Search

Dark matter is one of the great mysteries of contemporary science. In the first part of this work, we covered some general concepts that will serve as an introduction to the more specific topics analysed in this second part, such as the hypothetical particles that could constitute dark matter, and the experiments and detection techniques that have been implemented. [ABSTRACT FROM AUTHOR]

Many theories, such as the unification theories that would include gravitation, predict deviations from Newtonian inverse-square law (ISL) at short range. Many high precision experiments have been performed, but additional experiments are still of high scientific importance. Here, we discuss the torque thermal noise caused by residual gas damping, especially the effect of squeeze-film damping, in a proposed ISL experiment at the range of tens of microns. In such experiments, torsion pendulums are usually used to probe the torque interactions between the detector and the attractor, of which the thermal noise should be considered carefully due to the high sensitivity. By introducing a thermal accommodation coefficient, we can accurately model the torque noise of the residual gas damping as a combination of elastic and inelastic collisions. The results show that the noise will increase significantly at short separations between the pendulum and the surrounding components. In particular, when the separation is smaller than 40 μm, the squeeze-film damping may be larger than the internal damping of the pendulum used in present experiments, and become the fundamental limit for the experiments in the shorter range. [ABSTRACT FROM AUTHOR]

Gravitational waves allow us to test general relativity in the highly dynamical regime. While current observations have been consistent with waves emitted by quasi-circular binaries, eccentric binaries may also produce detectable signals in the near future with ground- and space-based detectors. We here explore how tests of general relativity scale with the orbital eccentricity of the source during the inspiral of compact objects up to e ∼ 0.8. We use a new, third post-Newtonian-accurate, eccentric waveform model for the inspiral of compact objects, which is fast enough for Bayesian parameter estimation and model selection, and highly accurate for modeling moderately eccentric inspirals. We derive and incorporate the eccentric corrections to this model induced in Brans–Dicke theory and in Einstein–dilaton–Gauss–Bonnet gravity at leading post-Newtonian order, which suggest a straightforward eccentric extension of the parameterized post-Einsteinian formalism. We explore the upper limits that could be set on the coupling parameters of these modified theories through both a confidence-interval- and Bayes-factor-based approach, using a Markov-Chain Monte Carlo and a trans-dimensional, reversible-jump, Markov-Chain Monte Carlo method. We find projected constraints with signals from sources with e ∼ 0.4 that are one order of magnitude stronger than that those obtained with quasi-circular binaries in advanced LIGO. In particular, eccentric gravitational waves detected at design sensitivity should be able to constrain the Brans–Dicke coupling parameter ω ≳ 3300 and the Gauss–Bonnet coupling parameter α1/2 ≲ 0.5 km at 90% confidence. Although the projected constraint on ω is weaker than other current constraints, the projected constraint on α1/2 is 10 times stronger than the current gravitational wave bound. [ABSTRACT FROM AUTHOR]

This review article presents the progress made over the last decade, since the introduction of effective field theories (EFTs) into post-Newtonian (PN) gravity. These have been put forward in the context of gravitational waves (GWs) from the compact binary inspiral. The mature development of this interdisciplinary field has resulted in significant advances of wide interest to physics at several levels serving various purposes. The field has firmly demonstrated, that seemingly disparate physical domains, such as quantum field theory and classical gravity, are related, and that the EFT framework is a universal one, where it has been proven to supply a robust methodology to boost progress in the development of PN theory. In this review emphasis was put on an accessible pedagogic presentation of the field theoretic aspects of the subject, with the view, that these are in fact common across the whole of theoretical physics, rather than in their original narrow quantum context. The review is aimed at a broad audience, from general readers new to the field, to specialists and experts in related subjects. The review begins with an overview of the introduction of EFTs into classical gravity and their development. Then, the basic ideas, which form the conceptual foundation of EFTs, are provided, and the strategy of a multi-stage EFT framework, which is utilized for the PN binary inspiral problem, is outlined. The main body of the review is then dedicated to presenting in detail the study of each of the effective theories at each of the intermediate scales in the problem, up to the actual GW observables. First, the EFT for a single compact object is considered, from which one proceeds to the EFT of a compact binary system, viewed as a composite particle with internal binding interactions. Finally, one arrives at the effective theory of the time-dependent multipole moments of the radiating system. The review is concluded with the multiple prospects of building on the progress in the field, and using further modern field theory insights and tools, to specifically address the study of GWs, as well as to broadly expand our fundamental understanding of gauge and gravity theories across the classical and quantum regimes. [ABSTRACT FROM AUTHOR]

