194 research outputs found
Post-Newtonian effects of planetary gravity on the perihelion shift
We consider a coplanar system comprised of a massive central body (a star), a
less massive secondary (a planet) on a circular orbit, and a test particle on a
bound orbit exterior to that of the secondary. The gravitational pull exerted
on the test particle by the secondary acts as a small perturbation, wherefore
the trajectory of the particle can be described as an ellipse of a precessing
perihelion. While the apsidal motion is defined overwhelmingly by the Newtonian
portion of the secondary's gravity, the post-Newtonian portion, too, brings its
tiny input. We explore whether this input may be of any astrophysical relevance
in the next few decades. We demonstrate that the overall post-Newtonian input
of the secondary's gravity can be split into two parts. One can be expressed
via the orbital angular momentum of the secondary, another via its orbital
radius. Despite some moderately large numerical factors showing up in the
expressions for these two parts, the resulting post-Newtonian contributions
from the secondary's gravity into the apsidal motion of the test particle turn
out to be small enough to be neglected in the near-future measurements.Comment: 5 pages, 1 figure, 1 table; accepted by MNRA
On the recently determined anomalous perihelion precession of Saturn
The astronomer E.V. Pitjeva, by analyzing with the EPM2008 ephemerides a
large number of planetary observations including also two years (2004-2006) of
normal points from the Cassini spacecraft, phenomenologically estimated a
statistically significant non-zero correction to the usual
Newtonian/Einsteinian secular precession of the longitude of the perihelion of
Saturn, i.e. \Delta\dot\varpi_Sat = -0.006 +/- 0.002 arcsec/cy; the formal,
statistical error is 0.0007 arcsec/cy. It can be explained neither by any of
the standard classical and general relativistic dynamical effects
mismodelled/unmodelled in the force models of the EPM2008 ephemerides nor by
several exotic modifications of gravity recently put forth to accommodate
certain cosmological/astrophysical observations without resorting to dark
energy/dark matter. Both independent analyses by other teams of astronomers and
further processing of larger data sets from Cassini will be helpful in
clarifying the nature and the true existence of the anomalous precession of the
perihelion of Saturn.Comment: LaTex2e, 14 pages, no figures, 2 tables. Accepted by The Astronomical
Journal (AJ
Solar System planetary orbital motions and dark matter
In this paper we explicitly work out the effects that a spherically symmetric
distribution of dark matter with constant density would induce on the Keplerian
orbital elements of the Solar System planets and compare them with the latest
results in planetary orbit determination from the EPM2004 ephemerides. It turns
out that the longitudes of perihelia and the mean longitudes are affected by
secular precessions. The resulting upper bounds on dark matter density,
obtained from the EPM2004 formal errors in the determined mean longitude shifts
over 90 years, lie in the range 10^-19-10^-20 g cm^-3 with a peak of 10^-22 g
cm^-3 for Mars. Suitable combinations of the planetary mean longitudes and
perihelia, which cancel out the aliasing impact of some of the unmodelled or
mismodelled forces of the dynamical models of EPM2004, yield a global upper
bound of 7 10^-20 g cm^-3 and 4 10^-19 g cm^-3, respectively.Comment: Latex, 8 pages, 2 tables, no figures, 8 references. Revised version
with improved analysi
Is it possible to measure the Lense-Thirring effect on the orbits of the planets in the gravitational field of the Sun?
Here we explore a novel approach in order to try to measure the
post-Newtonian 1/c^2 Lense-Thirring secular effect induced by the
gravitomagnetic field of the Sun on the planetary orbital motion. Due to the
relative smallness of the solar angular momentum J and the large values of the
planetary semimajor axes a, the gravitomagnetic precessions, which affect the
nodes Omega and the perihelia omega and are proportional to J/a^3, are of the
order of 10^-3 arcseconds per century only for, e.g., Mercury. This value lies
just at the edge of the present-day observational sensitivity in reconstructing
the planetary orbits, although future missions to Mercury like Messenger and
BepiColombo could allow to increase it. The major problems come from the main
sources of systematic errors. They are the aliasing classical precessions
induced by the multipolar expansion of the Sun's gravitational potential and
the classical secular N-body precessions which are of the same order of
magnitude or much larger than the Lense-Thirring precessions of interest. This
definitely rules out the possibility of analyzing only one orbital element of,
e.g., Mercury. In order to circumvent these problems, we propose a suitable
linear combination of the orbital residuals of the nodes of Mercury, Venus and
Mars which is, by construction, independent of such classical secular
precessions. A 1-sigma reasonable estimate of the obtainable accuracy yields a
36% error. Since the major role in the proposed combination is played by the
Mercury's node, it could happen that the new, more accurate ephemerides
available in future thanks to the Messenger and BepiColombo missions will offer
an opportunity to improve the present unfavorable situation.Comment: LaTex2e, A&A macros, 6 pages, no figure, 3 tables. Substantial
revision. More realistic conclusions. Estimations of the impact of
BepiColombo presente
Gravitomagnetism and the Earth-Mercury range
We numerically work out the impact of the general relativistic Lense-Thirring
effect on the Earth-Mercury range caused by the gravitomagnetic field of the
rotating Sun. The peak-to peak nominal amplitude of the resulting time-varying
signal amounts to 1.75 10^1 m over a temporal interval 2 yr. Future
interplanetary laser ranging facilities should reach a cm-level in ranging to
Mercury over comparable timescales; for example, the BepiColombo mission, to be
launched in 2014, should reach a 4.5 - 10 cm level over 1 - 8 yr. We looked
also at other Newtonian (solar quadrupole mass moment, ring of the minor
asteroids, Ceres, Pallas, Vesta, Trans-Neptunian Objects) and post-Newtonian
(gravitoelectric Schwarzschild solar field) dynamical effects on the
Earth-Mercury range. They act as sources of systematic errors for the
Lense-Thirring signal which, in turn, if not properly modeled, may bias the
recovery of some key parameters of such other dynamical features of motion.
Their nominal peak-to-peak amplitudes are as large as 4 10^5 m (Schwarzschild),
3 10^2 m (Sun's quadrupole), 8 10^1 m (Ceres, Pallas, Vesta), 4 m (ring of
minor asteroids), 8 10^-1 m (Trans-Neptunian Objects). Their temporal patterns
are different with respect to that of the gravitomagnetic signal.Comment: LaTex2e, 19 pages, 2 tables, 6 figures. Small typo in pag. 1406 of
the published version fixe
Dark Energy, Induced Gravity and Broken Scale Invariance
We study the cosmological evolution of an induced gravity model with a
self-interacting scalar field and in the presence of matter and
radiation. Such model leads to Einstein Gravity plus a cosmological constant as
a stable attractor among homogeneous cosmologies and is therefore a viable
dark-energy (DE) model for a wide range of scalar field initial conditions and
values for its positive coupling to the Ricci curvature .Comment: 6 pages, 5 figures, 1 table: final version accepted for publication
in PL
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