Newtonian Predictions Research Articles

A critical review of recent Gaia wide binary gravity tests

ABSTRACT Over the last couple of years, the appearance of the third data release from the Gaia satellite has triggered various wide binary low acceleration gravity tests. Wide binaries with typical total masses $\approx 1.0 - 1.6\,\mathrm{ M}_{\odot }$ and separations above a few thousand au probe the low acceleration $a \lesssim a_{0}$ regime, where at galactic and larger scales gravitational anomalies typically attributed to the presence of an as yet undetected dark matter component appear, where $a_{0} \approx 1.2\times 10^{-10}$ m s$^{-2}$ is the acceleration scale of Modified Newtonian Dynamics (MOND). Thus, studies of the relative velocities and separations on the plane of the sky, $v_{2\mathrm{ D}}$ and $s_{2\mathrm{ D}}$, respectively, of wide binary stars extending to separations above a few kau, provide an independent approach on the empirical study of gravity in the interesting $a \lesssim a_{0}$ acceleration range. Two independent groups, through complementary approaches, have obtained evidence for a departure from Newtonian predictions in the low acceleration regime, in consistency with MOND expectations for wide binary orbits in the Solar Neighbourhood. Two other groups however, have instead reported results showing a clear preference for Newtonian gravity over various MOND alternatives tested, over the same low acceleration regime. We here take a critical look at the various studies in question, from sample selection to statistical treatment of the wide binary relative velocities obtained. We discover a couple of critical problems in the formal design and statistical implementation shared by the two latter groups, and show explicitly how these yield biased conclusions.

Retarded Gravity in Disk Galaxies

Disk galaxies have a typical dimension of a few tens of kiloparsecs. It follows from the theory of general relativity that any signal originating from the galactic center will be noticed at the outskirts of the galaxy only tens of thousands of years later. This retardation effect, however, is absent in modelling used to calculate rotation curves throughout entire galaxies and their external gas. The considerable differences between Newtonian predictions and observed velocities are currently removed either by assuming dark matter or by suggesting various modifications to the laws of gravity, MOND being a long standing alternative to Newtonian gravity. In previous papers we have shown that by applying general relativity in a rigorous fashion, without neglecting retardation, one can explain the rotational velocities of galactic matter without modifying gravity or adding dark matter. Moreover, it was shown that dark matter effects, as they appear in gravitational lensing, the Tully-Fisher relation, and mass estimations based on the virial theorem could also be explained as retarded-gravity effects. It must be noted, however, that the proposed theory relies on the existence of a mass flow (of a changing rate) into the galaxy; a requirement that was not directly observed. In the original paper on the subject only one galaxy (M33) was analysed in detail. This was later amended with a published study of eleven galaxies. Here we give a more comprehensive retardation analysis of 143 galaxies of different types from the SPARC Galaxy collection. We show that in most cases we obtain very accurate fits to the data.

Strong constraints on the gravitational law from Gaia DR3 wide binaries

ABSTRACT We test Milgromian dynamics (MOND) using wide binary stars (WBs) with separations of 2–30 kAU. Locally, the WB orbital velocity in MOND should exceed the Newtonian prediction by $\approx 20~{{\ \rm per\ cent}}$ at asymptotically large separations given the Galactic external field effect (EFE). We investigate this with a detailed statistical analysis of Gaia DR3 data on 8611 WBs within 250 pc of the Sun. Orbits are integrated in a rigorously calculated gravitational field that directly includes the EFE. We also allow line-of-sight contamination and undetected close binary companions to the stars in each WB. We interpolate between the Newtonian and Milgromian predictions using the parameter αgrav, with 0 indicating Newtonian gravity and 1 indicating MOND. Directly comparing the best Newtonian and Milgromian models reveals that Newtonian dynamics is preferred at 19σ confidence. Using a complementary Markov Chain Monte Carlo analysis, we find that $\alpha _{\rm {grav}} = -0.021^{+0.065}_{-0.045}$, which is fully consistent with Newtonian gravity but excludes MOND at 16σ confidence. This is in line with the similar result of Pittordis and Sutherland using a somewhat different sample selection and less thoroughly explored population model. We show that although our best-fitting model does not fully reproduce the observations, an overwhelmingly strong preference for Newtonian gravity remains in a considerable range of variations to our analysis. Adapting the MOND interpolating function to explain this result would cause tension with rotation curve constraints. We discuss the broader implications of our results in light of other works, concluding that MOND must be substantially modified on small scales to account for local WBs.