In general relativity, Mercury's orbit becomes approximately elliptical and the its perihelion has thus an additional advance. We demonstrate, meanwhile, that in comparison of those given by Newton's theory of gravitation for the orbit of the Mercury, the circumference and the area are reduced by 40.39 km and 2.35 × 109 km2, respectively, besides the major-axis contraction pointed out recently, and all are produced by the curved space within Einstein's theory of gravitation. Since the resolution power of present astronomical distance measurement technology reaches one kilometer, the shrinkage of Mercury's orbit can then be observable. [ABSTRACT FROM AUTHOR]

We consider the application of both conservation of momentum and Newton’s laws to the Moon in an assumed circular orbit about the Earth. The inadequacy of some texts in applying Newton’s laws is considered. [ABSTRACT FROM AUTHOR]

Taking a novel approach, this paper discusses the structure of compact stars, an important topic in theoretical astrophysics. Adopting Newtonian gravitation, we solve the hydrostatic equilibrium equation by imposing a simple parametrization for the mass density inside the star. The solutions of the equilibrium equation are carried out without numerical integration, with the aim of determining a few global properties of white dwarfs and neutron stars. The global properties of compact stars are thus provided by simple algebraic relationships. The model is intended as an introductory approach to the study of compact stars at an undergraduate or graduate level. [ABSTRACT FROM AUTHOR]

In this paper the consequences of quantum gravitational effects in cosmological voids are studied through the use of the well-known and reliably calculable long-range quantum corrections to the gravitational potential. The line-element corresponding to these quantum-modified voids in a Universe possessing a cosmological constant is obtained. It is shown that the quantum vacuum in the voids is interpretable, through Einstein's equations, as a highly rarefied effective anisotropic fluid permeating the voids. Contrary to the common belief that in our current epoch violations of the energy conditions only take place in relatively small regions of the Universe, it is argued that theremay be extremely tiny quantum violations of the weak energy condition in cosmological voids and, therefore, in enormous regions occupying most of the volume of the Universe. [ABSTRACT FROM AUTHOR]

The LIGO and Virgo Scientific Collaborations have cataloged ten confident detections from binary black holes and one from binary neutron stars in their first two observing runs, which has already brought up an immense desire among the scientists to study the Universe and to extend the knowledge of astrophysics from these compact objects. One of the fundamental noise sources limiting the achievable detector bandwidth is given by Newtonian noise arising from terrestrial gravity fluctuations. It is important to model Newtonian noise spectra very accurately as it cannot be monitored directly using current technology. In this article, we show the reduction in the Newtonian noise curve obtained by more accurately modelling the current configuration of the Virgo observatory. In Virgo, there are clean rooms or recess like structures underneath each test mirror forming the main two Fabry–Perot arm cavities of the detector. We compute the displacements originating from an isotropic Rayleigh field including the recess structure. We find an overall strain noise reduction factor of 2 in the frequency band from 12 to about 15 Hz relative to previous models. The reduction factor depends on frequency and also varies between individual test masses. [ABSTRACT FROM AUTHOR]

The Newtonian constant of gravitation G historically has the largest relative uncertainty over all other fundamental constants with some discrepancies in values between different measurements. We propose a new scheme to measure G by detecting the position of a test mass in a precision displacement sensor induced by a force modulation from periodically rotating source masses. To seek different kinds of experimental setups, laser interferometers for the gravitational wave detection and optically-levitated microspheres are analyzed. The high sensitivity of the gravitational wave detectors to the displacement is advantageous to have a high signal-to-noise ratio of 10−6 with a few hours of the measurement time, whereas the tunability of parameters in optically-levitated microspheres can enable competitive measurements with a smaller scale setup dedicated to the G measurement. To achieve an accuracy of G better than currently available measurements, developments in force calibration is essential. These measurements can provide an alternative method to measure G precisely, potentially leading to the improvement in the accuracy of G, as well as a better search for non-Newtonian gravity at a length scale of  ∼1 m. [ABSTRACT FROM AUTHOR]

