A down to earth model of gravisensing or Newton's Law of Gravitation from the apple's perspective

NASA Technical Reports Server (NTRS)

Wayne, R.; Staves, M. P.

1996-01-01

The physiology of gravity perception in plants is examined and a model of gravitational pressure is explained and compared to the statolith model. The gravitational pressure model is based on studies of tension and compression of the plasma membrane against the extracellular matrix. Further studies examine the role of peptides or enzymes that inhibit a compression receptor and calcium channels.

Test of Newtonian gravity at short range using pico-precision displacement sensor

NASA Astrophysics Data System (ADS)

Akiyama, Takashi; Hata, Maki; Ninomiya, Kazufumi; Nishio, Hironori; Ogawa, Naruya; Sekiguchi, Yuta; Watanabe, Kentaro; Murata, Jiro

2009-10-01

Recent theoretical models of physics beyond the standard model, including attempts to resolve the hierarchy problem, predict deviations from the Newtonian gravity at short distances below millimeters. Present NEWTON project aims an experimental test of the inverse-square law at the millimeter scale, using a torsion pendulum with a pico-precision displacement sensor, which was originally developed for the micron precision optical alignment system (OASys) for the PHENIX muon tracking chambers at RHIC, using digital image analysis technique. In order to examine the gravitational force at short range scale around micrometers, we have developed a new apparatus NEWTON-III, which can determine the local gravitational acceleration by measuring the motion of the torsion pendulum. In this presentation, the development status and the results of the NEWTON-experiment will be reported.

Gravitation and Special Relativity from Compton Wave Interactions at the Planck Scale: An Algorithmic Approach

NASA Technical Reports Server (NTRS)

Blackwell, William C., Jr.

2004-01-01

In this paper space is modeled as a lattice of Compton wave oscillators (CWOs) of near- Planck size. It is shown that gravitation and special relativity emerge from the interaction between particles Compton waves. To develop this CWO model an algorithmic approach was taken, incorporating simple rules of interaction at the Planck-scale developed using well known physical laws. This technique naturally leads to Newton s law of gravitation and a new form of doubly special relativity. The model is in apparent agreement with the holographic principle, and it predicts a cutoff energy for ultrahigh-energy cosmic rays that is consistent with observational data.

Gravitational forces and moments on spacecraft

NASA Technical Reports Server (NTRS)

Kane, T. R.; Likins, P. W.

1975-01-01

The solution of problems of attitude dynamics of spacecraft and the influence of gravitational forces and moments is examined. Arguments are presented based on Newton's law of gravitation, and employing the methods of Newtonian (vectorial) mechanics, with minimal recourse to the classical concepts of potential theory. The necessary ideas were developed and relationships were established to permit the representation of gravitational forces and moments exerted on bodies in space by other bodies, both in terms involving the mass distribution properties of the bodies, and in terms of vector operations on those scalar functions classically described as gravitational potential functions.

Orbital Motion of Electrically Charged Spheres in Microgravity

ERIC Educational Resources Information Center

Banerjee, Shubho; Andring, Kevin; Campbell, Desmond; Janeski, John; Keedy, Daniel; Quinn, Sean; Hoffmeister, Brent

2008-01-01

The similar mathematical forms of Coulomb's law and Newton's law of gravitation suggest that two uniformly charged spheres should be able to orbit each other just as two uniform spheres of mass are known to do. In this paper we describe an experiment that we performed to demonstrate such an orbit. This is the first published account of a…

Analytical modeling of soliton interactions in a nonlocal nonlinear medium analogous to gravitational force

NASA Astrophysics Data System (ADS)

Zeng, Shihao; Chen, Manna; Zhang, Ting; Hu, Wei; Guo, Qi; Lu, Daquan

2018-01-01

We illuminate an analytical model of soliton interactions in lead glass by analogizing to a gravitational force system. The orbits of spiraling solitons under a long-range interaction are given explicitly and demonstrated to follow Newton's second law of motion and the Binet equation by numerical simulations. The condition for circular orbits is obtained and the oscillating orbits are proved not to be closed. We prove the analogy between the nonlocal nonlinear optical system and gravitational system and specify the quantitative relation of the quantity between the two models.

NASA Educational Briefs for the Classroom. Orbits of Bodies in Space

NASA Technical Reports Server (NTRS)

1982-01-01

The difference between an orbit and a revolution is explained and it is shown why space shuttle Columbia's period of revolution was longer than its orbital period. Parameters of orbits examined include apoapsis, periapsis, apogee, perigee, aphelion, perihelion, orbital plane, and inclination. Orbit velocity and duration, Newton's law of gravitation, and Kepler's three laws of motion are considered. The principles involved in geostationary satellites are also explored.

Copernican Mathematics: Calculating Periods and Distances of the Planets

ERIC Educational Resources Information Center

Rosenkrantz, Kurt J.

2004-01-01

The heliocentric, or Sun-centered model, one of the most important revolutions in scientific thinking, allowed Nicholas Copernicus to calculate the periods, relative distances, and approximate orbital shapes of all the known planets, thereby paving the way for Kepler's laws and Newton's formation of gravitation. Recreating Copernicus's…

Gradiometry and gravitomagnetic field detection

NASA Technical Reports Server (NTRS)

Mashhoon, Bahram

1989-01-01

Gravitomagnetism was apparently first introduced into physics about 120 years ago when major developments in electrodynamics and the strong similarity between Coulomb's law of electricity and Newton's law of gravity led to the hypothesis that mass current generates a fundamental force of gravitational origin analogous to the magnetic force caused by charge current. According to general relativity, the rotation of a body leads to the dragging of the local inertial frames. In the weak-field approximation, the dragging frequency can be interpreted, up to a constant proportionality factor, as a gravitational magnetic field. There is, as yet, no direct evidence regarding the existence of such a field. The possibility is examined of detecting the gravitomagnetic field of the Earth by gravity gradiometry.

How do stars form

NASA Astrophysics Data System (ADS)

Tscharnuter, W. M.

1980-02-01

Modes and model concept of star formation are reviewed, beginning with the theory of Kant (1755), via Newton's exact mathematical formulation of the laws of motion, his recognition of the universal validity of general gravitation, to modern concepts and hypotheses. Axisymmetric and spherically symmetric collapse models are discussed, and the origin of double and multiple star systems is examined.

Ramsey's method of separated oscillating fields and its application to gravitationally induced quantum phase shifts

DOE Office of Scientific and Technical Information (OSTI.GOV)

Abele, H.; Jenke, T.; Leeb, H.

2010-03-15

We propose to apply Ramsey's method of separated oscillating fields to the spectroscopy of the quantum states in the gravity potential above a horizontal mirror. This method allows a precise measurement of quantum mechanical phaseshifts of a Schroedinger wave packet bouncing off a hard surface in the gravitational field of the Earth. Measurements with ultracold neutrons will offer a sensitivity to Newton's law or hypothetical short-ranged interactions, which is about 21 orders of magnitude below the energy scale of electromagnetism.

How Spherical Is a Cube (Gravitationally)?

NASA Astrophysics Data System (ADS)

Sanny, Jeff; Smith, David

2015-02-01

An important concept that is presented in the discussion of Newton's law of universal gravitation is that the gravitational effect external to a spherically symmetric mass distribution is the same as if all of the mass of the distribution were concentrated at the center.1,2 By integrating over ring elements of a spherical shell, we show that the gravitational force on a point mass outside the shell is the same as that of a particle with the same mass as the shell at its center. This derivation works for objects with spherical symmetry while depending on the fact that the gravitational force between two point masses varies inversely as the square of their separation.3 If these conditions are not met, then the problem becomes more difficult. In this paper, we remove the condition of spherical symmetry and examine the gravitational force between two uniform cubes.

The Discovery of Gravitational Repulsion by Johannes Droste

NASA Astrophysics Data System (ADS)

McGruder, Charles Hosewell; VanDerMeer, B. Wieb

2018-01-01

In 1687 Newton published his universal law of gravitation, which states that the gravitational force is always attractive. This law is based on our terrestrial experience with slowly moving bodies (v << c). In 1915 Einstein completed his theory of general relativity (also referred to as Einstein’s Theory of Gravitation), which is valid not just for slowly moving bodies but also for those with relativistic velocities. In 1916 Johannes Droste submitted a PhD thesis on general relativity to his advisor, H.A. Lorentz. In it he calculated the motion of a particle in what he called a “single center” and today we call the Schwarzschild field and found that highly relativistic particles experience gravitational repulsion. Thus, his thesis written in Dutch and never before translated contains the discovery of gravitational repulsion. Because of its historical importance we translate the entire section of his thesis containing the discovery of gravitational repulsion. We also translate his thesis in the hope of clearing up a major historical misconception. Namely, that David Hilbert in 1917 discovered gravitational repulsion. In fact, Hilbert rediscovered it, apparently completely independent of Droste’s work. Finally we note that one of the biggest mysteries of astrophysics is the question of how highly energetic particles in relativistic jets and cosmic rays are accelerated. It has been suggested that gravitational repulsion is the mechanism responsible for these phenomena. An historical understanding of gravitational repulsion is therefore pertinent.

General relativity exactly described in terms of Newton's laws within curved geometries

NASA Astrophysics Data System (ADS)

Savickas, D.

2014-07-01

Many years ago Milne and McCrea showed in their well-known paper that the Hubble expansion occurring in general relativity could be exactly described by the use of Newtonian mechanics. It will be shown that a similar method can be extended to, and used within, curved geometries when Newton's second law is expressed within a four-dimensional curved spacetime. The second law will be shown to yield an equation that is exactly identical to the geodesic equation of motion of general relativity. This in itself yields no new information concerning relativity since the equation is mathematically identical to the relativistic equation. However, when the time in the second law is defined to have a constant direction as effectively occurs in Newtonian mechanics, and no longer acts as a fourth dimension as exists in relativity theory, it separates into a vector equation in a curved three-dimensional space and an additional second scalar equation that describes conservation of energy. It is shown that the curved Newtonian equations of motion define the metric coefficients which occur in the Schwarzschild solution and that they also define its equations of motion. Also, because the curved Newtonian equations developed here use masses as gravitational sources, as occurs in Newtonian mechanics, they make it possible to derive the solution for other kinds of mass distributions and are used here to find the metric equation for a thin mass-rod and the equation of motion for a mass particle orbiting it in its relativistic gravitational field.

Why did Einstein reject the November tensor in 1912-1913, only to come back to it in November 1915?

NASA Astrophysics Data System (ADS)

Weinstein, Galina

2018-05-01

The question of Einstein's rejection of the November tensor is re-examined in light of conflicting answers by several historians. I discuss these conflicting conjectures in view of three questions that should inform our thinking: Why did Einstein reject the November tensor in 1912, only to come back to it in 1915? Why was it hard for Einstein to recognize that the November tensor is a natural generalization of Newton's law of gravitation? Why did it take him three years to realize that the November tensor is not incompatible with Newton's law? I first briefly describe Einstein's work in the Zurich Notebook. I then discuss a number of interpretive conjectures formulated by historians and what may be inferred from them. Finally, I offer a new combined conjecture that answers the above questions.

Graviton mass bounds from an analysis of bright star trajectories at the Galactic Center

NASA Astrophysics Data System (ADS)

Zakharov, Alexander; Jovanović, Predrag; Borka, Dusko; Jovanović, Vesna Borka

2017-03-01

In February 2016 the LIGO & VIRGO collaboration reported the discovery of gravitational waves in merging black holes, therefore, the team confirmed GR predictions about an existence of black holes and gravitational waves in the strong gravitational field limit. Moreover, in their papers the joint LIGO & VIRGO team presented an upper limit on graviton mass such as mg < 1.2 × 10-22 eV (Abbott et al. 2016). So, the authors concluded that their observational data do not show any violation of classical general relativity. We show that an analysis of bright star trajectories could constrain graviton mass with a comparable accuracy with accuracies reached with gravitational wave interferometers and the estimate is consistent with the one obtained by the LIGO & VIRGO collaboration. This analysis gives an opportunity to treat observations of bright stars near the Galactic Center as a useful tool to obtain constraints on the fundamental gravity law such as modifications of the Newton gravity law in a weak field approximation. In that way, based on a potential reconstruction at the Galactic Center we obtain bounds on a graviton mass.

The moon-Earth system...As a vacuum gravity energy machine? A Hint about the Nature of Universal Gravity that May Have Been Overlooked

NASA Astrophysics Data System (ADS)

Masters, Roy

2011-10-01

We revisit the theories describing the moon raising the tides by virtue of pull gravity combined with the moon's centripetal angular momentum. We show that if gravity is considered as the attractive interaction between individual bodies, then a laboring moon doing work would have fallen to earth eons ago. Isaac Newton's laws of motion cannot work with pull gravity, but they do with Einstein's gravity as a property of the universe, which produces a continuous infusion of energy. In other words, the moon-Earth system becomes the first observable vacuum gravity energy machine. In other words the dynamics of what appears to be a closed system has been producing energy that continues raising the tides into perpetuity along with the force needed for the moon to escape the Earth's gravitational pull 4cm per year. All this is in defiance of Newton's first law which says ``If no force is added to a body it cannot accelerate.'' In this theory, a flowing space-time curves with three dimensions of force. A (flowing) spatial fabric bends around mass and displaces the inverse square field vanishing point property of matter with the appearance of a push-force square of the distance. In other words, the immeasurable universal gravity field appears as measurable local gravitation, concentrating universal gravitational pressure with the square of the distance from the very point was supposed to have disappeared. Needless to say such ``gravity'' necessitates a different beginning.

The mechanics and physics of fracturing: application to thermal aspects of crack propagation and to fracking.

PubMed

Cherepanov, Genady P

2015-03-28

By way of introduction, the general invariant integral (GI) based on the energy conservation law is presented, with mention of cosmic, gravitational, mass, elastic, thermal and electromagnetic energy of matter application to demonstrate the approach, including Coulomb's Law generalized for moving electric charges, Newton's Law generalized for coupled gravitational/cosmic field, the new Archimedes' Law accounting for gravitational and surface energy, and others. Then using this approach the temperature track behind a moving crack is found, and the coupling of elastic and thermal energies is set up in fracturing. For porous materials saturated with a fluid or gas, the notion of binary continuum is used to introduce the corresponding GIs. As applied to the horizontal drilling and fracturing of boreholes, the field of pressure and flow rate as well as the fluid output from both a horizontal borehole and a fracture are derived in the fluid extraction regime. The theory of fracking in shale gas reservoirs is suggested for three basic regimes of the drill mud permeation, with calculating the shape and volume of the local region of the multiply fractured rock in terms of the pressures of rock, drill mud and shale gas. © 2015 The Author(s) Published by the Royal Society. All rights reserved.

Numeric calculation of celestial bodies with spreadsheet analysis

NASA Astrophysics Data System (ADS)

Koch, Alexander

2016-04-01

The motion of the planets and moons in our solar system can easily be calculated for any time by the Kepler laws of planetary motion. The Kepler laws are a special case of the gravitational law of Newton, especially if you consider more than two celestial bodies. Therefore it is more basic to calculate the motion by using the gravitational law. But the problem is, that by gravitational law it is not possible to calculate the state of motion with only one step of calculation. The motion has to be numerical calculated for many time intervalls. For this reason, spreadsheet analysis is helpful for students. Skills in programmes like Excel, Calc or Gnumeric are important in professional life and can easily be learnt by students. These programmes can help to calculate the complex motions with many intervalls. The more intervalls are used, the more exact are the calculated orbits. The sutdents will first get a quick course in Excel. After that they calculate with instructions the 2-D-coordinates of the orbits of Moon and Mars. Step by step the students are coding the formulae for calculating physical parameters like coordinates, force, acceleration and velocity. The project is limited to 4 weeks or 8 lessons. So the calcualtion will only include the calculation of one body around the central mass like Earth or Sun. The three-body problem can only be shortly discussed at the end of the project.

Short distance modification of the quantum virial theorem

NASA Astrophysics Data System (ADS)

Zhao, Qin; Faizal, Mir; Zaz, Zaid

2017-07-01

In this letter, we will analyse the deformation of a semi-classical gravitational system from minimal measurable length scale. In the semi-classical approximation, the gravitational field will be analysed as a classical field, and the matter fields will be treated quantum mechanically. Thus, using this approximation, this system will be represented by a deformation of Schrödinger-Newton equation by the generalised uncertainty principle (GUP). We will analyse the effects of this GUP deformed Schrödinger-Newton equation on the behaviour of such a semi-classical gravitational system. As the quantum mechanical virial theorem can be obtained using the Schrödinger-Newton equation, a short distance modification of the Schrödinger-Newton equation will also result in a short distance modification of the quantum mechanical virial theorem.

Milgrom's revision of Newton's laws - Dynamical and cosmological consequences

NASA Technical Reports Server (NTRS)

Felten, J. E.

1984-01-01

Milgrom's (1983) recent revision of Newtonian dynamics was introduced to eliminate the inference that large quantities of invisible mass exist in galaxies. It is shown by simple examples that a Milgrom acceleration, in the form presented so far, implies other far-reaching changes in dynamics. The momentum of an isolated system is not conserved, and the usual theorem for center-of-mass motion of any system does not hold. Naive applications require extreme caution. The model fails to provide a complete description of particle dynamics and should be thought of as a revision of Kepler's laws rather than Newton's. The Milgrom acceleration also implies fundamental changes in cosmology. A quasi-Newtonian calculation adapted from Newtonian cosmology suggests that a 'Milgrom universe' will recollapse even if the classical closure parameter Omega is much less than unity. The solution, however, fails to satisfy the cosmological principle. Reasons for the breakdown of this calculation are examined. A new theory of gravitation will be needed before the behavior of a Milgrom universe can be predicted.

Milgrom's revision of cosmic dynamics: Amending Newton's laws or Keplers?

NASA Technical Reports Server (NTRS)

Felten, J. E.

1983-01-01

Milgrom's recent revision of Newtonian dynamics was introduced to eliminate the inference that large quantities of invisible mass exist in galaxies. Simple examples show that a Milgrom acceleration, in the form presented so far, imply other far-reaching changes in dynamics. The momentum of an isolated system is not conserved, and the usual theorem for center-of-mass motion of any system does not hold. Naive applications require extreme caution. The model fails to provide a complete description of particle dynamics and should be thought of as a revision of Kepler's laws rather than Newton's. The Milgrom acceleration also implies fundamental changes in cosmology. A quasi-Newtonian calculation adapted from Newtonian cosmology suggests that a Milgrom universe will recollapse even if the classical closure parameter theta is less than 1. The solution, however, fails to satisfy the cosmological principle. Reasons for the breakdown of this calculation are examined. A theory of gravitation needed before the behavior of a Milgrom universe can be predicted.

Development of diagnostic test instruments to reveal level student conception in kinematic and dynamics

NASA Astrophysics Data System (ADS)

Handhika, J.; Cari, C.; Suparmi, A.; Sunarno, W.; Purwandari, P.

2018-03-01

The purpose of this research was to develop a diagnostic test instrument to reveal students' conceptions in kinematics and dynamics. The diagnostic test was developed based on the content indicator the concept of (1) displacement and distance, (2) instantaneous and average velocity, (3) zero and constant acceleration, (4) gravitational acceleration (5) Newton's first Law, (6) and Newton's third Law. The diagnostic test development model includes: Diagnostic test requirement analysis, formulating test-making objectives, developing tests, checking the validity of the content and the performance of reliability, and application of tests. The Content Validation Index (CVI) results in the category are highly relevant, with a value of 0.85. Three questions get negative Content Validation Ratio CVR) (-0.6), after revised distractors and clarify visual presentation; the CVR become 1 (highly relevant). This test was applied, obtained 16 valid test items, with Cronbach Alpha value of 0.80. It can conclude that diagnostic test can be used to reveal the level of students conception in kinematics and dynamics.

NRL (Naval Research Laboratory) Plasma Formulary. Revised.

DTIC Science & Technology

1983-01-01

EQUATIONS Name Rationalized inks Gaussian Faday’s law V xE -- !-s VxE--l1p .aD -l3D 4i" Ampere’slta xH-VxH -- +J VxH -- .- +- J at C at C Poison’s eqution...energy density Froude Fr t V (gL ) 1/2 (Inertial forces/gravitational or VINL buoyancy forces) t/2 Gay- Lussac Ga I/PA T (Relative volume change...112 Alfvin speed a Newton’s- law heat coefficient, k x " aA T aix Volumetric expansion coefficient, dV/ V - )dT r Bulk modulus (units m/it 2 ) AR, A

Gravity, black holes, and the universe

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nicolson, I.

1981-01-01

The book treats current understandings of the nature and properties of gravity, with particular emphasis on its role in the physics of black holes and the structure and evolution of the universe as a whole. The development of modern ideas on force, motion and gravity is traced from the systems of Aristotle and Ptolemy through the work of Copernicus, Galileo and Kepler to Newton's law of universal gravitation and Einstein's general theory of relativity. Particular attention is then given to the role of gravity in stellar motions and to the phenomena determined by the immense gravitational forces associated with bodiesmore » of such great density, including relativistic effects, tidal forces, space-time effects, event horizons, rotation, mass and electrical charge, the existence of naked singularities and white holes, and black-hole thermodynamics. The existence of actual black holes in the universe is considered, and various black-hole candidates in the Galaxy, quasars and galactic nuclei are indicated. The role of gravity in cosmology is then examined, with attention given to the implications of general relativity, the Hubble law, the age of the universe, the density of the universe and its eventual fate. Possible alternative to general relativity as a theory of gravitation are considered, including theories of variable gravitational constant, grand unified theories, and quantum gravity.« less

Gravity, black holes and the universe

NASA Astrophysics Data System (ADS)

Nicolson, I.

The book treats current understandings of the nature and properties of gravity, with particular emphasis on its role in the physics of black holes and the structure and evolution of the universe as a whole. The development of modern ideas on force, motion and gravity is traced from the systems of Aristotle and Ptolemy through the work of Copernicus, Galileo and Kepler to Newton's law of universal gravitation and Einstein's general theory of relativity. Particular attention is then given to the role of gravity in stellar motions and to the phenomena determined by the immense gravitational forces associated with bodies of such great density, including relativistic effects, tidal forces, space-time effects, event horizons, rotation, mass and electrical charge, the existence of naked singularities and white holes, and black-hole thermodynamics. The existence of actual black holes in the universe is considered, and various black-hole candidates in the Galaxy, quasars and galactic nuclei are indicated. The role of gravity in cosmology is then examined, with attention given to the implications of general relativity, the Hubble law, the age of the universe, the density of the universe and its eventual fate. Possible alternative to general relativity as a theory of gravitation are considered, including theories of variable gravitational constant, grand unified theories, and quantum gravity.

The Broad Iron K-alpha line of Cygnus X-1 as Seen by XMM-Newton in the EPIC-pn Modified Timing Mode

NASA Technical Reports Server (NTRS)

Duro, Refiz; Dauser, Thomas; Wilms, Jorn; Pottschmidt, Katja; Nowak, Michael A.; Fritz, Sonja; Kendziorra, Eckhard; Kirsch, Marcus G. F.; Reynolds, Christopher S.; Staubert, Rudiger

2011-01-01

We present the analysis of the broadened, flourescent iron K(alpha) line in simultaneous XMM-Newton and RXTE data from the black hole Cygnus X-I. The XMM-Newton data were taken in a modified version of the Timing Mode of the EPIC-pn camera. In this mode the lower energy threshold of the instrument is increased to 2.8 keV to avoid telemetry drop outs due to the brightness of the source, while at the same time preserving the signal to noise ratio in the Fe K(alpha) band. We find that the best-fit spectrum consists of the sum of an exponentially cut-off power-law and relativistically smeared, ionized reflection. The shape of the broadened Fe K(alpha) feature is due to strong Compton broadening combined with relativistic broadening. Assuming a standard, thin accretion disk, the black hole is close to maximally rotating. Key words. X-rays: binaries - black hole physics - gravitation

The Newton constant and gravitational waves in some vector field adjusting mechanisms

DOE Office of Scientific and Technical Information (OSTI.GOV)

Santillán, Osvaldo P.; Scornavacche, Marina, E-mail: firenzecita@hotmail.com, E-mail: marina.scorna@hotmail.com

At the present, there exist some Lorentz breaking scenarios which explain the smallness of the cosmological constant at the present era [1]–[2]. An important aspect to analyze is the propagation of gravitational waves and the screening or enhancement of the Newton constant G {sub N} in these models. The problem is that the Lorentz symmetry breaking terms may induce an unacceptable value of the Newton constant G {sub N} or introduce longitudinal modes in the gravitational wave propagation. Furthermore this breaking may spoil the standard dispersion relation ω= ck . In [3] the authors have presented a model suggesting thatmore » the behavior of the gravitational constant is correct for asymptotic times. In the present work, an explicit checking is made and we finally agree with these claims. Furthermore, it is suggested that the gravitational waves are also well behaved for large times. In the process, some new models with the same behavior are obtained, thus enlarging the list of possible adjustment mechanisms.« less

Trajectories of bright stars at the Galactic Center as a tool to evaluate a graviton mass

NASA Astrophysics Data System (ADS)

Zakharov, Alexander; Jovanović, Predrag; Borka, Dusko; Jovanović, Vesna Borka

2016-10-01

Scientists worked in Saint-Petersburg (Petrograd, Leningrad) played the extremely important role in creation of scientific school and development of general relativity in Russia. Very recently LIGO collaboration discovered gravitational waves [1] predicted 100 years ago by A. Einstein. In the papers reporting about this discovery, the joint LIGO & VIRGO team presented an upper limit on graviton mass such as mg < 1.2 × 10-22eV [1, 2]. The authors concluded that their observational data do not show violations of classical general relativity because the graviton mass limit is very small. We show that an analysis of bright star trajectories could bound graviton mass with a comparable accuracy with accuracies reached with gravitational wave interferometers and expected with forthcoming pulsar timing observations for gravitational wave detection. This analysis gives an opportunity to treat observations of bright stars near the Galactic Center as a tool for an evaluation specific parameters of the black hole and also to obtain constraints on the fundamental gravity law such as a modifications of Newton gravity law in a weak field approximation. In that way, based on a potential reconstruction at the Galactic Center we give a bounds on a graviton mass.

Mechanics

NASA Astrophysics Data System (ADS)

Cox, John

2014-05-01

Part 1. The Winning of the Principles: 1. Introduction; 2. The beginnings of statics. Archimedes. Problem of the lever and of the centre of gravity; 2. Experimental verification and applications of the principle of the lever; 3. The centre of gravity; 4. The balance; 5. Stevinus of Bruges. The principle of the inclined plane; 6. The parallelogram of forces; 7. The principle of virtual work; 8. Review of the principles of statics; 9. The beginnings of dynamics. Galileo. The problem of falling bodies; 10. Huyghens. The problem of uniform motion in a circle. 'Centrifugal force'; 11. Final statement of the principles of dynamics. Extension to the motions of the heavenly bodies. The law of universal gravitation. Newton; Part II. Mathematical Statement of the Principles: Introduction; 12. Kinematics; 13. Kinetics of a particle moving in a straight line. The laws of motion; 14. Experimental verification of the laws of motion. Atwood's machine; 15. Work and energy; 16. The parallelogram law; 17. The composition and resolution of forces. Resultant. Component. Equilibrium; 18. Forces in one plane; 19. Friction; Part III. Application to Various Problems: 20. Motion on an inclined plane. Brachistochrones; 21. Projectiles; 22. Simple harmonic motion; 23. The simple pendulum; 24. Central forces. The law of gravitation; 25. Impact and impulsive forces; Part IV. The Elements of Rigid Dynamics: 26. The compound pendulum. Huyghens' solution; 27. D'alembert's principle; 28. Moment of inertia; 29. Experimental determination of moments of inertia; 30. Determination of the value of gravity by Kater's pendulum; 31. The constant of gravitation, or weighing the Earth. The Cavendish experiment; Answers to the examples; Index.