Breakdown of the Newton–Einstein Standard Gravity at Low Acceleration in Internal Dynamics of Wide Binary Stars

A gravitational anomaly is found at weak gravitational acceleration g N ≲ 10−9 m s−2 from analyses of the dynamics of wide binary stars selected from the Gaia DR3 database that have accurate distances, proper motions, and reliably inferred stellar masses. Implicit high-order multiplicities are required and the multiplicity fraction is calibrated so that binary internal motions agree statistically with Newtonian dynamics at a high enough acceleration of ≈10−8 m s−2. The observed sky-projected motions and separation are deprojected to the 3D relative velocity v and separation r through a Monte Carlo method, and a statistical relation between the Newtonian acceleration g N ≡ GM/r 2 (where M is the total mass of the binary system) and a kinematic acceleration g ≡ v 2/r is compared with the corresponding relation predicted by Newtonian dynamics. The empirical acceleration relation at ≲10−9 m s−2 systematically deviates from the Newtonian expectation. A gravitational anomaly parameter δ obs−newt between the observed acceleration at g N and the Newtonian prediction is measured to be: δ obs−newt = 0.034 ± 0.007 and 0.109 ± 0.013 at g N ≈ 10−8.91 and 10−10.15 m s−2, from the main sample of 26,615 wide binaries within 200 pc. These two deviations in the same direction represent a 10σ significance. The deviation represents a direct evidence for the breakdown of standard gravity at weak acceleration. At g N = 10−10.15 m s−2, the observed to Newton-predicted acceleration ratio is . This systematic deviation agrees with the boost factor that the AQUAL theory predicts for kinematic accelerations in circular orbits under the Galactic external field.

Short-range forces due to Lorentz-symmetry violation

Complementing previous theoretical and experimental work, we explore new types of short-range modifications to Newtonian gravity arising from spacetime-symmetry breaking. The first non-perturbative, i.e. to all orders in coefficients for Lorentz-symmetry breaking, are constructed in the Newtonian limit. We make use of the generic symmetry-breaking terms modifying the gravity sector and examine the isotropic coefficient limit. The results show new kinds of force law corrections, going beyond the standard Yukawa parameterization. Further, there are ranges of the values of the coefficients that could make the resulting forces large compared to the Newtonian prediction at short distances. Experimental signals are discussed for typical test mass arrangements.

Investigation of heat transfer and pressure drop in a porous media with internal heat generation

Heat transfer by forced convection of turbulent flow in a cylindrical channel composed of a porous medium with internally generated heat is studied experimentally in this paper. The pressure drop through the channel is determined experimentally and numerically. Steel spheres are used to form a porous channel and electromagnetic induction heating method is used to uniformly generate internal heating in these spheres. Dry air is used as the working fluid during cooling of the heated spheres. The length and inside diameter of the heated copper test section are 500 and 47 mm, respectively. The experiments are carried out for regimes of turbulent flow with Reynolds number based on the spheres diameter (Red), which ranges from 490 to 5490. The impact of various parameters, which include internal heat generation (Q), sphere diameter (d = 6, 8, 10, and 14 mm), and dry air inlet velocity, on heat transfer by forced convection are studied. The pressure drop data agree with the Newtonian prediction. The results show that decreasing porosity of the channel by 6% increases heat transfer by 38% approximately at the same Red, in the range of Red (750–3000). Increasing Red increases heat transfer at the same porosity. The maximum raise in Nusselt number is 20% with raising internal heat generation by 80% at the same porosity, and the pressure drop increases by 200% with decreasing porosity by 6% at the same Red, in the range of Red (750–3000). Increasing Red by 100% increases the pressure drop by 200% approximately at the same porosity, in the range of Red (1000–4000).

A Microfluidic Prototype for High-Frequency, Large Strain Oscillatory Flow Rheometry.

We introduce a “Rheo-chip” prototypical rheometer which is able to characterise model fluids under oscillatory flow at frequencies f up to 80 Hz and nominal strain up to 350, with sample consumption of less than 1 mL, and with minimum inertial effects. Experiments carried out with deionized (DI) water demonstrate that the amplitude of the measured pressure drop falls below the Newtonian prediction at 3 Hz. By introducing a simple model which assumes a linear dependence between the back force and the dead volume within the fluid chambers, the frequency response of both and of the phase delay could be modeled more efficiently. Such effects need to be taken into account when using this type of technology for characterising the frequency response of non-Newtonian fluids.

