Relativistic Effects in the Motion of the Moon

The main general relativistic effects in the motion of the Moon are briefly reviewed. The possibility of detection of the solar gravitomagnetic contributions to the mean motions of the lunar node and perigee is discussed.Comment: LaTeX file, no figures, 13 pages, to appear in: 'Testing relativistic gravity in space', edited by C. Laemmerzahl, C.W.F. Everitt and F.W. Hehl (Springer, Berlin 2000

Geodetic precession and frame dragging observed far from massive objects and close to a gyroscope

Total precession (geodetic precession and frame dragging) depends on the velocity of each source of gravitation, which means that it depends on the choice of the coordinate system. We consider the latter as an anomaly specifically in the Gravity Probe B experiment, we investigated it and solved this anomaly. Thus, we proved that if our present expression for the geodetic precession is correct, then the frame dragging should be 25% less than its predicted value.Comment: 11 page

Research of Gravitation in Flat Minkowski Space

In this paper it is introduced and studied an alternative theory of gravitation in flat Minkowski space. Using an antisymmetric tensor, which is analogous to the tensor of electromagnetic field, a non-linear connection is introduced. It is very convenient for studying the perihelion/periastron shift, deflection of the light rays near the Sun and the frame dragging together with geodetic precession, i.e. effects where angles are involved. Although the corresponding results are obtained in rather different way, they are the same as in the General Relativity. The results about the barycenter of two bodies are also the same as in the General Relativity. Comparing the derived equations of motion for the $n$-body problem with the Einstein-Infeld-Hoffmann equations, it is found that they differ from the EIH equations by Lorentz invariant terms of order $c^{-2}$.Comment: 28 page

New Upper Limit of Terrestrial Equivalence Principle Test for Rotating Extended Bodies

Improved terrestrial experiment to test the equivalence principle for rotating extended bodies is presented, and a new upper limit for the violation of the equivalence principle is obtained at the level of 1.6$10^{\text{-7}}$, which is limited by the friction of the rotating gyroscope. It means the spin-gravity interaction between the extended bodies has not been observed at this level.Comment: 4 page

Tensor-scalar gravity and binary-pulsar experiments

Some recently discovered nonperturbative strong-field effects in tensor-scalar theories of gravitation are interpreted as a scalar analog of ferromagnetism: "spontaneous scalarization". This phenomenon leads to very significant deviations from general relativity in conditions involving strong gravitational fields, notably binary-pulsar experiments. Contrary to solar-system experiments, these deviations do not necessarily vanish when the weak-field scalar coupling tends to zero. We compute the scalar "form factors" measuring these deviations, and notably a parameter entering the pulsar timing observable gamma through scalar-field-induced variations of the inertia moment of the pulsar. An exploratory investigation of the confrontation between tensor-scalar theories and binary-pulsar experiments shows that nonperturbative scalar field effects are already very tightly constrained by published data on three binary-pulsar systems. We contrast the probing power of pulsar experiments with that of solar-system ones by plotting the regions they exclude in a generic two-dimensional plane of tensor-scalar theories.Comment: 35 pages, REVTeX 3.0, uses epsf.tex to include 9 Postscript figure

Testing gravity to second post-Newtonian order: a field-theory approach

A new, field-theory-based framework for discussing and interpreting tests of gravity, notably at the second post-Newtonian (2PN) level, is introduced. Contrary to previous frameworks which attempted at parametrizing any conceivable deviation from general relativity, we focus on the best motivated class of models, in which gravity is mediated by a tensor field together with one or several scalar fields. The 2PN approximation of these "tensor-multi-scalar" theories is obtained thanks to a diagrammatic expansion which allows us to compute the Lagrangian describing the motion of N bodies. In contrast with previous studies which had to introduce many phenomenological parameters, we find that the 2PN deviations from general relativity can be fully described by only two new 2PN parameters, epsilon and zeta, beyond the usual (Eddington) 1PN parameters beta and gamma. It follows from the basic tenets of field theory, notably the absence of negative-energy excitations, that (beta-1), epsilon and zeta (as well as any new parameter entering higher post-Newtonian orders) must tend to zero with (gamma-1). It is also found that epsilon and zeta do not enter the 2PN equations of motion of light. Therefore, light-deflection or time-delay experiments cannot probe any theoretically motivated 2PN deviation from general relativity, but they can give a clean access to (gamma-1), which is of greatest significance as it measures the basic coupling strength of matter to the scalar fields. Because of the importance of self-gravity effects in neutron stars, binary-pulsar experiments are found to constitute a unique testing ground for the 2PN structure of gravity. A simplified analysis of four binary pulsars already leads to significant constraints: |epsilon| < 7x10^-2, |zeta| < 6x10^-3.Comment: 63 pages, 11 figures.ps.tar.gz.uu, REVTeX 3.