From Newton to Einstein.

ERIC Educational Resources Information Center

Ryder, L. H.

1987-01-01

Discusses the history of scientific thought in terms of the theories of inertia and absolute space, relativity and gravitation. Describes how Sir Isaac Newton used the work of earlier scholars in his theories and how Albert Einstein used Newton's theories in his. (CW)

Calibration of gravitational radiation antenna by dynamic Newton field

NASA Astrophysics Data System (ADS)

Suzuki, T.; Tsubono, K.; Kuroda, K.; Hirakawa, H.

1981-07-01

A method is presented of calibrating antennas for gravitational radiation. The method, which used the dynamic Newton field of a rotating body, is suitable in experiments for frequencies up to several hundred hertz. What is more, the method requires no hardware inside the vacuum chamber of the antenna and is particularly convenient for calibration of low-temperature antenna systems.

Letting students discover the power, and the limits, of simple models: Coulomb's law

NASA Astrophysics Data System (ADS)

Bohacek, Peter; Vonk, Matthew; Dill, Joseph; Boehm, Emma

2017-09-01

The inverse-square law pops up all over. It's a simplified model of reality that describes light, sound, gravity, and static electricity. But when it's brought up in class, students are often just handed the equations. They rarely have an opportunity to discover Coulomb's law or Newton's law of gravitation for themselves. It's not hard to understand why. A quantitative demonstration of Coulomb's law can be difficult. The forces are smaller than many force sensors can measure and static electricity tends to be finicky. In addition, off-the-shelf units are expensive or difficult to use. As a result, many instructors skip this lab in favor of qualitative demonstrations or simulations. Adolf Cortel sought to remedy this by designing a straightforward experiment for measuring Coulomb's law using charged metalized-glass spheres (Christmas ornaments) and an electronic balance. Building on Cortel's design, we've made a series of video-based experiments that students can use to discover the relationships that underlie electric force.

3, 2, 1 … Discovering Newton's Laws

NASA Astrophysics Data System (ADS)

Lutz, Joe; Sylvester, Kevin; Oliver, Keith; Herrington, Deborah

2017-03-01

"For every action there is an equal and opposite reaction." "Except when a bug hits your car window, the car must exert more force on the bug because Newton's laws only apply in the physics classroom, right?" Students in our classrooms were able to pick out definitions as well as examples of Newton's three laws; they could recite the laws and even solve for force, mass, and acceleration. However, when given "real world" questions, they would quickly revert to naive explanations. This frustration led to an examination of our approach to teaching Newton's laws. Like many, we taught Newton's laws in their numerical order—first, second, and then third. Students read about the laws, copied definitions, and became proficient with vocabulary before they applied the laws in a lab setting. This paper discusses how we transformed our teaching of Newton's laws by flipping the order (3, 2, 1) and putting the activity before concept, as well as how these changes affected student outcomes.

Newton's absolute time and space in general relativity

NASA Astrophysics Data System (ADS)

Gautreau, Ronald

2000-04-01

I describe a reference system in a spherically symmetric gravitational field that is built around times recorded by radially moving geodesic clocks. The geodesic time coordinate t and the curvature spatial radial coordinate R result in spacetime descriptions of the motion of the geodesic clocks that are exactly identical with equations following from Newton's absolute time and space used with his inverse square law. I show how to use the resulting Newtonian/general-relativistic equations for geodesic clocks to generate exact relativistic metric forms in terms of the coordinates (R,t). Newtonian theory does not describe light. However, the motion of light can be determined from the (R,t) general-relativistic metric forms obtained from Newtonian theory by setting ds2(R,t)=0. In this sense, a theory of light can be related to absolute time and space of Newtonian gravitational theory. I illustrate the (R,t) methodology by first solving the equations that result from a Newtonian picture and then examining the exact metric forms for the general-relativistic problems of the Schwarzschild field, gravitational collapse and expansion of a zero-pressure perfect fluid, and zero-pressure big-bang cosmology. I also briefly describe other applications of the Newtonian/general-relativistic formulation to: embedding a Schwarzschild mass into cosmology; continuously following an expanding universe from radiation to matter domination; Dirac's Large Numbers hypothesis; the incompleteness of Kruskal-Szekeres spacetime; double valuedness in cosmology; and the de Sitter universe.

Turning around Newton's Second Law

ERIC Educational Resources Information Center

Goff, John Eric

2004-01-01

Conceptual and quantitative difficulties surrounding Newton's second law often arise among introductory physics students. Simply turning around how one expresses Newton's second law may assist students in their understanding of a deceptively simple-looking equation.

Integrating Scientific Methods and Knowledge into the Teaching of Newton's Theory of Gravitation: An Instructional Sequence for Teachers' and Students' Nature of Science Education

ERIC Educational Resources Information Center

Develaki, Maria

2012-01-01

The availability of teaching units on the nature of science (NOS) can reinforce classroom instruction in the subject, taking into account the related deficiencies in textbook material and teacher training. We give a sequence of teaching units in which the teaching of Newton's gravitational theory is used as a basis for reflecting on the…

The Treatment of the Laws of Dynamics in Higher Level Schools.

ERIC Educational Resources Information Center

Kikoin, I. K.

1979-01-01

Describes how Newton's three laws of dynamics are taught in high school in the Soviet Union. Rejects introducing Newton's second law as an equation defining mass as a proportionality constant. Shows how the concept of mass can be introduced independently of Newton's Law. (GA)

Flow properties of concentrated suspensions

NASA Technical Reports Server (NTRS)

Hattori, K.; Izumi, K.

1984-01-01

The viscosity and flow behavior of a concentrated suspension, with special emphasis on fresh concrete containing a superplasticizer, is analyzed according to Newton's law of viscosity. The authors interpreted Newton's law in a new way, and explain non-Newton flow from Newton's law. The outline of this new theory is given. Viscosity of suspensions, and the effect of dispersants are analyzed.

"On Second Thoughts…": Changes of Mind as an Indication of Competing Knowledge Structures

NASA Astrophysics Data System (ADS)

Wilson, Kate F.; Low, David J.

2015-09-01

A review of student answers to diagnostic questions concerned with Newton's Laws showed a tendency for some students to change their answer to a question when the following question caused them to think more about the situation. We investigate this behavior and interpret it in the framework of the resource model; in particular, a weak Newton's Third Law structure being dominated by an inconsistent Newton's Second Law (or "Net Force") structure, in the absence of a strong, consistent Newtonian structure. This observation highlights the hidden problem in instruction where the implicit use of Newton's Third Law is dominated by the explicit conceptual and mathematical application of Newton's Second Law, both within individual courses and across a degree program. To facilitate students' development of a consistent Newtonian knowledge structure, it is important that instructors highlight the interrelated nature of Newton's Laws in problem solving.

Was Newton right? A search for non-Newtonian behavior of weak-field gravity

NASA Astrophysics Data System (ADS)

Boynton, Paul; Moore, Michael; Newman, Riley; Berg, Eric; Bonicalzi, Ricco; McKenney, Keven

2014-06-01

Empirical tests of Einstein's metric theory of gravitation, even in the non-relativistic, weak-field limit, could play an important role in judging theory-driven extensions of the current Standard Model of fundamental interactions. Guided by Galileo's work and his own experiments, Newton formulated a theory of gravity in which the force of attraction between two bodies is independent of composition and proportional to the inertia of each, thereby transparently satisfying Galileo's empirically informed conjecture regarding the Universality of Free Fall. Similarly, Einstein honored the manifest success of Newton's theory by assuring that the linearized equations of GTR matched the Newtonian formalism under "classical" conditions. Each of these steps, however, was explicitly an approximation raised to the status of principle. Perhaps, at some level, Newtonian gravity does not accurately describe the physical interaction between uncharged, unmagnetized, macroscopic bits of ordinary matter. What if Newton were wrong? Detecting any significant deviation from Newtonian behavior, no matter how small, could provide new insights and possibly reveal new physics. In the context of physics as an empirical science, for us this yet unanswered question constitutes sufficient motivation to attempt precision measurements of the kind described here. In this paper we report the current status of a project to search for violation of the Newtonian inverse square law of gravity.

The Cooling Law and the Search for a Good Temperature Scale, from Newton to Dalton

ERIC Educational Resources Information Center

Besson, Ugo

2011-01-01

The research on the cooling law began with an article by Newton published in 1701. Later, many studies were performed by other scientists confirming or confuting Newton's law. This paper presents a description and an interpretation of Newton's article, provides a short overview of the research conducted on the topic during the 18th century, and…

Ellipsoidal terrain correction based on multi-cylindrical equal-area map projection of the reference ellipsoid

NASA Astrophysics Data System (ADS)

Ardalan, A. A.; Safari, A.

2004-09-01

An operational algorithm for computation of terrain correction (or local gravity field modeling) based on application of closed-form solution of the Newton integral in terms of Cartesian coordinates in multi-cylindrical equal-area map projection of the reference ellipsoid is presented. Multi-cylindrical equal-area map projection of the reference ellipsoid has been derived and is described in detail for the first time. Ellipsoidal mass elements with various sizes on the surface of the reference ellipsoid are selected and the gravitational potential and vector of gravitational intensity (i.e. gravitational acceleration) of the mass elements are computed via numerical solution of the Newton integral in terms of geodetic coordinates {λ,ϕ,h}. Four base- edge points of the ellipsoidal mass elements are transformed into a multi-cylindrical equal-area map projection surface to build Cartesian mass elements by associating the height of the corresponding ellipsoidal mass elements to the transformed area elements. Using the closed-form solution of the Newton integral in terms of Cartesian coordinates, the gravitational potential and vector of gravitational intensity of the transformed Cartesian mass elements are computed and compared with those of the numerical solution of the Newton integral for the ellipsoidal mass elements in terms of geodetic coordinates. Numerical tests indicate that the difference between the two computations, i.e. numerical solution of the Newton integral for ellipsoidal mass elements in terms of geodetic coordinates and closed-form solution of the Newton integral in terms of Cartesian coordinates, in a multi-cylindrical equal-area map projection, is less than 1.6×10-8 m2/s2 for a mass element with a cross section area of 10×10 m and a height of 10,000 m. For a mass element with a cross section area of 1×1 km and a height of 10,000 m the difference is less than 1.5×10-4m2/s2. Since 1.5× 10-4 m2/s2 is equivalent to 1.5×10-5m in the vertical direction, it can be concluded that a method for terrain correction (or local gravity field modeling) based on closed-form solution of the Newton integral in terms of Cartesian coordinates of a multi-cylindrical equal-area map projection of the reference ellipsoid has been developed which has the accuracy of terrain correction (or local gravity field modeling) based on the Newton integral in terms of ellipsoidal coordinates.

Fundamentals of Physics, Volume 1, (Chapters 1 - 21)

NASA Astrophysics Data System (ADS)

Walker, Jearl

2004-01-01

Chapter 1. Measurement 1. How does the appearance of a new type of cloud signal changes in Earth's atmosphere? 1-1 What Is Physics? 1-2 Measuring Things. 1-3 The International System of Units. 1-4 Changing Units. 1-5 Length. 1-6 Time. 1-7 Mass. Review & Summary. Problems. Chapter 2. Motion Along a Straight Line. What causes whiplash injury in rear-end collisions of cars? 2-1 What Is Physics? 2-2 Motion. 2-3 Position and Displacement. 2-4 Average Velocity and Average Speed. 2-5 Instantaneous Velocity and Speed. 2-6 Acceleration. 2-7 Constant Acceleration: A Special Case. 2-8 Another Look at Constant Acceleration. 2-9 Free-Fall Acceleration. 2-10 Graphical Integration in Motion Analysis. 2 Review & Summary. Questions. Problems. Chapter 3. Vectors. How does an ant know the way home with no guiding clues on the desert plains? 3-1 What Is Physics? 3-2 Vectors and Scalars. 3-3 Adding Vectors Geometrically. 3-4 Components of Vectors. 3-5 Unit Vectors. 3-6 Adding Vectors by Components. 3-7 Vectors and the Laws of Physics. 3-8 Multiplying Vectors. Review & Summary. Questions. Problems. Chapter 4. Motion in Two and Three Dimensions. In a motorcycle jump for record distance, where does the jumper put the second ramp? 4-1 What Is Physics? 4-2 Position and Displacement. 4-3 Average Velocity and Instantaneous Velocity. 4-4 Average Acceleration and Instantaneous Acceleration. 4-5 Projectile Motion. 4-6 Projectile Motion Analyzed. 4-7 Uniform Circular Motion. 4-8 Relative Motion in One Dimension. 4-9 Relative Motion in Two Dimensions. Review & Summary. Questions. Problems. Chapter 5. Force and Motion--I. When a pilot takes off from an aircraft carrier, what causes the compulsion to .y the plane into the ocean? 5-1 What Is Physics? 5-2 Newtonian Mechanics. 5-3 Newton's First Law. 5-4 Force. 5-5 Mass. 5-6 Newton's Second Law. 5-7 Some Particular Forces. 5-8 Newton's Third Law. 5-9 Applying Newton's Laws. Review & Summary. Questions. Problems. Chapter 6. Force and Motion--II. Can a Grand Prix race car be driven upside down on a ceiling? 6-1 What Is Physics? 6-2 Friction. 6-3 Properties of Friction. 6-4 The Drag Force and Terminal Speed. 6-5 Uniform Circular Motion. Review & Summary. Questions. Problems. Chapter 7. Kinetic Energy and Work. In an epidural procedure, what sensations clue a surgeon that the needle has reached the spinal canal? 7-1 What Is Physics? 7-2 What Is Energy? 7-3 Kinetic Energy. 7-4 Work. 7-5 Work and Kinetic Energy. 7-6 Work Done by the Gravitational Force. 7-7 Work Done by a Spring Force. 7-8 Work Done by a General Variable Force. 7-9 Power. Review & Summary. Questions. Problems. Chapter 8. Potential Energy and Conservation of Energy. In rock climbing, what subtle factor determines if a falling climber will snap the rope? 8-1 What Is Physics? 8-2 Work and Potential Energy. 8-3 Path Independence of Conservative Forces. 8-4 Determining Potential Energy Values. 8-5 Conservation of Mechanical Energy. 8-6 Reading a Potential Energy Curve. 8-7 Work Done on a System by an External Force. 8-8 Conservation of Energy. Review & Summary. Questions. Problems. Chapter 9. Center of Mass and Linear Momentum. Does the presence of a passenger reduce the fatality risk in head-on car collisions? 9-1 What Is Physics? 9-2 The Center of Mass. 9-3 Newton's Second Law for a System of Particles. 9-4 Linear Momentum. 9-5 The Linear Momentum of a System of Particles. 9-6 Collision and Impulse. 9-7 Conservation of Linear Momentum. 9-8 Momentum and Kinetic Energy in Collisions. 9-9 Inelastic Collisions in One Dimension. 9-10 Elastic Collisions in One Dimension. 9-11 Collisions in Two Dimensions. 9-12 Systems with Varying Mass: A Rocket. Review & Summary. Questions. Problems. Chapter 10. Rotation. What causes roller-coaster headache? 10-1 What Is Physics? 10-2 The Rotational Variables. 10-3 Are Angular Quantities Vectors? 10-4 Rotation with Constant Angular Acceleration. 10-5 Relating the Linear and Angular Variables. 10-6 Kinetic Energy of Rotation. 10-7 Calculating the Rotational Inertia. 10-8 Torque. 10-9 Newton's Second Law for Rotation. 10-10 Work and Rotational Kinetic Energy. Review & Summary. Questions. Problems. Chapter 11. Rolling, Torque, and Angular Momentum. When a jet-powered car became supersonic in setting the land-speed record, what was the danger to the wheels? 11-1 What Is Physics? 11-2 Rolling as Translation and Rotation Combined. 11-3 The Kinetic Energy of Rolling. 11-4 The Forces of Rolling. 11-5 The Yo-Yo. 11-6 Torque Revisited. 11-7 Angular Momentum. 11-8 Newton's Second Law in Angular Form. 11-9 The Angular Momentum of a System of Particles. 11-10 The Angular Momentum of a Rigid Body Rotating About a Fixed Axis. 11-11 Conservation of Angular Momentum. 11-12 Precession of a Gyroscope. Review & Summary. Questions. Problems. Chapter 12. Equilibrium and Elasticity. What injury can occur to a rock climber hanging by a crimp hold? 12-1 What Is Physics? 12-2 Equilibrium. 12-3 The Requirements of Equilibrium. 12-4 The Center of Gravity. 12-5 Some Examples of Static Equilibrium. 12-6 Indeterminate Structures. 12-7 Elasticity. Review & Summary. Questions. Problems. Chapter 13. Gravitation. What lies at the center of our Milky Way galaxy? 13-1 What Is Physics? 13-2 Newton's Law of Gravitation. 13-3 Gravitation and the Principle of Superposition. 13-4 Gravitation Near Earth's Surface. 13-5 Gravitation Inside Earth. 13-6 Gravitational Potential Energy. 13-7 Planets and Satellites: Kepler's Laws. 13-8 Satellites: Orbits and Energy. 13-9 Einstein and Gravitation. Review & Summary. Questions. Problems. Chapter 14. Fluids. What causes ground effect in race car driving? 14-1 What Is Physics? 14-2 What Is a Fluid? 14-3 Density and Pressure. 14-4 Fluids at Rest. 14-5 Measuring Pressure. 14-6 Pascal's Principle. 14-7 Archimedes' Principle. 14-8 Ideal Fluids in Motion. 14-9 The Equation of Continuity. 14-10 Bernoulli's Equation. Review & Summary. Questions. Problems. Chapter 15. Oscillations. What is the "secret" of a skilled diver's high catapult in springboard diving? 15-1 What Is Physics? 15-2 Simple Harmonic Motion. 15-3 The Force Law for Simple Harmonic Motion. 15-4 Energy in Simple Harmonic Motion. 15-5 An Angular Simple Harmonic Oscillator. 15-6 Pendulums. 15-7 Simple Harmonic Motion and Uniform Circular Motion. 15-8 Damped Simple Harmonic Motion. 15-9 Forced Oscillations and Resonance. Review & Summary. Questions. Problems. Chapter 16. Waves--I. How can a submarine wreck be located by distant seismic stations? 16-1 What Is Physics? 16-2 Types of Waves. 16-3 Transverse and Longitudinal Waves. 16-4 Wavelength and Frequency. 16-5 The Speed of a Traveling Wave. 16-6 Wave Speed on a Stretched String. 16-7 Energy and Power of a Wave Traveling Along a String. 16-8 The Wave Equation. 16-9 The Principle of Superposition for Waves. 16-10 Interference of Waves. 16-11 Phasors. 16-12 Standing Waves. 16-13 Standing Waves and Resonance. Review & Summary. Questions. Problems. Chapter 17. Waves--II. How can an emperor penguin .nd its mate among thousands of huddled penguins? 17-1 What Is Physics? 17-2 Sound Waves. 17-3 The Speed of Sound. 17-4 Traveling Sound Waves. 17-5 Interference. 17-6 Intensity and Sound Level. 17-7 Sources of Musical Sound. 17-8 Beats. 17-9 The Doppler Effect. 17-10 Supersonic Speeds, Shock Waves. Review & Summary. Questions. Problems. Chapter 18. Temperature, Heat, and the First Law of Thermodynamics. How can a dead rattlesnake detect and strike a reaching hand? 18-1 What Is Physics? 18-2 Temperature. 18-3 The Zeroth Law of Thermodynamics. 18-4 Measuring Temperature. 18-5 The Celsius and Fahrenheit Scales. 18-6 Thermal Expansion. 18-7 Temperature and Heat. 18-8 The Absorption of Heat by Solids and Liquids. 18-9 A Closer Look at Heat and Work. 18-10 The First Law of Thermodynamics. 18-11 Some Special Cases of the First Law of Thermodynamics. 18-12 Heat Transfer Mechanisms. Review & Summary. Questions. Problems. Chapter 19. The Kinetic Theory of Gases. How can cooling steam inside a railroad tank car cause the car to be crushed? 19-1 What Is Physics? 19-2 Avogadro's Number. 19-3 Ideal Gases. 19-4 Pressure, Temperature, and RMS Speed. 19-5 Translational Kinetic Energy. 19-6 Mean Free Path. 19-7 The Distribution of Molecular Speeds. 19-8 The Molar Speci.c Heats of an Ideal Gas. 19-9 Degrees of Freedom and Molar Speci.c Heats. 19-10 A Hint of Quantum Theory. 19-11 The Adiabatic Expansion of an Ideal Gas. Review & Summary. Questions. Problems. Chapter 20. Entropy and the Second Law of Thermodynamics. Why is the popping of popcorn irreversible? 20-1 What Is Physics? 20-2 Irreversible Processes and Entropy. 20-3 Change in Entropy. 20-4 The Second Law of Thermodynamics. 20-5 Entropy in the Real World: Engines. 20-6 Entropy in the Real World: Refrigerators. 20-7 The Ef.ciencies of Real Engines. 20-8 A Statistical View of Entropy. Review & Summary. Questions. Problems. Appendices. A The International System of Units (SI). B Some Fundamental Constants of Physics. C Some Astronomical Data. D Conversion Factors. E Mathematical Formulas. F Properties of the Elements. G Periodic Table of the Elements. Answers to Checkpoints and Odd-Numbered Questions and Problems. Index.

Teaching Newton's Third Law of Motion in the Presence of Student Preconception

ERIC Educational Resources Information Center

Poon, C. H.

2006-01-01

The concept of interaction that underlies Newton's Laws of Motion is compared with the students' commonsense ideas of force and motion. An approach to teaching Newton's Third Law of Motion is suggested that focuses on refining the student's intuitive thinking on the nature of interaction.

A physical process of the radial acceleration of disc galaxies

NASA Astrophysics Data System (ADS)

Wilhelm, Klaus; Dwivedi, Bhola N.

2018-03-01

An impact model of gravity designed to emulate Newton's law of gravitation is applied to the radial acceleration of disc galaxies. Based on this model (Wilhelm et al. 2013), the rotation velocity curves can be understood without the need to postulate any dark matter contribution. The increased acceleration in the plane of the disc is a consequence of multiple interactions of gravitons (called `quadrupoles' in the original paper) and the subsequent propagation in this plane and not in three-dimensional space. The concept provides a physical process that relates the fit parameter of the acceleration scale defined by McGaugh et al. (2016) to the mean free path length of gravitons in the discs of galaxies. It may also explain the gravitational interaction at low acceleration levels in MOdification of the Newtonian Dynamics (MOND, Milgrom 1983, 1994, 2015, 2016). Three examples are discussed in some detail: the spiral galaxies NGC 7814, NGC 6503 and M 33.

Extending Newton's Universal Theory of Gravity

NASA Astrophysics Data System (ADS)

Aisenberg, Sol

2011-11-01

This should remove the mystery of Dark Matter. Newton's universal theory of gravity only used the observations of the motion of planets in our solar system. Hubble later used observations of fixed stars in the universe, and showed that the fixed stars were actually galaxies with very large numbers of stars. Newton's universal law of gravity could not explain these new observations without the mystery of dark matter for the additional gravity. In science, when a theory is not able to explain new observations it is necessary to modify the theory or abandon the theory. Rubin observed flat (constant velocity) rotation curves for stars in spiral galaxies. Dark matter was proposed to provide the missing gravity. The equation balancing gravitational force and centripetal force is M*G=v*v*r and for the observed constant velocity v this requires M*G to be a linear function of distance r. If the linear dependence is instead assigned to G instead of M to give a new value for Gn as G+A*r, this will explain the observations in the cosmos and also in our solar system for small r. See ``The Misunderstood Universe'' for more details.

Can Newton's Third Law Be "Derived" from the Second?

NASA Astrophysics Data System (ADS)

Gangopadhyaya, Asim; Harrington, James

2017-04-01

Newton's laws have engendered much discussion over several centuries. Today, the internet is awash with a plethora of information on this topic. We find many references to Newton's laws, often discussions of various types of misunderstandings and ways to explain them. Here we present an intriguing example that shows an assumption hidden in Newton's third law that is often overlooked. As is well known, the first law defines an inertial frame of reference and the second law determines the acceleration of a particle in such a frame due to an external force. The third law describes forces exerted on each other in a two-particle system, and allows us to extend the second law to a system of particles. Students are often taught that the three laws are independent. Here we present an example that challenges this assumption. At first glance, it seems to show that, at least for a special case, the third law follows from the second law. However, a careful examination of the assumptions demonstrates that is not quite the case. Ultimately, the example does illustrate the significance of the concept of mass in linking Newton's dynamical principles.

Spontaneous Lorentz and diffeomorphism violation, massive modes, and gravity

NASA Astrophysics Data System (ADS)

Bluhm, Robert; Fung, Shu-Hong; Kostelecký, V. Alan

2008-03-01

Theories with spontaneous local Lorentz and diffeomorphism violation contain massless Nambu-Goldstone modes, which arise as field excitations in the minimum of the symmetry-breaking potential. If the shape of the potential also allows excitations above the minimum, then an alternative gravitational Higgs mechanism can occur in which massive modes involving the metric appear. The origin and basic properties of the massive modes are addressed in the general context involving an arbitrary tensor vacuum value. Special attention is given to the case of bumblebee models, which are gravitationally coupled vector theories with spontaneous local Lorentz and diffeomorphism violation. Mode expansions are presented in both local and spacetime frames, revealing the Nambu-Goldstone and massive modes via decomposition of the metric and bumblebee fields, and the associated symmetry properties and gauge fixing are discussed. The class of bumblebee models with kinetic terms of the Maxwell form is used as a focus for more detailed study. The nature of the associated conservation laws and the interpretation as a candidate alternative to Einstein-Maxwell theory are investigated. Explicit examples involving smooth and Lagrange-multiplier potentials are studied to illustrate features of the massive modes, including their origin, nature, dispersion laws, and effects on gravitational interactions. In the weak static limit, the massive mode and Lagrange-multiplier fields are found to modify the Newton and Coulomb potentials. The nature and implications of these modifications are examined.

Constraining the range of Yukawa gravity interaction from S2 star orbits II: bounds on graviton mass

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zakharov, A.F.; Jovanović, P.; Borka, D.

2016-05-01

Recently LIGO collaboration discovered gravitational waves [1] predicted 100 years ago by A. Einstein. Moreover, in the key paper reporting about the discovery, the joint LIGO and VIRGO team presented an upper limit on graviton mass such as m {sub g} < 1.2 × 10{sup −22} eV [2] (see also more details in another LIGO paper [3] dedicated to a data analysis to obtain such a small constraint on a graviton mass). Since the graviton mass limit is so small the authors concluded that their observational data do not show violations of classical general relativity. We consider another opportunity tomore » evaluate a graviton mass from phenomenological consequences of massive gravity and show that an analysis of bright star trajectories could bound graviton mass with a comparable accuracy with accuracies reached with gravitational wave interferometers and expected with forthcoming pulsar timing observations for gravitational wave detection. It gives an opportunity to treat observations of bright stars near the Galactic Center as a wonderful tool not only for an evaluation specific parameters of the black hole but also to obtain constraints on the fundamental gravity law such as a modifications of Newton gravity law in a weak field approximation. In particular, we obtain bounds on a graviton mass based on a potential reconstruction at the Galactic Center.« less

Can Newton's Third Law Be "Derived" from the Second?

ERIC Educational Resources Information Center

Gangopadhyaya, Asim; Harrington, James

2017-01-01

Newton's laws have engendered much discussion over several centuries. Today, the internet is awash with a plethora of information on this topic. We find many references to Newton's laws, often discussions of various types of misunderstandings and ways to explain them. Here we present an intriguing example that shows an assumption hidden in…

Making More Plausible What is Hard To Believe: Historical Justifications and Illustrations of Newton's Third Law.

