Orbital effects of a monochromatic plane gravitational wave with ultra-low frequency incident on a gravitationally bound two-body system

We analytically compute the long-term orbital variations of a test particle orbiting a central body acted upon by an incident monochromatic plane gravitational wave. We assume that the characteristic size of the perturbed two-body system is much smaller than the wavelength of the wave. Moreover, we also suppose that the wave's frequency is much smaller than the particle's orbital one. We make neither a priori assumptions about the direction of the wavevector nor on the orbital geometry of the planet. We find that, while the semi-major axis is left unaffected, the eccentricity, the inclination, the longitude of the ascending node, the longitude of pericenter and the mean anomaly undergo non-vanishing long-term changes. They are not secular trends because of the slow modulation introduced by the tidal matrix coefficients and by the orbital elements themselves. They could be useful to indepenedently constrain the ultra-low frequency waves which may have been indirectly detected in the BICEP2 experiment. Our calculation holds, in general, for any gravitationally bound two-body system whose characteristic frequency is much larger than the frequency of the external wave. It is also valid for a generic perturbation of tidal type with constant coefficients over timescales of the order of the orbital period of the perturbed particle.Comment: LaTex2e, 24 pages, no figures, no tables. Changes suggested by the referees include

Observational constraints on spatial anisotropy of G from orbital motions

A phenomenological anisotropic variation \Delta G/G of the Newtonian gravitational coupling parameter G, if real, would affect the orbital dynamics of a two-body gravitationally bound system in a specific way. We analytically work out the long-term effects that such a putative modification of the usual Newtonian inverse-square law would induce on the trajectory of a test particle orbiting a central mass. Without making any a-priori simplifying assumptions concerning the orbital configuration of the test particle, it turns out that its osculating semi-major axis a, eccentricity e, pericenter \varpi and mean anomaly M undergo long-term temporal variations, while the inclination I and the node \Omega are left unaffected. Moreover, the radial and the transverse components of the position and the velocity vectors r and v of the test particle experience non-vanishing changes per orbit, contrary to the out-of-plane ones. Then, we compute our theoretical predictions for some of the major bodies of the solar system by orienting the gradient of G(r) towards the Galactic Center and keeping it fixed over the characteristic timescales involved. By comparing our calculation to the latest observational determinations for the same bodies, we infer \Delta G/G <= 10^-17 over about 1 au. Finally, we consider also the Supermassive Black Hole hosted by the Galactic Center in Sgr A^* and the main sequence star S2 orbiting it in about 16 yr, obtaining just \Delta G/G <= 10^-2 over 1 kau.Comment: LaTex2e, 18 pages, no figures, 4 tables. Accepted by Classical and Quantum Gravity (CQG). Typo fixed. Reference update