Letter: Sagnac Interferometry and Non–Newtonian Gravity

2010

Many of today's gravity theories predict the existence of a non-Newtonian Yukawa-type correction to the gravitational potential. New experimental techniques, such as Sagnac interferometry, may help in exploring the range λ ≥ 10 14 m where such forces are possibly measurable. It is expected that future space missions will operate in this range, which has not been examined for a very long time. Restricting ourselves to an Earth orbiting satellite we follow a perturbing-potential approach applied on the Lagrange planetary equations, in order to study the effect of such a non-Newtonian potential in the range λ ∼ = 1.073R E . This is achieved by calculating the time rates of change of the orbital elements for the earth orbiting satellite GRACE-A. All these time rates have been calculated on the Keplerian and the precessing Keplerian ellipse of the body under study. Of all the orbital elements, the argument of the perigee is most affected by this potential.

Yukawa-type effects in satellite dynamics

2010

Yukawa-type potential effects in the anomalistic period of celestial bodies

Mioc

2010

Several contemporary modified models of gravity predict the existence of a non-Newtonian Yukawa-type correction to the classical gravitational potential. We study the motion of a secondary celestial body under the influence of the corrected gravitational force of a primary. We derive two equations to approximate the periastron time rate of change and its total variation over one revolution (i.e., the difference between the anomalistic period and the Keplerian period) under the influence of the non-Newtonian radial acceleration. Kinematically, this influence produces apsidal motion. We performed numerical estimations for Mercury, for the companion star of the pulsar PSR 1913+16, and for the extrasolar Planet b of the star HD 80606. We also considered the case of the artificial Earth satellite GRACE-A, but the results present a low degree of reliability from a practical standpoint.

Calculation of radar signal delays in the vicinity of the Sun due to the contribution of a Yukawa correction term in the gravitational potential

2011

There has been a renewed interest in the recent years in the possibility of deviations from the predictions of Newton's "inverse-square law" of universal gravitation. One of the reasons for renewing this interest lies in various theoretical attempts to construct a unified elementary particle theory, in which there is a natural prediction of new forces over macroscopic distances. Therefore the existence of such a force would only coexist with gravity, and in principle could only be detected as a deviation from the inverse square law, or in the "universality of free fall" experiments. New experimental techniques such that of Sagnac interferometry can help explore the range of the Yukawa correction λ ≥ 10 14 m where such forces might be present. It may be, that future space missions might be operating in this range which has been unexplored for very long time. To study the effect of the Yukawa correction to the gravitational potential and its corresponding signal delay in the vicinity of the Sun, we use a spherically symmetric modified space time metric where the Yukawa correction its added to the gravitational potential. Next, the Yukawa correction contribution to the signal delay is evaluated. In the case where the distance of closest approach is much less than the range λ, it results to a signal time delay that satisfies the relation t (b < λ) ∼ = 37.7t (b = λ). I. Haranas ( )