ERIC Educational Resources Information Center

Gauld, Colin

1998-01-01

Reports that many students do not believe Newton's law of action and reaction and suggests ways in which its plausibility might be enhanced. Reviews how this law has been made more plausible over time by Newton and those who succeeded him. Contains 25 references. (DDR)

3, 2, 1 ... Discovering Newton's Laws

ERIC Educational Resources Information Center

Lutz, Joe; Sylvester, Kevin; Oliver, Keith; Herrington, Deborah

2017-01-01

"For every action there is an equal and opposite reaction." "Except when a bug hits your car window, the car must exert more force on the bug because Newton's laws only apply in the physics classroom, right?" Students in our classrooms were able to pick out definitions as well as examples of Newton's three laws; they could…

The Clock Mission Optis

NASA Astrophysics Data System (ADS)

Dittus, Hansjörg; Lämmerzahl, Claus

Clocks are an almost universal tool for exploring the fundamental structure of theories related to relativity. For future clock experiments, it is important for them to be performed in space. One mission which has the capability to perform and improve all relativity tests based on clocks by several orders of magnitude is OPTIS. These tests consist of (i) tests of the isotropy of light propagation (from which information about the matter sector which the optical resonators are made of can also be drawn), (ii) tests of the constancy of the speed of light, (iii) tests of the universality of the gravitational redshift by comparing clocks based on light propagation, like light clocks and various atomic clocks, (iv) time dilation based on the Doppler effect, (v) measuring the absolute gravitational redshift, (vi) measuring the perihelion advance of the satellite's orbit by using very precise tracking techniques, (vii) measuring the Lense-Thirring effect, and (viii) testing Newton's gravitational potential law on the scale of Earth-bound satellites. The corresponding tests are not only important for fundamental physics but also indispensable for practical purposes like navigation, Earth sciences, metrology, etc.

Classical Mechanics: A Modern Introduction

NASA Astrophysics Data System (ADS)

McCall, Martin W.

2000-12-01

Classical Mechanics is a clear introduction to the subject, combining a user-friendly style with an authoritative approach, whilst requiring minimal prerequisite mathematics - only elementary calculus and simple vectors are presumed. The text starts with a careful look at Newton's Laws, before applying them in one dimension to oscillations and collisions. More advanced applications - including gravitational orbits, rigid body dynamics and mechanics in rotating frames - are deferred until after the limitations of Newton's inertial frames have been highlighted through an exposition of Einstein's Special Relativity. The examples given throughout are often unusual for an elementary text, although they are made accessible through discussion and diagrams. Complete revision summaries are given at the end of each chapter, together with problems designed to be both illustrative and challenging. Features: * Comprehensive introduction to classical mechanics and relativity * Many novel examples, e.g. stability of the universe, falling cats, crickets bats and snooker * Includes many problems with numerical answers * Revision notes at the end of each chapter

Soft X-Ray Emission Lines from a Relativistic Accretion Disk in MCG -6-30-15 and Mrk 766

NASA Technical Reports Server (NTRS)

Branduardi-Raymont, G.; Sako, M.; Kahn, S. M.; Brinkman, A. C.; Kaastra, J. S.; Page, M. J.

2000-01-01

XMM-Newton Reflection Grating Spectrometer (RGS) spectra of the Narrow Line Seyfert 1 galaxies MCG -6-30-15 and Mrk 766 are physically and spectroscopically inconsistent with standard models comprising a power-law continuum absorbed by either cold or ionized matter. We propose that the remarkably similar features detected in both objects in the 5 - 35 A band are H-like oxygen, nitrogen, and carbon emission lines, gravitation- ally redshifted and broadened by relativistic effects in the vicinity of a Kerr black hole. We discuss the implications of our interpretation, and demonstrate that the derived parameters can be physically self-consistent.

Solutions To the Problem of Impact in the 17th and 18th Centuries and Teaching Newton's Third Law Today.

ERIC Educational Resources Information Center

Gauld, Colin

1998-01-01

Compares the ideas of young people about Newton's third law, focusing on youth of today and youth of the 17th and 18th centuries. Examines the use of Newton's third law in understanding impact phenomena in the 17th and 18th centuries. Contains 46 references. (DDR)

Philosophical Concepts in Physics

NASA Astrophysics Data System (ADS)

Cushing, James T.

1998-01-01

Preface; Part I. The Scientific Enterprise: 1. Ways of knowing; 2. Aristotle and Francis Bacon; 3. Science and metaphysics; Part II. Ancient and Modern Models of the Universe: 4. Observational astronomy and the Ptolemaic model; 5. The Copernican model and Kepler's laws; 6. Galileo on motion; Part III. The Newtonian Universe: 7. Newton's Principia; 8. Newton's law of universal gravitation; 9. Some old questions revisited; Part IV. A Perspective: 10. Galileo's Letter to the Grand Duchess; 11. An overarching Newtonian framework; 12. A view of the world based on science: determinism; Part V. Mechanical Versus Electrodynamical World Views: 13. Models of the aether; 14. Maxwell's theory; 15. The Kaufmann experiments; Part VI. The Theory of Relativity: 16. The background to and essentials of special relativity; 17. Further logical consequences of Einstein's postulates; 18. General relativity and the expanding universe; Part VII. The Quantum World and the Completeness of Quantum Mechanics: 19. The road to quantum mechanics; 20. 'Copenhage' quantum mechanics; 21. Is quantum mechanics complete?; Part VIII. Some Philosophical Lessons from Quantum Mechanics: 22. The EPR paper and Bell's theorem; 23. An alternative version of quantum mechanics; 24. An essential role for historical contingency?; Part IX. A Retrospective: 25. The goals of science and the status of its knowledge; Notes; General references; Bibliography; Author index; Subject index.

Students' Concepts of Force: The Importance of Understanding Newton's Third Law.

ERIC Educational Resources Information Center

Brown, David E.

1989-01-01

Reports various misconceptions of Newton's third law obtained from interviews and written tests of high school students. Suggests putting emphasis on the third law in physics teaching. Ten references are listed. (YP)

Demonstrations of the Action and Reaction Law and the Energy Conservation Law Using Fine Spherical Plastic Beads

ERIC Educational Resources Information Center

Khumaeni, A.; Tanaka, S.; Kobayashi, A.; Lee, Y. I.; Kurniawan, K. H.; Ishii, K.; Kagawa, K.

2008-01-01

Equipment for demonstrating Newton's third law and the energy conservation law in mechanics have successfully been constructed utilizing fine spherical plastic beads in place of metal ball bearings. To demonstrate Newton's third law, special magnetized Petri dishes were employed as objects, while to examine the energy conservation law, a…

Infinity and Newton's Three Laws of Motion

NASA Astrophysics Data System (ADS)

Lee, Chunghyoung

2011-12-01

It is shown that the following three common understandings of Newton's laws of motion do not hold for systems of infinitely many components. First, Newton's third law, or the law of action and reaction, is universally believed to imply that the total sum of internal forces in a system is always zero. Several examples are presented to show that this belief fails to hold for infinite systems. Second, two of these examples are of an infinitely divisible continuous body with finite mass and volume such that the sum of all the internal forces in the body is not zero and the body accelerates due to this non-null net internal force. So the two examples also demonstrate the breakdown of the common understanding that according to Newton's laws a body under no external force does not accelerate. Finally, these examples also make it clear that the expression `impressed force' in Newton's formulations of his first and second laws should be understood not as `external force' but as `exerted force' which is the sum of all the internal and external forces acting on a given body, if the body is infinitely divisible.

Integrating Gender and Group Differences into Bridging Strategy

NASA Astrophysics Data System (ADS)

Yılmaz, Serkan; Eryılmaz, Ali

2010-08-01

The main goal of this study was to integrate gender and group effect into bridging strategy in order to assess the effect of bridging analogy-based instruction on sophomore students' misconceptions in Newton's Third Law. Specifically, the authors developed and benefited from anchoring analogy diagnostic test to merge the effect of group and gender into the strategy. Newton's third law misconception test, attitude scale toward Newton's third law, and classroom observation checklists were the other measuring tools utilized throughout this quasi-experimental study. The researchers also developed or used several teaching/learning materials such as gender and group splitted concept diagrams, lesson plans, gender splitted frequency tables, make sense scales, PowerPoint slides, flash cards, and demonstrations. The convenience sample of the study chosen from the accessible population involved 308 students from two public universities. The results of multivariate analysis of covariance indicated that the bridging strategy had a significant effect on students' misconceptions in Newton's third law whereas it had no significant effect on students' attitudes toward Newton's third law.

On improving the algorithm efficiency in the particle-particle force calculations

NASA Astrophysics Data System (ADS)

Kozynchenko, Alexander I.; Kozynchenko, Sergey A.

2016-09-01

The problem of calculating inter-particle forces in the particle-particle (PP) simulation models takes an important place in scientific computing. Such simulation models are used in diverse scientific applications arising in astrophysics, plasma physics, particle accelerators, etc., where the long-range forces are considered. The inverse-square laws such as Coulomb's law of electrostatic forces and Newton's law of universal gravitation are the examples of laws pertaining to the long-range forces. The standard naïve PP method outlined, for example, by Hockney and Eastwood [1] is straightforward, processing all pairs of particles in a double nested loop. The PP algorithm provides the best accuracy of all possible methods, but its computational complexity is O (Np2), where Np is a total number of particles involved. Too low efficiency of the PP algorithm seems to be the challenging issue in some cases where the high accuracy is required. An example can be taken from the charged particle beam dynamics where, under computing the own space charge of the beam, so-called macro-particles are used (see e.g., Humphries Jr. [2], Kozynchenko and Svistunov [3]).

Cool in the kitchen: Radiation, conduction, and the Newton ``hot block'' experiment

NASA Astrophysics Data System (ADS)

Silverman, Mark P.; Silverman, Christopher R.

2000-02-01

Despite frequent reference to Newton's law of cooling in physics and math books, the paper in which Newton reported this law is quite obscure and rarely cited. We have managed to acquire a copy of this paper and discuss the interesting experiment that Newton did in his kitchen. Surprisingly, the paper contains no procedural details or data of any experiments measuring the rate at which a hot object cools. We have performed our own kitchen experiments to investigate the cooling of (a) the burner of an electric range and (b) a block of Styrofoam. Newton's law provides a poor model for both systems, whose th! ! ermal energy loss we can much better understand by examining closely the effects of radiation and conduction.

The Amateur Scientist.

ERIC Educational Resources Information Center

Walker, Jearl

1983-01-01

Three physics experiments are described, minimizing difficulties for amateur experimenters. One experiment demonstrates the Doppler shift of light, converting the phenomenon into sound. The second measures Planck's constant. The third measures the universal gravitational constant, which does the same in Newton's theory of gravitation. (Author/JN)

Demonstrating Newton's Third Law: Changing Aristotelian Viewpoints.

ERIC Educational Resources Information Center

Roach, Linda E.

1992-01-01

Suggests techniques to help eliminate students' misconceptions involving Newton's Third Law. Approaches suggested include teaching physics from a historical perspective, using computer programs with simulations, rewording the law, drawing free-body diagrams, and using demonstrations and examples. (PR)

Oil, Earth mass and gravitational force.

PubMed

Moustafa, Khaled

2016-04-01

Fossil fuels are intensively extracted from around the world faster than they are renewed. Regardless of direct and indirect effects of such extractions on climate change and biosphere, another issue relating to Earth's internal structure and Earth mass should receive at least some interest. According to the Energy Information Administration (EIA), about 34 billion barrels of oil (~4.7 trillion metric tons) and 9 billion tons of coal have been extracted in 2014 worldwide. Converting the amounts of oil and coal extracted over the last 3 decades and their respective reserves, intended to be extracted in the future, into mass values suggests that about 355 trillion tons, or ~5.86∗10(-9) (~0.0000000058)% of the Earth mass, would be 'lost'. Although this is a tiny percentage, modeling the potential loss of Earth mass may help figuring out a critical threshold of mass loss that should not be exceeded. Here, I briefly discuss whether such loss would have any potential consequences on the Earth's internal structure and on its gravitational force based on the Newton's law of gravitation that links the attraction force between planets to their respective masses and the distance that separate them. Copyright © 2016 Elsevier B.V. All rights reserved.

Alternative to particle dark matter

NASA Astrophysics Data System (ADS)

Khoury, Justin

2015-01-01

We propose an alternative to particle dark matter that borrows ingredients of modified Newtonian dynamics (MOND) while adding new key components. The first new feature is a dark matter fluid, in the form of a scalar field with small equation of state and sound speed. This component is critical in reproducing the success of cold dark matter for the expansion history and the growth of linear perturbations, but does not cluster significantly on nonlinear scales. Instead, the missing mass problem on nonlinear scales is addressed by a modification of the gravitational force law. The force law approximates MOND at large and intermediate accelerations, and therefore reproduces the empirical success of MOND at fitting galactic rotation curves. At ultralow accelerations, the force law reverts to an inverse-square law, albeit with a larger Newton's constant. This latter regime is important in galaxy clusters and is consistent with their observed isothermal profiles, provided the characteristic acceleration scale of MOND is mildly varying with scale or mass, such that it is 12 times higher in clusters than in galaxies. We present an explicit relativistic theory in terms of two scalar fields. The first scalar field is governed by a Dirac-Born-Infeld action and behaves as a dark matter fluid on large scales. The second scalar field also has single-derivative interactions and mediates a fifth force that modifies gravity on nonlinear scales. Both scalars are coupled to matter via an effective metric that depends locally on the fields. The form of this effective metric implies the equality of the two scalar gravitational potentials, which ensures that lensing and dynamical mass estimates agree. Further work is needed in order to make both the acceleration scale of MOND and the fraction at which gravity reverts to an inverse-square law explicitly dynamical quantities, varying with scale or mass.

Dramatic (and Simple!) Demonstration of Newton's Third Law

NASA Astrophysics Data System (ADS)

Feldman, Gerald

2011-02-01

An operational understanding of Newton's third law is often elusive for students. Typical examples of this concept are given for contact forces that are closer to the students' everyday experience. While this is a good thing in general, the reaction force can sometimes be taken for granted, and the students can miss the opportunity to really think about what is going on. In the case of magnetic forces, however, the notion of action at a distance actually requires a careful inspection of the forces involved and thereby promotes a more detailed analysis of the situation. In this paper, a simple demonstration of Newton's third law is presented in the context of a magnet falling through a hollow conducting tube. The results are unambiguous and lead the students to an irrefutable verification of Newton's third law.

Cool in the Kitchen: Radiation, Conduction, and the Newton "Hot Block" Experiment.

ERIC Educational Resources Information Center

Silverman, Mark P.; Silverman, Christopher R.

2000-01-01

Discusses the history of the development of Newton's Law of Cooling. Describes an experiment conducted in the kitchen that is designed to test the rate of cooling of a hot block of iron. Finds that Newton's law does not represent very well the mechanism of heat loss. (Contains over 10 references.) (WRM)

Conformal and projective symmetries in Newtonian cosmology

NASA Astrophysics Data System (ADS)

Duval, C.; Gibbons, G. W.; Horváthy, P. A.

2017-02-01

Definitions of non-relativistic conformal transformations are considered both in the Newton-Cartan and in the Kaluza-Klein-type Eisenhart/Bargmann geometrical frameworks. The symmetry groups that come into play are exemplified by the cosmological, and also the Newton-Hooke solutions of Newton's gravitational field equations. It is shown, in particular, that the maximal symmetry group of the standard cosmological model is isomorphic to the 13-dimensional conformal-Newton-Cartan group whose conformal-Bargmann extension is explicitly worked out. Attention is drawn to the appearance of independent space and time dilations, in contrast with the Schrödinger group or the Conformal Galilei Algebra.

f(R) gravity and chameleon theories

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brax, Philippe; Bruck, Carsten van de; Davis, Anne-Christine

2008-11-15

We analyze f(R) modifications of Einstein's gravity as dark energy models in the light of their connection with chameleon theories. Formulated as scalar-tensor theories, the f(R) theories imply the existence of a strong coupling of the scalar field to matter. This would violate all experimental gravitational tests on deviations from Newton's law. Fortunately, the existence of a matter dependent mass and a thin-shell effect allows one to alleviate these constraints. The thin-shell condition also implies strong restrictions on the cosmological dynamics of the f(R) theories. As a consequence, we find that the equation of state of dark energy is constrainedmore » to be extremely close to -1 in the recent past. We also examine the potential effects of f(R) theories in the context of the Eoet-wash experiments. We show that the requirement of a thin shell for the test bodies is not enough to guarantee a null result on deviations from Newton's law. As long as dark energy accounts for a sizeable fraction of the total energy density of the Universe, the constraints that we deduce also forbid any measurable deviation of the dark energy equation of state from -1. All in all, we find that both cosmological and laboratory tests imply that f(R) models are almost coincident with a {lambda}CDM model at the background level.« less

Imbalance of Ecosystems and the Modified Newton's 3 Laws of Change

NASA Astrophysics Data System (ADS)

Lin, H.

2013-12-01

Sustainability calls for the unity of human knowledge that bridges the present "two cultures" gulf between the sciences and the humanities, and the transition from the age of machine to the age of the environment quests for harmony with nature (so-called eco-civilization). Ecosystems are fundamentally different from machines, where individual components contain complex organisms instead of identical nonliving entities. Because of heterogeneity, diversity, self-organization, and openness, imbalances abound in nature. These are reflected in entropy increase over time (S > 0) and gradient persistence over space (F > 0). In this paper, three modified Newton's laws of change for ecosystems are suggested, and examples of imbalances from landscape-soil-water-ecosystem-climate will be illustrated. ● Newton's 1st law of motion: ∑F=0 → dv/dt=0. i.e., if net force acting on an object is zero, then the object's velocity remains unchanged. Modified Newton's 1st law of change (imbalance #1): ∑F>0 → dv/dt≥0. i.e., unavoidable forcing exists in nature (∑F>0), thus change always happens; however, with inertia/resistance in some systems or minimum threshold needed to change, dv/dt≥0. ● Newton's 2nd law of motion: ∑F=ma. i.e., acceleration is inversely proportional to body mass. Modified Newton's 2nd law of change (imbalance #2): ∑F≠ma. i.e., either 1) it is hard to make change because of resilience, self-adjustment, nonlinearity of interactions-feedbacks in living systems (∑F≥ma), or 2) there is possible threshold behavior or sudden collapse of a system (∑F

Changing the Order of Newton's Laws--Why & How the Third Law Should Be First

ERIC Educational Resources Information Center

Stocklmayer, Sue; Rayner, John P.; Gore, Michael M.

2012-01-01

Newton's laws are difficult both for teachers and students at all levels. This is still the case despite a long history of critique of the laws as presented in the classroom. For example, more than 50 years ago Eisenbud and Weinstock proposed reformulations of the laws that put them on a sounder, more logically consistent base than is presented in…

Runners do not push off the ground but fall forwards via a gravitational torque.

PubMed

Romanov, Nicholas; Fletcher, Graham

2007-09-01

The relationship between the affect and timing of the four forces involved in running (gravity, ground reaction force, muscle force, and potential strain energy) is presented. These forces only increase horizontal acceleration of the centre of mass during stance but not flight. The current hierarchical models of running are critiqued because they do not show gravity, a constant force, in affect during stance. A new gravitational model of running is developed, which shows gravity as the motive force. Gravity is shown to cause a torque as the runner's centre of mass moves forward of the support foot. Ground reaction force is not a motive force but operates according to Newton's third law; therefore, the ground can only propel a runner forward in combination with muscle activity. However, leg and hip extensor muscles have consistently proven to be silent during leg extension (mid-terminal stance). Instead, high muscle-tendon forces at terminal stance suggest elastic recoil regains most of the centre of mass's height. Therefore, the only external motive force from mid-terminal stance is gravity via a gravitational torque, which causes a horizontal displacement. The aim of this paper is to establish a definitive biomechanical technique (Pose method) that is easily taught to runners (Romanov, 2002): falling forwards via a gravitational torque while pulling the support foot rapidly from the ground using the hamstring muscles.

Why Do Things Fall? How to Explain Why Gravity Is Not a Force

ERIC Educational Resources Information Center

Stannard, Warren B.

2018-01-01

In most high school physics classes, gravity is described as an attractive force between two masses as formulated by Newton over 300 years ago. Einstein's general theory of relativity implies that gravitational effects are instead the result of a "curvature" of space-time. However, explaining why things fall without resorting to Newton's…

An explanation of forms of planetary orbits and estimation of angular shift of the Mercury' perihelion using the statistical theory of gravitating spheroidal bodies

NASA Astrophysics Data System (ADS)

Krot, A. M.

2013-09-01

This work develops a statistical theory of gravitating spheroidal bodies to calculate the orbits of planets and explore forms of planetary orbits with regard to the Alfvén oscillating force [1] in the Solar system and other exoplanetary systems. The statistical theory of formation of gravitating spheroidal bodies has been proposed in [2]-[5]. Starting the conception for forming a spheroidal body inside a gas-dust protoplanetary nebula, this theory solves the problem of gravitational condensation of a gas-dust protoplanetary cloud with a view to planetary formation in its own gravitational field [3] as well as derives a new law of the Solar system planetary distances which generalizes the wellknown laws [2], [3]. This work also explains an origin of the Alfvén oscillating force modifying forms of planetary orbits within the framework of the statistical theory of gravitating spheroidal bodies [5]. Due to the Alfvén oscillating force moving solid bodies in a distant zone of a rotating spheroidal body have elliptic trajectories. It means that orbits for the enough remote planets from the Sun in Solar system are described by ellipses with focus in the origin of coordinates and with small eccentricities. The nearby planet to Sun named Mercury has more complex trajectory. Namely, in case of Mercury the angular displacement of a Newtonian ellipse is observed during its one rotation on an orbit, i.e. a regular (century) shift of the perihelion of Mercury' orbit occurs. According to the statistical theory of gravitating spheroidal bodies [2]-[5] under the usage of laws of celestial mechanics in conformity to cosmogonic bodies (especially, to stars) it is necessary to take into account an extended substance called a stellar corona. In this connection the stellar corona can be described by means of model of rotating and gravitating spheroidal body [5]. Moreover, the parameter of gravitational compression α of a spheroidal body (describing the Sun, in particular) has been estimated on the basis of the linear size of its kernel, i.e. the thickness of a visible part of the solar corona. Really, NASA' astronomer S. Odenwald in his notice «How thick is the solar corona?» wrote: "The corona actually extends throughout the entire solar system as a "wind" of particles, however, the densist parts of the corona is usually seen not more than about 1-2 solar radii from the surface or about 690,000 to 1.5 million kilometers at the equator. Near the poles, it seems to be a bit flatter..." [6]. In the fact, as mentioned in [5], a recession of plots of dependences of relative brightness of components of spectrum of the Solar corona occurs on distance of 3-3.5 radii from the center, i.e. on 2-2.5 radii from the edge of the solar disk. Thus, accepting thickness of a visible part of the solar corona equal to Δ = 2R (here R is radius of the solar disk) we find that r* = R + Δ = 3R , where r* =1/ α . In other words, the parameter of gravitational compression 2 α =1/ r* of a spheroidal body in case of the Sun with its corona (for which the equatorial radius ofdisk R = 6.955ṡ108 m) can be estimated by the value [2]-[5]: 2.29701177718 10 (m ) (3 ) 1 19 2 2 = ≈ ṡ - - R α . (1) So, the procedure of finding α is based on the known 3σ -rule in the statistical theory. Really, as shown in the monograph [5], namely the solar corona accounting under calculation of perturbed orbit of the planet of Mercury allows to find the estimation of a displacement of perihelion of Mercury' orbit for the one period within the framework of the statistical theory of gravitating spheroidal bodies. As it is known, on a way of specification of the law of Newton using the general relativity theory the Mercury problem solving was found [5]. Nevertheless, from a common position of the statistical theory of gravitating spheroidal bodies the points of view as Leverrier (about existence of an unknown matter) and Einstein (about insufficiency of the theory of Newton) practically differ nothing. Really, there exist plasma as well as gas-dust substance around of kernel of cosmogonic body (in particular, the solar corona in case of the Sun), i.e. the account of circumstance that forming cosmogonic bodies have not precise outlines and are represented by means of spheroidal forms demands some specification of the Newton' law in connection with a gravitating spheroidal body [2]-[5]. So, with the purpose of Mercury' trajectory finding within the framework of the statistical theory of gravitating and rotating spheroidal bodies it is necessary to estimate gravitational potential in nearby removal from the Sun, i.e. in a remote zone of a gravitational field and in immediate proximity to a kernel of a rotating spheroidal body. Taking into account that the orbit of planet Mercury entirely lays in one plane of polar angle θ =θ 0 = const we should use the formula [5]: 0 2 2 1 0 sin () * ɛ θ γ ϕ - = - > r r M g r r , (2) where r* =1/ α , α is a parameter of gravitational compression of a spheroidal body, M is its mass, γ is the Newtonian gravitational constant, ɛ 0 is a geometrical eccentricity of kernel of a rotating and gravitating spheroidal body (2 1 ɛ 0 << ) [2]-[5]. This work shows that in view of greatest proximity on distance to the Sun and essential inclination of orbit of Mercury the projection of a point of perihelion of its orbit can directly get in a nearby vicinity of the Sun, namely, in the visible part of the solar corona. In the monograph [5], using Binet' equation and formula (2) the equation of disturbed orbit of a planet (the Mercury) in a vicinity of a kernel of a rotating and gravitating spheroidal body has been derived. The obtained relation expresses the equation of the so-called "disturbed" ellipse in polar coordinates with the origin of coordinates in focus, i.e. the planet Mercury is moving on a precessing elliptic orbit in view of the fact that there is a modulating multiplier of a phase (or azimuth angle). So, within the framework of the statistical theory of gravitating spheroidal bodies the required angular moving of Newtonian ellipse during one turn of Mercury on the disturbed orbit (or displacement of perihelion of its orbit for the period) has been estimated [5]: 2 2 2 2 0 (1 )2 (3 ) a e e ṡ - + ṡ = α π ɛ δɛ , (3) where through a and e a major semi-axis and an eccentricity of Mercury's orbit are designated respectively, α is a parameter of gravitational compression (1) and ɛ 0 is a geometrical eccentricity of kernel of a rotating and gravitating spheroidal body (the Sun) [5]. Thus, according to the proposed formula (3) the turn of perihelion of Mercury' orbit is equal to 43.93'' in century that well is consistent with conclusions of the general relativity theory of Einstein (whose analogous estimation is equal to 43.03'') and astronomical observation data (43.11 ± 0.45'') [5].

Gravitational effective action at second order in curvature and gravitational waves

NASA Astrophysics Data System (ADS)

Calmet, Xavier; Capozziello, Salvatore; Pryer, Daniel

2017-09-01

We consider the full effective theory for quantum gravity at second order in curvature including non-local terms. We show that the theory contains two new degrees of freedom beyond the massless graviton: namely a massive spin-2 ghost and a massive scalar field. Furthermore, we show that it is impossible to fine-tune the parameters of the effective action to eliminate completely the classical spin-2 ghost because of the non-local terms in the effective action. Being a classical field, it is not clear anyway that this ghost is problematic. It simply implies a repulsive contribution to Newton's potential. We then consider how to extract the parameters of the effective action and show that it is possible to measure, at least in principle, the parameters of the local terms independently of each other using a combination of observations of gravitational waves and measurements performed by pendulum type experiments searching for deviations of Newton's potential.

Infrared modification of gravity from conformal symmetry

NASA Astrophysics Data System (ADS)

Gegenberg, Jack; Rahmati, Shohreh; Seahra, Sanjeev S.

