Orbital precession due to central-force perturbations

Adkins, Gregory S.; McDonnell, Jordan

doi:10.1103/physrevd.75.082001

Cited by 90 publications

(79 citation statements)

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“…can be obtained from (16); let us now work out the secular precession of the pericentre of a test particle induced by (17) in the case β − 2 < 0. By proceeding as in Section 2 we get (see also [28])…”

Section: The Power-law Corrections In the F (R) Extended Theories Of mentioning

confidence: 90%

Solar System Tests of Some Models of Modified Gravity Proposed to Explain Galactic Rotation Curves without Dark Matter

Iorio

Ruggiero

2008

Scholarly Research Exchange

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We consider the recently estimated corrections Δω to the standard Newtonian/Einsteinian secular precessions of the longitudes of perihelia ω of several planets of the Solar System in order to evaluate whether they are compatible with the predicted anomalous precessions due to models of long-range modified gravity put forth to account for certain features of the rotation curves of galaxies without resorting to dark matter. In particular, we consider a logarithmic-type correction and a f (R) inspired powerlaw modification of the Newtonian gravitational potential. The results obtained by taking the ratio of the predicted apsidal rates for different pairs of planets show that the modifications of the Newtonian potentials examined in this paper are not compatible with the secular extra-precessions of the perihelia of the Solar System's planets estimated by E. V. Pitjeva as solve-for parameters processing almost one century of data with the latest EPM ephemerides.

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Section: The Power-law Corrections In the F (R) Extended Theories Of mentioning

confidence: 90%

Solar System Tests of Some Models of Modified Gravity Proposed to Explain Galactic Rotation Curves without Dark Matter

Iorio

Ruggiero

2008

Scholarly Research Exchange

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“…(16) loses its meaning for e → 0 since it yields 0/0. Other derivations of either the Yukawa-type secular precession of the pericenter or its advance per orbit can be found in, e.g., [35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54]. All of them make use of different level of approximations in either the magnitude of the length scale λ or the orbital configuration of the test particle.…”

Section: Introductionmentioning

confidence: 99%

Constraints from orbital motions around the Earth of the environmental fifth-force hypothesis for the OPERA superluminal neutrino phenomenology

Iorio¹

2012

J. High Energ. Phys.

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“…and this is just equation (30) from [1] up to the applied notations. The extreme simplicity of this back-of-envelope derivation demonstrates clearly that the real backbone behind the Adkins and McDonnell perihelion precession formula is the Hamilton's vector, the lost sparkling diamond of introductory level mechanics.…”

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confidence: 99%

Remark on orbital precession due to central-force perturbations

Chashchina

Силагадзе

2008

Phys. Rev. D

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This is a comment on the recent paper by G. S. Adkins and J. McDonnell "Orbital precession due to central-force perturbations" published in Phys. Rev. D75 (2007), 082001 [arXiv:gr-qc/0702015]. We show that the main result of this paper, the formula for the precession of Keplerian orbits induced by central-force perturbations, can be obtained very simply by the use of Hamilton's vector.In the recent paper G. S. Adkins and J. McDonnell reconsidered the old problem of perihelion precession of Keplerian orbits under the influence of arbitrary central-force perturbations. Their main result is the formula for perihelion precession in the form of a one-dimensional integral convenient for numerical calculations.The reason why this well studied and essentially textbook problem [2] came into the focus of the current research is the recent usage of this classical effect to constrain hypothetical modifications of Newtonian gravity from higher dimensional models [3], as well as the density of dark matter in the solar system [4].Traditionally the simplest way to study the perihelion motion is the use of the Runge-Lenz vector [5,6]. The Runge-Lenz vectoris the extra constant of motion originated from the hidden symmetry of the Coulomb/Kepler problem [7]. Here α = GmM , L is the angular momentum vector and v is the relative velocity of a planet of mass m with respect to the Sun of mass M . Geometrically the Runge-Lenz vector points towards the perihelion. Therefore its precession rate is just the precession rate of the perihelion [8].However, we will use not the Runge-Lenz vector but its less known cousin, the Hamilton vector [9,10,11,12] where ϕ is the polar angle in the orbit plane. This very useful vector constant of motion of the Kepler problem was well known in the past, but mysteriously disappeared from textbooks after the first decade of the twentieth century [9,11,12,13]. Of course, A and u are not independent constants of motion. The relation between them isRemembering that the magnitude of the Runge-Lenz vector is A = α e, where e is the eccentricity of the orbit [5], we get from (3) the magnitude of the Hamilton vectorIf the potential U (r) contains a small central-force perturbation V (r) besides the Coulomb binding potential,the Hamilton vector (as well as the Runge-Lenz vector) ceases to be conserved and begins to precess with the same rate as the Runge-Lenz vector, because according to (3) the two vectors are perpendicular.To calculate the precession rate of the Hamilton vector we first find its time derivativėwhere µ = mM m+M is the reduced mass. To get (5), we have used Newton's equation of motion for˙ v and the equatioṅ e ϕ = −φ e r .

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Orbital precession due to central-force perturbations

Cited by 90 publications

References 26 publications

Solar System Tests of Some Models of Modified Gravity Proposed to Explain Galactic Rotation Curves without Dark Matter

Solar System Tests of Some Models of Modified Gravity Proposed to Explain Galactic Rotation Curves without Dark Matter

Constraints from orbital motions around the Earth of the environmental fifth-force hypothesis for the OPERA superluminal neutrino phenomenology

Remark on orbital precession due to central-force perturbations

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