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In this paper we examine the recently introduced Dvali-Gabadadze-Porrati (DGP) gravity model. We use a space-time metric in which the local gravitation source dominates the metric over the contributions from the cosmological flow. Anticipating ideal possible solar system effects, we derive expressions for the signal time delays in the vicinity of the Sun, and for various ranges of the angle theta of the signal approach. The time contribution due to DGP correction to the metric is found to be proportional to b^3/2/c²r₀. For r₀ equal to 5 Mpc and theta in the range [-Pi/3, Pi/3], delta t is equal to 0.0001233 ps. This delay is extremely small to be measured by today's technology, but it could be probably measurable by future experiments.

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 lamda > = 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 , it results to a signal time delay that satisfies the relation t(b

In the study of an Earth orbiting satellite, the terms of the series expansion of the Earth's gravitational potential can be expressed as functions of the eccentricity of the satellite. These functions are also known as eccentricity functions. The series expansion of these functions given by Kaula [2] appears to result in instabilities at high eccentricities. When calculating the eccentricity functions, researchers resort to numerical integration techniques instead. The approach followed in this contribution bypasses the problem of instability at high eccentricities by using a Hansen coefficient definition. As a test, we first calculate analytical expressions for various known eccentricity functions and then we proceed with the calculation of the eccentricity functions associated with degree and order 20, 30, 40, 50 sectorial harmonic coefficient expansion of the gravitational potential. Our calculation demonstrates the efficiency of Hansen coefficient approach that differs from that given by Kaula. It is efficient, fast, and can easily be performed with the help of a personal computer, with no instabilities at higher eccentricities.

We study the effects of a non-singular gravitational potential on satellite orbits calculating the corresponding changes of its orbital elements, using Gauss' planetary equations. We derive two non-zero expressions for the changes of the argument of the perigee and the mean anomaly, and we compare them to those derived by the general theory relativity. Using the GRACE satellite system, we obtain numerical results from which we conclude that the effect of such a potential, on the perigee cannot be separated from that of general relativity. Furthermore we conclude that the effect on the mean anomaly can probably be observed by today's technology.

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, can help in exploring the range Lamda > 10¹⁴, 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 Lamda=1.073 R. 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.

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.