6 research outputs found
Secular increase of the Astronomical Unit and perihelion precessions as tests of the Dvali-Gabadadze-Porrati multi-dimensional braneworld scenario
An unexpected secular increase of the Astronomical Unit, the length scale of
the Solar System, has recently been reported by three different research groups
(Krasinsky and Brumberg, Pitjeva, Standish). The latest JPL measurements amount
to 7+-2 m cy^-1. At present, there are no explanations able to accommodate such
an observed phenomenon, neither in the realm of classical physics nor in the
usual four-dimensional framework of the Einsteinian General Relativity. The
Dvali-Gabadadze-Porrati braneworld scenario, which is a multi-dimensional model
of gravity aimed to the explanation of the observed cosmic acceleration without
dark energy, predicts, among other things, a perihelion secular shift, due to
Lue and Starkman, of 5 10^-4 arcsec cy^-1 for all the planets of the Solar
System. It yields a variation of about 6 m cy^-1 for the Earth-Sun distance
which is compatible at 1-sigma level with the observed rate of the Astronomical
Unit. The recently measured corrections to the secular motions of the perihelia
of the inner planets of the Solar System are in agreement, at 1-sigma level,
with the predicted value of the Lue-Starkman effect for Mercury and Mars and at
2-sigma level for the Earth.Comment: LaTex2e, 7 pages, no figures, no tables, 13 references. Minor
correction
On the effects of the Dvali-Gabadadze-Porrati braneworld gravity on the orbital motion of a test particle
In this paper we explicitly work out the secular perturbations induced on all
the Keplerian orbital elements of a test body to order O(e^2) in the
eccentricity e by the weak-field long-range modifications of the usual
Newton-Einstein gravity due to the Dvali-Gabadadze-Porrati (DGP) braneworld
model. The Gauss perturbative scheme is used. It turns out that the argument of
pericentre and the mean anomaly are affected by secular rates which are
independent of the semimajor axis of the orbit of the test particle. The first
nonvaishing eccentricity-dependent corrections are of order O(e^2). For
circular orbits the Lue-Starkman (LS) effect on the pericentre is obtained.
Some observational consequences are discussed for the Solar System planetary
mean longitudes lambda which would undergo a 1.2\cdot 10^-3 arcseconds per
century braneworld secular precession. According to recent data analysis over
92 years for the EPM2004 ephemerides, the 1-sigma formal accuracy in
determining the Martian mean longitude amounts to 3\cdot 10^-3 milliarcseconds,
while the braneworld effect over the same time span would be 1.159
milliarcseconds. The major limiting factor is the 2.6\cdot 10^-3 arcseconds per
century systematic error due to the mismodelling in the Keplerian mean motion
of Mars. A suitable linear combination of the mean longitudes of Mars and Venus
may overcome this problem. The formal, 1-sigma obtainable observational
accuracy would be \sim 7%. The systematic error due to the present-day
uncertainties in the solar quadrupole mass moment, the Keplerian mean motions,
the general relativistic Schwarzschild field and the asteroid ring would amount
to some tens of percent.Comment: LaTex2e, 23 pages, 5 tables, 1 figure, 37 references. Second-order
corrections in eccentricity explicitly added. Typos corrected. References
update
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.
Tidal Dynamics in Cosmological Spacetimes
We study the relative motion of nearby free test particles in cosmological
spacetimes, such as the FLRW and LTB models. In particular, the influence of
spatial inhomogeneities on local tidal accelerations is investigated. The
implications of our results for the dynamics of the solar system are briefly
discussed. That is, on the basis of the models studied in this paper, we
estimate the tidal influence of the cosmic gravitational field on the orbit of
the Earth around the Sun and show that the corresponding temporal rate of
variation of the astronomical unit is negligibly small.Comment: 12 pages, no figures, REVTeX 4.0; appendix added, new references, and
minor changes throughout; to appear in Classical and Quantum Gravity; v4:
error in (A24) of Appendix A corrected, results and conclusions unchanged. We
thank L. Iorio for pointing out the erro