Using only five photographs of the Sun at different dates, we show that the mass of the Sun can be calculated using a telescope, a camera, and Kepler’s third law. With these photographs we are able to calculate the distance between the Sun and the Earth at different dates over a period of time of about three months. These distances allow us to obtain the correct elliptical orbit of Earth, proving Kepler’s first law. Analysis of the data extracted from the photographs is performed using an analytical optimization approach that allows us to find the parameters of the elliptical orbit. Also, it is shown that the five data points fit an ellipse using a geometrical scheme. The obtained parameters are in very good agreement with the ones for Earth’s orbit, allowing us to foresee the future positions of Earth along its trajectory. The parameters for the orbit are used to calculate the Sun’s mass by applying Kepler’s third law and Newton’s law for gravitation. This method gives a result which is in excellent agreement with the correct value for the Sun’s mass. Thus, over a time span of about three months, any student is capable to calculate the mass of the Sun with only five photographs, a telescope and a camera. [ABSTRACT FROM AUTHOR]

In 1936, Albert Einstein wrote a brief article where he suggested the possibility that a massive object acted as a lens, amplifying the brightness of a star. As time went by, this phenomenon—known as gravitational lensing—has become a powerful research tool in astrophysics. The simplest and symmetrical expression of a gravitational lens is known as an Einstein ring. This model has recently allowed the measurement of the mass of a star, the white dwarf Stein 2051 B. The purpose of this work is to show an accessible and up-to-date introduction to the effect of gravitational lensing, focused on the Einstein ring and the measurement of the mass of Stein 2051 B. The intended audience of this article are non-graduate students of physics and similar fields of study, and requires only a basic knowledge of classical physics, modern physics, algebra and trigonometry. [ABSTRACT FROM AUTHOR]

We recently suggested a nonlocal modification of Einstein’s field equations in which Newton’s constant G was promoted to a covariant differential operator . The latter contains two independent contributions which operate respectively in the infrared (IR) and ultraviolet (UV) energy regimes. In the light of the recent direct gravitational radiation measurements we aim to determine the UV-modified 1.5 post-Newtonian radiative quadrupole moment of a generic n-body system. We eventually use these preliminary results in the context of a binary system and observe that in the limit vanishing UV parameters we precisely recover the corresponding general relativistic results. Moreover we notice that the leading order deviation of the UV-modified radiative quadrupole moment numerically coincides with findings obtained in the framework of calculations performed previously in the context of the perihelion precession of Mercury. [ABSTRACT FROM AUTHOR]

The influence of the planets, and planetary alignment on the Earth’s tides is addressed. Starting from Newton’s law of gravitation, the tidal influence of any celestial body is expressed in terms of its apparent size and its density. From this, planetary alignment can be seen to contribute at most tenths of a millimetre to a tide and so is unlikely to be a significant contributor to exceptional tidal events. The likely causes of extreme tidal events are outlined: when the Sun and Moon are each closest to Earth, equinox, and weather—in particular extreme air pressure, rainfall, and wind. We conclude with the long-term influence of the planets on the Earth’s orbit and thus on the Sun’s tidal effect (with timescales of the order of 100 000 years), and planetary influence on the Moon’s orbit. [ABSTRACT FROM AUTHOR]

We investigate the accretion process for static spherically symmetric geometry, i.e., magnetically charged regular black hole with isotropic fluid. We obtain generalized expressions for the velocity (), speed of sound (), energy density () and accretion rate () at the critical point near the regular black hole during the accretion process. We also plot these physical parameters against fixed values of charge, mass and different values of equation of state parameter to study the process of accretion. We find that radial velocity and energy density of the fluid remain positive and negative as well as rate of change of mass is increased and decreased for dust, stiff, quintessence fluid and phantom-like fluid, respectively. [ABSTRACT FROM AUTHOR]

