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We examine the Poynting-Robertson (PR) effect under the influence of a logarithmic predicted as a correction to the Newtonian gravitational potential in the solar system. Our motivation emanates from the fact that today’s gravitational theories predict various corrections such that exponential, logarithmic to describe and understand the existence of dark matter, postulated to resolve discrepancies in astrophysical observations in today’s accepted theories of gravity. By saying that we simply mean that our main interest is to calculate the times that dust particles take to reach the Earth’s orbit and derive analytical expressions for the time changes of basic orbital elements in the influence of the PR effect. We use dust particle starting at a distance $r = 2.7~\text{AU}$ or approximately in the asteroid belt. In a first order perturbation treatment we obtain time solutions for the orbital elements of semi major axis, eccentricity, and mean motion, as well as expressions for the time taken for these particles to reach Earth’s orbit. We find that for circular orbits in a logarithmic potential the time taken to reach Earth is slightly larger that the elliptical orbits. Newtonian potential circular orbits require more times when compared to the logarithmic ones. Finally elliptical orbits time to reach Earth are of the same order of magnitude with a dependence on the eccentricity, density, and particle diameter.

We study the motion of a secondary celestial body under the influence of a corrected gravitational potential in a modified Newtonian dynamics scenario. Furthermore we look within the Milky-way where the first correction to the potential results from a modified Poisson equation, and includes two mew terms one of which is of the form $\ln(r/r_{\max})$ and the other is associated with the cosmological constant lambda $\varLambda $ added to the Newtonian potential. The regions of influence of the two potentials are associated with regions of interested bounded by the conditions $r < r_{\max}$ for the Newtonian potential, $r > r_{\max}$ the logarithmic correction to the potential relating to the term $(\nabla \phi )^{2}$ in the Poisson equation for the gravitational field that has matter density $\rho $ , and finally, the domain where $r \gg r_{\max}$ the potential scales as $c^{2}\varLambda r^{2}$ and the cosmological constant lambda dominates. Next using an average disturbing potential we integrate Lagrange’s planetary equations and we obtain analytical expressions for the average time rates of change of the orbital elements using our sun as an example. We find that both dark matter and cosmological constant affect only the argument of the perigalaktikon point as well as the mean anomaly.

We explore the dynamics and stability of the two-body problem by modifying the Newtonian potential with the Yukawa potential. This model may be considered a theory of modified gravity; where the interaction is not simply the Kepler solution for large distance. We investigate stability by deriving the Jacobian of the linearized matrix equation and evaluating the eigenvalues of the various equilibrium points calculated during the analysis. The subcases of a purely Yukawa and purely Newtonian potential are also explored.

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 $8.557 \times 10^{6}$ yr and for elliptic orbits of eccentricities $e =0.1, 0.5$ require times of $9.396 \times 10^{6}$ and $2.129 \times 10^{6}$ yr respectively to reach Earth’s orbit. Finally, various cases of the Yukawa potential are studied and the corresponding particle times to reach Earth’s are derived per case along with numerical results for circular and various elliptical orbits.

We use a non-singular potential that appears in the literature under the influence of which the Poynting- Robertson effect is studied. For that, dust particles originat- ing within the asteroid belt are used, in circular and elliptic orbits, and expressions for the semimajor axis as a function of time are obtained. The derived expressions are written in terms of the two basic dust particle parameters, namely the density and the diameter. In both cases, we obtain expres- sions for the time that the dust particles take to reach the orbit of Earth under the action of the non-singular poten- tial and solar radiation. For the non-singular potential, dust particles of diameter 10 −3 m in circular and elliptical orbits require times of the order of 4.058 × 10 7 and 2.823 × 10 7 y to reach the orbit of the Earth respectively. Finally, the de- rived expressions and numerical results are compared with those of the Newtonian potential.

A generalized uncertainty principle admitting a minimal measurable length contains a parameter of which the numerical value needs to be fixed. In fact, the application of the Generalized Uncertainty Principle (GUP) to some quantum mechanical problems offers different values for the upper bound of the GUP dimensionless parameter \(\alpha_{0}\). In this work, by applying a GUP which is linear and quadratic in the \(\Delta P\) correction to Newton’s law of gravity, and then using the stability condition of the circular orbits of the planets, we propose an upper bound for \(\alpha_{0}\). By using the astronomical data of the Solar System objects, a new and severe constraint on the upper bound of the parameter \(\alpha_{0}\) is derived. Also, using the modified Newtonian potential, inspired by a GUP which is linear and quadratic in \(\Delta P\), we investigate the possibility of measuring the relevant parameter \(\alpha_{0}\) through observables provided by the Galileo Navigation Satellite System.

The (Newton + Yukawa)-type gravitational potential V(r)=−(γM/r)[1+Aexp (−r/B)](γ= the gravitational constant as measured at infinity, M= the mass of the source, A, B are constants) is considered in the framework of the Sciama linear approach to Mach’s principle. The coupling constant A of the Yukawa component is found to be related to the mass density and size of the observable (causally connected) universe.

If the photon were to have a rest mass near the best present upper limit,m≲3×10−53 g, Maxwell's equations would be inapplicable over distances exceeding about 1015 cm, with profound implications for cosmic electrodynamics. This paper deals with electrodynamic and gravitational effects of the non-Maxwellian stresses which would be associated with large-scale magnetic fields in quasi-static plasmas in these circumstances. The existence of moderately dense interstellar gas clouds with relatively strong magnetization shows thatm≲10−58 g. General relativity must be used to calculate even the ‘Newtonian’ gravitational effects of electromagnetic fields, and it is shown here that the Newtonian potential caused by the non-Maxwellian stresses just cancels that caused by the non-Maxwellian energy density. Previous arguments based on the latter alone are therefore invalid.

We study the effects of a non singular gravitational potential on satellite orbits by deriving the corresponding time rates of change of its orbital elements. This is achieved by expanding the non singular potential into power series up to second order. This series contains three terms, the first being the Newtonian potential and the other two, (first order term)and (second order term), express deviations of the singular potential from the Newtonian. These deviations from the Newtonian potential are taken as disturbing potential terms in the Lagrange planetary equations that provide the time rates of change of the orbital elements of a satellite in a non singular gravitational field. We split these effects into secular, low and high frequency components and we evaluate them numerically using the low Earth orbiting mission Gravity Recovery and Climate Experiment (GRACE). We show that the secular effect of the second order disturbing term on the perigee and the mean anomaly are, 4.307 10^-9/a and -2.533 10^-15/a respectively. These effects, are far too small and most likely cannot easily be observed with todays technology. Numerical evaluation of the low and high frequency effects of the disturbing term on low Earth orbiters like GRACE are very small and undetectable by current observational means., Comment: 9 pages