2016-03-01

We reconsider a gauge theory of gravity in which the gauge group is the conformal group SO(4,2), and the action is of the Yang-Mills form, quadratic in the curvature. The resulting gravitational theory exhibits local conformal symmetry and reduces to Weyl-squared gravity under certain conditions. When the theory is linearized about flat spacetime, we find that matter which couples to the generators of special conformal transformations reproduces Newton's inverse square law. Conversely, matter which couples to generators of translations induces a constant and possibly repulsive force far from the source, which may be relevant for explaining the late-time acceleration of the Universe. The coupling constant of the theory is dimensionless, which means that it is potentially renormalizable.

Internal models and prediction of visual gravitational motion.

PubMed

Zago, Myrka; McIntyre, Joseph; Senot, Patrice; Lacquaniti, Francesco

2008-06-01

Baurès et al. [Baurès, R., Benguigui, N., Amorim, M.-A., & Siegler, I. A. (2007). Intercepting free falling objects: Better use Occam's razor than internalize Newton's law. Vision Research, 47, 2982-2991] rejected the hypothesis that free-falling objects are intercepted using a predictive model of gravity. They argued instead for "a continuous guide for action timing" based on visual information updated till target capture. Here we show that their arguments are flawed, because they fail to consider the impact of sensori-motor delays on interception behaviour and the need for neural compensation of such delays. When intercepting a free-falling object, the delays can be overcome by a predictive model of the effects of gravity on target motion.

Newton's Laws, Euler's Laws and the Speed of Light

ERIC Educational Resources Information Center

Whitaker, Stephen

2009-01-01

Chemical engineering students begin their studies of mechanics in a department of physics where they are introduced to the mechanics of Newton. The approach presented by physicists differs in both perspective and substance from that encountered in chemical engineering courses where Euler's laws provide the foundation for studies of fluid and solid…

Astronomical and Cosmological Symbolism in Art Dedicated to Newton and Einstein

NASA Astrophysics Data System (ADS)

Sinclair, R.

2013-04-01

Separated by two and a half centuries, Isaac Newton (1642-1727) and Albert Einstein (1879-1955) had profound impacts on our understanding of the universe. Newton established our understanding of universal gravitation, which was recast almost beyond recognition by Einstein. Both discovered basic patterns behind astronomical phenomena and became the best-known scientists of their respective periods. I will describe here how artists of the 18th and 20th centuries represented the achievements of Newton and Einstein. Representations of Newton express reverence, almost an apotheosis, portraying him as the creator of the universe. Einstein, in a different age, is represented often as a comic figure, and only rarely do we find art that hints at the profound view of the universe he developed.

Magnetic Levitation and Newton's Third Law

ERIC Educational Resources Information Center

Aguilar, Horacio Munguia

2007-01-01

Newton's third law is often misunderstood by students and even their professors, as has already been pointed out in the literature. Application of the law in the context of electromagnetism can be especially problematic, because the idea that the forces of "action" and "reaction" are equal and opposite independent of the medium through which they…

Teaching Newton's Laws with the iPod Touch in Conceptual Physics

ERIC Educational Resources Information Center

Kelly, Angela M.

2011-01-01

One of the greatest challenges in teaching physics is helping students achieve a conceptual understanding of Newton's laws. I find that students fresh from middle school can sometimes recite the laws verbatim ("An object in motion stays in motion..." and "For every action..."), but they rarely demonstrate a working knowledge of…

Students' Understanding on Newton's Third Law in Identifying the Reaction Force in Gravity Interactions

ERIC Educational Resources Information Center

Zhou, Shaona; Zhang, Chunbin; Xiao, Hua

2015-01-01

In the past three decades, previous researches showed that students had various misconceptions of Newton's Third Law. The present study focused on students' difficulties in identifying the third-law force pair in gravity interaction situations. An instrument involving contexts with gravity and non-gravity associated interactions was designed and…

Spacetime Dynamics and Slow Neutrino Background

NASA Astrophysics Data System (ADS)

Zhang, Tianxi

2018-06-01

Space is a form of existence of matter, while time is a measure of change of the matter in the space. Issac Newton suggested that the space and time are absolute, not affected by matter and its motion. His first law of motion or the law of inertia says that, without net force acts on it, an object in motion remains the motion in a straight line at a constant speed. Ernest Mach proposed that the inertia of a body results from the gravitational interaction on the body by the rest of the entire universe. As mass is a measure of inertia, Mach’s principle can be simply stated as mass here is affected by matter there. On the basis of Mach’s principle, Albert Einstein considered the space and time to be relative and developed two theories of relativities. One called special relativity describes the effect of motion on spacetime and the other called general relativity describes the effect of matter on spacetime. Recently, the author has further considered reactions of the influenced spacetime on the moving objects, including photons. A moving object including a photon, because of its continuously keeping on displacement, disturbs the rest of the entire universe or distorts/curves the spacetime. The distorted or curved spacetime then generates an effective gravitational force to act back on the moving object or photon, so that reduces the object inertia or photon frequency. Considering the disturbance of spacetime by a photon is extremely weak, the author has modelled the effective gravitational force to be Newtonian and derived a new redshift-distance relation that not only perfectly explained the redshift-distance measurement of distant type Ia supernovae but also inherently obtained Hubble’s law as an approximate at small redshift. In this study, we will further analyse the reaction of the influenced spacetime on moving neutrinos and demonstrate the creation of slow neutrino (or tired neutrino) background that may be gravitationally orbiting around clusters, galaxies, and any celestial objects to play a role of dark mater in explaining the excess of galactic and clustery rotations. This work was supported by NSF/REU (Grant #: PHY-1559870) at Alabama A & M University.

Measurement-based perturbation theory and differential equation parameter estimation with applications to satellite gravimetry

NASA Astrophysics Data System (ADS)

Xu, Peiliang

2018-06-01

The numerical integration method has been routinely used by major institutions worldwide, for example, NASA Goddard Space Flight Center and German Research Center for Geosciences (GFZ), to produce global gravitational models from satellite tracking measurements of CHAMP and/or GRACE types. Such Earth's gravitational products have found widest possible multidisciplinary applications in Earth Sciences. The method is essentially implemented by solving the differential equations of the partial derivatives of the orbit of a satellite with respect to the unknown harmonic coefficients under the conditions of zero initial values. From the mathematical and statistical point of view, satellite gravimetry from satellite tracking is essentially the problem of estimating unknown parameters in the Newton's nonlinear differential equations from satellite tracking measurements. We prove that zero initial values for the partial derivatives are incorrect mathematically and not permitted physically. The numerical integration method, as currently implemented and used in mathematics and statistics, chemistry and physics, and satellite gravimetry, is groundless, mathematically and physically. Given the Newton's nonlinear governing differential equations of satellite motion with unknown equation parameters and unknown initial conditions, we develop three methods to derive new local solutions around a nominal reference orbit, which are linked to measurements to estimate the unknown corrections to approximate values of the unknown parameters and the unknown initial conditions. Bearing in mind that satellite orbits can now be tracked almost continuously at unprecedented accuracy, we propose the measurement-based perturbation theory and derive global uniformly convergent solutions to the Newton's nonlinear governing differential equations of satellite motion for the next generation of global gravitational models. Since the solutions are global uniformly convergent, theoretically speaking, they are able to extract smallest possible gravitational signals from modern and future satellite tracking measurements, leading to the production of global high-precision, high-resolution gravitational models. By directly turning the nonlinear differential equations of satellite motion into the nonlinear integral equations, and recognizing the fact that satellite orbits are measured with random errors, we further reformulate the links between satellite tracking measurements and the global uniformly convergent solutions to the Newton's governing differential equations as a condition adjustment model with unknown parameters, or equivalently, the weighted least squares estimation of unknown differential equation parameters with equality constraints, for the reconstruction of global high-precision, high-resolution gravitational models from modern (and future) satellite tracking measurements.

Illustrating Newton's Second Law with the Automobile Coast-Down Test.

ERIC Educational Resources Information Center

Bryan, Ronald A.; And Others

1988-01-01

Describes a run test of automobiles for applying Newton's second law of motion and the concept of power. Explains some automobile thought-experiments and provides the method and data of an actual coast-down test. (YP)

The Earth, the Moon and Conservation of Momentum

ERIC Educational Resources Information Center

Brunt, Marjorie; Brunt, Geoff

2013-01-01

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.

Discovery Science: Newton All around You.

ERIC Educational Resources Information Center

Prigo, Robert; Humphrey, Gregg

1993-01-01

Presents activities for helping elementary students learn about Newton's third law of motion. Several activity cards demonstrate the concept of the law of action and reaction. The activities require only inexpensive materials that can be found around the house. (SM)

I ``Saw'' Newton's Three Laws

NASA Astrophysics Data System (ADS)

Shaw, Mike

2012-11-01

Would you like to build an inexpensive, highly visible, quickly assembled device that dramatically illustrates Newton's three laws of motion? This model incorporates sturdiness, high-profile visibility, and a student interest component that is sure to capture and hold their attention.

Objects in Motion

ERIC Educational Resources Information Center

Damonte, Kathleen

2004-01-01

One thing scientists study is how objects move. A famous scientist named Sir Isaac Newton (1642-1727) spent a lot of time observing objects in motion and came up with three laws that describe how things move. This explanation only deals with the first of his three laws of motion. Newton's First Law of Motion says that moving objects will continue…

XMM-Newton study of the lensing cluster of galaxies CL 0024+17

NASA Astrophysics Data System (ADS)

Zhang, Y.-Y.; Böhringer, H.; Mellier, Y.; Soucail, G.; Forman, W.

2005-01-01

We present a detailed gravitational mass measurement based on the XMM-Newton imaging spectroscopy analysis of the lensing cluster of galaxies CL 0024+17 at z=0.395. The emission appears approximately symmetric. However, on the scale of r ˜ 3.3' some indication of elongation is visible in the northwest-southeast (NW-SE) direction from the hardness ratio map (HRM). Within 3', we measure a global gas temperature of 3.52 ± 0.17 keV, metallicity of 0.22 ± 0.07, and bolometric luminosity of 2.9 ± 0.1 × 1044 h-270 erg s-1. We derive a temperature distribution with an isothermal temperature of 3.9 keV to a radius of 1.5' and a temperature gradient in the outskirts (1.3'

On the Minimal Accuracy Required for Simulating Self-gravitating Systems by Means of Direct N-body Methods

NASA Astrophysics Data System (ADS)

Portegies Zwart, Simon; Boekholt, Tjarda

2014-04-01

The conservation of energy, linear momentum, and angular momentum are important drivers of our physical understanding of the evolution of the universe. These quantities are also conserved in Newton's laws of motion under gravity. Numerical integration of the associated equations of motion is extremely challenging, in particular due to the steady growth of numerical errors (by round-off and discrete time-stepping and the exponential divergence between two nearby solutions. As a result, numerical solutions to the general N-body problem are intrinsically questionable. Using brute force integrations to arbitrary numerical precision we demonstrate empirically that ensembles of different realizations of resonant three-body interactions produce statistically indistinguishable results. Although individual solutions using common integration methods are notoriously unreliable, we conjecture that an ensemble of approximate three-body solutions accurately represents an ensemble of true solutions, so long as the energy during integration is conserved to better than 1/10. We therefore provide an independent confirmation that previous work on self-gravitating systems can actually be trusted, irrespective of the intrinsically chaotic nature of the N-body problem.

A Magnetic Set-Up to Help Teach Newton's Laws

ERIC Educational Resources Information Center

Panijpan, Bhinyo; Sujarittham, Thanida; Arayathanitkul, Kwan; Tanamatayarat, Jintawat; Nopparatjamjomras, Suchai

2009-01-01

A set-up comprising a magnetic disc, a solenoid and a mechanical balance was used to teach first-year physics students Newton's third law with the help of a free body diagram. The image of a floating magnet immobilized by the solenoid's repulsive force should help dispel a common misconception of students as regards the first law: that stationary…

Catch as Catch Can: The History of the Theory of Gravitational Capture.

ERIC Educational Resources Information Center

Osipov, Y.

1992-01-01

Traces cosmogonic history of solar system from Laplace's hypothesis of revolving gas nebulae, to Newton's two-body problem with its mathematical impossibility of gravitational capture, to the isosceles three-body problem of Schmidt and Sitnikov with its notion of partial capture, and finally to the total capture model of Alexeyev verified by the…

The role of competing knowledge structures in undermining learning: Newton's second and third laws

NASA Astrophysics Data System (ADS)

Low, David J.; Wilson, Kate F.

2017-01-01

We investigate the development of student understanding of Newton's laws using a pre-instruction test (the Force Concept Inventory), followed by a series of post-instruction tests and interviews. While some students' somewhat naive, pre-existing models of Newton's third law are largely eliminated following a semester of teaching, we find that a particular inconsistent model is highly resilient to, and may even be strengthened by, instruction. If test items contain words that cue students to think of Newton's second law, then students are more likely to apply a "net force" approach to solving problems, even if it is inappropriate to do so. Additional instruction, reinforcing physical concepts in multiple settings and from multiple sources, appears to help students develop a more connected and consistent level of understanding. We recommend explicitly encouraging students to check their work for consistency with physical principles, along with the standard checks for dimensionality and order of magnitude, to encourage reflective and rigorous problem solving.

Analysis of Newton's Third Law Questions on the Force Concepts Inventory at Georgia State University

NASA Astrophysics Data System (ADS)

Oakley, Christopher; Thoms, Brian

2012-03-01

A major emphasis of the Physics Education Research program at Georgia State University is an effort to assess and improve students' understanding of Newton's Laws concepts. As part of these efforts the Force Concepts Inventory (FCI) has been given to students in both the algebra-based and calculus-based introductory physics sequences. In addition, the algebra-based introductory physics sequence is taught in both a SCALE-UP and a traditional lecture format. The results of the FCI have been analyzed by individual question and also as categorized by content. The analysis indicates that students in both algebra and calculus-based courses are successful at overcoming Aristotelian misconceptions regarding Newton's Third Law (N3) in the context of a stationary system. However, students are less successful on N3 questions involving objects in constant motion or accelerating. Interference between understanding of Newton's Second and Third Laws as well as other possible explanations for lower student performance on N3 questions involving non-stationary objects will be discussed.

Interpreting Recoil for Undergraduate Students

NASA Astrophysics Data System (ADS)

Elsayed, Tarek A.

2012-04-01

The phenomenon of recoil is usually explained to students in the context of Newton's third law. Typically, when a projectile is fired, the recoil of the launch mechanism is interpreted as a reaction to the ejection of the smaller projectile. The same phenomenon is also interpreted in the context of the conservation of linear momentum, which is closely related to Newton's third law. Since the actual microscopic causes of recoil differ from one problem to another, some students (and teachers) may not be satisfied with understanding recoil through the principles of conservation of linear momentum and Newton's third law. For these students, the origin of the recoil motion should be presented in more depth.

Clustering of galaxies with f(R) gravity

NASA Astrophysics Data System (ADS)

Capozziello, Salvatore; Faizal, Mir; Hameeda, Mir; Pourhassan, Behnam; Salzano, Vincenzo; Upadhyay, Sudhaker

2018-02-01

Based on thermodynamics, we discuss the galactic clustering of expanding Universe by assuming the gravitational interaction through the modified Newton's potential given by f(R) gravity. We compute the corrected N-particle partition function analytically. The corrected partition function leads to more exact equations of state of the system. By assuming that the system follows quasi-equilibrium, we derive the exact distribution function that exhibits the f(R) correction. Moreover, we evaluate the critical temperature and discuss the stability of the system. We observe the effects of correction of f(R) gravity on the power-law behaviour of particle-particle correlation function also. In order to check the feasibility of an f(R) gravity approach to the clustering of galaxies, we compare our results with an observational galaxy cluster catalogue.

The Effect of Using a Visual Representation Tool in a Teaching-Learning Sequence for Teaching Newton's Third Law

ERIC Educational Resources Information Center

Savinainen, Antti; Mäkynen, Asko; Nieminen, Pasi; Viiri, Jouni

2017-01-01

This paper presents a research-based teaching-learning sequence (TLS) that focuses on the notion of interaction in teaching Newton's third law (N3 law) which is, as earlier studies have shown, a challenging topic for students to learn. The TLS made systematic use of a visual representation tool--an interaction diagram (ID)--highlighting…

Short-range inverse-square law experiment in space

NASA Technical Reports Server (NTRS)

Paik, H. J.; Moody, M. V.

2002-01-01

Newton's inverse-square law is a cornerstone of General Relativity. Its validity has been demonstrated to better than one part in thousand in ranges greater than 1 cm. The range below 1 mm has been left largely unexplored, due to the difficulties associated with designing sensitive short-range experiments. However, the theoretical rationale for testing Newton's law at ranges below 1 mm has become very strong recently.

Rule-governed Approaches to Physics--Newton's Third Law.

ERIC Educational Resources Information Center

Maloney, David P.

1984-01-01

Describes an approach to assessing the use of rules in solving problems related to Newton's third law of motion. Discusses the problems used, method of questioning, scoring of problem sets, and a general overview of the use of the technique in aiding the teacher in dealing with student's conceptual levels. (JM)

Newton's Law of Cooling Revisited

ERIC Educational Resources Information Center

Vollmer, M.

2009-01-01

The cooling of objects is often described by a law, attributed to Newton, which states that the temperature difference of a cooling body with respect to the surroundings decreases exponentially with time. Such behaviour has been observed for many laboratory experiments, which led to a wide acceptance of this approach. However, the heat transfer…

Demonstrating Kinematics and Newton's Laws in a Jump

ERIC Educational Resources Information Center

Kamela, Martin

2007-01-01

When students begin the study of Newton's laws they are generally comfortable with static equilibrium type problems, but dynamic examples where forces are not constant are more challenging. The class exercise presented here helps students to develop an intuitive grasp of both the position-velocity-acceleration relation and the force-acceleration…

Reconstruction of the two-dimensional gravitational potential of galaxy clusters from X-ray and Sunyaev-Zel'dovich measurements

NASA Astrophysics Data System (ADS)

Tchernin, C.; Bartelmann, M.; Huber, K.; Dekel, A.; Hurier, G.; Majer, C. L.; Meyer, S.; Zinger, E.; Eckert, D.; Meneghetti, M.; Merten, J.

2018-06-01

Context. The mass of galaxy clusters is not a direct observable, nonetheless it is commonly used to probe cosmological models. Based on the combination of all main cluster observables, that is, the X-ray emission, the thermal Sunyaev-Zel'dovich (SZ) signal, the velocity dispersion of the cluster galaxies, and gravitational lensing, the gravitational potential of galaxy clusters can be jointly reconstructed. Aims: We derive the two main ingredients required for this joint reconstruction: the potentials individually reconstructed from the observables and their covariance matrices, which act as a weight in the joint reconstruction. We show here the method to derive these quantities. The result of the joint reconstruction applied to a real cluster will be discussed in a forthcoming paper. Methods: We apply the Richardson-Lucy deprojection algorithm to data on a two-dimensional (2D) grid. We first test the 2D deprojection algorithm on a β-profile. Assuming hydrostatic equilibrium, we further reconstruct the gravitational potential of a simulated galaxy cluster based on synthetic SZ and X-ray data. We then reconstruct the projected gravitational potential of the massive and dynamically active cluster Abell 2142, based on the X-ray observations collected with XMM-Newton and the SZ observations from the Planck satellite. Finally, we compute the covariance matrix of the projected reconstructed potential of the cluster Abell 2142 based on the X-ray measurements collected with XMM-Newton. Results: The gravitational potentials of the simulated cluster recovered from synthetic X-ray and SZ data are consistent, even though the potential reconstructed from X-rays shows larger deviations from the true potential. Regarding Abell 2142, the projected gravitational cluster potentials recovered from SZ and X-ray data reproduce well the projected potential inferred from gravitational-lensing observations. We also observe that the covariance matrix of the potential for Abell 2142 reconstructed from XMM-Newton data sensitively depends on the resolution of the deprojected grid and on the smoothing scale used in the deprojection. Conclusions: We show that the Richardson-Lucy deprojection method can be effectively applied on a grid and that the projected potential is well recovered from real and simulated data based on X-ray and SZ signal. The comparison between the reconstructed potentials from the different observables provides additional information on the validity of the assumptions as function of the projected radius.

Non-Relativistic Twistor Theory and Newton-Cartan Geometry

NASA Astrophysics Data System (ADS)

Dunajski, Maciej; Gundry, James

2016-03-01

We develop a non-relativistic twistor theory, in which Newton-Cartan structures of Newtonian gravity correspond to complex three-manifolds with a four-parameter family of rational curves with normal bundle O oplus O(2)}. We show that the Newton-Cartan space-times are unstable under the general Kodaira deformation of the twistor complex structure. The Newton-Cartan connections can nevertheless be reconstructed from Merkulov's generalisation of the Kodaira map augmented by a choice of a holomorphic line bundle over the twistor space trivial on twistor lines. The Coriolis force may be incorporated by holomorphic vector bundles, which in general are non-trivial on twistor lines. The resulting geometries agree with non-relativistic limits of anti-self-dual gravitational instantons.

Bohlin transformation: the hidden symmetry that connects Hooke to Newton

NASA Astrophysics Data System (ADS)

Saggio, Maria Luisa

2013-01-01

Hooke's name is familiar to students of mechanics thanks to the law of force that bears his name. Less well-known is the influence his findings had on the founder of mechanics, Isaac Newton. In a lecture given some twenty years ago, W Arnol'd pointed out the outstanding contribution to science made by Hooke, and also noted the controversial issue of the attribution of important discoveries to Newton that were actually inspired by Hooke. It therefore seems ironic that the two most famous force laws, named after Hooke and Newton, are two geometrical aspects of the same law. This relationship, together with other illuminating aspects of Newtonian mechanics, is described in Arnol'd's book and is worth remembering in standard physics courses. In this didactical paper the duality of the two forces is expounded and an account of the more recent contributions to the subject is given.

A Simple Derivation of Kepler's Laws without Solving Differential Equations

ERIC Educational Resources Information Center

Provost, J.-P.; Bracco, C.

2009-01-01

Proceeding like Newton with a discrete time approach of motion and a geometrical representation of velocity and acceleration, we obtain Kepler's laws without solving differential equations. The difficult part of Newton's work, when it calls for non-trivial properties of ellipses, is avoided by the introduction of polar coordinates. Then a simple…

Newton's First Law: A Learning Cycle Approach

ERIC Educational Resources Information Center

McCarthy, Deborah

2005-01-01

To demonstrate how Newton's first law of motion applies to students' everyday lives, the author developed a learning cycle series of activities on inertia. The discrepant event at the heart of these activities is sure to elicit wide-eyed stares and puzzled looks from students, but also promote critical thinking and help bring an abstract concept…

Learning, Retention, and Forgetting of Newton's Third Law throughout University Physics

ERIC Educational Resources Information Center

Sayre, Eleanor C.; Franklin, Scott V.; Dymek, Stephanie; Clark, Jessica; Sun, Yifei

2012-01-01

We present data from a between-student study on student response to questions on Newton's third law given in two introductory calculus-based physics classes (Mechanics and Electromagnetism) at a large northeastern university. Construction of a response curve reveals subtle dynamics in student learning not capturable by pretesting and post-testing.…

Student Teachers' Levels of Understanding and Model of Understanding about Newton's Laws of Motion

ERIC Educational Resources Information Center

Saglam-Arslan, Aysegul; Devecioglu, Yasemin

2010-01-01

This study was conducted to determine the level of student teachers' understandings of Newton's laws of motion and relating these levels to identify student teachers' models of understanding. An achievement test composed of two parts comprising 12 open ended questions was constructed and given to 45 pre-service classroom teachers. The first part…

Model Analysis of Fine Structures of Student Models: An Example with Newton's Third Law.

ERIC Educational Resources Information Center

Bao, Lei; Hogg, Kirsten; Zollman, Dean

2002-01-01

Studies the role of context in students' uses of alternative conceptual models by using Newton's third law. Identifies four contextual features that are frequently used by students in their reasoning. Probes the effects of specific contextual features on student reasoning using a multiple-choice survey. (Contains 39 references.) (Author/YDS)

Students' Concept of Force: The Importance of Understanding Newton's Third Law.

ERIC Educational Resources Information Center

Brown, David E.

This paper analyzes the misconceptions high school students have about force and suggests that the misunderstanding of Newton's third law is the key to these misconceptions. Clinical interview and diagnostic test data (N=104) indicates that many students have a naive view of force as an acquired or innate property of single objects rather than…

Applying the Science of Learning to the Learning of Science: Newton's Second Law of Motion

ERIC Educational Resources Information Center

Lemmer, Miriam

2018-01-01

Science teaching and learning require knowledge about how learning takes place (cognition) and how learners interact with their surroundings (affective and sociocultural factors). The study reported on focussed on learning for understanding of Newton's second law of motion from a cognitive perspective that takes social factors into account. A…

Experimentally Building a Qualitative Understanding of Newton's Second Law

ERIC Educational Resources Information Center

Gates, Joshua

2014-01-01

Newton's second law is one of the cornerstones of the introductory physics curriculum, but it can still trouble a large number of students well after its introduction, hobbling their ability to apply the concept to problem solving and to related concepts, such as momentum, circular motion, and orbits. While there are several possibilities for…

Terrain Correction on the moving equal area cylindrical map projection of the surface of a reference ellipsoid

NASA Astrophysics Data System (ADS)

Ardalan, A.; Safari, A.; Grafarend, E.

2003-04-01

An operational algorithm for computing the ellipsoidal terrain correction based on application of closed form solution of the Newton integral in terms of Cartesian coordinates in the cylindrical equal area map projected surface of a reference ellipsoid has been developed. As the first step the mapping of the points on the surface of a reference ellipsoid onto the cylindrical equal area map projection of a cylinder tangent to a point on the surface of reference ellipsoid closely studied and the map projection formulas are computed. Ellipsoidal mass elements with various sizes on the surface of the reference ellipsoid is considered and the gravitational potential and the vector of gravitational intensity of these mass elements has been computed via the solution of Newton integral in terms of ellipsoidal coordinates. The geographical cross section areas of the selected ellipsoidal mass elements are transferred into cylindrical equal area map projection and based on the transformed area elements Cartesian mass elements with the same height as that of the ellipsoidal mass elements are constructed. Using the close form solution of the Newton integral in terms of Cartesian coordinates the potential of the Cartesian mass elements are computed and compared with the same results based on the application of the ellipsoidal Newton integral over the ellipsoidal mass elements. The results of the numerical computations show that difference between computed gravitational potential of the ellipsoidal mass elements and Cartesian mass element in the cylindrical equal area map projection is of the order of 1.6 × 10-8m^2/s^2 for a mass element with the cross section size of 10 km × 10 km and the height of 1000 m. For a 1 km × 1 km mass element with the same height, this difference is less than 1.5 × 10-4 m^2}/s^2. The results of the numerical computations indicate that a new method for computing the terrain correction based on the closed form solution of the Newton integral in terms of Cartesian coordinates and with accuracy of ellipsoidal terrain correction has been achieved! In this way one can enjoy the simplicity of the solution of the Newton integral in terms of Cartesian coordinates and at the same time the accuracy of the ellipsoidal terrain correction, which is needed for the modern theory of geoid computations.

Dramatic (and Simple!) Demonstration of Newton's Third Law

ERIC Educational Resources Information Center

Feldman, Gerald

2011-01-01

An operational understanding of Newton's third law is often elusive for students. Typical examples of this concept are given for contact forces that are closer to the students' everyday experience. While this is a good thing in general, the reaction force can sometimes be taken for granted, and the students can miss the opportunity to really think…

Virtual Petaflop Simulation: Parallel Potential Solvers and New Integrators for Gravitational Systems

NASA Technical Reports Server (NTRS)

Lake, George; Quinn, Thomas; Richardson, Derek C.; Stadel, Joachim

1999-01-01

"The orbit of any one planet depends on the combined motion of all the planets, not to mention the actions of all these on each other. To consider simultaneously all these causes of motion and to define these motions by exact laws allowing of convenient calculation exceeds, unless I am mistaken, the forces of the entire human intellect" -Isaac Newton 1687. Epochal surveys are throwing down the gauntlet for cosmological simulation. We describe three keys to meeting the challenge of N-body simulation: adaptive potential solvers, adaptive integrators and volume renormalization. With these techniques and a dedicated Teraflop facility, simulation can stay even with observation of the Universe. We also describe some problems in the formation and stability of planetary systems. Here, the challenge is to perform accurate integrations that retain Hamiltonian properties for 10(exp 13) timesteps.