Symmetry and conservation law are discussed on the Finsler manifold M. We adopt the point Finsler approach, where we consider the geometry on a point manifold M not on TM. Generalized vector fields are defined on oriented curves on M, and Finsler non-linear connections are considered on M, not on the tangent space TM. Killing vector fields K are defined as generalized vector fields as , and the Killing symmetry is also reformulated simply as by using the Killing 1-form and the spray operator defined by using the non-linear connection. is related to the generalization of Killing tensors on the Finsler manifold, and our ansatz of and give an analytical method of finding higher derivative conserved quantities, which may be called hidden conserved quantities. We show two examples: the Carter constant on Kerr spacetime and the Runge–Lentz vectors in Newtonian gravity. [ABSTRACT FROM AUTHOR]

Newton’s law of universal gravitation underpins our understanding of the dynamics of the Solar System and of a good portion of the observable universe. Generally, in the classroom or in textbooks, the law is presented initially in a qualitative way and at some point during the exposition its mathematical formulation is written on the blackboard and some quantitative consequences are discussed. In the present paper we argue that this approach can be improved by the use of plausibility arguments. [ABSTRACT FROM AUTHOR]

The purpose of this work is to study the effectiveness of our introductory mechanics instructions in changing students’ misconceptions about Newtonian concepts. We gave the force concept inventory (FCI) test to 341 of our students twice, before and after instructions. The data were analyzed using a method first reported by Martín-Blas et al (2010 Eur. J. Eng. Educ. 35 597–606). We examined all of the known misconceptions found in the original paper by Hestenes et al (1992 Phys. Teach. 30 141–51) and determined the dominant ones from students’ incorrect answers for each of the 30 questions in the inventory. By comparing the dominant misconceptions held by our students in the pre- and post-tests, we were able to determine which ones were unchangeable by instructions and students couldn’t overcome. Results indicate some overall improvement in students’ performance but also the existence of very resistive to change misconceptions that were not affected by instructions. [ABSTRACT FROM AUTHOR]

The measurement of the Newtonian gravity constant G is a formidable task. Starting from the first determination made by Henry Cavendish in 1798, several attempts have been made in order to improve knowledge of its value. Nevertheless, despite these efforts, its uncertainty has decreased only by a factor of ten per century. Cold atom interferometry represents a conceptually different technique to challenge the G measurement, a feature that is crucial in order to identify discrepancies among previous measurements. In this review paper, after a short introduction on the traditional measurement techniques, I will describe and discuss past and ongoing G determination based on atom interferometry, highlighting for each of them the most significant aspects. [ABSTRACT FROM AUTHOR]

We construct a self-consistent relativistic Newtonian analogue corresponding to gravitational static spherical symmetric spacetime geometries, starting directly from a generalized scalar relativistic gravitational action in a Newtonian framework, which gives geodesic equations of motion identical to those of the parent metric. Consequently, the derived velocity-dependent relativistic scalar potential, which is a relativistic generalization of the Newtonian gravitational potential, exactly reproduces the relativistic gravitational features corresponding to any static spherical symmetric spacetime geometry in its entirety, including all the experimentally tested gravitational effects in the weak field up to the present. This relativistic analogous potential is expected to be quite useful in studying a wide range of astrophysical phenomena, especially in strong field gravity. [ABSTRACT FROM AUTHOR]

Pulsars orbiting around the black hole (BH) at our galactic center provide us with a unique testing site for gravity. In this work, we propose an approach to probe the gravity around the BH introducing two phenomenological parameters which characterize deviation from the vacuum Einstein theory. The two phenomenological parameters are associated with the energy–momentum tensor in the framework of the Einstein theory. Therefore, our approach can be regarded as the complement to the parametrized post-Newtonian framework in which phenomenological parameters are introduced for deviation of gravitational theories from general relativity. In our formulation, we take into account the possibility of existence of a relativistic and exotic matter component. Since the pulsars can be regarded as test particles, as the first step, we consider geodesic motion in the system composed of a central BH and a perfect fluid whose distribution is static and spherically symmetric. It is found that the mass density of the fluid and a parameter of the equation of state can be determined with precision with if the density on the pulsar orbit is larger than . [ABSTRACT FROM AUTHOR]

