Experimental feasibility of measuring the gravitational redshift of light using dispersion in optical fibers

This paper describes a new class of experiments that use dispersion in optical fibers to convert the gravitational frequency shift of light into a measurable phase shift or time delay. Two conceptual models are explored. In the first model, long counter-propagating pulses are used in a vertical fiber optic Sagnac interferometer. The second model uses optical solitons in vertically separated fiber optic storage rings. We discuss the feasibility of using such an instrument to make a high precision measurement of the gravitational frequency shift of light.Comment: 11 pages, 12 figure

Long-term evolution of orbits about a precessing oblate planet. 3. A semianalytical and a purely numerical approach

Construction of a theory of orbits about a precessing oblate planet, in terms of osculating elements defined in a frame of the equator of date, was started in Efroimsky and Goldreich (2004) and Efroimsky (2005, 2006). We now combine that analytical machinery with numerics. The resulting semianalytical theory is then applied to Deimos over long time scales. In parallel, we carry out a purely numerical integration in an inertial Cartesian frame. The results agree to within a small margin, for over 10 Myr, demonstrating the applicability of our semianalytical model over long timescales. This will enable us to employ it at the further steps of the project, enriching the model with the tides, the pull of the Sun, and the planet's triaxiality. Another goal of our work was to check if the equinoctial precession predicted for a rigid Mars could have been sufficient to repel the orbits away from the equator. We show that for low initial inclinations, the orbit inclination reckoned from the precessing equator of date is subject only to small variations. This is an extension, to non-uniform precession given by the Colombo model, of an old result obtained by Goldreich (1965) for the case of uniform precession and a low initial inclination. However, near-polar initial inclinations may exhibit considerable variations for up to +/- 10 deg in magnitude. Nevertheless, the analysis confirms that an oblate planet can, indeed, afford large variations of the equinoctial precession over hundreds of millions of years, without repelling its near-equatorial satellites away from the equator of date: the satellite inclination oscillates but does not show a secular increase. Nor does it show secular decrease, a fact that is relevant to the discussion of the possibility of high-inclination capture of Phobos and Deimos