Abstract:
Very recently authors in [1] proposed a new Generalized Uncertainty Principle (or GUP) with a linear term in Plank length. In this Letter the effect of this linear term is studied perturbatively in the context of Keplerian orbits. The angle by which the perihelion of the orbit revolves over a complete orbital cycle is computed. The result is applied in the context of the precession of the perihelion of Mercury. As a consequence we get a lower bound of the new intermediate length scale offered by the GUP which is approximately 40 orders of magnitude below Plank length.

Abstract:
The longitude of the perihelion advance of Mercury was calculated for the
two and ten-body problem by using a correction to the balance between the force
given by the Newton 2^{nd} law of motion and the Newton gravitational
force. The corresponding system of differential equations was solved
numerically. The correction, that expresses the apparent mass variation with
the body speed, has a trend that is different from those that usually appear in
the electron theory and in the special theory of relativity. The calculated
intrinsic precession was ~42.95 arc-sec/cy for the Sun-Mercury system and
~42.98 arc-sec/cy when the difference between the corrected model and the Newtonian
model, for the 10-body problem, is taken.

Abstract:
In this talk relativistic corrections due to Geroch-Hansen multipoles for perihelion precession and node line precession of orbits in a stationary axially symmetric vacuum spacetime endowed with a plane of symmetry will be shown. Patterns of regularity will be discussed.

Abstract:
Gravitational Thomas Precession (GTP) is the name given to Thomas Precession when the acceleration is caused by a gravitational force field. The GTP gives a negative contribution of 7.163 arcsec/century for the anomalous perihelion advance of Mercury's orbit. This effect seems to be of some concern for the General Relativity.

Abstract:
The precession of Mercury's perihelion is reinspected by the principle of least action. The anomalous advancement of the apside line that is customarily accounted by the theory of general relativity, is ascribed to the gravitational effect due to the entire Universe. When the least action is written in the Sun's frame of reference, the residual rotation is seen to stem from inertia due to all bodies in the Universe. Since mass corresponds to a bound form of energy, gravity, as any other force, can be described as an energy density difference between a system of bodies and its surrounding energy densities that are dispersed throughout the Universe. According to the principle of least action the Universe is expanding by combustion of mass to radiation in the quest of equilibrating the bound forms of energy with "zero-density surroundings" in least time. Keywords: cosmological principle; energy density; energy dispersal; evolution; gravity; the principle of least action

Abstract:
We calculate the perihelion precession delta for nearly circular orbits in a central potential V(r). Differently from other approaches to this problem, we do not assume that the potential is close to the Newtonian one. The main idea in the deduction is to apply the underlying symmetries of the system to show that delta must be a function of r V''(r)/V'(r), and to use the transformation behaviour of delta in a rotating system of reference. This is equivalent to say, that the effective potential can be written in a one-parameter set of possibilities as sum of centrifugal potential and potential of the central force. We get a universal formula for delta. It has to be read as follows: a circular orbit at this value r exists and is stable if and only if this delta is a well-defined real; and if this is the case, then the angular difference from one perihelion to the next one for nearly circular orbits at this r is exactly 2 pi + delta. Then we show how to apply this result to examples of recent interest like modified Newtonian gravity and linearized fourth-order gravity. In the second part of the paper, we generalize this universal formula to static spherically symmetric space-times. For the Schwarzschild black hole with mass parameter m > 0 it leads to a surprisingly unknown formula. It represents a strict result and is applicable for all values r > 6m and is in good agreement with the fact that stable circular orbits exist for r > 6m only.

Abstract:
Among all the theories proposed to explain the 'anomalous' perihelion precession of Mercury's orbit announced in 1859 by Le Verrier, the general theory of relativity proposed by Einstein in November 1915, alone could calculate Mercury's 'anomalous' precession with a precision demanded by observational accuracy. Since Mercury's precession was a directly derived result of the full general theory, it was viewed by Einstein as the most critical test of general relativity, amongst the three tests proposed by him. With the advent of the space age, the observational accuracy level has improved further and it became possible to detect this precession for other planetary orbits of the solar system -- viz., Venus and the Earth. This conclusively proved that the phenomenon of 'anomalous' perihelion precession of planetary orbits is really a relativistic effect. Our previous papers presented the mathematical model and the computed value of the relativistic perihelion precession of Mercury's orbit using an alternate relativistic gravitational model, which is a remodeled form of Einstein's relativity theories, and which retained only experimentally proven principles and has been enriched by the benefits of almost a century-long relativity experimentation including the space age experiments. Using this model, we present in this paper the computed values of the relativistic precession of Venus and the Earth, which compare well with the predictions of general relativity and also are in agreement with the observed values within the range of uncertainty.

Abstract:
If the concepts underlying Effective Theory were appreciated from the earliest days of Newtonian gravity, Le Verrier's announcement in 1845 of the anomalous perihelion precession of Mercury would have been no surprise. Furthermore, the size of the effect could have been anticipated through "naturalness" arguments well before the definitive computation in General Relativity. Thus, we have an illustration of how Effective Theory concepts can guide us in extending our knowledge to "new physics", and not just in how to reduce larger theories to restricted (e.g., lower energy) domains.

Abstract:
A updated numerical evaluation of the Newtonian component of Mercury’s
perihelion advance over more than two centuries starting from about the year
2000 is made using the Euler’s algorithm as well as a modified Euler algorithm.
Results are given for about the last 30 years of this interval which show that
the precession rate may be substantially higher than what it is believed to be.

Abstract:
Quite exotic relativistic objects known as wormholes are hypothetical candidates for central machine of active galactic nuclei as well as black holes. We find the magnitude of the perihelion precession and the deflection of light in gravitational field of a wormhole and compare them with those for a black hole. The impact parameter is taken to be much larger than the wormhole throat size. We show that the relative difference between results for a black hole and a wormhole may be significant and amount to tens of percent.