We investigate how a Higgs mechanism could be responsible for the emergence of gravity in extensions of Einstein theory, with a suitable low energy limit. In this scenario, at high energies, symmetry restoration could ‘turn off’ gravity, with dramatic implications for cosmology and quantum gravity. The sense in which gravity is muted depends on the details of the implementation. In the most extreme case gravity’s dynamical degrees of freedom would only be unleashed after the Higgs field acquires a non-trivial vacuum expectation value, with gravity reduced to a topological field theory in the symmetric phase. We might also identify the Higgs and the Brans–Dicke fields in such a way that in the unbroken phase Newton’s constant vanishes, decoupling matter and gravity. We discuss the broad implications of these scenarios. [ABSTRACT FROM AUTHOR]

We study Kaluza–Klein reduction in Newton–Cartan gravity. In particular we show that dimensional reduction and the nonrelativistic limit commute. The resulting theory contains Galilean electromagnetism and a nonrelativistic scalar. It provides the first example of back-reacted couplings of scalar and vector matter to Newton–Cartan gravity. This back-reaction is interesting as it sources the spatial Ricci curvature, providing an example where nonrelativistic gravity is more than just a Newtonian potential. [ABSTRACT FROM AUTHOR]

A sinusoidally time-varying pattern of the values of Newton’s constant of gravitation G measured in Earth-based laboratories over the last few decades has been recently reported in the literature. We put to the test the hypothesis that the aforementioned harmonic variation may pertain to G itself in a direct and independent way. We numerically integrated the ad hoc modified equations of motion of the major bodies of the Solar System, finding that the orbits of the planets would be altered by an unacceptably larger amount in view of the present-day high accuracy astrometric measurements. In the case of Saturn, its geocentric right ascension α, declination δ and range ρ would be affected by up to milliarcseconds and 105 km, respectively; the present-day residuals of such observables are as little as about 4 milliarcseconds and 10−1 km, respectively. We analytically calculated the long-term orbital effects induced by the putative harmonic variation of G at hand, finding non-zero rates of change for the semimajor axis a, the eccentricity e and the argument of pericenter ω of a test particle. For the LAGEOS satellite, an orbital increase as large as 3.9 m yr−1 is predicted, in contrast with the observed decay of −0.203 ± 0.035 m yr−1. An anomalous perihelion precession as large as 14 arcseconds per century is implied for Saturn, while latest observations constrain it to the 10−4 arcseconds per century level. The rejection level provided by the Mercury’s perihelion rate is of the same order of magnitude. [ABSTRACT FROM AUTHOR]

We show how the correction to the calculation of the mass in the original relativistic model of a rotating star by Hartle (1967 Astrophys. J.150 1005–29), found recently by Reina and Vera (2015 Class. Quantum Grav.32 155008), appears in the Newtonian limit, and that the correcting term is indeed present, albeit hidden, in the original Newtonian approach by Chandrasekhar (1933 Mon. Not. Roy. Astr. Soc.93 390–406). [ABSTRACT FROM AUTHOR]

A precessing source frame, constructed using the Newtonian orbital angular momentum , can be invoked to model inspiral gravitational waves from generic spinning compact binaries. An attractive feature of such a precessing convention is its ability to remove all spin precession induced modulations from the orbital phase evolution. However, this convention usually employs a post-Newtonian (PN) accurate precessional equation, appropriate for the PN accurate orbital angular momentum , to evolve the -based precessing source frame. This influenced us to develop inspiral waveforms for spinning compact binaries in a precessing convention that explicitly employ to describe the binary orbits. Our approach introduces certain additional 3PN order terms in the evolution equations for the orbital phase and frequency with respect to the usual -based implementation of the precessing convention. We examine the practical implications of these additional terms by computing the match between inspiral waveforms that employ and -based precessing conventions. The match estimates are found to be smaller than the optimal value, namely 0.97, for a non-negligible fraction of unequal mass spinning compact binaries. [ABSTRACT FROM AUTHOR]

