bound |a_2| < 2
\times 10^-9 m^2. Although the astronomical bounds are weaker, they are still
of interest in the case that the effective form of f(R) is modified in
different regions, perhaps through the chameleon mechanism. Assuming the
laboratory bound is universal, we conclude that the propagating Ricci scalar
mode cannot be excited by astrophysical sources.Comment: 19 pages, 1 figure; typos in Sec. VIII. A. correcte

- â€¦