The flyby anomaly: a multivariate analysis approach

[EN] The flyby anomaly is the unexpected variation of the asymptotic post-encounter velocity of a spacecraft with respect to the pre-encounter velocity as it performs a slingshot manoeuvre. This effect has been detected in, at least, six flybys of the Earth but it has not appeared in other recent flybys. In order to find a pattern in these, apparently contradictory, data several phenomenological formulas have been proposed but all have failed to predict a new result in agreement with the observations. In this paper we use a multivariate dimensional analysis approach to propose a fitting of the data in terms of the local parameters at perigee, as it would occur if this anomaly comes from an unknown fifth force with latitude dependence. Under this assumption, we estimate the range of this force around 300 km .Acedo Rodríguez, L. (2017). The flyby anomaly: a multivariate analysis approach. Astrophysics and Space Science. 362(2):1-7. doi:10.1007/s10509-017-3025-zS173622Acedo, L.: Adv. Space Res. 54, 788 (2014). 1505.06884Acedo, L.: Universe 1, 422 (2015a)Acedo, L.: Galaxies 3, 113 (2015b)Acedo, L.: Mon. Not. R. Astron. Soc. 463(2), 2119 (2016)Acedo, L., Bel, L.: Astron. Nachr. (2016). 1602.03669Adler, S.L.: Int. J. Mod. Phys. A 25, 4577 (2010). 0908.2414 . doi: 10.1142/S0217751X10050706Adler, S.L.: In: Proceedings of the Conference in Honour of Murray Gellimann’s 80th Birthday, p. 352 (2011). doi: 10.1142/9789814335614_0032Anderson, J.D., Laing, P.A., Lau, E.L., Liu, A.S., Nieto, M.M., Turyshev, S.G.: Phys. Rev. D 65(8), 082004 (2002). gr-qc/0104064 . doi: 10.1103/PhysRevD.65.082004Anderson, J.D., Campbell, J.K., Ekelund, J.E., Ellis, J., Jordan, J.F.: Phys. Rev. Lett. 100(9), 091102 (2008). doi: 10.1103/PhysRevLett.100.091102Atchison, J.A., Peck, M.A., Streetman, B.J.: J. Guid. Control Dyn. 33, 1115 (2010). doi: 10.2514/1.47413Border, J.S., Pham, T., Bedrossian, A., Chang, C.: 2015 Delta Differential One-way Ranging in Dsn Telecommunication Link Design Handbook (810-005). http://deepspace.jpl.nasa.gov/dsndocs/810-005/210/210A.pdf . Accessed: 2016-11-17Burns, J.A.: Am. J. Phys. 44(10), 944 (1976). doi: 10.1119/1.10237Busack, H.-J.: arXiv e-prints 1312.1139 (2013)Butrica, A.J.: In: From Engineering Science to Big Science: The NACA and NASA Collier Trophy Research Project Winners, p. 251 (1998)Cahill, R.T.: arXiv e-prints 0804.0039 (2008)Chamberlin, A., Yeomans, D., Giorgini, J., Chodas, P.: 2016 Horizons Ephemeris System. http://ssd.jpl.nasa.gov/horizons.cgi . Accessed: 2016-10-27Danby, J.M.A.: Fundamentals of Celestial Mechanics, 2nd edn. Willmann-Bell, Richmond (1988)Dickey, J.O., Bender, P.L., Faller, J.E., Newhall, X.X., Ricklefs, R.L., Ries, J.G., Shelus, P.J., Veillet, C., Whipple, A.L., Wiant, J.R., Williams, J.G., Yoder, C.F.: Science 265, 482 (1994). doi: 10.1126/science.265.5171.482Feng, J.L., Fornal, B., Galon, I., Gardner, S., Somolinsky, J., Tait, T.M.P., Tanedo, P.: Phys. Rev. Lett. 117, 071803 (2016). doi: 10.1103/PhysRevLett.117.071803Fischbach, E., Buncher, J.B., Gruenwald, J.T., Jenkins, J.H., Krause, D.E., Mattes, J.J., Newport, J.R.: Space Sci. Rev. 145, 285 (2009). doi: 10.1007/s11214-009-9518-5Folkner, W.M., Williamns, J.G., Boggs, D.H., Park, R.S., Kuchynka, P.: IPN Progress Report 42(196) (2014)Franklin, A., Fischback, E.: The Rise and Fall of the Fifth Force. Discovery, Pursuit, and Justification in Modern Physics, 2nd edn. Springer, New York (2016)Hackmann, E., Lämmerzahl, C.: In: 38th COSPAR Scientific Assembly. COSPAR Meeting, vol. 38, p. 3 (2010)Hafele, J.C.: arXiv e-prints 0904.0383 (2009)Iorio, L.: Sch. Res. Exch. 2009 807695 (2009). 0811.3924 . doi: 10.3814/2009/807695Iorio, L.: Astron. J. 142, 68 (2011a). 1102.4572 . doi: 10.1088/0004-6256/142/3/68Iorio, L.: Mon. Not. R. Astron. Soc. 415, 1266 (2011b). 1102.0212Iorio, L.: Galaxies 1, 192 (2013). 1306.3166Iorio, L.: Int. J. Mod. Phys. D 24, 1530015 (2015). 1412.7673Jouannic, B., Noomen, R., van den IJSel, J.A.A.: In: Proceedings of the 25th International Symposium on Space Flight Dynamics ISSFD, Munich (Germany), 2015Krasinsky, G.A., Brumberg, V.A.: Celest. Mech. Dyn. Astron. 90, 267 (2004)Lämmerzahl, C., Preuss, O., Dittus, H.: In: Dittus, H., Lämmerzahl, C., Turyshev, S.G. (eds.) Lasers, Clocks and Drag-Free Control: Exploration of Relativistic Gravity in Space. Astrophysics and Space Science Library, vol. 349, p. 75 (2008). doi: 10.1007/978-3-540-34377-6_3McCulloch, M.E.: Mon. Not. R. Astron. Soc. 389, 57 (2008). 0806.4159 . doi: 10.1111/j.1745-3933.2008.00523.xPinheiro, M.J.: Phys. Lett. A 378, 3007 (2014). 1404.1101Pinheiro, M.J.: Mon. Not. R. Astron. Soc. 461(4), 3948 (2016)Rievers, B., Lämmerzahl, C.: Ann. Phys. 523, 439 (2011). 1104.3985 . doi: 10.1002/andp.201100081Thompson, P.F., Abrahamson, M., Ardalan, S., Bordi, J.: In: 24th AAS/AIAA Space Flight Mechanics Meeting, Santa Fe, New Mexico, January 26–30, 2014, 2014. http://hdl.handle.net/2014/45519Turyshev, S.G., Toth, V.T.: Living Rev. Relativ. 13, 4 (2010). 1001.3686 . doi: 10.12942/lrr-2010-4Turyshev, S.G., Toth, V.T., Kinsella, G., Lee, S.-C., Lok, S.M., Ellis, J.: Phys. Rev. Lett. 108(24), 241101 (2012). 1204.2507 . doi: 10.1103/PhysRevLett.108.241101Vallado, D.A.: Fundamentals of Astrodynamics and Applications, 2nd edn. (2004)Williams, J.G., Turyshev, S.G., Boggs, D.H.: Phys. Rev. Lett. 93(26), 261101 (2004). gr-qc/0411113 . doi: 10.1103/PhysRevLett.93.26110

