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

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 ≥ 1014 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 ( ) Department of Physics and Astronomy, York University, 4700 Keele Street, Toronto, Ontario, M3J 1P3, Canada e-mail: [email protected] O. Ragos Department of Mathematics, Faculty of Sciences, University of Patras, 26500 Patras, Greece e-mail: [email protected]