Deviations from Newton's law in supersymmetric large extra dimensions

NASA Astrophysics Data System (ADS)

Callin, P.; Burgess, C. P.

2006-09-01

Deviations from Newton's inverse-squared law at the micron length scale are smoking-gun signals for models containing supersymmetric large extra dimensions (SLEDs), which have been proposed as approaches for resolving the cosmological constant problem. Just like their non-supersymmetric counterparts, SLED models predict gravity to deviate from the inverse-square law because of the advent of new dimensions at sub-millimeter scales. However SLED models differ from their non-supersymmetric counterparts in three important ways: (i) the size of the extra dimensions is fixed by the observed value of the dark energy density, making it impossible to shorten the range over which new deviations from Newton's law must be seen; (ii) supersymmetry predicts there to be more fields in the extra dimensions than just gravity, implying different types of couplings to matter and the possibility of repulsive as well as attractive interactions; and (iii) the same mechanism which is purported to keep the cosmological constant naturally small also keeps the extra-dimensional moduli effectively massless, leading to deviations from general relativity in the far infrared of the scalar-tensor form. We here explore the deviations from Newton's law which are predicted over micron distances, and show the ways in which they differ and resemble those in the non-supersymmetric case.

ON THE MINIMAL ACCURACY REQUIRED FOR SIMULATING SELF-GRAVITATING SYSTEMS BY MEANS OF DIRECT N-BODY METHODS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Portegies Zwart, Simon; Boekholt, Tjarda

2014-04-10

The conservation of energy, linear momentum, and angular momentum are important drivers of our physical understanding of the evolution of the universe. These quantities are also conserved in Newton's laws of motion under gravity. Numerical integration of the associated equations of motion is extremely challenging, in particular due to the steady growth of numerical errors (by round-off and discrete time-stepping and the exponential divergence between two nearby solutions. As a result, numerical solutions to the general N-body problem are intrinsically questionable. Using brute force integrations to arbitrary numerical precision we demonstrate empirically that ensembles of different realizations of resonant three-bodymore » interactions produce statistically indistinguishable results. Although individual solutions using common integration methods are notoriously unreliable, we conjecture that an ensemble of approximate three-body solutions accurately represents an ensemble of true solutions, so long as the energy during integration is conserved to better than 1/10. We therefore provide an independent confirmation that previous work on self-gravitating systems can actually be trusted, irrespective of the intrinsically chaotic nature of the N-body problem.« less

Testing the strong equivalence principle with the triple pulsar PSR J 0337 +1715

NASA Astrophysics Data System (ADS)

Shao, Lijing

2016-04-01

Three conceptually different masses appear in equations of motion for objects under gravity, namely, the inertial mass, mI , the passive gravitational mass, mP, and the active gravitational mass, mA. It is assumed that, for any objects, mI=mP=mA in the Newtonian gravity, and mI=mP in the Einsteinian gravity, oblivious to objects' sophisticated internal structure. Empirical examination of the equivalence probes deep into gravity theories. We study the possibility of carrying out new tests based on pulsar timing of the stellar triple system, PSR J 0337 +1715 . Various machine-precision three-body simulations are performed, from which, the equivalence-violating parameters are extracted with Markov chain Monte Carlo sampling that takes full correlations into account. We show that the difference in masses could be probed to 3 ×1 0-8 , improving the current constraints from lunar laser ranging on the post-Newtonian parameters that govern violations of mP=mI and mA=mP by thousands and millions, respectively. The test of mP=mA would represent the first test of Newton's third law with compact objects.

Historical Development of Newton's Laws of Motion and Suggestions for Teaching Content

ERIC Educational Resources Information Center

Chang, Wheijen; Bell, Beverley; Jones, Allister

2014-01-01

A review of the history of Newton's Laws of Motion illustrates that the historical development gradually shifted away from intuitive experiences and daily life conventions towards a scientific regulated perspective. Three stages of the historical development are discussed, i.e. prior to the Principia, the 3rd (last) edition of the Principia,…

The influence of implementation of interactive lecture demonstrations (ILD) conceptual change oriented toward the decreasing of the quantity students that misconception on the Newton's first law

NASA Astrophysics Data System (ADS)

Kurniawan, Yudi; Suhandi, Andi; Hasanah, Lilik

2016-02-01

This paper aims to know the influence of implementation of ILD conceptual change oriented (ILD-CC) toward the decreasing of the quantity of students that misconception on the Newton's First Law. The Newton's First Law misconceptions separated into five sub-misconceptions. This research is a quantitative research with one group pretest-posttest design. The samples of this research were 32 students on 9th grade of junior high school in Pandeglang, Banten, Indonesia. The diagnostic test is a multiple-choice form with three-tier test format. The result of this study found that there was decreasing of the quantity of students that misconception on the Newton's First Law. The largest percentage in the decreasing of the number of the students that misconception was on the Misconception 4 about 80, 77%. The Misconception 4 is "The cause of tendency of the body passenger that sat upright on the accelerated bus from motionless bus suddenly to backward be a backward force". For the future studies, it suggested to combine other methods to optimize the decreasing the number of students that misconception.

Deductive Reasoning to Teach Newton's Law of Motion

ERIC Educational Resources Information Center

Lee, Han Su; Park, Jongwon

2013-01-01

Finding out about and then understanding the forces acting on a moving object, based on a description of the change in motion of this object, is an important part of the conceptual understanding of Newton's law of motion. Using Hempel's deductive-normative model for scientific explanation, we developed a deductive explanation task (DET),…

Introducing the Notion of Bare and Effective Mass via Newton's Second Law of Motion

ERIC Educational Resources Information Center

Pinto, Marcus Benghi

2007-01-01

The concepts of bare and effective mass are widely used within modern physics. Their meaning is discussed in advanced undergraduate and graduate courses such as solid state physics, nuclear physics and quantum field theory. Here I discuss how these concepts may be introduced together with the discussion of Newton's second law of motion. The…

Snowboard Jumping, Newton's Second Law and the Force on Landing

ERIC Educational Resources Information Center

O'Shea, Michael J.

2004-01-01

An application of Newton's second law to a snowboarder dropping off a vertical ledge shows that the average normal force during landing (force exerted by the ground on the snowboarder) is determined by four factors. It is shown that the flexing of the legs, the softness of the snow, the angle of the landing surface and the forward motion of the…

Development and Application of a Rubric for Evaluating Students' Performance on Newton's Laws of Motion

ERIC Educational Resources Information Center

Kocakulah, Mustafa Sabri

2010-01-01

This study aims to develop and apply a rubric to evaluate the solutions of pre-service primary science teachers to questions about Newton's Laws of Motion. Two groups were taught the topic using the same teaching methods and administered four questions before and after teaching. Furthermore, 76 students in the experiment group were instructed…

Pre-Service Science Teachers' PCK: Inconsistency of Pre-Service Teachers' Predictions and Student Learning Difficulties in Newton's Third Law

ERIC Educational Resources Information Center

Zhou, Shaona; Wang, Yanlin; Zhang, Chunbin

2016-01-01

There is widespread agreement that science learning always builds upon students' existing ideas and that science teachers should possess knowledge of learners. This study aims at investigating pre-service science teachers' knowledge of student misconceptions and difficulties, a crucial component of PCK, on Newton's Third Law. A questionnaire was…

From Schawlow to Newton: An educational return

NASA Astrophysics Data System (ADS)

Sathe, D.

Newton's laws of motion and his theory of gravitation are known for over 300 years. However, investigations of educators, from various countries and carried out in the last quarter of the 20t h century, show that the Aristotelian ideas keep persisting among students - in spite of learning thes e topics in schools and colleges. In the traditional examinations students do give answers in accordance with Newton's laws but in questionnaires of educators they ignore Newtonian laws unknowingly, and quite naturally give answers along the Aristotelian line of thought. Why do they give such contrasting answers? Should we take for granted that their understanding of Newtonian laws is satisfactory because of their correct answers in traditional exams, though not in questionnaires? Can these contrasting views affect their interest in physics? These are some questions that warrant our attention earnestly, as we gear up for the research and teaching in 21s t century. The author felt the need of focusing attention on the logical aspects of the subject, due to the global character of said problem. His decision was strengthened greatly, in late1970s, by the philosophy of Dennis Sciama and hence author's dedication of a letter to the editor to his memory, in the COSPAR Info. Bulletin /1/. Being a trained biochemist, author started looking for points, missed by the earlier educators - that means author started following the advice of Arthur Schawlow /2/ in late 1970s, though unknowingly. Sadly, author came to know of it after dedicating a lecture to the memory of Abdus Salam in a symposium in Samarkand, Uzbekistan. Therefore he is dedicating this presentation to the memory of Arthur Schawlow. According to the present author, the persistence of Aristotelian ideas and consequent contrasting performances of students are due to the logical conflicts between the basic concepts of physics itself. For example, the conflict between the treatment of uniform circular motion and the concept of work motivate students to ignore the centripetal force as choose the tangential force as the resultant force. This is how the said contrast becomes a logical barrier in the comprehension of uniform circular motion and related topics. More information of work of others will also be provided, for the sake of comparison with author's work - leading to some new directions to be explored in the 21s t century. References: 1. Sathe, Dileep V. [Dec. 2001] COSPAR Information Bulletin #152, p. 53. 2. Chu, Steven, [August 1999] Physics World, V: 12, N: 8, p. 49.

Implementing WebQuest Based Instruction on Newton's Second Law

ERIC Educational Resources Information Center

Gokalp, Muhammed Sait; Sharma, Manjula; Johnston, Ian; Sharma, Mia

2013-01-01

The purpose of this study was to investigate how WebQuests can be used in physics classes for teaching specific concepts. The study had three stages. The first stage was to develop a WebQuest on Newton's second law. The second stage involved developing a lesson plan to implement the WebQuest in class. In the final stage, the WebQuest was…

Newton's Law: Not so Simple after All

ERIC Educational Resources Information Center

Robertson, William C.; Gallagher, Jeremiah; Miller, William

2004-01-01

One of the most basic concepts related to force and motion is Newton's first law, which essentially states, "An object at rest tends to remain at rest unless acted on by an unbalanced force. An object in motion in a straight line tends to remain in motion in a straight line unless acted upon by an unbalanced force." Judging by the time and space…

Student's preconception and anxiety when they solve multi representation concepts in Newton laws and it's application

NASA Astrophysics Data System (ADS)

Cari, C.; Suparmi, A.; Handhika, J.

2016-11-01

The purpose of this study was to describe of preconceptions and anxieties students in solving the representation concepts in newton laws and it's application. This research was conducted for junior undergraduate student's in physics department (36 Students) and physics education (31 Students). The method used in this study is a qualitative descriptive. The data was collection using test for multirepresentation concept, questionnaires for anxiety, and interviews. Based on the analysis it can be concluded that (1) the higher is anxiety, the higher is unconsistency (67,16%), (2) the higher is anxiety, the higher is consistency but wrong answer (29,85%), (3) the lower is anxiety, the higher is consistency of right answer (2,98%). Mostly students have understood fewer physics concept in newtons laws.

XMM-NEWTON SLEW SURVEY OBSERVATIONS OF THE GRAVITATIONAL WAVE EVENT GW150914

DOE Office of Scientific and Technical Information (OSTI.GOV)

Troja, E.; Read, A. M.; Tiengo, A.

The detection of the first gravitational wave (GW) transient GW150914 prompted an extensive campaign of follow-up observations at all wavelengths. Although no dedicated XMM-Newton observations have been performed, the satellite passed through the GW150914 error region during normal operations. Here we report the analysis of the data taken during these satellite slews performed two hours and two weeks after the GW event. Our data cover 1.1 and 4.8 deg{sup 2} of the final GW localization region. No X-ray counterpart to GW150914 is found down to a sensitivity of 6 × 10{sup −13} erg cm{sup −2} s{sup −1} in the 0.2–2more » keV band. Nevertheless, these observations show the great potential of XMM-Newton slew observations for searching for the electromagnetic counterparts of GW events. A series of adjacent slews performed in response to a GW trigger would take ≲1.5 days to cover most of the typical GW credible region. We discuss this scenario and its prospects for detecting the X-ray counterpart of future GW detections.« less

The History of the Cooling Law: When the Search for Simplicity Can Be an Obstacle

ERIC Educational Resources Information Center

Besson, Ugo

2012-01-01

This paper presents an historical overview of the research on the cooling law, from Newton until the beginning of 20th century, and provides some suggestions for the use of this history as a resource for teaching. This history begins with a description and an interpretation of Newton's earlier work in 1701 and an overview of studies confirming or…

From Newton's Second Law to Huygens's Principle: Visualizing Waves in a Large Array of Masses Joined by Springs

ERIC Educational Resources Information Center

Dolinko, A. E.

2009-01-01

By simulating the dynamics of a bidimensional array of springs and masses, the propagation of conveniently generated waves is visualized. The simulation is exclusively based on Newton's second law and was made to provide insight into the physics of wave propagation. By controlling parameters such as the magnitude of the mass and the elastic…

Teachers' Beliefs about the Role of Interaction in Teaching Newtonian Mechanics and Its Influence on Students' Conceptual Understanding of Newton's Third Law

ERIC Educational Resources Information Center

Jauhiainen, Johanna; Koponen, Ismo T.; Lavonen, Jari

2006-01-01

Students' conceptual understanding of Newton's third law has been the subject of numerous studies. These studies have often pointed out the importance of addressing the concept of interaction in teaching Newtonian mechanics. In this study, teachers were interviewed in order to examine how they understand interaction and use it in their…

The Effect of Group Work on Misconceptions of 9th Grade Students about Newton's Laws

ERIC Educational Resources Information Center

Ergin, Serap

2016-01-01

In this study, the effect of group work and traditional method on 9th grade students' misconceptions about Newton Laws was investigated. The study was conducted in three classes in an Anatolian Vocational High School in Ankara/Turkey in the second term of the 2014-2015 academic year. Two of these classes were chosen as the experimental group and…

Lazy Days: An Active Way to Put Newton's First Law into Motion (or Rest)

ERIC Educational Resources Information Center

Roemmele, Christopher; Sederberg, David

2017-01-01

Students are better able to understand Newton's first law when they build from their own personal experiences of bicycling, skateboarding, or riding in a car. Most have experienced a tumble when their skateboard or bicycle comes to an abrupt stop. Alternately in a car, your body continues moving when the brakes are applied and you feel the force…

Leadership for Sustainable Development From the Perspective of a Woman Physicist

NASA Astrophysics Data System (ADS)

Williams, Elvira S.

2005-10-01

What skills make a great leader? What policies lead to great programs? Answers to these challenging questions must be formulated and implemented by leaders who are successful regardless of the type organization interested in sustainable development. Leadership from both a career and an organizational viewpoint will be discussed from the perspective of a woman physicist. Implications of laws of classical and modern physics will be used in this discussion as tools for tailoring tactics for coarse- and fine-tuned guidance systems for successful leadership aimed at sustainable development. Specifically, implications of Newton's first, second and third laws of motion and the law of universal gravitation from classical physics are applied to leadership. The results are interpreted against the more refined findings of both quantum and chaos physics theories that indicate our inability to precisely predict outcomes of any event. Also, the refined theories support the notion that everything in the universe interacts with everything else in the universe at some level, so that nothing is completely isolated from anything else. Therefore, skill sets and program policies based on an interacting, all-inclusive, or holistic approaches are the ones that are most likely to generate great leaders and great programs, since these are the ones less likely to omit significant factors that could contribute to creation of great leaders.

Disturbance Reduction Control Design for the ST7 Flight Validation Experiment

NASA Technical Reports Server (NTRS)

Maghami, P. G.; Hsu, O. C.; Markley, F. L.; Houghton, M. B.

2003-01-01

The Space Technology 7 experiment will perform an on-orbit system-level validation of two specific Disturbance Reduction System technologies: a gravitational reference sensor employing a free-floating test mass, and a set of micro-Newton colloidal thrusters. The ST7 Disturbance Reduction System is designed to maintain the spacecraft's position with respect to a free-floating test mass to less than 10 nm/Hz, over the frequency range of 1 to 30 mHz. This paper presents the design and analysis of the coupled, drag-free and attitude control systems that close the loop between the gravitational reference sensor and the micro-Newton thrusters, while incorporating star tracker data at low frequencies. A full 18 degree-of-freedom model, which incorporates rigid-body models of the spacecraft and two test masses, is used to evaluate the effects of actuation and measurement noise and disturbances on the performance of the drag-free system.

Bell's theorem, the measurement problem, Newton's self-gravitation and its connections to violations of the discrete symmetries C, P, T

NASA Astrophysics Data System (ADS)

Hiesmayr, Beatrix C.

2015-07-01

About 50 years ago John St. Bell published his famous Bell theorem that initiated a new field in physics. This contribution discusses how discrete symmetries relate to the big open questions of quantum mechanics, in particular: (i) how correlations stronger than those predicted by theories sharing randomness (Bell's theorem) relate to the violation of the CP symmetry and the P symmetry; and its relation to the security of quantum cryptography, (ii) how the measurement problem (“why do we observe no tables in superposition?”) can be polled in weakly decaying systems, (iii) how strongly and weakly interacting quantum systems are affected by Newton's self gravitation. These presented preliminary results show that the meson-antimeson systems and the hyperon- antihyperon systems are a unique laboratory to tackle deep fundamental questions and to contribute to the understand what impact the violation of discrete symmetries has.

Optical analogues of the Newton-Schrödinger equation and boson star evolution.

PubMed

Roger, Thomas; Maitland, Calum; Wilson, Kali; Westerberg, Niclas; Vocke, David; Wright, Ewan M; Faccio, Daniele

2016-11-14

Many gravitational phenomena that lie at the core of our understanding of the Universe have not yet been directly observed. An example in this sense is the boson star that has been proposed as an alternative to some compact objects currently interpreted as being black holes. In the weak field limit, these stars are governed by the Newton-Schrodinger equation. Here we present an optical system that, under appropriate conditions, identically reproduces such equation in two dimensions. A rotating boson star is experimentally and numerically modelled by an optical beam propagating through a medium with a positive thermal nonlinearity and is shown to oscillate in time while also stable up to relatively high densities. For higher densities, instabilities lead to an apparent breakup of the star, yet coherence across the whole structure is maintained. These results show that optical analogues can be used to shed new light on inaccessible gravitational objects.

Optical analogues of the Newton-Schrödinger equation and boson star evolution

NASA Astrophysics Data System (ADS)

Roger, Thomas; Maitland, Calum; Wilson, Kali; Westerberg, Niclas; Vocke, David; Wright, Ewan M.; Faccio, Daniele

2016-11-01

Many gravitational phenomena that lie at the core of our understanding of the Universe have not yet been directly observed. An example in this sense is the boson star that has been proposed as an alternative to some compact objects currently interpreted as being black holes. In the weak field limit, these stars are governed by the Newton-Schrodinger equation. Here we present an optical system that, under appropriate conditions, identically reproduces such equation in two dimensions. A rotating boson star is experimentally and numerically modelled by an optical beam propagating through a medium with a positive thermal nonlinearity and is shown to oscillate in time while also stable up to relatively high densities. For higher densities, instabilities lead to an apparent breakup of the star, yet coherence across the whole structure is maintained. These results show that optical analogues can be used to shed new light on inaccessible gravitational objects.

Tests of Mach's Principle With a Mechanical Oscillator

NASA Technical Reports Server (NTRS)

Millis, Marc G. (Technical Monitor); Cramer, John G.; Fey, Curran W.; Casissi, Damon V.

2004-01-01

James F. Woodward has made a prediction, based on Sciama's formulation of Mach's Principle in the framework of general relativity, that in the presence of an energy flow the inertial mass of an object may undergo sizable variations, changing as the second time derivative of the energy. We describe an attempt to test for the predicted effect with a charging capacitor, using a technique that does not require an unbalanced force or any local violation of Newton s 3rd law of motion. We attempt to observe: (1) the gravitational effect of the varying mass and (2) the effect of the mass variation on a driven harmonic oscillator with the charging capacitor as the oscillating mass. We report on the predicted effect, the design and implementation of the measurement apparatus, and initial experience with the apparatus. At this time, however, we will not report on observations of the presence or absence of the Woodward effect.

An introduction to tensor calculus, relativity and cosmology /3rd edition/

NASA Astrophysics Data System (ADS)

Lawden, D. F.

This textbook introduction to the principles of special relativity proceeds within the context of cartesian tensors. Newton's laws of motion are reviewed, as are the Lorentz transformations, Minkowski space-time, and the Fitzgerald contraction. Orthogonal transformations are described, and invariants, gradients, tensor derivatives, contraction, scalar products, divergence, pseudotensors, vector products, and curl are defined. Special relativity mechanics are explored in terms of mass, momentum, the force vector, the Lorentz transformation equations for force, calculations for photons and neutrinos, the development of the Lagrange and Hamilton equations, and the energy-momentum tensor. Electrodynamics is investigated, together with general tensor calculus and Riemmanian space. The General Theory of Relativity is presented, along with applications to astrophysical phenomena such as black holes and gravitational waves. Finally, analytical discussions of cosmological problems are reviewed, particularly Einstein, de Sitter, and Friedmann universes, redshifts, event horizons, and the redshift.

Newton's Strange Collisions.

ERIC Educational Resources Information Center

Erlichson, Herman

1995-01-01

Discusses Newton's apparent oversight of the role of energy considerations in collisions between two spherical bodies related to the third corollary of his "Laws of Motion." Investigates several theories that provide solutions to the mysterious oversight. (LZ)

Teichmuller Space Resolution of the EPR Paradox

NASA Astrophysics Data System (ADS)

Winterberg, Friedwardt

2013-04-01

The mystery of Newton's action-at-a-distance law of gravity was resolved by Einstein with Riemann's non-Euclidean geometry, which permitted the explanation of the departure from Newton's law for the motion of Mercury. It is here proposed that the similarly mysterious non-local EPR-type quantum correlations may be explained by a Teichmuller space geometry below the Planck length, for which an experiment for its verification is proposed.

How College Students' Conceptions of Newton's Second and Third Laws Change through Watching Interactive Video Vignettes: A Mixed Methods Study

ERIC Educational Resources Information Center

Engelman, Jonathan

2016-01-01

Changing student conceptions in physics is a difficult process and has been a topic of research for many years. The purpose of this study was to understand what prompted students to change or not change their incorrect conceptions of Newtons Second or Third Laws in response to an intervention, Interactive Video Vignettes (IVVs), designed to…

Conceptual and Laboratory Exercise to Apply Newton's Second Law to a System of Many Forces

ERIC Educational Resources Information Center

Mungan, Carl E.

2012-01-01

A pair of objects on an inclined plane are connected together by a string. The upper object is then connected to a fixed post via a spring. The situation is first analysed as a classroom exercise in using free-body diagrams to solve Newton's second law for a system of objects upon which many different kinds of force are acting (string tension,…

Quantum mechanics from Newton's second law and the canonical commutation relation [X, P] = i

NASA Astrophysics Data System (ADS)

Palenik, Mark C.

2014-07-01

Despite the fact that it has been known since the time of Heisenberg that quantum operators obey a quantum version of Newton's laws, students are often told that derivations of quantum mechanics must necessarily follow from the Hamiltonian or Lagrangian formulations of mechanics. Here, we first derive the existing Heisenberg equations of motion from Newton's laws and the uncertainty principle using only the equations F=\\frac{dP}{dt}, P=m\\frac{dV}{dt}, and [X, P] = i. Then, a new expression for the propagator is derived that makes a connection between time evolution in quantum mechanics and the motion of a classical particle under Newton's laws. The propagator is solved for three cases where an exact solution is possible: (1) the free particle; (2) the harmonic oscillator; and (3) a constant force, or linear potential in the standard interpretation. We then show that for a general for a general force F(X), by Taylor expanding X(t) in time, we can use this methodology to reproduce the Feynman path integral formula for the propagator. Such a picture may be useful for students as they make the transition from classical to quantum mechanics and help solidify the equivalence of the Hamiltonian, Lagrangian, and Newtonian pictures of physics in their minds.

Newton's second law and the multiplication of distributions

NASA Astrophysics Data System (ADS)

Sarrico, C. O. R.; Paiva, A.

2018-01-01

Newton's second law is applied to study the motion of a particle subjected to a time dependent impulsive force containing a Dirac delta distribution. Within this setting, we prove that this problem can be rigorously solved neither by limit processes nor by using the theory of distributions (limited to the classical Schwartz products). However, using a distributional multiplication, not defined by a limit process, a rigorous solution emerges.

How College Students' Conceptions of Newton's Second and Third Laws Change Through Watching Interactive Video Vignettes: A Mixed Methods Study

NASA Astrophysics Data System (ADS)

Engelman, Jonathan

Changing student conceptions in physics is a difficult process and has been a topic of research for many years. The purpose of this study was to understand what prompted students to change or not change their incorrect conceptions of Newtons Second or Third Laws in response to an intervention, Interactive Video Vignettes (IVVs), designed to overcome them. This study is based on prior research reported in the literature which has found that a curricular framework of elicit, confront, resolve, and reflect (ECRR) is important for changing student conceptions (McDermott, 2001). This framework includes four essential parts such that during an instructional event student conceptions should be elicited, incorrect conceptions confronted, these conflicts resolved, and then students should be prompted to reflect on their learning. Twenty-two undergraduate student participants who completed either or both IVVs were studied to determine whether or not they experienced components of the ECRR framework at multiple points within the IVVs. A fully integrated, mixed methods design was used to address the study purpose. Both quantitative and qualitative data were collected iteratively for each participant. Successive data collections were informed by previous data collections. All data were analyzed concurrently. The quantitative strand included a pre/post test that participants took before and after completing a given IVV and was used to measure the effect of each IVV on learning. The qualitative strand included video of each participant completing the IVV as well as an audio-recorded video elicitation interview after the post-test. The qualitative data collection was designed to describe student experiences with each IVV as well as to observe how the ECRR framework was experienced. Collecting and analyzing data using this mixed methods approach helped develop a more complete understanding of how student conceptions of Newtons Second and Third Laws changed through completion of IVVs and how the ECRR framework was experienced. In answering the research questions, two major conclusions were reached: (1) while the ECRR framework was experienced in both the Newtons 2nd Law and Newtons 3rd Law IVVs, these experiences were qualitatively different from each other and these differences help support the differences in gain scores on the post-tests for the participants; and (2) both IVVs were able to change certain misconceptions associated with either Newtons 2nd or 3rd laws more than others. Therefore, in researching student experiences while completing the Newtons 2nd Law and Newtons 3rd Law IVVs, I determined that a complete, sequential experience of the elicit, confront, resolve, reflect framework led to the greatest change in student conceptions. This dissertation adds to the field of physics education through finding the positive impact of the ECRR framework, as IVVs are still being created and disseminated. Physics educators and researchers interested in conceptual change can use these findings to provide evidence on what students think when interacting with videos designed to change their conceptions. Finally, this dissertation supports the conceptual change literature in that the full, sequential experience involving each component of the ECRR framework led to a change in student conceptions.

No slip gravity

NASA Astrophysics Data System (ADS)

Linder, Eric V.

