Effects in the Anomalistic Period of Celestial Bodies due to a Logarithmic Correction to the Newtonian Gravitational Potential

We study the motion of a secondary celestial body under the influence of the logarithmic corrected gravitational force of a primary one. This kind of correction was introduced by Fabris et al. (2009). We derive two equations to compute the rate of change of the periastron w.r.t. the eccentric anomaly and its total variation over one revolution, In a kinematical sense, this influence produces an apsidal motion. We perform numerical estimations for Mercury and for the companion star of the pulsar PSR 1913+16. We also consider the case of the artificial Earth satellite GRACE-A, but the results present a low degree of reliability from a practical standpointComment: 12 pages, 5 figures, Published in Astrophysics and Space Science, 201

The Lense-Thirring Effect in the Anomalistic Period of Celestial Bodies

In the weak field and slow motion approximation, the general relativistic field equations are linearized, resembling those of the electromagnetic theory. In a way analogous to that of a moving charge generating a magnetic field, a mass-energy current can produce a gravitomagnetic field. In this contribution, the motion of a secondary celestial body is studied under the influence of the gravitomagnetic force generated by a spherical primary. More specifically, two equations are derived 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). Kinematically, this influence results to an apsidal motion. The aforementioned quantities are numerically estimated for Mercury, the companion star of the pulsar PSR 1913+16, the companion planet of the star HD 80606 and the artificial Earth satellite GRACE-A. The case of the artificial Earth satellite GRACE-A is also considered, but the results present a low degree of reliability from a practical standpoint

Kretschmann Invariant and Relations Between Spacetime Singularities Entropy and Information

Curvature invariants are scalar quantities constructed from tensors that represent curvature. One of the most basic polynomial curvature invariants in general relativity is the Kretschmann scalar. This study is an investigation of this curvature invariant and the connection of geometry to entropy and information of different metrics and black holes. The scalar gives the curvature of the spacetime as a function of the radial distance r in the vicinity as well as inside of the black hole. We derive the Kretschmann Scalar (KS) first for a fifth force metric that incorporates a Yukawa correction, then for a Yukawa type of Schwarzschild black hole, for a Reissner-Nordstrom black hole and finally an internal star metric. Then we investigate the relation and derive the curvature’s dependence on the entropy S and number of information N. Finally we discuss the settings in which the entropy’s full range of positive and negative values would have a meaningful interpretation. The Kretschmann scalar helps us understand the black hole’s appearance as a “whole entity”. It can be applied in solar mass size black holes, neutron stars or supermassive black holes at the center of various galaxies

The Poynting–Robertson Effect in the Newtonian Potential with a Yukawa Correction

We consider a Yukawa-type gravitational potential combined with the Poynting-Robertson effect. Dust particles originating within the asteroid belt and moving on circular and elliptic trajectories are studied and expressions for the time rate of change of their orbital radii and semimajor axes, respectively, are obtained. These expressions are written in terms of basic particle parameters, namely their density and diameter. Then, they are applied to produce expressions for the time required by the dust particles to reach the orbit of Earth. For the Yukawa gravitational potential, dust particles of diameter 10-3 m in circular orbits require times of the order of 8.557 x 106 y and for elliptic orbits of eccentricities e = 0.1, 0.5 require times of 9.396 x 106 and 2.129 x 106 y respectively to reach Earth\u27s orbit. Finally, various cases of the Yukawa potential are studied and the corresponding particle times to reach Earth\u27s are derived per case along with numerical results for circular and various elliptical orbits

The Lens-Thirring effect in the anomalistic period of celestial bodies

In the weak field and slow motion approximation, the general relativistic field equations are linearized, resembling those of the electromagnetic theory. In a way analogous to that of a moving charge generating a magnetic field, a mass energy current can produce a gravitomagnetic field. In this contribution, the motion of a secondary celestial body is studied under the influence of the gravitomagnetic force generated by a spherical primary. More specifically, two equations are derived 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). Kinematically, this influence results to an apsidal motion. The aforementioned quantities are numerically estimated for Mercury, the companion star of the pulsar PSR 1913 plus 16, the companion planet of the star HD 80606 and the artificial Earth satellite GRACE A. The case of the artificial Earth satellite GRACE A is also considered, but the results present a low degree of reliability from a practical standpoint.Comment: 12 pages, 5 Figure

