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

Testing the gravitational interaction in the field of the Earth via satellite laser ranging and the Laser Ranged Satellites Experiment (LARASE)

In this work, the Laser Ranged Satellites Experiment (LARASE) is presented. This is a research program that aims to perform new refined tests and measurements of gravitation in the field of the Earth in the weak field and slow motion (WFSM) limit of general relativity (GR). For this objective we use the free available data relative to geodetic passive satellite lasers tracked from a network of ground stations by means of the satellite laser ranging (SLR) technique. After a brief introduction to GR and its WFSM limit, which aims to contextualize the physical background of the tests and measurements that LARASE will carry out, we focus on the current limits of validation of GR and on current constraints on the alternative theories of gravity that have been obtained with the precise SLR measurements of the two LAGEOS satellites performed so far. Afterward, we present the scientific goals of LARASE in terms of upcoming measurements and tests of relativistic physics. Finally, we introduce our activities and we give a number of new results regarding the improvements to the modelling of both gravitational and non-gravitational perturbations to the orbit of the satellites. These activities are a needed prerequisite to improve the forthcoming new measurements of gravitation. An innovation with respect to the past is the specialization of the models to the LARES satellite, especially for what concerns the modelling of its spin evolution, the neutral drag perturbation and the impact of Earth's solid tides on the satellite orbit