8,073 research outputs found
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
Density of dark matter in Solar system and perihelion precession of planets
Direct relation is pointed out between the secular perihelion precession of a
planet and the density of dark matter at its orbit. It is valid under the only
assumption that the density is spherically-symmetric, with the center
coinciding with the Sun. This relation, combined with the observational data on
perihelion precession of planets, results in upper limits on local values of
the dark matter density in the Solar system.Comment: 4 pages; some explanations on derivation of master formula adde
The impact of the new CHAMP and GRACE Earth gravity models on the measurement of the general relativistic Lense--Thirring effect with the LAGEOS and LAGEOS II satellites
Among the effects predicted by the General Theory of Relativity for the
orbital motion of a test particle, the post-Newtonian gravitomagnetic
Lense-Thirring effect is very interesting and, up to now, there is not yet an
undisputable experimental direct test of it. To date, the data analysis of the
orbits of the existing geodetic LAGEOS and LAGEOS II satellites has yielded a
test of the Lense-Thirring effect with a claimed accuracy of 20%-30%. According
to some scientists such estimates could be optimistic. Here we wish to discuss
the improvements obtainable in this measurement, in terms of reliability of the
evaluation of the systematic error and reduction of its magnitude, due to the
new CHAMP and GRACE Earth gravity models.Comment: LaTex2e, 6 pages, no figures, no tables. Paper presented at 2nd CHAMP
science meeting, Potsdam, 1-4 September 200
Gravitomagnetic time-varying effects on the motion of a test particle
We study the effects of a time-varying gravitomagnetic field on the motion of
test particles. Starting from recent results, we consider the gravitomagnetic
field of a source whose spin angular momentum has a linearly time-varying
magnitude. The acceleration due to such a time-varying gravitomagnetic field is
considered as a perturbation of the Newtonian motion, and we explicitly
evaluate the effects of this perturbation on the Keplerian elements of a closed
orbit. The theoretical predictions are compared with actual astronomical and
astrophysical scenarios, both in the solar system and in binary pulsars
systems, in order to evaluate the impact of these effects on real systems.Comment: 8 pages, RevTeX; revised to match the version accepted for
publication in General Relativity and Gravitatio
On the possibility of measuring the Earth's gravitomagnetic force in a new laboratory experiment
In this paper we propose, in a preliminary way, a new Earth-based laboratory
experiment aimed to the detection of the gravitomagnetic field of the Earth. It
consists of the measurement of the difference of the circular frequencies of
two rotators moving along identical circular paths, but in opposite directions,
on a horizontal friction-free plane in a vacuum chamber placed at South Pole.
The accuracy of our knowledge of the Earth's rotation from VLBI and the
possibility of measuring the rotators'periods over many revolutions should
allow for the feasibility of the proposed experiment.Comment: Latex2e, 8 pages, no figures, no tables, accepted for publication by
Classical and Quantum Gravity. Typo corrected in the formula of the error in
the difference of the orbital period
The relativistic precession of the orbits
The relativistic precession can be quickly inferred from the nonlinear polar
orbit equation without actually solving it.Comment: Accepted for publication in Astrophysics & Space Scienc
LAGEOS-type Satellites in Critical Supplementary Orbit Configuration and the Lense-Thirring Effect Detection
In this paper we analyze quantitatively the concept of LAGEOS--type
satellites in critical supplementary orbit configuration (CSOC) which has
proven capable of yielding various observables for many tests of General
Relativity in the terrestrial gravitational field, with particular emphasis on
the measurement of the Lense--Thirring effect.Comment: LaTex2e, 20 pages, 7 Tables, 6 Figures. Changes in Introduction,
Conclusions, reference added, accepted for publication in Classical and
Quantum Gravit
Will the recently approved LARES mission be able to measure the Lense-Thirring effect at 1%?