Research has shown that project-based learning promotes student interest in science and improves understanding of scientific content. Fostering student motivation is particularly important in accelerated science and technology programmes for talented students, which are often demanding and time-consuming. Current texts provide little guidance on ways to employ challenging, open-ended investigations in physics suitable for the more capable students. This paper presents a project-based approach for teaching Newton’s laws in a programme for talented eighth-grade students. Evidence from student work demonstrates that project-based learning is a feasible classroom practice, challenging yet fulfilling for both students and teachers. [ABSTRACT FROM AUTHOR]

We formulate within a generalized distributional approach the treatment of the stability against radial perturbations for both neutral and charged stratified stars in Newtonian and Einstein's gravity. We obtain from this approach the boundary conditions connecting any two phases within a star and underline its relevance for realistic models of compact stars with phase transitions, owing to the modification of the star's set of eigenmodes with respect to the continuous case. [ABSTRACT FROM AUTHOR]

Newtonian gravity was formulated as a geometrodynamic theory as far back as in 1930s by Elie Cartan, in what is named aptly as Newton–Cartan space time. Though there are several approaches of realizing the algebraic structure of the Newton–Cartan geometry from a contraction of the relativistic results, a dynamical (field theoretic) realization of it is lacking. In this paper we present such a realization from the localization of the Galilean symmetry of nonrelativistic matter field theories. [ABSTRACT FROM AUTHOR]

This paper briefly reviews recent short-range gravity experiments that were performed at below laboratory scales to test the Newtonian inverse square law of gravity. To compare the sensitivities of these measurements, estimates using the conventional Yukawa parametrization are introduced. Since these experiments were triggered by the prediction of the large extra-dimension model, experiments performed at different length scales are compared with this prediction. In this paper, a direct comparison between laboratory-scale experiments and the LHC results is presented for the first time. A laboratory experiment is shown to determine the best limit at and . In addition, new analysis results are described for atomic systems used as gravitational microlaboratories. [ABSTRACT FROM AUTHOR]

Metric theories of gravity are studied, beginning with a general action that is quadratic in curvature and allows arbitrary inverse powers of the dʼAlembertian operator, resulting in infrared non-local extensions of general relativity. The field equations are derived in full generality and their consistency is checked by verifying the Bianchi identities. The weak-field limit is computed and a straightforward algorithm is presented to infer the post-Newtonian corrections directly from the action. This is then applied to various infrared gravity models including non-local dark energy and non-local massive gravity models. Generically, the Newtonian potentials are not identical and deviate from the behaviour at large distances. However, the former does not occur in a specific class of theories that does not introduce additional degrees of freedom in flat spacetime. A new non-local model within this class is proposed, defined by the exponential of the inverse dʼAlembertian. This model exhibits novel features, such as the weakening of the gravity in the infrared, suggesting de-gravitation of the cosmological constant. [ABSTRACT FROM AUTHOR]

In this paper we propose a mathematical model to describe a theoretical device able to simulate an inverse-square force on a test mass moving on a horizontal plane. We use two pulleys, a counterweight, a wire and a smooth rail, in addition to the test mass. The tension of the wire (i.e. the attractive force on the test mass) is determined by the position of a counterweight free to move on a rail placed under the plane. The profile of the rail is calculated in order to obtain the required Newtonian force. Details of this calculation are reported in the paper, and numerical simulations are provided in order to investigate the stability of the orbits under the effect of the main friction forces and other perturbative effects. This work points out that there are some criticalities intrinsic to the apparatus and gives some suggestions about how to minimize their impact. [ABSTRACT FROM AUTHOR]

Conventional approaches to incorporating general relativistic effects into the dynamics of N-body systems containing central black holes, or of hierarchical triple systems with a relativistic inner binary, may not be adequate when the goal is to study the evolution of the system over a timescale related to relativistic secular effects, such as the precession of the pericenter. For such problems, it may be necessary to include post-Newtonian (PN) ‘cross terms’ in the equations of motion in order to capture relativistic effects consistently over the long timescales. Cross terms are PN terms that explicitly couple the two-body relativistic perturbations with the Newtonian perturbations due to other bodies in the system. In this paper, we show that the total energy of a hierarchical triple system is manifestly conserved to Newtonian order over the relativistic pericenter precession timescale of the inner binary if and only if PN cross-term effects in the equations of motion are taken carefully into account. [ABSTRACT FROM AUTHOR]