Physics 101: The visual systems ability to learn and integrate Newtonian predictions

Physics 101: The visual systems ability to learn and integrate Newtonian predictions

The secret of planets’ perihelion between Newton and Einstein

Abstract Three different approaches show that, contrary to a longstanding conviction older than 160 years, the advance of Mercury’s perihelion can be achieved in Newtonian gravity with a very high precision by correctly analyzing the situation without neglecting Mercury’s mass. General relativity remains more precise than Newtonian physics, but Newtonian framework is more powerful than researchers and astronomers were thinking till now, at least for the case of Mercury. The Newtonian formula of the advance of planets’ perihelion breaks down for the other planets. The predicted Newtonian result is indeed too large for Venus and Earth. Therefore, it is also shown that corrections due to gravitational and rotational time dilation, in an intermediate framework which analyzes gravity between Newton and Einstein, solve the problem. By adding such corrections, a result consistent with the one of general relativity is indeed obtained. Thus, the most important results of this paper are two: (i) It is not correct that Newtonian theory cannot predict the anomalous rate of precession of the perihelion of planets’ orbit. The real problem is instead that a pure Newtonian prediction is too large. (ii) Perihelion’s precession can be achieved with the same precision of general relativity by extending Newtonian gravity through the inclusion of gravitational and rotational time dilation effects. This second result is in agreement with a couple of recent and interesting papers of Hansen, Hartong and Obers. Differently from such papers, in the present work the importance of rotational time dilation is also highlighted. Finally, it is important to stress that a better understanding of gravitational effects in an intermediate framework between Newtonian theory and general relativity, which is one of the goals of this paper, could, in principle, be crucial for a subsequent better understanding of the famous Dark Matter and Dark Energy problems.

Dynamic Equilibrium Equations in Unified Mechanics Theory

Traditionally dynamic analysis is done using Newton’s universal laws of the equation of motion. According to the laws of Newtonian mechanics, the x, y, z, space-time coordinate system does not include a term for energy loss, an empirical damping term “C” is used in the dynamic equilibrium equation. Energy loss in any system is governed by the laws of thermodynamics. Unified Mechanics Theory (UMT) unifies the universal laws of motion of Newton and the laws of thermodynamics at ab-initio level. As a result, the energy loss [entropy generation] is automatically included in the laws of the Unified Mechanics Theory (UMT). Using unified mechanics theory, the dynamic equilibrium equation is derived and presented. One-dimensional free vibration analysis with frictional dissipation is used to compare the results of the proposed model with that of a Newtonian mechanics equation. For the proposed entropy generation equation in the system, the trend of predictions is comparable with the reported experimental results and Newtonian mechanics-based predictions.

Newtonian Predictions Are Integrated With Sensory Information in 3D Motion Perception

Because the motions of everyday objects obey Newtonian mechanics, perhaps these laws or approximations thereof are internalized by the brain to facilitate motion perception. Shepard’s seminal investigations of this hypothesis demonstrated that the visual system fills in missing information in a manner consistent with kinematic constraints. Here, we show that perception relies on internalized regularities not only when filling in missing information but also when available motion information is inconsistent with the expected outcome of a physical event. When healthy adult participants (Ns = 11, 11, 12, respectively, in Experiments 1, 2, and 3) viewed 3D billiard-ball collisions demonstrating varying degrees of consistency with Newtonian mechanics, their perceptual judgments of postcollision trajectories were biased toward the Newtonian outcome. These results were consistent with a maximum-likelihood model of sensory integration in which perceived target motion following a collision is a reliability-weighted average of a sensory estimate and an internal prediction consistent with Newtonian mechanics.

Tidal Disruptions of Main-sequence Stars. IV. Relativistic Effects and Dependence on Black Hole Mass

Abstract Using a suite of fully relativistic hydrodynamic simulations applied to main-sequence stars with realistic internal density profiles, we examine full and partial tidal disruptions across a wide range of black hole mass ( ) and stellar mass ( ) as larger M BH leads to stronger relativistic effects. For fixed M ⋆, as M BH increases, the ratio of the maximum pericenter distance yielding full disruptions ( ) to its Newtonian prediction rises rapidly, becoming triple the Newtonian value for , while the ratio of the energy width of the stellar debris for full disruptions to the Newtonian prediction decreases steeply, resulting in a factor of 2 correction at . We provide approximate formulae that express the relativistic corrections of both and the energy width relative to their Newtonian approximate estimates. For partial disruptions, we find that the fractional remnant mass for a given ratio of the pericenter to is higher for larger M BH. These results have several implications. As M BH increases above , the cross section for complete disruptions is suppressed by competition with direct capture. However, the cross-section ratio for partial to complete disruptions depends only weakly on M BH. The relativistic correction to the debris energy width delays the time of peak mass-return rate and diminishes the magnitude of the peak return rate. For , the M BH-dependence of the full disruption cross section and the peak mass-return rate and time is influenced more by relativistic effects than by Newtonian dynamics.