2018-03-01

A subclass of the Horndeski modified gravity theory we call No Slip Gravity has particularly interesting properties: 1) a speed of gravitational wave propagation equal to the speed of light, 2) equality between the effective gravitational coupling strengths to matter and light, Gmatter and Glight, hence no slip between the metric potentials, yet difference from Newton's constant, and 3) suppressed growth to give better agreement with galaxy clustering observations. We explore the characteristics and implications of this theory, and project observational constraints. We also give a simple expression for the ratio of the gravitational wave standard siren distance to the photon standard candle distance, in this theory and others, and enable a direct comparison of modified gravity in structure growth and in gravitational waves, an important crosscheck.

When Newton's cooling law doesn't hold

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tarnow, E.

1994-01-01

What is the fastest way to cool something If the object is macroscopic it is to lower the surrounding temperature as much as possible and let Newton's cooling law take effect. If we enter the microscopic world where quantum mechanics rules, this procedure may no longer be the best. This is shown in a simple example where we calculate the optimum cooling rate for an asymmetric two-state system.

FMA Live! at Hardy Middle School

NASA Image and Video Library

2013-09-16

With the help of a student participant, "FMA Live!" crew members explain Newton's second law of motion during a performance of "FMA Live!" at Hardy Middle School in Washington on Monday, Sept. 16th, 2013. "FMA Live!" is a program sponsored by NASA and Honeywell that teaches Newton's three laws of motion mixed with dance and music. The program travels across the country and has reached nearly 300,000 students.Photo Credit: (NASA/Jay Westcott)

FMA Live! at Hardy Middle School

NASA Image and Video Library

2013-09-16

With the help of a student participant, "FMA Live!" crew members explain Newton's first law of motion during a performance of "FMA Live!" at Hardy Middle School in Washington on Monday, Sept. 16th, 2013. "FMA Live!" is a program sponsored by NASA and Honeywell that teaches Newton's three laws of motion mixed with dance and music. The program travels across the country and has reached nearly 300,000 students.Photo Credit: (NASA/Jay Westcott)

Relativistic Iron K Emission and Absorption in the Seyfert 1.9 Galaxy MCG-05-23-16

NASA Technical Reports Server (NTRS)

Braito, V.; Reeves, J. N.; Dewangan, G. C.; George, I.; Griffiths, R.; Markowitz, A.; Nandra, K.; Porquet, D.; Ptak, A.; Turner, T. J.;

Large & Small: Exploring the Laws of Nature

ERIC Educational Resources Information Center

Creutz, E.

1976-01-01

Illustrates how both large entities (such as stars and galaxies) and small entities (such as fundamental particles) obey the same physical laws. Discusses quantum mechanics, Newton's laws, and general relativity. (MLH)

Challenging the cosmological constant

NASA Astrophysics Data System (ADS)

Kaloper, Nemanja

2007-09-01

We outline a dynamical dark energy scenario whose signatures may be simultaneously tested by astronomical observations and laboratory experiments. The dark energy is a field with slightly sub-gravitational couplings to matter, a logarithmic self-interaction potential with a scale tuned to ˜10 eV, as is usual in quintessence models, and an effective mass m influenced by the environmental energy density. Its forces may be suppressed just below the current bounds by the chameleon-like mimicry, whereby only outer layers of mass distributions, of thickness 1/m, give off appreciable long range forces. After inflation and reheating, the field is relativistic, and attains a Planckian expectation value before Hubble friction freezes it. This can make gravity in space slightly stronger than on Earth. During the matter era, interactions with nonrelativistic matter dig a minimum close to the Planck scale. However, due to its sub-gravitational matter couplings the field will linger away from this minimum until the matter energy density dips below ˜10 eV. Then it starts to roll to the minimum, driving a period of cosmic acceleration. Among the signatures of this scenario may be dark energy equation of state w≠-1, stronger gravity in dilute mediums, that may influence BBN and appear as an excess of dark matter, and sub-millimeter corrections to Newton's law, close to the present laboratory limits.

Dimensionally regularized Tsallis' statistical mechanics and two-body Newton's gravitation

NASA Astrophysics Data System (ADS)

Zamora, J. D.; Rocca, M. C.; Plastino, A.; Ferri, G. L.

2018-05-01

Typical Tsallis' statistical mechanics' quantifiers like the partition function and the mean energy exhibit poles. We are speaking of the partition function Z and the mean energy 〈 U 〉 . The poles appear for distinctive values of Tsallis' characteristic real parameter q, at a numerable set of rational numbers of the q-line. These poles are dealt with dimensional regularization resources. The physical effects of these poles on the specific heats are studied here for the two-body classical gravitation potential.

New interpretation of matter-antimatter asymmetry based on branes and possible observational consequences

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cai Ronggen; Li Tong; Li Xueqian

2007-11-15

Motivated by the alpha-magnetic-spectrometer (AMS) project, we assume that after the big bang or inflation epoch, antimatter was repelled onto one brane which is separated from our brane where all the observational matter resides. It is suggested that CP may be spontaneously broken, the two branes would correspond to ground states for matter and antimatter, respectively. Generally a complex scalar field which is responsible for the spontaneous CP violation, exists in the space between the branes. The matter and antimatter on the two branes attract each other via gravitational force, meanwhile the scalar field causes a Casimir effect to resultmore » in a repulsive force against the gravitation. We find that the Casimir force is much stronger than the gravitational force, as long as the separation of the two branes is small. Thus at early epoch after the big bang, the two branes were closer and then have been separated by the Casimir repulsive force from each other. The trend will continue until the separation is sufficiently large and then the gravitational force observed in our four-space would obviously deviate from the Newton's universal gravitational law. We suppose that there is a potential barrier at the brane boundary, which is similar to the surface tension for a water membrane. The barrier prevents the matter (antimatter) particles from entering the space between two branes and jump from one brane to another. However, by the quantum tunneling, a sizable antimatter flux may come to our brane and be observed by the AMS. In this work by considering two possible models, i.e. the naive flat space-time and Randall-Sundrum models, and using the observational data on the visible matter in our universe as inputs, we derive the antimatter flux which comes to our detector in the nonrelativistic approximation and make a rough numerical estimate of possible numbers of antihelium at AMS.« less

Émilie Du Châtelet's interpretation of the laws of motion in the light of 18th century mechanics.

PubMed

Reichenberger, Andrea

2018-06-01

Émilie Du Châtelet is well known for her French translation of Newton's Philosophiae Naturalis Principia Mathematica. It is the first and only French translation of Newton's magnum opus. The complete work appeared in 1759 under the title Principes mathématiques de la philosophie naturelle, par feue Madame la Marquise Du Chastellet. Before translating Newton's Principia, Du Châtelet worked on her Institutions de physique. In this book she defended the Leibnizian concept of living forces - vis viva. This paper argues that both of these works were part of a critical transformation and consolidation of post-Newtonian mechanics in the early 18th century, beyond Newton and Leibniz. This will be shown by comparing Du Châtelet's translation of Newton's axioms with her own formulations of the laws of motion in light of Thomas Le Seur's and François Jacquier's Geneva edition which holds a special place among the several editions of the Principia that appeared in the early 18th century. Copyright © 2018 Elsevier Ltd. All rights reserved.

Teaching Newton's Laws with the iPod Touch in Conceptual Physics

NASA Astrophysics Data System (ADS)

Kelly, Angela M.

2011-04-01

One of the greatest challenges in teaching physics is helping students achieve a conceptual understanding of Newton's laws. I find that students fresh from middle school can sometimes recite the laws verbatim ("An object in motion stays in motion…" and "For every action…"), but they rarely demonstrate a working knowledge of how to apply them to observable phenomena. As a firm believer in inquiry-based teaching methods, I like to develop activities where students can experiment and construct understandings based on relevant personal experiences. Consequently, I am always looking for exciting new technologies that can readily demonstrate how physics affects everyday things. In a conceptual physics class designed for ninth-graders, I created a structured activity where students applied Newton's laws to a series of free applications downloaded on iPod Touches. The laws had been introduced during the prior class session with textual descriptions and graphical representations. The course is offered as part of the Enlace Latino Collegiate Society, a weekend enrichment program for middle and high school students in the Bronx. The majority of students had limited or no prior exposure to physics concepts, and many attended high schools where physics was not offered at all.

FMA Live! at Hardy Middle School

NASA Image and Video Library

2013-09-16

Two teachers at Hardy Middle School square off in foam suits as "FMA Live!" crew members explain Newton's third law of motion during a performance of "FMA Live!" at Hardy Middle School in Washington on Monday, Sept. 16th, 2013. "FMA Live!" is a program sponsored by NASA and Honeywell that teaches Newton's three laws of motion mixed with dance and music. The program travels across the country and has reached nearly 300,000 students.Photo Credit: (NASA/Jay Westcott)

On trajectories of rolling marbles in cones and other funnels

NASA Astrophysics Data System (ADS)

White, Gary D.

2013-12-01

We report on theoretical and experimental results for a ball that rolls without slipping on a surface of revolution, whose symmetry axis is aligned with a uniform gravitational field, particularly investigating both near-circular orbits and scattering-type orbits in cones. The experimental data give support for the theoretical treatment, a non-trivial application of Newton's second law that expands on our previous work and related work of others. Our findings refine those from a recent article in this journal, and largely replicate those obtained from an earlier Lagrangian approach, adding some new details and commentary. While the orbits of marbles rolling in cones do not match inverse-square-law orbits quantitatively (e.g., instead of Kepler's 3rd law, we have T2∝R), we argue that students should experience these qualitative phenomena—precession of orbits, escape velocity behavior, spin-orbit coupling, conservation laws for angular momentum, energy, and spin projection—as much for the fun and kinesthetic impressions as for the raw learning. We also report on a heretofore largely ignored variable in the exploration of rolling orbits in a gravity well: the marble's spin about its own axis as it rolls. Experimenters can, intentionally or not, vary this initial condition and produce different orbital periods for a given orbital radius—a distinctly non-celestial behavior. Careful selection of the initial spin direction and speed for a particular cone can result in marble orbits that mimic the planetary ellipses.

XMM-Newton Observations of the Toothbrush and Sausage Clusters

NASA Astrophysics Data System (ADS)

Kara, S.; Mernier, F.; Ezer, C.; Akamatsu, H.; Ercan, E.

2017-10-01

Galaxy clusters are the largest gravitationally-bound objects in the universe. The member galaxies are embedded in a hot X-ray emitting Intra Cluster Medium (ICM) that has been enriched with metals produced by supernovae over the last billion years. Here we report new results from XMM-Newton archival observations of the merging clusters 1RXSJ0603.3+4213 and CIZA J2242.8+5301. These two clusters, also known as the Toothbrush and Sausage clusters, respectively, show a large radio relic associated with a merger shock North of their respective core. We show the distribution of the metal abundances with respect to the merger structures in these two clusters. The results are derived from spatially resolved X-ray spectra from the EPIC instrument on board XMM-Newton.

Fundamentals of Physics, Part 2 (Chapters 12-20)

NASA Astrophysics Data System (ADS)

Halliday, David; Resnick, Robert; Walker, Jearl

2003-12-01

Chapter 12 Equilibrium and Elasticity. What injury can occur to a rock climber hanging by a crimp hold? 12-1 What Is Physics? 12-2 Equilibrium. 12-3 The Requirements of Equilibrium. 12-4 The Center of Gravity. 12-5 Some Examples of Static Equilibrium. 12-6 Indeterminate Structures. 12-7 Elasticity. Review & Summary Questions Problems. Chapter 13 Gravitation. What lies at the center of our Milky Way galaxy? 13-1 What Is Physics? 13-2 Newton's Law of Gravitation. 13-3 Gravitation and the Principle of Superposition. 13-4 Gravitation Near Earth's Surface. 13-5 Gravitation Inside Earth. 13-6 Gravitational Potential Energy. 13-7 Planets and Satellites: Kepler's Laws. 13-8 Satellites: Orbits and Energy. 13-9 Einstein and Gravitation. Review & Summary Questions Problems. Chapter 14 Fluids. What causes ground effect in race car driving? 14-1 What Is Physics? 14-2 What Is a Fluid? 14-3 Density and Pressure. 14-4 Fluids at Rest. 14-5 Measuring Pressure. 14-6 Pascal's Principle. 14-7 Archimedes' Principle. 14-8 Ideal Fluids in Motion. 14-9 The Equation of Continuity. 14-10 Bernoulli's Equation. Review & SummaryQuestionsProblems. Chapter 15 Oscillations. What is the "secret" of a skilled diver's high catapult in springboard diving? 15-1 What Is Physics? 15-2 Simple Harmonic Motion. 15-3 The Force Law for Simple Harmonic Motion. 15-4 Energy in Simple Harmonic Motion. 15-5 An Angular Simple Harmonic Oscillator. 15-6 Pendulums. 15-7 Simple Harmonic Motion and Uniform Circular Motion. 15-8 Damped Simple Harmonic Motion. 15-9 Forced Oscillations and Resonance. Review & Summary Questions Problems. Chapter 16 Waves--I. How can a submarine wreck be located by distant seismic stations? 16-1 What Is Physics? 16-2 Types of Waves. 16-3 Transverse and Longitudinal Waves. 16-4 Wavelength and Frequency. 16-5 The Speed of a Traveling Wave. 16-6 Wave Speed on a Stretched String. 16-7 Energy and Power of a Wave Traveling Along a String. 16-8 The Wave Equation. 16-9 The Principle of Superposition for Waves. 16-10 Interference of Waves. 16-11 Phasors. 16-12 Standing Waves. 16-13 Standing Waves and Resonance. Review & Summary Questions Problems. Chapter 17 Waves--II. How can an emperor penguin .nd its mate among thousands of huddled penguins? 17-1 What Is Physics? 17-2 Sound Waves. 17-3 The Speed of Sound. 17-4 Traveling Sound Waves. 17-5 Interference. 17-6 Intensity and Sound Level. 17-7 Sources of Musical Sound. 17-8 Beats. 17-9 The Doppler Effect. 17-10 Supersonic Speeds, Shock Waves. Review & Summary Questions Problems. Chapter 18 Temperature, Heat, and the First Law of Thermodynamics. How can a dead rattlesnake detect and strike a reaching hand? 18-1 What Is Physics?. 18-2 Temperature. 18-3 The Zeroth Law of Thermodynamics. 18-4 Measuring Temperature. 18-5 The Celsius and Fahrenheit Scales. 18-6 Thermal Expansion. 18-7 Temperature and Heat. 18-8 The Absorption of Heat by Solids and Liquids. 18-9 A Closer Look at Heat and Work. 18-10 The First Law of Thermodynamics. 18-11 Some Special Cases of the First Law of Thermodynamics. 18-12 Heat Transfer Mechanisms. Review & Summary Questions Problems. Chapter 19 The Kinetic Theory of Gases. How can cooling steam inside a railroad tank car cause the car to be crushed? 19-1 What Is Physics? 19-2 Avogadro's Number. 19-3 Ideal Gases. 19-4 Pressure, Temperature, and RMS Speed. 19-5 Translational Kinetic Energy. 19-6 Mean Free Path. 19-7 The Distribution of Molecular Speeds. 19-8 The Molar Speci.c Heats of an Ideal Gas. 19-9 Degrees of Freedom and Molar Speci.c Heats. 19-10 A Hint of Quantum Theory. 19-11 The Adiabatic Expansion of an Ideal Gas. Review & Summary Questions Problems. Chapter 20 Entropy and the Second Law of Thermodynamics. Why is the popping of popcorn irreversible? 20-1 What Is Physics? 20-2 Irreversible Processes and Entropy. 20-3 Change in Entropy. 20-4 The Second Law of Thermodynamics. 20-5 Entropy in the Real World: Engines. 20-6 Entropy in the Real World: Refrigerators. 20-7 The Ef.ciencies of Real Engines. 20-8 A Statistical View of Entropy. Review & Summary Questions Problems. Appendices. A The International System of Units (SI). B Some Fundamental Constants of Physics. C Some Astronomical Data. D Conversion Factors. E Mathematical Formulas. F Properties of the Elements. G Periodic Table of the Elements. Answers to Checkpoints and Odd-Numbered Questions and Problems. Index.

Precision Timing of PSR J0437-4715: An Accurate Pulsar Distance, a High Pulsar Mass, and a Limit on the Variation of Newton's Gravitational Constant

NASA Astrophysics Data System (ADS)

Verbiest, J. P. W.; Bailes, M.; van Straten, W.; Hobbs, G. B.; Edwards, R. T.; Manchester, R. N.; Bhat, N. D. R.; Sarkissian, J. M.; Jacoby, B. A.; Kulkarni, S. R.

2008-05-01

Analysis of 10 years of high-precision timing data on the millisecond pulsar PSR J0437-4715 has resulted in a model-independent kinematic distance based on an apparent orbital period derivative, dot Pb , determined at the 1.5% level of precision (Dk = 157.0 +/- 2.4 pc), making it one of the most accurate stellar distance estimates published to date. The discrepancy between this measurement and a previously published parallax distance estimate is attributed to errors in the DE200 solar system ephemerides. The precise measurement of dot Pb allows a limit on the variation of Newton's gravitational constant, |Ġ/G| <= 23 × 10-12 yr-1. We also constrain any anomalous acceleration along the line of sight to the pulsar to |a⊙/c| <= 1.5 × 10-18 s-1 at 95% confidence, and derive a pulsar mass, mpsr = 1.76 +/- 0.20 M⊙, one of the highest estimates so far obtained.

Controller Design for the ST7 Disturbance Reduction System

NASA Technical Reports Server (NTRS)

Maghami, Peiman; Markley, F. Landis; Dennehey, Neil; Houghton, Martin B.; Folkner, William M.; Bauer, Frank (Technical Monitor)

2002-01-01

The Space Technology 7 experiment will perform an on-orbit system-level validation of two specific Disturbance Reduction System technologies: a gravitational reference sensor employing a free-floating test mass and a set of micro-Newton colloidal thrusters. The Disturbance Reduction System is designed to maintain a spacecraft's position with respect to the free-floating test mass to less than 10 nm/ square root of Hz, over the frequency range 10(exp -3) Hz to 10(exp -2) Hz. This paper presents the design and analysis of the coupled drag-free and attitude control system that closes the loop between the gravitational reference sensor and the micro-Newton thrusters while incorporating star tracker data at low frequencies. The effects of actuation and measurement noise and disturbances on the spacecraft and test masses are evaluated in a seven-degree-of-freedom planar model incorporating two translational and one rotational degrees of freedom for the spacecraft and two translational degrees of freedom for each test mass.

Origins of Newton's First Law

NASA Astrophysics Data System (ADS)

Hecht, Eugene

2015-02-01

Anyone who has taught introductory physics should know that roughly a third of the students initially believe that any object at rest will remain at rest, whereas any moving body not propelled by applied forces will promptly come to rest. Likewise, about half of those uninitiated students believe that any object moving at a constant speed must be continually pushed if it is to maintain its motion.1 That's essentially Aristotle's law of motion and it is so "obviously" borne out by experience that it was accepted by scholars for 2000 years, right through the Copernican Revolution. But, of course, it's fundamentally wrong. This paper tells the story of how the correct understanding, the law of inertia, evolved and how Newton came to make it his first law.

Complex large-scale convection of a viscous incompressible fluid with heat exchange according to Newton's law

NASA Astrophysics Data System (ADS)

Gorshkov, A. V.; Prosviryakov, E. Yu.

2017-12-01

The paper considers the construction of analytical solutions to the Oberbeck-Boussinesq system. This system describes layered Bénard-Marangoni convective flows of an incompressible viscous fluid. The third-kind boundary condition, i. e. Newton's heat transfer law, is used on the boundaries of a fluid layer. The obtained solution is analyzed. It is demonstrated that there is a fluid layer thickness with tangential stresses vanishing simultaneously, this being equivalent to the existence of tensile and compressive stresses.

Monitoring Global Geophysical Fluids by Space Geodesy

NASA Technical Reports Server (NTRS)

Chao, Benjamin F.; Dehant, V.; Gross, R. S.; Ray, R. D.; Salstein, D. A.; Watkins, M.

1999-01-01

Since its establishment on 1/1/1998 by the International Earth Rotation Service, the Coordinating Center for Monitoring Global Geophysical Fluids (MGGF) and its seven Special Bureaus have engaged in an effort to support and facilitate the understanding of the geophysical fluids in global geodynamics research. Mass transports in the atmosphere-hydrosphere-solid Earth-core system (the "global geophysical fluids") will cause the following geodynamic effects on a broad time scale: (1) variations in the solid Earth's rotation (in length-of-day and polar motion/nutation) via the conservation of angular momentum and effected by torques at the fluid-solid Earth interface; (2) changes in the global gravitational field according to Newton's gravitational law; and (3) motion in the center of mass of the solid Earth relative to that of the whole Earth ("geocenter") via the conservation of linear momentum. These minute signals have become observable by space geodetic techniques, primarily VLBI, SLR, GPS, and DORIS, with ever increasing precision/accuracy and temporal/spatial resolution. Each of the seven Special Bureaus within MGGF is responsible for calculations related to a specific Earth component or aspect -- Atmosphere, Ocean, Hydrology, Ocean Tides, Mantle, Core, and Gravity/Geocenter. Angular momenta and torques, gravitational coefficients, and geocenter shift will be computed for geophysical fluids based on global observational data, and from state-of-the-art models, some of which assimilate such data. The computed quantities, algorithm and data formats are standardized. The results are archived and made available to the scientific research community. This paper reports the status of the MGGF activities and current results.

The Conservation Principles and Kepler's Laws of Planetary Motion

ERIC Educational Resources Information Center

Motz, Lloyd

1975-01-01

Derives Kepler's three laws of planetary motion algebraically from conservation principles without introducing Newton's law of force explicitly. This procedure can be presented to students who have had no more than high school algebra. (Author)

Why do things fall? How to explain why gravity is not a force

NASA Astrophysics Data System (ADS)

Stannard, Warren B.

2018-03-01

In most high school physics classes, gravity is described as an attractive force between two masses as formulated by Newton over 300 years ago. Einstein’s general theory of relativity implies that gravitational effects are instead the result of a ‘curvature’ of space-time. However, explaining why things fall without resorting to Newton’s gravitational force can be difficult. This paper introduces some simple graphical and visual analogies and models which are suitable for the introduction of Einstein’s theory of general relativity at a high school level. These models provide an alternative to Newton’s gravitational force and help answer the simple question: why do things fall?

The Fourth Law of Motion in Classical Mechanics and Electrodynamics

NASA Astrophysics Data System (ADS)

Pinheiro, Mario J.

2010-01-01

Newton's second law has limited scope of application when transient phenomena are at stake. We endeavor here to consider a modification of Newton's second law in order to take into account sudden change (surge) of angular momentum or linear momentum. It is shown that space react back according to a kind of induction law that is related to inertia, but also appears to give evidence of a "fluidic" nature of space itself. The back-reaction is quantified by the time rate of the angular momentum flux threading a surface, mass dependent, and bearing similarity to the quantum mechanics phase shift, present in the Aharonov-Bohm and Aharonov-Casher effects, thus giving evidence of the property of vacuum polarization, a phenomena which is relative to local space. It is formulated a kind of (qualitative) Lenz law that gives an explanation to precession.

Measurement of Newton's constant using a torsion balance with angular acceleration feedback.

PubMed

Gundlach, J H; Merkowitz, S M

2000-10-02

We measured Newton's gravitational constant G using a new torsion balance method. Our technique greatly reduces several sources of uncertainty compared to previous measurements: (1) It is insensitive to anelastic torsion fiber properties; (2) a flat plate pendulum minimizes the sensitivity due to the pendulum density distribution; (3) continuous attractor rotation reduces background noise. We obtain G = (6.674215+/-0.000092) x 10(-11) m3 kg(-1) s(-2); the Earth's mass is, therefore, M = (5.972245+/-0.000082) x 10(24) kg and the Sun's mass is M = (1.988435+/-0.000027) x 10(30) kg.

Intuitive Physics.

ERIC Educational Resources Information Center

McCloskey, Michael

1983-01-01

Although Newton's laws of motion are well known, studies have shown that many people have misconceptions about the motions of objects. Subjects of these studies tend to follow a theory held in the three centuries before Newton (impetus theory). This theory and studies examining misconceptions about motion are discussed. (JN)

Are ecological and evolutionary theories scientific?

PubMed

Murray, B G

2001-05-01

Scientists observe nature, search for generalizations, and provide explanations for why the world is as it is. Generalizations are of two kinds. The first are descriptive and inductive, such as Boyle's Law. They are derived from observations and therefore refer to observables (in this case, pressure and volume). The second are often imaginative and form the axioms of a deductive theory, such as Newton's Laws of Motion. They often refer to unobservables (e.g. inertia and gravitation). Biology has many inductive generalizations (e.g. Bergmann's Rule and 'all cells arise from preexisting cells') but few, if any, recognized universal laws and virtually no deductive theory. Many biologists and philosophers of biology have agreed that predictive theory is inappropriate in biology, which is said to be more complex than physics, and that one can have nonpredictive explanations, such as the neo-Darwinian Theory of Evolution by Natural Selection. Other philosophers dismiss nonpredictive, explanatory theories, including evolutionary 'theory', as metaphysics. Most biologists do not think of themselves as philosophers or give much thought to the philosophical basis of their research. Nevertheless, their philosophy shows in the way they do research. The plethora of ad hoc (i.e. not universal) hypotheses indicates that biologists are reluctant inductivists in that the search for generalization does not have a high priority. Biologists test their hypotheses by verification. Theoretical physicists, in contrast, are deductive unifiers and test their explanatory hypotheses by falsification. I argue that theoretical biology (concerned with unobservables, such as fitness and natural selection) is not scientific because it lacks universal laws and predictive theory. In order to make this argument, I review the differences between verificationism and falsificationism, induction and deduction, and descriptive and explanatory laws. I show how these differ with a specific example of a successful and still useful (even if now superseded as explanatory) deductive theory, Newton's Theory of Motion. I also review some of the philosophical views expressed on these topics because philosophers seem to be even more divided than biologists, which is not at all helpful. The fact that biology does not have predictive theories does not constitute irrefutable evidence that it cannot have them. The only way to falsify this philosophical hypothesis, however, is to produce a predictive theory with universal biological laws. I have proposed such a theory, but it has been presented piecemeal. At the end of this paper, I bring the pieces together into a deductive theory on the evolution of life history traits (e.g. clutch size, mating relationships, sexual size dimorphism).

Supporting the learning of Newton's laws with graphical data

NASA Astrophysics Data System (ADS)

Piggott, David

Teaching physics provides the opportunity for a very unique interaction between students and instructor that is not found in chemistry or biology. Physics has a heavy emphasis on trying to alter students' misconceptions about how things work in the real word. In chemistry and microbiology this is not an issue because the topics of discussion in those classes are a new experience for the students. In the case of physics the students have everyday experience with the different concepts discussed. This causes the students to build incorrect mental models explaining how different things work. In order to correct these mental models physics teachers must first get the students to vocalize these misconceptions. Then the teacher must confront the students with an example that exposes the false nature of their model. Finally, the teacher must help the student resolve these discrepancies and form the correct model. This study attempts to resolve these discrepancies by giving the students concrete evidence via graphs of Newton's laws. The results reported here indicate that this method of eliciting the misconception, confronting the misconception, and resolving the misconception is successful with Newton's third law, but only marginally successful for first and second laws.

Newton's laws of motion in the form of a Riccati equation.

PubMed

Nowakowski, Marek; Rosu, Haret C

2002-04-01

We discuss two applications of a Riccati equation to Newton's laws of motion. The first one is the motion of a particle under the influence of a power law central potential V(r)=kr(epsilon). For zero total energy we show that the equation of motion can be cast in the Riccati form. We briefly show here an analogy to barotropic Friedmann-Robertson-Lemaitre cosmology where the expansion of the universe can be also shown to obey a Riccati equation. A second application in classical mechanics, where again the Riccati equation appears naturally, are problems involving quadratic friction. We use methods reminiscent to nonrelativistic supersymmetry to generalize and solve such problems.