Einsteinʼs general relativity predicts that the intrinsic rotation of an astronomical body leads to a general-relativistic contribution to its gravitational field. One of the consequences of general relativity is the so called Lense–Thirring effect, which has been a subject of many theoretical and experimental investigations during the last decades. In this article the model of a rigidly rotating, homogeneous, oblate spheroid will be analyzed with respect to its gravito-magnetic properties beyond the Lense–Thirring contribution to its gravitational field. As a consequence, a scalar, gravito-magnetic potential containing all the information about the spheroidʼs gravito-magnetic field will be derived. Based upon these results, general-relativistic effects like the gravito-magnetic gyroscope precession and the so called G-clock effect in the vicinity of the rotating spheroid will be treated with post-Newtonian accuracy. [ABSTRACT FROM AUTHOR]

The rotation curves of spiral galaxies suggest that either a considerable fraction of the galactic mass must be dark matter, or that one of Newtonʼs laws needs revision at accelerations less than . We have endeavored to search for evidence of the latter in a terrestrial laboratory. A sensitive torsion balance was employed to measure small accelerations due to gravity. No deviations from the predictions of Newtonʼs law were found down to 1 × 10−12 m s−2. [ABSTRACT FROM AUTHOR]

Recently, U. Das and B. Mukhopadhyay proposed that the Chandrasekhar limit of a white dwarf could reach a new high level (2.58M⊙) if a superstrong magnetic field were considered (Das U and Mukhopadhyay B 2013 Phys. Rev. Lett. 110 071102), where the structure of the strongly magnetized white dwarf (SMWD) is calculated in the framework of Newtonian theory (NT). As the SMWD has a far smaller size, in contrast with the usual expectation, we found that there is an obvious general relativistic effect (GRE) in the SMWD. For example, for the SMWD with a one Landau level system, the super-Chandrasekhar mass limit in general relativity (GR) is approximately 16.5% lower than that in NT. More interestingly, the maximal mass of the white dwarf will be first increased when the magnetic field strength keeps on increasing and reaches the maximal value M = 2.48M⊙ with BD = 391.5. Then if we further increase the magnetic fields, surprisingly, the maximal mass of the white dwarf will decrease when one takes the GRE into account. [ABSTRACT FROM AUTHOR]

Students’ misconceptions about Newton's second law in frictionless outer space were investigated. The research was formed according to an epistemic game theoretical framework. The term ‘epistemic’ refers to students’ participation in problem-solving activities as a means of constructing new knowledge. The term ‘game’ refers to a coherent activity that consists of moves and rules. A set of questions in which students are asked to solve two similar Newton's second law problems, one of which is on the Earth and the other in outer space, was administered to 116 undergraduate students. The findings indicate that there is a significant difference between students’ epistemic game preferences and race-type (outer space or frictional surface) question. So students who used Newton's second law on the ground did not apply this law and used primitive reasoning when it came to space. Among these students, voluntary interviews were conducted with 18 students. Analysis of interview transcripts showed that: (1) the term ‘space’ causes spontaneity among students that prevents the use of the law; (2) students hesitate to apply Newton's second law in space due to the lack of a condition—the friction; (3) students feel that Newton's second law is not valid in space for a variety of reasons, but mostly for the fact that the body in space is not in contact with a surface. [ABSTRACT FROM AUTHOR]

The three-body problem, which describes three masses interacting through Newtonian gravity without any restrictions imposed on the initial positions and velocities of these masses, has attracted the attention of many scientists for more than 300 years. In this paper, we present a review of the three-body problem in the context of both historical and modern developments. We describe the general and restricted (circular and elliptic) three-body problems, different analytical and numerical methods of finding solutions, methods for performing stability analysis and searching for periodic orbits and resonances. We apply the results to some interesting problems of celestial mechanics. We also provide a brief presentation of the general and restricted relativistic three-body problems, and discuss their astronomical applications. [ABSTRACT FROM AUTHOR]