51 research outputs found
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
SpecScan: A Utility Program for Generating Numerical Data from Printed Forms of Spectra or Other Signals
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