Fundamentals of Physics, Part 1 (Chapters 1-11)

NASA Astrophysics Data System (ADS)

Halliday, David; Resnick, Robert; Walker, Jearl

2003-12-01

Chapter 1.Measurement. How does the appearance of a new type of cloud signal changes in Earth's atmosphere? 1-1 What Is Physics? 1-2 Measuring Things. 1-3 The International System of Units. 1-4 Changing Units. 1-5 Length. 1-6 Time. 1-7 Mass. Review & Summary. Problems. Chapter 2.Motion Along a Straight Line. What causes whiplash injury in rear-end collisions of cars? 2-1 What Is Physics? 2-2 Motion. 2-3 Position and Displacement. 2-4 Average Velocity and Average Speed. 2-5 Instantaneous Velocity and Speed. 2-6 Acceleration. 2-7 Constant Acceleration: A Special Case. 2-8 Another Look at Constant Acceleration. 2-9 Free-Fall Acceleration. 2-10 Graphical Integration in Motion Analysis. Review & Summary. Questions. Problems. Chapter 3.Vectors. How does an ant know the way home with no guiding clues on the deser t plains? 3-2 Vectors and Scalars. 3-3 Adding Vectors Geometrically. 3-4 Components of Vectors. 3-5 Unit Vectors. 3-6 Adding Vectors by Components. 3-7 Vectors and the Laws of Physics. 3-8 Multiplying Vectors. Review & Summary. Questions. Problems. Chapter 4.Motion in Two and Three Dimensions. In a motorcycle jump for record distance, where does the jumper put the second ramp? 4-1 What Is Physics? 4-2 Position and Displacement. 4-3 Average Velocity and Instantaneous Velocity. 4-4 Average Acceleration and Instantaneous Acceleration. 4-5 Projectile Motion. 4-6 Projectile Motion Analyzed. 4-7 Uniform Circular Motion. 4-8 Relative Motion in One Dimension. 4-9 Relative Motion in Two Dimensions. Review & Summary. Questions. Problems. Chapter 5.Force and Motion-I. When a pilot takes off from an aircraft carrier, what causes the compulsion to fly the plane into the ocean? 5-1 What Is Physics? 5-2 Newtonian Mechanics. 5-3 Newton's First Law. 5-4 Force. 5-5 Mass. 5-6 Newton's Second Law. 5-7 Some Particular Forces. 5-8 Newton's Third Law. 5-9 Applying Newton's Laws. Review & Summary. Questions. Problems. Chapter 6.Force and Motion-II. Can a Grand Prix race car be driven upside down on a ceiling? 6-1 What Is Physics? 6-2 Friction. 6-3 Properties of Friction. 6-4 The Drag Force and Terminal Speed. 6-5 Uniform Circular Motion. Review & Summary. Questions. Problems. Chapter 7.Kinetic Energy and Work. In an epidural procedure, what sensations clue a surgeon that the needle has reached the spinal canal? 7-1 What Is Physics? 7-2 What Is Energy? 7-3 Kinetic Energy. 7-4 Work. 7-5 Work and Kinetic Energy. 7-6 Work Done by the Gravitational Force. 7-7 Work Done by a Spring Force. 7-8 Work Done by a General Variable Force. 7-9 Power. Review & Summary. Questions. Problems. Chapter 8.Potential Energy and Conservation of Energy. In rock climbing, what subtle factor determines if a falling climber will snap the rope? 8-1 What Is Physics? 8-2 Work and Potential Energy. 8-3 Path Independence of Conservative Forces. 8-4 Determining Potential Energy Values. 8-5 Conservation of Mechanical Energy. 8-6 Reading a Potential Energy Curve. 8-7 Work Done on a System by an External Force. 8-8 Conservation of Energy. Review & Summary. Questions. Problems. Chapter 9.Center of Mass and Linear Momentum. Does the presence of a passenger reduce the fatality risk in head-on car collisions? 9-1 What Is Physics? 9-2 The Center of Mass. 9-3 Newton's Second Law for a System of Particles. 9-4 Linear Momentum. 9-5 The Linear Momentum of a System of Particles. 9-6 Collision and Impulse. 9-7 Conservation of Linear Momentum. 9-8 Momentum and Kinetic Energy in Collisions. 9-9 Inelastic Collisions in One Dimension. 9-10 Elastic Collisions in One Dimension. 9-11 Collisions in Two Dimensions. 9-12 Systems with Varying Mass: A Rocket. Review & Summary. Questions. Problems. Chapter 10.Rotation. What causes roller-coaster headache? 10-1 What Is Physics? 10-2 The Rotational Variables. 10-3 Are Angular Quantities Vectors? 10-4 Rotation with Constant Angular Acceleration. 10-5 Relating the Linear and Angular Variables. 10-6 Kinetic Energy of Rotation. 10-7 Calculating the Rotational Inertia. 10-8 Torque. 10-9 Newton's Second Law for Rotation. 10-10 Work and Rotational Kinetic Energy. Review & Summary. Questions. Problems. Chapter 11.Rolling, Torque, and Angular Momentum. When a jet-powered car became supersonic in setting the land-speed record, what was the danger to the wheels? 11-1 What Is Physics? 11-2 Rolling as Translation and Rotation Combined. 11-3 The Kinetic Energy of Rolling. 11-4 The Forces of Rolling. 11-5 The Yo-Yo. 11-6 Torque Revisited. 11-7 Angular Momentum. 11-8 Newton's Second Law in Angular Form. 11-9 The Angular Momentum of a System of Particles. 11-10 The Angular Momentum of a Rigid Body Rotating About a Fixed Axis. 11-11 Conservation of Angular Momentum. 11-12 Precession of a Gyroscope. Review & Summary. Questions. Problems. Appendix A: The International System of Units (SI). Appendix B: Some Fundamental Constants of Physics. Appendix C: Some Astronomical Data. Appendix D: Conversion Factors. Appendix E: Mathematical Formulas. Appendix F: Properties of the Elements. Appendix G: Periodic Table of the Elements. Answers to Checkpoints and Odd-Numbered Questions and Problems. Index.

The attraction of the pyramids: virtual realization of Hutton's suggestion to improve Maskelyne's 1774 Earth density estimate

NASA Astrophysics Data System (ADS)

Smallwood, John R.

2018-01-01

Charles Hutton suggested in 1821 that the pyramids of Egypt be used to site an experiment to measure the deflection of the vertical by a large mass. The suggestion arose as he had estimated the attraction of a Scottish mountain as part of Nevil Maskelyne's (1774) "Schiehallion Experiment", a demonstration of Isaac Newton's law of gravitational attraction and the earliest reasonable quantitative estimate of Earth's mean density. I present a virtual realization of an experiment at the Giza pyramids to investigate how Hutton's concept might have emerged had it been undertaken as he suggested. The attraction of the Great Pyramid would have led to inward north-south deflections of the vertical totalling 1.8 arcsec (0.0005°), and east-west deflections totalling 2.0 arcsec (0.0006°), which although small, would have been within the contemporaneous detectable range, and potentially given, as Hutton wished, a more accurate Earth density measurement than he reported from the Schiehallion experiment.

On the geometry of the space-time and motion of the spinning bodies

NASA Astrophysics Data System (ADS)

Trenčevski, Kostadin

2013-03-01

In this paper an alternative theory about space-time is given. First some preliminaries about 3-dimensional time and the reasons for its introduction are presented. Alongside the 3-dimensional space (S) the 3-dimensional space of spatial rotations (SR) is considered independently from the 3-dimensional space. Then it is given a model of the universe, based on the Lie groups of real and complex orthogonal 3 × 3 matrices in this 3+3+3-dimensional space. Special attention is dedicated for introduction and study of the space S × SR, which appears to be isomorphic to SO(3,ℝ) × SO(3,ℝ) or S 3 × S 3. The influence of the gravitational acceleration to the spinning bodies is considered. Some important applications of these results about spinning bodies are given, which naturally lead to violation of Newton's third law in its classical formulation. The precession of the spinning axis is also considered.

Definitions of Complexity are Notoriously Difficult

NASA Astrophysics Data System (ADS)

Schuster, Peter

Definitions of complexity are notoriously difficult if not impossible at all. A good working hypothesis might be: Everything is complex that is not simple. This is precisely the way in which we define nonlinear behavior. Things appear complex for different reasons: i) Complexity may result from lack of insight, ii) complexity may result from lack of methods, and (iii) complexity may be inherent to the system. The best known example for i) is celestial mechanics: The highly complex Pythagorean epicycles become obsolete by the introduction of Newton's law of universal gravitation. To give an example for ii), pattern formation and deterministic chaos became not really understandable before extensive computer simulations became possible. Cellular metabolism may serve as an example for iii) and is caused by the enormous complexity of biochemical reaction networks with up to one hundred individual reaction fluxes. Nevertheless, only few fluxes are dominant in the sense that using Pareto optimal values for them provides near optimal values for all the others...

The Lighter Side of Gravity

NASA Astrophysics Data System (ADS)

Narlikar, Jayant Vishnu

1996-10-01

From the drop of an apple to the stately dance of the galaxies, gravity is omnipresent in the Cosmos. Even with its high profile, gravity is the most enigmatic of all the known basic forces in nature. The Lighter Side of Gravity presents a beautifully clear and completely nontechnical introduction to the phenomenon of this force in all its manifestations. Astrophysicist Jayant Narlikar begins with an historical background to the discovery of the law of gravitation by Isaac Newton in the seventeenth century. Using familiar analogies, interesting anecdotes, and numerous illustrations to get across subtle effects and difficult points to readers, he goes on to describe the general theory of relativity and some of its strange and unfamiliar ideas such as curved spacetime, the bending of light, and black holes. Since first publication in 1982 (W.H. Freeman), Dr. Narlikar has brought his book completely up to date and expanded it to include the discovery of gigantic gravitational lenses in space, the findings of the Cosmic Background Explorer (COBE) satellite, the detection of dark matter in galaxies, the investigation of the very early Universe, and other new ideas in cosmology. This lucid and stimulating book presents a clear approach to the intriguing phenomenon of gravity for everyone who has ever felt caught in its grip. Jayant Narlikar is the winner of many astronomical prizes and the author of Introduction to Cosmology (Cambridge University Press, 1993).

On the photo-gravitational restricted four-body problem with variable mass

NASA Astrophysics Data System (ADS)

Mittal, Amit; Agarwal, Rajiv; Suraj, Md Sanam; Arora, Monika

2018-05-01

This paper deals with the photo-gravitational restricted four-body problem (PR4BP) with variable mass. Following the procedure given by Gascheau (C. R. 16:393-394, 1843) and Routh (Proc. Lond. Math. Soc. 6:86-97, 1875), the conditions of linear stability of Lagrange triangle solution in the PR4BP are determined. The three radiating primaries having masses m1, m2 and m3 in an equilateral triangle with m2=m3 will be stable as long as they satisfy the linear stability condition of the Lagrangian triangle solution. We have derived the equations of motion of the mentioned problem and observed that there exist eight libration points for a fixed value of parameters γ (m at time t/m at initial time, 0<γ≤1 ), α (the proportionality constant in Jeans' law (Astronomy and Cosmogony, Cambridge University Press, Cambridge, 1928), 0≤α≤2.2), the mass parameter μ=0.005 and radiation parameters qi, (0< qi≤1, i=1, 2, 3). All the libration points are non-collinear if q2≠ q3. It has been observed that the collinear and out-of-plane libration points also exist for q2=q3. In all the cases, each libration point is found to be unstable. Further, zero velocity curves (ZVCs) and Newton-Raphson basins of attraction are also discussed.

Causal holographic information does not satisfy the linearized quantum focusing condition

NASA Astrophysics Data System (ADS)

Fu, Zicao; Marolf, Donald; Qi, Marvin

2018-04-01

The Hubeny-Rangamani causal holographic information (CHI) defined by a region R of a holographic quantum field theory (QFT) is a modern version of the idea that the area of event horizons might be related to an entropy. Here the event horizon lives in a dual gravitational bulk theory with Newton's constant G bulk, and the relation involves a factor of 4 G bulk. The fact that CHI is bounded below by the von Neumann entropy S suggests that CHI is coarse-grained. Its properties could thus differ markedly from those of S. In particular, recent results imply that when d ≤ 4 holographic QFTs are perturbatively coupled to d-dimensional gravity, the combined system satisfies the so-called quantum focusing condition (QFC) at leading order in the new gravitational coupling G d when the QFT entropy is taken to be that of von Neumann. However, by studying states dual to spherical bulk (anti-de Sitter) Schwarschild black holes in the conformal frame for which the boundary is a (2 + 1)-dimensional de Sitter space, we find the QFC defined by CHI is violated even when perturbing about a Killing horizon and using a single null congruence. Since it is known that a generalized second law (GSL) holds in this context, our work demonstrates that the QFC is not required in order for an entropy, or an entropy-like quantity, to satisfy such a GSL.

Normalization and Implementation of Three Gravitational Acceleration Models

NASA Technical Reports Server (NTRS)

Eckman, Randy A.; Brown, Aaron J.; Adamo, Daniel R.; Gottlieb, Robert G.

2016-01-01

Unlike the uniform density spherical shell approximations of Newton, the consequence of spaceflight in the real universe is that gravitational fields are sensitive to the asphericity of their generating central bodies. The gravitational potential of an aspherical central body is typically resolved using spherical harmonic approximations. However, attempting to directly calculate the spherical harmonic approximations results in at least two singularities that must be removed to generalize the method and solve for any possible orbit, including polar orbits. Samuel Pines, Bill Lear, and Robert Gottlieb developed three unique algorithms to eliminate these singularities. This paper documents the methodical normalization of two of the three known formulations for singularity-free gravitational acceleration (namely, the Lear and Gottlieb algorithms) and formulates a general method for defining normalization parameters used to generate normalized Legendre polynomials and Associated Legendre Functions (ALFs) for any algorithm. A treatment of the conventional formulation of the gravitational potential and acceleration is also provided, in addition to a brief overview of the philosophical differences between the three known singularity-free algorithms.

Systemic venous drainage: can we help Newton?

PubMed

Corno, Antonio F

2007-06-01

In recent years substantial progress occurred in the techniques of cardiopulmonary bypass, but the factor potentially limiting the flexibility of cardiopulmonary bypass remains the drainage of the systemic venous return. In the daily clinical practice of cardiac surgery, the amount of systemic venous return on cardiopulmonary bypass is directly correlated with the amount of the pump flow. As a consequence, the pump flow is limited by the amount of venous return that the pump is receiving. On cardiopulmonary bypass the amount of venous drainage depends upon the central venous pressure, the height differential between patient and inlet of the venous line into the venous reservoir, and the resistance in the venous cannula(s) and circuit. The factors determining the venous return to be taken into consideration in cardiac surgery are the following: (a) characteristics of the individual patient; (b) type of planned surgical procedure; (c) type of venous cannula(s); (d) type of circuit for cardiopulmonary bypass; (e) strategy of cardiopulmonary bypass; (f) use of accessory mechanical systems to increased the systemic venous return. The careful pre-operative evaluation of all the elements affecting the systemic venous drainage, including the characteristics of the individual patient and the type of required surgical procedure, the choice of the best strategy of cardiopulmonary bypass, and the use of the most advanced materials and tools, can provide a systemic venous drainage substantially better than what it would be allowed by the simple "Law of universal gravitation" by Isaac Newton.

Constraints on Cosmic Strings from the LIGO-Virgo Gravitational-Wave Detectors

NASA Technical Reports Server (NTRS)

Aasi, J.; Abadie, J.; Abbott, B.P.; Abbott, R.; Abbott, T.; Abernathy, M.R.; Accadia, T.; Adams, C.; Adams, T.; Adhikari, R.X.;

Fun-Filled Physics.

ERIC Educational Resources Information Center

Dana, Thomas M.; And Others

1993-01-01

Presents a unit of three lessons to teach Newton's Laws of Motion. After rotating through learning centers, answering questions, and recording observations, students are asked to generate a "class law" that explains the scientific phenomenon they observed. (MDH)

Gravitational mass of positron from LEP synchrotron losses.

PubMed

Kalaydzhyan, Tigran

2016-07-27

General relativity(GR) is the current description of gravity in modern physics. One of the cornerstones of GR, as well as Newton's theory of gravity, is the weak equivalence principle (WEP), stating that the trajectory of a freely falling test body is independent of its internal structure and composition. WEP is known to be valid for the normal matter with a high precision. However, due to the rarity of antimatter and weakness of the gravitational forces, the WEP has never been confirmed for antimatter. The current direct bounds on the ratio between the gravitational and inertial masses of the antihydrogen do not rule out a repulsive nature for the antimatter gravity. Here we establish an indirect bound of 0.13% on the difference between the gravitational and inertial masses of the positron (antielectron) from the analysis of synchrotron losses at the Large Electron-Positron collider (LEP). This serves as a confirmation of the conventional gravitational properties of antimatter without common assumptions such as, e.g., coupling of gravity to virtual particles, dynamics of distant astrophysical sources and the nature of absolute gravitational potentials.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sakstein, Jeremy; Wilcox, Harry; Bacon, David

The Beyond Horndeski class of alternative gravity theories allow for Self-accelerating de-Sitter cosmologies with no need for a cosmological constant. This makes them viable alternatives to ΛCDM and so testing their small-scale predictions against General Relativity is of paramount importance. These theories generically predict deviations in both the Newtonian force law and the gravitational lensing of light inside extended objects. Therefore, by simultaneously fitting the X-ray and lensing profiles of galaxy clusters new constraints can be obtained. In this work, we apply this methodology to the stacked profiles of 58 high-redshift (0.1 < z < 1.2) clusters using X-ray surfacemore » brightness profiles from the XMM Cluster Survey and weak lensing profiles from CFHTLenS. By performing a multi-parameter Markov chain Monte Carlo analysis, we are able to place new constraints on the parameters governing deviations from Newton's law Υ{sub 1} = −0.11{sup +0.93}{sub −0.67} and light bending Υ{sub 2} = −0.22{sup +1.22}{sub −1.19}. Both constraints are consistent with General Relativity, for which Υ{sub 1} = Υ{sub 2} = 0. We present here the first observational constraints on Υ{sub 2}, as well as the first extragalactic measurement of both parameters.« less

Mass and Dynamical Structures of the Lensing Clusters CL0024+17 and CL2244+02

NASA Technical Reports Server (NTRS)

Forman, William; Mushotzky, Richard (Technical Monitor)

2004-01-01

We present a detailed gravitational mass measurement based on the XMM-Newton imaging spectroscopy analysis of the lensing cluster of galaxies CL0024+17 at $z = 0.395$. The emission appears approximately symmetric. However, on the scale of $r\\sim3.3'$, some indication of elongation is visible in the northwest-southeast direction from the hardness ratio map. Within $3'$, we measure a global gas temperature of $3.52\\pm0.17$ keV, metallicity of $0.22\\pm0.07$, and a bolometric luminosity of $2.9\\pm0. l\\times10(exp 44)$ erg/s. We derive a temperature distribution with an isothermal temperature of 3.9 keV up to a radius of $1.5'$ and a strong temperature gradient in the outskirts ($1.3' less than r less than 3.3'$). Under the assumption of hydrostatic equilibrium, we measure the gravitational mass and gas mass fraction to be $M-{200} = 2.0\\pm0.3\\times 10(exp 14)$ solar masses and $f-{gas} = 0.20\\pm0.03$ at $r-{200} = 1.05$ Mpc (all for a Hubble constant of 70 km/sec/Mpc) using the observed gas temperature profile. The complex core structure is the key to explaining the discrepancy between the gravitational mass determined from the XMM-Newton observations and HST optical lensing measurements.

An XMM-Newton Observation of the Seyfert Galaxy 1H0419-577 in an Extreme Low State

NASA Technical Reports Server (NTRS)

Pounds, K. A.; Reeves, J. N.; Page, K. L.; O'Brien, P. T.

2003-01-01

Previous observations of the luminous Seyfert galaxy 1H 0419-577 have found its X-ray spectrum to range from that of a typical Seyfert 1 with 2-10 keV power law index Gamma approx. 1.9 to a much flatter power law of Gamma approx. 1.5 or less. We report here a new XMM-Newton observation which allows the low state spectrum to be studied in much greater detail than hitherto. We find a very hard spectrum (Gamma approx. 1.0) which exhibits broad features that can be modelled with the addition of an extreme relativistic Fe K emission line or with partial covering of the underlying continuum by a substantial column density of near-neutral gas. Both the EPIC and RGS data show evidence for strong line emission of OVII and OVIII requiring an extended region of low density photoionised gas in 1H 0419- 577. Comparison with an earlier XMM-Newton observation when 1H 0419-577 was X-ray bright indicates the dominant spectral variability occurs via a steep power law component.

Teaching Newton's 3rd law of motion using learning by design approach

NASA Astrophysics Data System (ADS)

Aquino, Jiezel G.; Caliguid, Mariel P.; Buan, Amelia T.; Magsayod, Joy R.; Lahoylahoy, Myrna E.

2018-01-01

This paper presents the process and implementation of Learning by Design Approach in teaching Newton's 3rd Law of Motion. A lesson activity from integrative STEM education was adapted, modified and enhanced through pilot testing. After revisions, the implementation was done to one class. The respondent's prior knowledge was first assessed by a pretest. PPIT (present the scenario, plan, implement and test) was the framework followed in the implementation of Learning by Design. Worksheets were then utilized to measure their conceptual understanding and perception. A score guide was also used to evaluate the student's output. Paired t-test analysis showed that there is a significant difference in the pretest and posttest achievement scores. This implies that the performance of the students have improved during the implementation of the Learning by Design. The Analysis of variance also depicts that the low, average and high benefited in the Learning by Design approach. The results of this study suggests that Learning by Design is an effective approach in teaching Newton's 3rd Law of Motion and thus be used in a Science classroom.

An XMM-Newton Observation of the Seyfert 1 Galaxy 1H 0419-577 in an Extreme Low State

NASA Technical Reports Server (NTRS)

Pounds, K. A.; Reeves, J. N.; Page, K. L.; OBrien, P. T.

2004-01-01

Previous observations of the luminous Seyfert 1 galaxy 1H 0419-577 have found its X-ray spectrum to range from that of a typical Seyfert 1 with 2-10 keV power law index Gamma approx. 1.9 to a much flatter power law of Gamma approx. 1.5 or less. We report here a new XMM-Newton observation which allows the low state spectrum to be studied in much greater detail than hitherto. We find a very hard spectrum (Gamma approx. 1.0), which exhibits broad features that can be modelled myth the addition of an extreme relativistic Fe K emission line or with partial covering of the underlying continuum by a substantial column density of near-neutral gas. Both the EPIC and RGS data show evidence for strong line emission of OVII and OVIII requiring an extended region of low density photoionised gas in 1H 0419-577. Comparison with an earlier XMM-Newton observation when 1H 0419-577 was 'X-ray bright' indicates the dominant spectral variability occurs via a steep power law component.

Predicting Mercury's precession using simple relativistic Newtonian dynamics

NASA Astrophysics Data System (ADS)

Friedman, Y.; Steiner, J. M.

2016-03-01

We present a new simple relativistic model for planetary motion describing accurately the anomalous precession of the perihelion of Mercury and its origin. The model is based on transforming Newton's classical equation for planetary motion from absolute to real spacetime influenced by the gravitational potential and introducing the concept of influenced direction.

Physics in our Universe

NASA Astrophysics Data System (ADS)

Conn Henry, Richard

2016-06-01

The recent detection of gravitational waves from the merger of two massive black holes means that we must now take Newton's approach to the Universe even more seriously than we have taken it since Principia: General Relativity has now been tested, as never before, and GR has passed with flying colors! In my poster I try to summarize all of fundamental physics taken together --- gravitation, dark energy, and particles. But the whole job is not yet done: mass + energy remains as a final frontier. It may be that the topology of 4-space is the answer: how I wish I were a mathematical topologist of great ability!

Evidence of Black Hole Spin in GX 339-4: XMM-Newton/EPIC-pn and RXTE Spectroscopy of the Very High State

NASA Astrophysics Data System (ADS)

Miller, J. M.; Fabian, A. C.; Reynolds, C. S.; Nowak, M. A.; Homan, J.; Freyberg, M. J.; Ehle, M.; Belloni, T.; Wijnands, R.; van der Klis, M.; Charles, P. A.; Lewin, W. H. G.

2004-05-01

We have analyzed spectra of the Galactic black hole GX 339-4 obtained through simultaneous 76 ks XMM-Newton/EPIC-pn and 10 ks Rossi X-Ray Timing Explorer observations during a bright phase of its 2002-2003 outburst. An extremely skewed, relativistic Fe Kα emission line and ionized disk reflection spectrum are revealed in these spectra. Self-consistent models for the Fe Kα emission-line profile and disk reflection spectrum rule out an inner disk radius compatible with a Schwarzschild black hole at more than the 8 σ level of confidence. The best-fit inner disk radius of (2-3)rg suggests that GX 339-4 harbors a black hole with a>=0.8-0.9 (where rg=GM/c2 and a=cJ/GM2, and assuming that reflection in the plunging region is relatively small). This confirms indications for black hole spin based on a Chandra spectrum obtained later in the outburst. The emission line and reflection spectrum also rule out a standard power-law disk emissivity in GX 339-4 a broken power-law form with enhanced emissivity inside ~6rg gives improved fits at more than the 8 σ level of confidence. The extreme red wing of the line and the steep emissivity require a centrally concentrated source of hard X-rays that can strongly illuminate the inner disk. Hard X-ray emission from the base of a jet-enhanced by gravitational light-bending effects-could create the concentrated hard X-ray emission; this process may be related to magnetic connections between the black hole and the inner disk. We discuss these results within the context of recent results from analyses of XTE J1650-500 and MCG -6-30-15, and of models for the inner accretion flow environment around black holes.

Anomalous cosmic-microwave-background polarization and gravitational chirality.

PubMed

Contaldi, Carlo R; Magueijo, João; Smolin, Lee

2008-10-03

We consider the possibility that gravity breaks parity, with left and right-handed gravitons coupling to matter with a different Newton's constant and show that this would affect their zero-point vacuum fluctuations during inflation. Should there be a cosmic background of gravity waves, the effect would translate into anomalous cosmic microwave background polarization. Nonvanishing temperature-magnetic (TB) mode [and electric-magnetic mode] components emerge, revealing interesting experimental targets. Indeed, if reasonable chirality is present a TB measurement would provide the easiest way to detect a gravitational wave background. We speculate on the theoretical implications of such an observation.

Zero-Totality in Action-Reaction Space:. A Generalization of Newton's Third Law?

NASA Astrophysics Data System (ADS)

Karam, Sabah E.

2013-09-01

In order to present the universe as a zero-totality the key concepts of nothingness and duality are required. Diaz and Rowlands introduce processes of conjugation, complexification, and dimensionalization using a universal alphabet and rewrite system to describe a physical universe composed of nilpotents. This paper will apply the concept of conjugation to the Newtonian duality actionreaction by introducing associated dual spaces called action space-reaction space. An attempt to generalize Newton's third law of motion, utilizing the concept of dual spaces, will follow in a manner suggestive of the zero-totality fermion-vacuum relationship.

An Introduction to Rockets - or - Never Leave Geeks Unsupervised

NASA Technical Reports Server (NTRS)

Mellett, Kevin

2006-01-01

An introduction to rockets along with a brief history Newton's third law is presented. The contents include: 1) What is a Rocket?; 2) A Brief History; 3) Newton's Third Law; 4) A Brief History; 5) Mission Requirements; 6) Some Orbital Measurements; 7) Self Eating Watermelon; 8) Orbital Inclinations; 9) 28.5 Equatorial Orbit; 10) 51.6 Orbit (ISS); 11) Polar Orbit; 12) Geostationary Orbit; 13) Liquid Rocket; 13) Liquids vs. Solids; 14) Liquids; 15) Systems Integration; 16) Integration (NFL!); 17) Guidance Systems; 18) Vectored Thrust; 19) Spin Stabilization; 20) Aerodynamic Stability (Fire Arrows); and 21) Center of Gravity & Center of Pressure.