Asymmetric periodic orbits in the photogravitational Copenhagen problem

AbstractIn this paper we study the Ox-asymmetric solutions of the planar photogravitational restricted three-body problem in the case of primaries with equal masses and equal values of the radiation pressure parameters. In particular, we are concerned with the families of asymmetric orbits which bifurcate from the well known families a, b, and c. Their evolution is examined via the numerical construction of series of the critical bifurcation points of a, b, and c with respect to the variation of the common radiation parameter q. We also present some illustrative cases of these families for several values of this parameter. In order to avoid the singularity due to binary collisions between the third body and one of the primaries, the equations of motion of the problem are regularized by using the Levi-Civita transformations

Radar Signal Delay in the Dvali-Gabadadze-Porrati Gravity in the Vicinity of the Sun

In this paper we examine the recently introduced Dvali Gabadadze Porrati gravity model. We use the 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 angles of the signal approach. We use the corresponding numerical value for the parameter r0 to be equal to 5 Mpc. In the vicinity of the Sun and with theta in the range -Pi/3 less than equal to theta less than equal to Pi/3, Deltat is equal to 0.0001233 ps. A time signal delay extremely small to measure by todays technology could be probably measurable in the future years to come, by various future experiments.Comment: 4 pages, Astrophysics Space Science, 201

Quantum and Post-Newtonian Effects in the Anomalistic Period and the Mean Motion of Celestial Bodies

We study the motion of a secondary celestial body under the influence of the corrected gravitational force of a primary. We study the effect of quantum and relativistic corrections to the gravitational potential of a primary body acting on the orbiting body. More specifically, two equations are derived to approximate the perigee/perihelion/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 quantum as well as post- Newtonian accelerations. Numerical results have been obtained for the artificial Earth satellite Molnya, Mercury, and, finally, the for the HW Vir c, planetary companion.Comment: 15 pages, 9 figures to be published in Astrophysics and Space Science Received: 15 January 2015 / Accepted: 1 June 2015. arXiv admin note: text overlap with arXiv:gr-qc/9310024 by other author

Heterotopic ossification in patients previously hospitalized in an intensive care unit

BACKGROUND: Heterotopic ossification (HO) is a potential complication in patients hospitalized in an intensive care unit (ICU). In this study we examined the association of HO diagnosed with three-phase bone scan (3pBS) in association with various parameters in patients previously hospitalized in ICU. MATERIAL AND METHODS: We retrieved patient records of the last 12 years subjected to 3pBS and diagnosed with HO from the Department of Nuclear Medicine (2004 up to 2016) and searched for a name match from ICU records. RESULTS: We found 61 patients that had a positive 3pBS for HO of whom 17 patients were hospitalized in the ICU. Among the 17 patients, twelve fulfilled the study criteria and were included in the study. The mean age was 38 years and 92% were males. HO was unilateral in 7 and bilateral in 5 patients. Patients with unilateral HO had up to 2 joints with HO, while those with bilateral had up to 4 joints. HO was most frequently observed in lower limbs, with hip being the most common joint affected. In the upper limbs, HO occurred predominantly in bilateral joints with elbow being the most frequently involved joint. Patients with longer duration of ICU stay had more joints affected. CONCLUSION: HO is a potential complication in patients with ICU hospitalization. Since 3pBS is an imaging method for early detection of HO, patients hospitalized in ICU should be screened with 3pBS for appropriate management

Linear Stability of Equilibrium Points in the Generalized Photogravitational Chermnykh's Problem

The equilibrium points and their linear stability has been discussed in the generalized photogravitational Chermnykh's problem. The bigger primary is being considered as a source of radiation and small primary as an oblate spheroid. The effect of radiation pressure has been discussed numerically. The collinear points are linearly unstable and triangular points are stable in the sense of Lyapunov stability provided $\mu< \mu_{Routh}=0.0385201$. The effect of gravitational potential from the belt is also examined. The mathematical properties of this system are different from the classical restricted three body problem