Phenomenology of the Lense-Thirring effect in the Solar System

Recent years have seen increasing efforts to directly measure some aspects of the general relativistic gravitomagnetic interaction in several astronomical scenarios in the solar system. After briefly overviewing the concept of gravitomagnetism from a theoretical point of view, we review the performed or proposed attempts to detect the Lense-Thirring effect affecting the orbital motions of natural and artificial bodies in the gravitational fields of the Sun, Earth, Mars and Jupiter. In particular, we will focus on the evaluation of the impact of several sources of systematic uncertainties of dynamical origin to realistically elucidate the present and future perspectives in directly measuring such an elusive relativistic effect.Comment: LaTex, 51 pages, 14 figures, 22 tables. Invited review, to appear in Astrophysics and Space Science (ApSS). Some uncited references in the text now correctly quoted. One reference added. A footnote adde

On the dark energy clustering properties

We highlight a viable mechanism leading to the formation of dark energy structures on sub-horizon cosmological scales, starting from linear perturbations in scalar-tensor cosmologies. We show that the coupling of the dark energy scalar field, or Quintessence, to the Ricci scalar induces a "dragging" of its density perturbations through the general relativistic gravitational potentials. We discuss, in particular, how this process forces dark energy to behave as a pressureless component if the cosmic evolution is dominated by non-relativistic matter. This property is also analyzed in terms of the effective sound speed of the dark energy, which correspondingly approaches the behavior of the dominant cosmological component, being effectively vanishing after matter-radiation equality. To illustrate this effect, we consider Extended Quintessence scenarios involving a quadratic coupling between the field and the Ricci scalar. We show that Quintessence density perturbations reach non-linearity at scales and redshifts relevant for the structure formation process, respecting all the existing constraints on scalar-tensor theories of Gravity. This study opens new perspectives on the standard picture of structure formation in dark energy cosmologies, since the Quintessence field itself, if non-minimally coupled to Gravity, may undergo clustering processes, eventually forming density perturbations exiting from the linear regime. A non-linear approach is then required to further investigate the evolution of these structures, and in particular their role in the dark haloes surrounding galaxies and clusters.Comment: 15 pages including three figures, final version accepted for publication by Phys.Rev.