3. Beautiful theories, ugly facts

‘Beautiful theories, ugly facts’ evaluates the theories on planetary systems, particularly the Solar System. In 1734, the Swedish polymath Emmanuel Swedenborg proposed that the Sun and all the planets condensed out of the same ball of gas, in what is probably the earliest statement of the nebular hypothesis. The nebular hypothesis entered something close to its modern form in the hands of the French mathematician Pierre-Simon Laplace, who in 1796 made the clear connection to Newtonian gravity. The angular momentum problem and the structure of a protoplanetary disk, the formation of rocky cores, and the gravitational accretion of gas in the disk also come under this topic.

Simultaneous determination of mass parameter and radial marker in Schwarzschild geometry

We show that mass parameter and radial marker values can be indirectly measured in thought experiments performed in Schwarzschild spacetime, without using the Newtonian limit of general relativity or approximations based on Euclidean geometry. Our approach involves different proper time quantifications as well as solutions to systems of algebraic equations, and aims to strengthen the conceptual independence of general relativity from Newtonian gravity.

Effective Potentials and Orbits in Weyl Conformastatic Slender Disk

By using geodesic equations to obtain a gravitational potential generated from a point-like source, we end up in the concept of a nearly Newtonian gravity to analyse effective potentials of quasi-circular orbits. By means of an approximate solution from an axially static and symmetric Weyl metric, we study an effective gravitational potential to obtain its related rotation curves, orbital planes and orbits. Moreover, using as initial condition a Plummer sphere, some prospects on star cluster disruption are also discussed in this framework.

The signature of the quadratic generalized uncertainty principle on the newtonian gravity and galaxy mass profile

In this study, we discuss the corrections implies by the presence of the general uncertainty principle (GUP) on Newton’s law of gravity by virtue of Verlinde’s proposal. We argue here that GUP leads to twofold modification, namely on the equipartition theorem and the holographic relation (Bekenstein-Hawking formula). Hence, following Verlinde’s proposal, we obtain quantum corrections term to the Newtonian gravity. In addition, we also report the quantum corrected mass profile of the galaxy. We restricted our derivation to first order in the GUP’s free parameter and compared it analytically with the other relevant works.

Additional Solar System Gravitational Anomalies

This article is motivated by uncertainty in experimental determinations of the gravitational constant, G, and numerous anomalies of up to 0.5 percent in Newtonian gravitational force on bodies within the solar system. The analysis sheds new light through six natural experiments within the solar system, which draw on published reports and astrophysical databases, and involve laboratory determinations of G, orbital dynamics of the planets and the moons of Earth and Mars, and non-gravitational acceleration (NGA) of ‘Oumuamua and comets. In each case, values are known for all variables in Newton’s Law , except for the gravitational constant, G. Analyses determine the gravitational constant’s observed value, , which—across the six settings—varies with the mass of the smaller, moving body, m, so that . While further work is required, this examination shows a scale-related Newtonian gravity effect at scales from benchtop to Solar System, which contributes to the understanding of symmetry in gravity and has possible implications for Newton’s Laws, dark matter, and formation of structure in the universe.

Dark Matter Axions, Non-Newtonian Gravity and Constraints on Them from Recent Measurements of the Casimir Force in the Micrometer Separation Range

We consider axionlike particles as the most probable constituents of dark matter, the Yukawa-type corrections to Newton’s gravitational law and constraints on their parameters following from astrophysics and different laboratory experiments. After a brief discussion of the results by Prof. Yu. N. Gnedin in this field, we turn our attention to the recent experiment on measuring the differential Casimir force between Au-coated surfaces of a sphere and the top and bottom of rectangular trenches. In this experiment, the Casimir force was measured over an unusually wide separation region from 0.2 to 8μm and compared with the exact theory based on first principles of quantum electrodynamics at nonzero temperature. We use the measure of agreement between experiment and theory to obtain the constraints on the coupling constant of axionlike particles to nucleons and on the interaction strength of a Yukawa-type interaction. The constraints obtained on the axion-to-nucleon coupling constant and on the strength of a Yukawa interaction are stronger by factors of 4 and 24, respectively, than those found previously from gravitational experiments and measurements of the Casimir force but weaker than the constraints following from a differential measurement where the Casimir force was nullified. Some other already performed and planned experiments aimed at searching for axions and non-Newtonian gravity are discussed, and their prospects are evaluated.

External field effect in gravity

In both Newtonian gravity and Einstein gravity there is no force on a test particle located inside a spherical cavity cut out of a static, spherically symmetric mass distribution. Inside the cavity exterior matter is decoupled and there is no external field effect that could act on the test particle. However, for potentials other than the Newtonian potential or for geometries other than Ricci flat ones this is no longer the case, and there then is an external field effect. We explore this possibility in various alternate gravity scenarios, and suggest that such (Machian) external field effects can serve as a diagnostic for gravitational theory.