Tidal Disruptions of Main-sequence Stars. I. Observable Quantities and Their Dependence on Stellar and Black Hole Mass

Abstract This paper introduces a series of papers presenting a quantitative theory for the tidal disruption of main-sequence stars by supermassive black holes. Using fully general relativistic hydrodynamics simulations and MESA-model initial conditions, we explore the pericenter-dependence of tidal disruption properties for eight stellar masses ( ) and six black hole masses ( ). We present here the results most relevant to observations. The effects of internal stellar structure and relativity decouple for both the disruption cross section and the characteristic energy width of the debris. Moreover, the full disruption cross section is almost independent of M ⋆ for M ⋆/M ⊙ ≲ 3. Independent of M ⋆, relativistic effects increase the critical pericenter distance for full disruption events by up to a factor of ∼3 relative to the Newtonian prediction. The probability of a direct capture is also independent of M ⋆; at M BH/M ⊙ ≃ 5 × 106 this probability is equal to the probability of a complete disruption. The breadth of the debris energy distribution ΔE can differ from the standard estimate by factors of 0.35 − 2, depending on M ⋆ and M BH, implying a corresponding change (∝(ΔE)−3/2) in the characteristic mass-return timescale. We provide analytic forms, suitable for use in both event rate estimates and parameter inference, to describe all these trends. For partial disruptions, we find a nearly universal relation between the star’s angular momentum and the fraction of M ⋆ remaining. Within the “empty loss-cone” regime, partial disruptions must precede full disruptions. These partial disruptions can drastically affect the rate and appearance of subsequent total disruptions.

Comparing Relativistic and Newtonian Motion Under a Constant Force Using Dimensional Analysis and Calculus

Students have difficulty bridging the conceptual gap between Newtonian and relativistic physics, and, consequently, the teaching of special relativity has been discussed extensively in the literature. A comprehensive list of such references is too large to include, but a brief list is given. In this paper, the author presents several exercises, comparing Newtonian and relativistic solutions to one-dimensional motion of a mass M acted upon by a constant force F. Calculations include the speed, time, and distance of travel for which the Newtonian and relativistic predictions differ by a given percentage. Relativistic motion under a constant force has been discussed previously, but the present treatment has important differences, which will be described below.

Embeddedness of Local Gravity in Perception & Action

Understanding and making predictions about the physical forces determining object motion could greatly facilitate the perception of dynamic events. To be optimal, trajectory judgments of a falling object should be consistent with the physical laws that govern object motion, however previous studies show that beliefs often violate Newtonian laws. The aim of this study was to determine whether human observers integrate Newtonian predictions of object motion with noisy sensory information to reduce ambiguity in the perception of dynamic events. When a ball rolls off a surface, the trajectory of its descent is determined by a relatively constant horizontal velocity and a downward acceleration caused by gravity. For this experiment, we simulated this dynamic event in virtual reality: participants viewed a marble-sized ball fall from a tabletop under two different horizontal velocities and seven different downward accelerations (one matching Earth’s gravity, three lower, and three higher, spanning the range from Mercury’s gravity to Jupiter’s gravity). On each trial, participants indicated the perceived trajectory of the falling ball by adjusting the curvature of a parabolic arc. Each participant’s internal prediction about local gravity in this virtual environment was assessed using trials where the ball rolled up to the edge of the tabletop, then disappeared, and the participant indicated the expected continuation of the trajectory (as opposed to the perceived trajectory indicated in other trials). Although participants’ internal predictions were biased to underestimate the true gravity of Earth (which may serve a practical role for guiding interceptive actions), their perceptual judgments reflected a combination of this prediction with the available visual information. Furthermore, the combination process appears to be consistent with maximum likelihood estimation, as the influence of the internal prediction increased proportionally with the amount of sensory noise, which we varied by manipulating the amount of time the ball’s descent was visible.

