Newtonian Limit of String-Dilaton Gravity

Capozziello, Salvatore; Lambiase, Gaetano

doi:10.1142/s0218271803003347

Cited by 12 publications

(9 citation statements)

References 20 publications

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“…Capozziello and Lambiase [18] studied the Newtonian limit of string-dilation gravity, and found a perturbing potential containing a linear combination of Yukawa, r 2 , and cosh(r/λ) terms. The Pioneer Anomaly, the anomalous acceleration of about 8.5×10 −10 m/s 2 for 20AU ≤ r ≤ 70AU directed towards the sun experienced by the Pioneer 10/11 spacecraft, has been a strong source of motivation for the development of modified theories of gravity.…”

Section: Summary and Discussionmentioning

confidence: 99%

Orbital precession due to central-force perturbations

Adkins

McDonnell

2007

Phys. Rev. D

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We calculate the precession of Keplerian orbits under the influence of arbitrary central-force perturbations. Our result is in the form of a one-dimensional integral that is straightforward to evaluate numerically. We demonstrate the effectiveness of our formula for the case of the Yukawa potential. We obtain analytic results for potentials of the form V(r) = \alpha r^n and V(r) = \alpha \ln(r/\lambda) in terms of the hypergeometric function {_2F_1} (1/2-n/2,1-n/2; 2; e^2), where e is the eccentricity. Our results reproduce the known general relativistic (n=-3), constant force (n=1), and cosmological constant (n=2) precession formulas. Planetary precessions are often used to constrain the sizes of hypothetical new weak forces--our results allow for more precise, and often stronger, constraints on such proposed new forces.Comment: 10 pages, 1 figur

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Section: Summary and Discussionmentioning

confidence: 99%

Orbital precession due to central-force perturbations

Adkins

McDonnell

2007

Phys. Rev. D

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“…Indeed, tells us that a long‐term change of e occurs only if the averaged extrapotential considered explicitly depends on ω and on time through M or, equivalently, E . Actually, the anomalous potentials arising in the majority of long‐range modified models of gravity are time‐independent and spherically symmetric (Dvali, Gabadadze & Porrati 2000; Capozziello et al 2001; Capozziello & Lambiase 2003; Dvali, Gruzinov & Zaldarriaga 2003; Kerr, Hauck & Mashhoon 2003; Allemandi et al 2005; Gruzinov 2005; Jaekel & Reynaud 2005a,b; Navarro & van Acoleyen 2005; Reynaud & Jaekel 2005; Apostolopoulos & Tetradis 2006; Brownstein & Moffat 2006; Capozziello, Cardone & Francaviglia 2006; Jaekel & Reynaud 2006a,b; Moffat 2006; Navarro & van Acoleyen 2006a,b; Sanders 2006; Adkins & McDonnell 2007; Adkins, McDonnell & Fell 2007; Bertolami et al 2007; Capozziello 2007; Capozziello & Francaviglia 2008; Nojiri & Odintsov 2007; Bertolami & Santos 2009; de Felice & Tsujikawa 2010; Ruggiero 2010; Sotiriou & Faraoni 2010; Fabrina et al 2011). Anomalous accelerations A exhibiting a dependence on the test particle’s velocity v were also proposed in different frameworks (Jaekel & Reynaud 2005a,b; Hořava 2009a,b; Kehagias & Sfetsos 2009).…”

Section: Exotic Models Of Modified Gravitymentioning

confidence: 99%

On the anomalous secular increase of the eccentricity of the orbit of the Moon

Iorio

2011

Monthly Notices of the Royal Astronomical Society

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A recent analysis of a Lunar Laser Ranging (LLR) data record spanning 38.7 yr revealed an anomalous increase of the eccentricity e of the lunar orbit amounting toė meas = (9 ± 3) × 10 −12 yr −1 . The present-day models of the dissipative phenomena occurring in the interiors of both the Earth and the Moon are not able to explain it. In this paper, we examine several dynamical effects, not modelled in the data analysis, in the framework of long-range modified models of gravity and of the standard Newtonian/Einsteinian paradigm. It turns out that none of them can accommodateė meas . Many of them do not even induce long-term changes in e; other models do, instead, yield such an effect, but the resulting magnitudes are in disagreement witḣ e meas . In particular, the general relativistic gravitomagnetic acceleration of the Moon due to the Earth's angular momentum has the right order of magnitude, but the resulting Lense-Thirring secular effect for the eccentricity vanishes. A potentially viable Newtonian candidate would be a trans-Plutonian massive object (Planet X/Nemesis/Tyche) since it, actually, would affect e with a non-vanishing long-term variation. On the other hand, the values for the physical and orbital parameters of such a hypothetical body required to obtain at least the right order of magnitude forė are completely unrealistic: suffices it to say that an Earth-sized planet would be at 30 au, while a jovian mass would be at 200 au. Thus, the issue of finding a satisfactorily explanation for the anomalous behaviour of the Moon's eccentricity remains open.

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“…Gravitational lensing, stellar hydrodynamics and Galactic rotation curves appear natural candidates as test-bed experiments [26][27][28][29][30][31]. In this field we have several contributions from various authors [32][33][34][35][36][37][38][39][40][41][42][43][44]. An interesting application concerns the study of the Casimir effect [45][46][47] in weak-field limit in the context of STFOG.…”

Section: Introductionmentioning

confidence: 99%

Virial theorem in scalar tensor fourth order gravity

2021

Self Cite

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In this paper, we study, in the Newtonian limit, the virial theorem in the context of a scalar tensor fourth order gravity. In particular, we show, that for a isolated galaxy in viral equilibrium, a specific class of scalar tensor fourth order gravity, i.e. $$f(R,\phi )+\omega (\phi )\,\phi _{;\alpha }\,\phi ^{;\alpha }$$ f ( R , ϕ ) + ω ( ϕ ) ϕ ; α ϕ ; α in not suitable to explain the large fraction of dark matter necessary to have the flatness of the galaxies rotation curves experimentally observed.

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Newtonian Limit of String-Dilaton Gravity

Cited by 12 publications

References 20 publications

Orbital precession due to central-force perturbations

Orbital precession due to central-force perturbations

On the anomalous secular increase of the eccentricity of the orbit of the Moon

Virial theorem in scalar tensor fourth order gravity

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