After the approval by the Italian Space Agency of the LARES satellite, which
should be launched at the end of 2009 with a VEGA rocket and whose claimed goal
is a about 1% measurement of the general relativistic gravitomagnetic
Lense-Thirring effect in the gravitational field of the spinning Earth, it is
of the utmost importance to reliably assess the total realistic accuracy that
can be reached by such a mission. The observable is a linear combination of the
nodes of the existing LAGEOS and LAGEOS II satellites and of LARES able to
cancel out the impact of the first two even zonal harmonic coefficients of the
multipolar expansion of the classical part of the terrestrial gravitational
potential representing a major source of systematic error. While LAGEOS and
LAGEOS II fly at altitudes of about 6000 km, LARES will be placed at an
altitude of 1450 km. Thus, it will be sensitive to much more even zonals than
LAGEOS and LAGEOS II. Their corrupting impact \delta\mu has been evaluated by
using the standard Kaula's approach up to degree L=70 along with the sigmas of
the covariance matrices of eight different global gravity solutions
(EIGEN-GRACE02S, EIGEN-CG03C, GGM02S, GGM03S, JEM01-RL03B, ITG-Grace02s,
ITG-Grace03, EGM2008) obtained by five institutions (GFZ, CSR, JPL, IGG, NGA)
with different techniques from long data sets of the dedicated GRACE mission.
It turns out \delta\mu about 100-1000% of the Lense-Thirring effect. An
improvement of 2-3 orders of magnitude in the determination of the high degree
even zonals would be required to constrain the bias to about 1-10%.Comment: Latex, 15 pages, 1 table, no figures. Final version matching the
published one in General Relativity and Gravitation (GRG
Conservative evaluation of the uncertainty in the LAGEOS-LAGEOS II Lense-Thirring test
We deal with the test of the general relativistic gravitomagnetic
Lense-Thirring effect currently ongoing in the Earth's gravitational field with
the combined nodes \Omega of the laser-ranged geodetic satellites LAGEOS and
LAGEOS II.
One of the most important source of systematic uncertainty on the orbits of
the LAGEOS satellites, with respect to the Lense-Thirring signature, is the
bias due to the even zonal harmonic coefficients J_L of the multipolar
expansion of the Earth's geopotential which account for the departures from
sphericity of the terrestrial gravitational potential induced by the
centrifugal effects of its diurnal rotation. The issue addressed here is: are
the so far published evaluations of such a systematic error reliable and
realistic? The answer is negative. Indeed, if the difference \Delta J_L among
the even zonals estimated in different global solutions (EIGEN-GRACE02S,
EIGEN-CG03C, GGM02S, GGM03S, ITG-Grace02, ITG-Grace03s, JEM01-RL03B, EGM2008,
AIUB-GRACE01S) is assumed for the uncertainties \delta J_L instead of using
their more or less calibrated covariance sigmas \sigma_{J_L}, it turns out that
the systematic error \delta\mu in the Lense-Thirring measurement is about 3 to
4 times larger than in the evaluations so far published based on the use of the
sigmas of one model at a time separately, amounting up to 37% for the pair
EIGEN-GRACE02S/ITG-Grace03s. The comparison among the other recent GRACE-based
models yields bias as large as about 25-30%. The major discrepancies still
occur for J_4, J_6 and J_8, which are just the zonals the combined
LAGEOS/LAGOES II nodes are most sensitive to.Comment: LaTex, 12 pages, 12 tables, no figures, 64 references. To appear in
Central European Journal of Physics (CEJP
A uniform treatment of the orbital effects due to a violation of the Strong Equivalence Principle in the gravitational Stark-like limit
We analytically work out several effects which a violation of the Strong
Equivalence Principle (SEP) induces on the orbital motion of a binary system
constituted of self-gravitating bodies immersed in a constant and uniform
external field. We do not restrict to the small eccentricity limit. Moreover,
we do not select any specific spatial orientation of the external polarizing
field. We explicitly calculate the SEP-induced mean rates of change of all the
osculating Keplerian orbital elements of the binary, the perturbation of the
projection of the binary orbit onto the line-of-sight, the shift of the radial
velocity, and the range and range-rate signatures and as well. We find that the
ratio of the SEP precessions of the node and the inclination of the binary
depends only on and the pericenter of the binary itself, being independent on
both the magnitude and the orientation of the polarizing field, and on the
semimajor axis, the eccentricity and the node of the binary. Our results, which
do not depend on any particular SEP-violating theoretical scheme, can be
applied to quite general astronomical and astrophysical scenarios. They can be
used to better interpret present and future SEP experiments, especially when
several theoretical SEP mechanisms may be involved, and to suitably design new
dedicated tests.Comment: LaTex2e, 14 pages, no figures, no tables, 42 references. To appear in
Classical and Quantum Gravity (CQG
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