Testing Newton/GR, MoND and quantised inertia on wide binaries

Wide binary stars are within the low-acceleration regime in which galactic rotation curves deviate from Newtonian or general relativistic predictions. It has recently been observed that their rotation rates are similarly anomalous in a way that dark matter cannot explain, since it must be smooth on these small scales to fit galaxy rotation curves. Here, it is shown that Newtonian/GR models cannot predict these wide binaries since dark matter cannot be applied. It is also shown that MoND cannot predict these systems. However, a model which assumes that inertia is due to Unruh radiation made inhomogeneous in space by relativistic horizons (QI, quantised inertia) can predict these wide binaries, and it has the advantage of not needing an adjustable parameter.

Detecting the general relativistic orbital precession of the exoplanet HD 80606b

We investigate the relativistic effects in the orbital motion of the exoplanet HD 80606b with a high eccentricity of e ≃ 0.93. We propose a method to detect these effects (notably the orbital precession) based on measuring the successive eclipse and transit times of the exoplanet. In the case of HD 80606b, we find that in ten years (after approximately 33 periods) the instants of transits and eclipses are delayed with respect to the Newtonian prediction by about three minutes due to relativistic effects. These effects can be detected by comparing at different epochs the time difference between a transit and the preceding eclipse, and should be measurable by comparing events already observed on HD 80606 in 2010 with the Spitzer satellite together with those to be observed in the future with the James Webb Space Telescope.

Challenging a Newtonian prediction through Gaia wide binaries

Under Newtonian dynamics, the relative motion of the components of a binary star should follow a Keplerian scaling with separation. Once orientation effects and a distribution of ellipticities are accounted for, dynamical evolution can be modeled to include the effects of Galactic tides and stellar mass perturbers, over the lifetime of the solar neighborhood. This furnishes a prediction for the relative velocity between the components of a binary and their projected separation. Taking a carefully selected small sample of 81 solar neighborhood wide binaries from the Hipparcos catalog, we identify these same stars in the recent Gaia DR2, to test the prediction mentioned using the latest and most accurate astrometry available. The results are consistent with the Newtonian prediction for projected separations below 7000 AU, but inconsistent with it at larger separations, where accelerations are expected to be lower than the critical [Formula: see text][Formula: see text]m.s[Formula: see text] value of MONDian gravity. This result challenges Newtonian gravity at low accelerations and shows clearly the appearance of gravitational anomalies of the type usually attributed to dark matter at galactic scales, now at much smaller stellar scales.

Galaxy two-point correlation function in general relativity

We perform theoretical and numerical studies of the full relativistic two-point galaxy correlation function, considering the linear-order scalar and tensor perturbation contributions and the wide-angle effects. Using the gauge-invariant relativistic description of galaxy clustering and accounting for the contributions at the observer position, we demonstrate that the complete theoretical expression is devoid of any long-mode contributions from scalar or tensor perturbations and it lacks the infrared divergences in agreement with the equivalence principle. By showing that the gravitational potential contribution to the correlation function converges in the infrared, our study justifies an IR cut-off (kIR ⩽ H0) in computing the gravitational potential contribution. Using the full gauge-invariant expression, we numerically compute the galaxy two-point correlation function and study the individual contributions in the conformal Newtonian gauge. We find that the terms at the observer position such as the coordinate lapses and the observer velocity (missing in the standard formalism) dominate over the other relativistic contributions in the conformal Newtonian gauge such as the source velocity, the gravitational potential, the integrated Sachs-Wolf effect, the Shapiro time-delay and the lensing convergence. Compared to the standard Newtonian theoretical predictions that consider only the density fluctuation and redshift-space distortions, the relativistic effects in galaxy clustering result in a few percent-level systematic errors beyond the scale of the baryonic acoustic oscillation (∼ 2% at 150 Mpc/h and redshift one). Our theoretical and numerical study provides a comprehensive understanding of the relativistic effects in the galaxy two-point correlation function, as it proves the validity of the theoretical prediction and accounts for effects that are often neglected in its numerical evaluation.

NGC 1052-DF2 and modified gravity (MOG) without dark matter

ABSTRACT We model the velocity dispersion of the ultradiffuse galaxy NGC 1052-DF2 using Newtonian gravity and modified gravity (MOG). The velocity dispersion predicted by MOG is higher than the Newtonian gravity prediction, but it is fully consistent with the observed velocity dispersion that is obtained from the motion of 10 globular clusters (GCs).