Precision Lunar Laser Ranging For Lunar and Gravitational Science

Laser ranging to retroreflector arrays placed on the lunar surface by the Apollo astronauts and the Soviet Lunar missions over the past 39 years have dramatically increased our understanding of gravitational physics along with Earth and Moon geophysics, geodesy, and dynamics. Significant advances in these areas will require placing modern retroreflectors and/or active laser ranging systems at new locations on the lunar surface. Ranging to new locations will enable better measurements of the lunar librations, aiding in our understanding of the interior structure of the moon. More precise range measurements will allow us to study effects that are too small to be observed by the current capabilities as well as enabling more stringent tests of Einstein's theory of General Relativity. Setting up retroreflectors was a key part of the Apollo missions so it is natural to ask if future lunar missions should include them as well. The Apollo retroreflectors are still being used today, and nearly 40 years of ranging data has been invaluable for scientific as well as other studies such as orbital dynamics. However, the available retroreflectors all lie within 26 degrees latitude of the equator, and the most useful ones within 24 degrees longitude of the sub-earth meridian. This clustering weakens their geometrical strength

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