On the effects of the Dvali-Gabadadze-Porrati braneworld gravity on the orbital motion of a test particle

Abstract

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.

arXiv commentLaTex2e, 23 pages, 5 tables, 1 figure, 37 references. Second-order corrections in eccentricity explicitly added. Typos corrected. References updated

References in corpus (9)

• 4D Gravity on a Brane in 5D Minkowski Space
• Classical and Quantum Consistency of the DGP Model
• Probing Newton's Constant on Vast Scales: DGP Gravity, Cosmic Acceleration and Large Scale Structure
• The Accelerated Universe and the Moon
• Gravitational Leakage into Extra Dimensions: Probing Dark Energy Using Local Gravity
• On the possibility of measuring the solar oblateness and some relativistic effects from planetary ranging
• Is it possible to measure the Lense-Thirring effect on the orbits of the planets in the gravitational field of the Sun?
• Secular increase of the Astronomical Unit and perihelion precessions as tests of the Dvali-Gabadadze-Porrati multi-dimensional braneworld scenario
• On the possibility of testing the Brane-World scenario with orbital motions in the Solar System

Cited by in corpus (24)

• Solar system effects in Schwarzschild--de Sitter spacetime
• Charged Particle Motion Around Rotating Black Hole in Braneworld Immersed in Magnetic Field
• Analysis of the Yukawa gravitational potential in $f(R)$ gravity I: semiclassical periastron advance
• Analysis of the Yukawa gravitational potential in $f(R)$ gravity II: relativistic periastron advance
• Perturbations of Self-Accelerated Universe
• Super-ASTROD: Probing primordial gravitational waves and mapping the outer solar system
• Cargese Lectures on Brane Induced Gravity
• Magnetized Particle Motion Around Black Hole in Braneworld
• Magnetic Fields of Spherical Compact Stars in Braneworld
• Dynamical determination of the Kuiper Belt's mass from motions of the inner planets of the Solar System
• Novel constraints on fifth forces and ultralight dark sector with asteroidal data
• Astronomical constraints on some long-range models of modified gravity
• Constraining the cosmological constant and the DGP gravity with the double pulsar PSR J0737-3039
• Solar system constraints on the Dvali-Gabadadze-Porrati braneworld theory of gravity
• Local cosmological effects of the order of H in the orbital motion of a binary system
• Fluid sphere: stability problem and dimensional constraint
• Effects in the Anomalistic Period of Celestial Bodies due to a Logarithmic Correction to the Newtonian Gravitational Potential
• Weyl conformastatic perihelion advance of small body objects
• Anomalous precession of planets on a Weyl conformastatic solution
• Mass Screening in Modified Gravity
• How the orbital period of a test particle is modified by the Dvali-Gabadadze-Porrati gravity?
• On the perspectives of testing the Dvali-Gabadadze-Porrati gravity model with the outer planets of the Solar System
• Spin precession in the Dvali-Gabadadze-Porrati braneworld scenario
• Radar Signal Delay in the Dvali-Gabadadze-Porrati Gravity in the Vicinity of the Sun