Schwarzschild and Kerr solutions of Einstein's field equation: An Introduction

NASA Astrophysics Data System (ADS)

Heinicke, Christian; Hehl, Friedrich W.

2015-12-01

Starting from Newton's gravitational theory, we give a general introduction into the spherically symmetric solution of Einstein's vacuum field equation, the Schwarzschild(-Droste) solution, and into one specific stationary axially symmetric solution, the Kerr solution. The Schwarzschild solution is unique and its metric can be interpreted as the exterior gravitational field of a spherically symmetric mass. The Kerr solution is only unique if the multipole moments of its mass and its angular momentum take on prescribed values. Its metric can be interpreted as the exterior gravitational field of a suitably rotating mass distribution. Both solutions describe objects exhibiting an event horizon, a frontier of no return. The corresponding notion of a black hole is explained to some extent. Eventually, we present some generalizations of the Kerr solution.

Action-reaction at a distance

NASA Astrophysics Data System (ADS)

Brand, Howard

2002-03-01

Lenz's law is used to demonstrate that Newton's third law includes forces acting at a distance. The action-reaction pair is the force on a magnet falling through a conducting tube at terminal velocity, and a force on the tube.

An insight into Newton's cooling law using fractional calculus

NASA Astrophysics Data System (ADS)

Mondol, Adreja; Gupta, Rivu; Das, Shantanu; Dutta, Tapati

2018-02-01

For small temperature differences between a heated body and its environment, Newton's law of cooling predicts that the instantaneous rate of change of temperature of any heated body with respect to time is proportional to the difference in temperature of the body with the ambient, time being measured in integer units. Our experiments on the cooling of different liquids (water, mustard oil, and mercury) did not fit the theoretical predictions of Newton's law of cooling in this form. The solution was done using both Caputo and Riemann-Liouville type fractional derivatives to check if natural phenomena showed any preference in mathematics. In both cases, we find that cooling of liquids has an identical value of the fractional derivative of time that increases with the viscosity of the liquid. On the other hand, the cooling studies on metal alloys could be fitted exactly by integer order time derivative equations. The proportionality constant between heat flux and temperature difference was examined with respect to variations in the depth of liquid and exposed surface area. A critical combination of these two parameters signals a change in the mode of heat transfer within liquids. The equivalence between the proportionality constants for the Caputo and Riemann-Liouville type derivatives is established.

Alternative theoretical method for motion of a sand-filled funnel experiment

NASA Astrophysics Data System (ADS)

Byrd, David; White, Gary

2001-11-01

In "Motion of a Sand-Filled Funnel," Peter Sullivan and Anna McLoon described how to use numerical methods and a Microsoft Excel spreadsheet to predict the motion of a variant of Atwood's machine with variable mass. They wrote for noncalculus-based physics classes, but we solve the same problem using the methods of calculus. Our method highlights the less-familiar but more accurate version of Newton's second law, ∑F =dp/dt. This can help introductory physics students understand a broader definition of Newton's second law and enhance their calculus skills. It also teaches students how to solve a variable-mass problem.

Normalization of Gravitational Acceleration Models

NASA Technical Reports Server (NTRS)

Eckman, Randy A.; Brown, Aaron J.; Adamo, Daniel R.

2011-01-01

Unlike the uniform density spherical shell approximations of Newton, the con- sequence of spaceflight in the real universe is that gravitational fields are sensitive to the nonsphericity of their generating central bodies. The gravitational potential of a nonspherical central body is typically resolved using spherical harmonic approximations. However, attempting to directly calculate the spherical harmonic approximations results in at least two singularities which must be removed in order to generalize the method and solve for any possible orbit, including polar orbits. Three unique algorithms have been developed to eliminate these singularities by Samuel Pines [1], Bill Lear [2], and Robert Gottlieb [3]. This paper documents the methodical normalization of two1 of the three known formulations for singularity-free gravitational acceleration (namely, the Lear [2] and Gottlieb [3] algorithms) and formulates a general method for defining normalization parameters used to generate normalized Legendre Polynomials and ALFs for any algorithm. A treatment of the conventional formulation of the gravitational potential and acceleration is also provided, in addition to a brief overview of the philosophical differences between the three known singularity-free algorithms.

Gravitational induction

NASA Astrophysics Data System (ADS)

Bini, Donato; Cherubini, Christian; Chicone, Carmen; Mashhoon, Bahram

2008-11-01

We study the linear post-Newtonian approximation to general relativity known as gravitoelectromagnetism (GEM); in particular, we examine the similarities and differences between GEM and electrodynamics. Notwithstanding some significant differences between them, we find that a special nonstationary metric in GEM can be employed to show explicitly that it is possible to introduce gravitational induction within GEM in close analogy with Faraday's law of induction and Lenz's law in electrodynamics. Some of the physical implications of gravitational induction are briefly discussed.

Gravitational decoherence, alternative quantum theories and semiclassical gravity

NASA Astrophysics Data System (ADS)

Hu, B. L.

2014-04-01

In this report we discuss three aspects: 1) Semiclassical gravity theory (SCG): 4 levels of theories describing the interaction of quantum matter with classical gravity. 2) Alternative Quantum Theories: Discerning those which are derivable from general relativity (GR) plus quantum field theory (QFT) from those which are not 3) Gravitational Decoherence: derivation of a master equation and examination of the assumptions which led to the claims of observational possibilities. We list three sets of corresponding problems worthy of pursuit: a) Newton-Schrödinger Equations in relation to SCG; b) Master equation of gravity-induced effects serving as discriminator of 2); and c) Role of gravity in macroscopic quantum phenomena.

Forces. Physical Science in Action[TM]. Schlessinger Science Library. [Videotape].

ERIC Educational Resources Information Center

2000

Forces are all around. Without them, there would be no movement. In fact, Sir Isaac Newton theorized that a force called inertia actually works to keep things exactly as they are at any given moment! Students will learn about Newton's laws and about how forces affect many aspects of life. With clear demonstrations and a unique hands-on activity,…

Newton's method applied to finite-difference approximations for the steady-state compressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Bailey, Harry E.; Beam, Richard M.

1991-01-01

Finite-difference approximations for steady-state compressible Navier-Stokes equations, whose two spatial dimensions are written in generalized curvilinear coordinates and strong conservation-law form, are presently solved by means of Newton's method in order to obtain a lifting-airfoil flow field under subsonic and transonnic conditions. In addition to ascertaining the computational requirements of an initial guess ensuring convergence and the degree of computational efficiency obtainable via the approximate Newton method's freezing of the Jacobian matrices, attention is given to the need for auxiliary methods assessing the temporal stability of steady-state solutions. It is demonstrated that nonunique solutions of the finite-difference equations are obtainable by Newton's method in conjunction with a continuation method.

A massive binary black-hole system in OJ 287 and a test of general relativity.

PubMed

Valtonen, M J; Lehto, H J; Nilsson, K; Heidt, J; Takalo, L O; Sillanpää, A; Villforth, C; Kidger, M; Poyner, G; Pursimo, T; Zola, S; Wu, J-H; Zhou, X; Sadakane, K; Drozdz, M; Koziel, D; Marchev, D; Ogloza, W; Porowski, C; Siwak, M; Stachowski, G; Winiarski, M; Hentunen, V-P; Nissinen, M; Liakos, A; Dogru, S

2008-04-17

Tests of Einstein's general theory of relativity have mostly been carried out in weak gravitational fields where the space-time curvature effects are first-order deviations from Newton's theory. Binary pulsars provide a means of probing the strong gravitational field around a neutron star, but strong-field effects may be best tested in systems containing black holes. Here we report such a test in a close binary system of two candidate black holes in the quasar OJ 287. This quasar shows quasi-periodic optical outbursts at 12-year intervals, with two outburst peaks per interval. The latest outburst occurred in September 2007, within a day of the time predicted by the binary black-hole model and general relativity. The observations confirm the binary nature of the system and also provide evidence for the loss of orbital energy in agreement (within 10 per cent) with the emission of gravitational waves from the system. In the absence of gravitational wave emission the outburst would have happened 20 days later.

Latency-information theory and applications: Part III. On the discovery of the space dual of the laws of motion in physics

NASA Astrophysics Data System (ADS)

Feria, Erlan H.

2008-04-01

In this third of a multi-paper series the discovery of a space dual for the laws of motion is reported and named the laws of retention. This space-time duality in physics is found to inherently surface from a latency-information theory (LIT) that is treated in the first two papers of this multi-paper series. A motion-coder and a retention-coder are fundamental elements of a LIT's recognition-communication system. While a LIT's motion-coder addresses motion-time issues of knowledge motion, a LIT's retention-coder addresses retention-space issues of knowledge retention. For the design of a motion-coder, such as a modulation-antenna system, the laws of motion in physics are used while for the design of a retention-coder, such as a write/read memory, the newly advanced laws of retention can be used. Furthermore, while the laws of motion reflect a configuration of space certainty, the laws of retention reflect a passing of time uncertainty. Since the retention duals of motion concepts are too many to cover in a single publication, the discussion will be centered on the retention duals for Newton's Principia and the gravitational law, Coulomb's electrical law, Maxwell's equations, Einstein's relativity theory, quantum mechanics, and the uncertainty principle. Furthermore the retention duals will be illustrated with an uncharged and non-rotating black hole (UNBH). A UNBH is the retention dual of a vacuum since the UNBH and vacuum offer, from a theoretical perspective, the least resistance to knowledge retention and motion, respectively. Using this space-time duality insight it will be shown that the speed of light in a vacuum of c M=2.9979 x 10 8 meters/sec has a retention dual, herein called the pace of dark in a UNBH of c R=6.1123 x 10 63 secs/m 3 where 'pace' refers to the expected retention-time per retention-space for the 'dark' knowledge residing in a black hole.

Stochastic modification of the Schrödinger-Newton equation

NASA Astrophysics Data System (ADS)

Bera, Sayantani; Mohan, Ravi; Singh, Tejinder P.

2015-07-01

The Schrödinger-Newton (SN) equation describes the effect of self-gravity on the evolution of a quantum system, and it has been proposed that gravitationally induced decoherence drives the system to one of the stationary solutions of the SN equation. However, the equation itself lacks a decoherence mechanism, because it does not possess any stochastic feature. In the present work we derive a stochastic modification of the Schrödinger-Newton equation, starting from the Einstein-Langevin equation in the theory of stochastic semiclassical gravity. We specialize this equation to the case of a single massive point particle, and by using Karolyhazy's phase variance method, we derive the Diósi-Penrose criterion for the decoherence time. We obtain a (nonlinear) master equation corresponding to this stochastic SN equation. This equation is, however, linear at the level of the approximation we use to prove decoherence; hence, the no-signaling requirement is met. Lastly, we use physical arguments to obtain expressions for the decoherence length of extended objects.

Satellite-Based Fusion of Image/Inertial Sensors for Precise Geolocation

DTIC Science & Technology

2009-03-01

largest contributor and is a valid approximation of orbital position prediction [15]. According to Newton, the gravitational force of the Earth onto an...steps in developing an image-aided navigation system for an orbiting satellite is the understanding of the satellite’s trajectory around the Earth . This...Development . . . . . . . . . . . . . . . . . . . . . . . . 77 4.2 Low Earth Orbit Simulation . . . . . . . . . . . . . . . . . . . . . . . 78 4.3 High Earth

Testing local Lorentz invariance with short-range gravity

DOE PAGES

Kostelecký, V. Alan; Mewes, Matthew

2017-01-10

The Newton limit of gravity is studied in the presence of Lorentz-violating gravitational operators of arbitrary mass dimension. The linearized modified Einstein equations are obtained and the perturbative solutions are constructed and characterized. We develop a formalism for data analysis in laboratory experiments testing gravity at short range and demonstrate that these tests provide unique sensitivity to deviations from local Lorentz invariance.

Il volto della Luna da Plutarco a Newton. Storia di una teoria ellenistica della gravità

NASA Astrophysics Data System (ADS)

Cappi, Alberto

2013-03-01

In his dialogue "De Facie quae in Orbe Lunae apparet", Plutarch includes a discussion on a non-Aristotelian theory of gravity. I describe how this theory could be developed during the Hellenistic period and its influence on the cosmological debate along the centuries until the beginning of modern science. (Text in Italian)

A Solar Sailcraft Simulation Application

ERIC Educational Resources Information Center

Celeda, Tomáš

2013-01-01

An application was created to encourage students' practical knowledge of gravitational fields, the law of conservation of energy and other phenomena, such as gravitational slingshots. The educational software simulates the flight of a solar sail spacecraft between two planets of the Solar System using the laws of gravity and radiation…

The changing source of X-ray reflection in the radio-intermediate Seyfert 1 galaxy III Zw 2

NASA Astrophysics Data System (ADS)

Gonzalez, A. G.; Waddell, S. G. H.; Gallo, L. C.

2018-03-01

We report on X-ray observations of the radio-intermediate, X-ray bright Seyfert 1 galaxy, III Zw 2, obtained with XMM-Newton, Suzaku, and Swift over the past 17 yr. The source brightness varies significantly over yearly time-scales, but more modestly over periods of days. Pointed observations with XMM-Newton in 2000 and Suzaku in 2011 show spectral differences despite comparable X-ray fluxes. The Suzaku spectra are consistent with a power-law continuum and a narrow Gaussian emission feature at ˜6.4 keV, whereas the earlier XMM-Newton spectrum requires a broader Gaussian profile and soft-excess below ˜2 keV. A potential interpretation is that the primary power-law emission, perhaps from a jet base, preferentially illuminates the inner accretion disc in 2000, but the distant torus in 2011. The interpretation could be consistent with the hypothesized precessing radio jet in III Zw 2 that may have originated from disc instabilities due to an ongoing merging event.

Learning Physics in a Water Park

ERIC Educational Resources Information Center

Cabeza, Cecilia; Rubido, Nicolás; Martí, Arturo C.

2014-01-01

Entertaining and educational experiments that can be conducted in a water park, illustrating physics concepts, principles and fundamental laws, are described. These experiments are suitable for students ranging from senior secondary school to junior university level. Newton's laws of motion, Bernoulli's equation, based on the conservation of…

A classification of event sequences in the influence network

NASA Astrophysics Data System (ADS)

Walsh, James Lyons; Knuth, Kevin H.

2017-06-01

We build on the classification in [1] of event sequences in the influence network as respecting collinearity or not, so as to determine in future work what phenomena arise in each case. Collinearity enables each observer to uniquely associate each particle event of influencing with one of the observer's own events, even in the case of events of influencing the other observer. We further classify events as to whether they are spacetime events that obey in the fine-grained case the coarse-grained conditions of [2], finding that Newton's First and Second Laws of motion are obeyed at spacetime events. A proof of Newton's Third Law under particular circumstances is also presented.

Gravitational attraction until relativistic equipartition of internal and translational kinetic energies

NASA Astrophysics Data System (ADS)

Bulyzhenkov, I. E.

2018-02-01

Translational ordering of the internal kinematic chaos provides the Special Relativity referents for the geodesic motion of warm thermodynamical bodies. Taking identical mathematics, relativistic physics of the low speed transport of time-varying heat-energies differs from Newton's physics of steady masses without internal degrees of freedom. General Relativity predicts geodesic changes of the internal heat-energy variable under the free gravitational fall and the geodesic turn in the radial field center. Internal heat variations enable cyclic dynamics of decelerated falls and accelerated takeoffs of inertial matter and its structural self-organization. The coordinate speed of the ordered spatial motion takes maximum under the equipartition of relativistic internal and translational kinetic energies. Observable predictions are discussed for verification/falsification of the principle of equipartition as a new basic for the ordered motion and self-organization in external fields, including gravitational, electromagnetic, and thermal ones.

The gravitational analog of Faraday's induction law

NASA Astrophysics Data System (ADS)

Zile, Daniel; Overduin, James

2015-04-01

Michael Faraday, the discoverer of electromagnetic induction, was convinced that there must also be a gravitational analog of this law, and he carried out drop-tower experiments in 1849 to look for the electric current induced in a coil by changes in gravitational flux through the coil. This work, now little remembered, was in some ways the first investigation of what we would now call a unified-field theory. We revisit Faraday's experiments in the light of current knowledge and ask what might be learned if they were to be performed today. We then review the gravitational analog for Faraday's law that arises within the vector (or gravito-electromagnetic) approximation to Einstein's theory of general relativity in the weak-field, low-velocity limit. This law relates spinning masses and induced ``mass currents'' rather than spinning charges and electric currents, but is otherwise remarkably similar to its electromagnetic counterpart. The predicted effects are completely unobservable in everyday settings like those envisioned by Faraday, but are thought to be relevant in astrophysical contexts like the accretion disks around collapsed stars, thus bearing out Faraday's remarkable intuition. Undergraduate student.

Preconceptions of Japanese Students Surveyed Using the Force and Motion Conceptual Evaluation

NASA Astrophysics Data System (ADS)

Ishimoto, Michi

2010-07-01

We assess the preconceptions of Japanese students about force and motion. The Force and Motion Conceptual Evaluation is a research-based, multiple-choice assessment of students' conceptual understanding of Newton's laws of motion and energy conservation. It is administered to determine the effectiveness of introductory mechanics curricula. In this study, the test was given to engineering students at the beginning of the first lecture of an introductory mechanics course for several years. Some students had minimal high school physics education, whereas the others had completed high school physics programs. To probe the students' preconceptions, we studied their test answers for each of the following categories: velocity, acceleration, Newton's first and second laws, Newton's third law, and energy conservation. We find that preconceptions, such as F ∝ mv, are prevalent among the students, regardless of their level of high school physics education. In the case of a collision between two objects, two preconceptions—a mass-dependent model and an action-dependent model—are prevalent. Typically, students combine the two models, with action dependency outweighing mass dependency. In the case of a sled sliding down a hill without friction at two heights and inclinations, a quarter of students used the height-dependent model to answer questions regarding speed and kinetic energy.

Lazy Days: An Active Way to Put Newton's First Law into Motion (or Rest)

NASA Astrophysics Data System (ADS)

Roemmele, Christopher; Sederberg, David

2017-05-01

Students are better able to understand Newton's first law when they build from their own personal experiences of bicycling, skateboarding, or riding in a car. Most have experienced a tumble when their skateboard or bicycle comes to an abrupt stop. Alternately in a car, your body continues moving when the brakes are applied and you feel the force of the seatbelt holding you in place. Start moving again and you feel your body pushed forward by the seat against your back. These common experiences provide good opportunities to learn about the concept of inertia (and to obey the law and wear seatbelts!). The state of motion of the rider does not change until an outside force is applied. We like to tell students to look at inertia as nature's way of "being lazy." This is how the name of this lab exercise, Lazy Days, is derived.

XMM-Newton X-ray and HST weak gravitational lensing study of the extremely X-ray luminous galaxy cluster Cl J120958.9+495352 ( z = 0.902)

DOE PAGES

Tholken, Sophia; Schrabback, Tim; Reiprich, Thomas H.; ...

2018-03-05

Here, observations of relaxed, massive, and distant clusters can provide important tests of standard cosmological models, for example by using the gas mass fraction. To perform this test, the dynamical state of the cluster and its gas properties have to be investigated. X-ray analyses provide one of the best opportunities to access this information and to determine important properties such as temperature profiles, gas mass, and the total X-ray hydrostatic mass. For the last of these, weak gravitational lensing analyses are complementary independent probes that are essential in order to test whether X-ray masses could be biased.

XMM-Newton X-ray and HST weak gravitational lensing study of the extremely X-ray luminous galaxy cluster Cl J120958.9+495352 ( z = 0.902)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tholken, Sophia; Schrabback, Tim; Reiprich, Thomas H.

Here, observations of relaxed, massive, and distant clusters can provide important tests of standard cosmological models, for example by using the gas mass fraction. To perform this test, the dynamical state of the cluster and its gas properties have to be investigated. X-ray analyses provide one of the best opportunities to access this information and to determine important properties such as temperature profiles, gas mass, and the total X-ray hydrostatic mass. For the last of these, weak gravitational lensing analyses are complementary independent probes that are essential in order to test whether X-ray masses could be biased.

Electrostatics of proteins in dielectric solvent continua. I. Newton's third law marries qE forces

NASA Astrophysics Data System (ADS)

Stork, Martina; Tavan, Paul

2007-04-01

The authors reformulate and revise an electrostatic theory treating proteins surrounded by dielectric solvent continua [B. Egwolf and P. Tavan, J. Chem. Phys. 118, 2039 (2003)] to make the resulting reaction field (RF) forces compatible with Newton's third law. Such a compatibility is required for their use in molecular dynamics (MD) simulations, in which the proteins are modeled by all-atom molecular mechanics force fields. According to the original theory the RF forces, which are due to the electric field generated by the solvent polarization and act on the partial charges of a protein, i.e., the so-called qE forces, can be quite accurately computed from Gaussian RF dipoles localized at the protein atoms. Using a slightly different approximation scheme also the RF energies of given protein configurations are obtained. However, because the qE forces do not account for the dielectric boundary pressure exerted by the solvent continuum on the protein, they do not obey the principle that actio equals reactio as required by Newton's third law. Therefore, their use in MD simulations is severely hampered. An analysis of the original theory has led the authors now to a reformulation removing the main difficulties. By considering the RF energy, which represents the dominant electrostatic contribution to the free energy of solvation for a given protein configuration, they show that its negative configurational gradient yields mean RF forces obeying the reactio principle. Because the evaluation of these mean forces is computationally much more demanding than that of the qE forces, they derive a suggestion how the qE forces can be modified to obey Newton's third law. Various properties of the thus established theory, particularly issues of accuracy and of computational efficiency, are discussed. A sample application to a MD simulation of a peptide in solution is described in the following paper [M. Stork and P. Tavan, J. Chem. Phys., 126, 165106 (2007).

Rockets: An Educator's Guide with Activities in Science, Mathematics, and Technology.

ERIC Educational Resources Information Center

National Aeronautics and Space Administration, Washington, DC.

This educational guide discusses rockets and includes activities in science, mathematics, and technology. It begins with background information on the history of rocketry, scientific principles, and practical rocketry. The sections on scientific principles and practical rocketry focus on Sir Isaac Newton's Three Laws of Motion. These laws explain…

Short-range inverse-square law experiment in space

NASA Technical Reports Server (NTRS)

Strayer, D.; Paik, H. J.; Moody, M. V.

2002-01-01

The objective of ISLES (Inverse-Square Law Experiment in Space) is to perform a null test ofNewton's law on the ISS with a resolution of one part in lo5 at ranges from 100 pm to 1 mm. ISLES will be sensitive enough to detect axions with the strongest allowed coupling and to test the string-theory prediction with R z 5 pm.

Viking radio science data analysis and synthesis. [rotation of Mars, solar system dynamics, and gravitational laws

NASA Technical Reports Server (NTRS)

Shapiro, I. I.

1984-01-01

The rotational motion of Mars and its geophysical ramifications were investigated. Solar system dynamics and the laws of gravitation were also studied. The planetary ephemeris program, which was the central element in data analysis for this project, is described in brief. Viking Lander data were used in the investigation.

Newton in Space

NASA Technical Reports Server (NTRS)

Herbert, Dexter (Editor)

1992-01-01

In this 'Liftoff to Learning' series video, astronauts (Charles Veach, Gregory Harbaugh, Donald McMonagle, Michael Coats, L. Blaine Hammond, Guion Bluford, Richard Hieb) from the STS-39 Mission use physical experiments and computer animation to explain how weightlessness and gravity affects everything and everyone onboard the Space Shuttle. The physics behind the differences between weight and mass, and the concepts of 'free fall', are demonstrated along with explanations and experiments of Sir Issac Newton's three laws of motion.

Abraham Pais Prize for History of Physics Talk: Henry Cavendish, John Michell, Weighing the Stars

NASA Astrophysics Data System (ADS)

McCormmach, Russell

2010-03-01

This talk is about an interaction between two 18th-century natural philosophers (physical scientists), Henry Cavendish and John Michell, and its most important outcome, the experiment of weighing the world (their name for it) using a torsion balance (our name for it). Michell was the most inventive of the 18th century English natural philosophers, and Cavendish was the first of his countrymen to possess abilities at all comparable with Newton's. By their interests and skills, they were drawn to one another. Both were universal natural philosophers, equally adept at building scientific instruments, performing experiments, constructing theory, and using mathematics; both had a penchant for exacting, quantitative work. Both also had fitful habits of publication, which did not begin to reveal the range of their work, to the mystification of later scientists and historians. Late in life, Cavendish and Michell turned their attention to the force that Newton had examined most completely, a singular triumph of his natural philosophy, the force of universal gravitation. Over the course of the 18th century, abundant evidence of attraction had been gathered from the motions of the earth, moon, planets, and comets, phenomena which span the intermediate range of masses, sizes, and distances. But in three domains of experience, involving the extreme upper and lower limits of masses and dimensions, the universality of gravitation remained an article of faith. These were the gravity of the ``fixed'' stars, the mutual attraction of terrestrial bodies, and the gravitation of light and other special substances. Michell took on himself the task of deducing observable consequences from each of these prospective instances of universal gravitation. Cavendish encouraged Michell, and he followed up the resulting observational and experimental questions. The experiment of weighing the world was the last experiment Mitchell planned and the last experiment Cavendish published. The capstone of two distinguished careers, the experiment outlived the world in which it was conceived and carried out. Today gravitation is at the center of the physics of the very small and the very large, and experiments that followed in Michell and Cavendish's footsteps find a place in it. The ``most important advance in experiments on gravitation,'' to quote an authority, ``was the introduction of the torsion balance'' by Michell and Cavendish and independently by Coulomb; ``it has been the basis of all the most significant experiments on gravitation ever since.'' Another authority traces the ``noble tradition of precision measurement to which we are heirs'' to Cavendish's experiment, which he calls the ``first modern physics experiment.''

Generalization of Rindler Potential at Cluster Scales in Randers-Finslerian Spacetime: a Possible Explanation of the Bullet Cluster 1E0657-558?

NASA Astrophysics Data System (ADS)

Chang, Zhe; Li, Ming-Hua; Lin, Hai-Nan; Li, Xin

2012-12-01

The data of the Bullet Cluster 1E0657-558 released on November 15, 2006 reveal that the strong and weak gravitational lensing convergence κ-map has an 8σ offset from the Σ-map. The observed Σ-map is a direct measurement of the surface mass density of the Intracluster medium (ICM) gas. It accounts for 83% of the averaged mass-fraction of the system. This suggests a modified gravity theory at large distances different from Newton's inverse-square gravitational law. In this paper, as a cluster scale generalization of Grumiller's modified gravity model (Phys. Rev. Lett.105 (2010) 211303), we present a gravity model with a generalized linear Rindler potential in Randers-Finslerian spacetime without invoking any dark matter. The galactic limit of the model is qualitatively consistent with the MOND and Grumiller's. It yields approximately the flatness of the rotational velocity profile at the radial distance of several kpcs and gives the velocity scales for spiral galaxies at which the curves become flattened. Plots of convergence κ for a galaxy cluster show that the peak of the gravitational potential has chances to lie on the outskirts of the baryonic mass center. Assuming an isotropic and isothermal ICM gas profile with temperature T = 14.8 keV (which is the center value given by observations), we obtain a good match between the dynamical mass MT of the main cluster given by collisionless Boltzmann equation and that given by the King β-model. We also consider a Randers+dark matter scenario and a Λ-CDM model with the NFW dark matter distribution profile. We find that a mass ratio η between dark matter and baryonic matter about 6 fails to reproduce the observed convergence κ-map for the isothermal temperature T taking the observational center value.

Newtonian Gravity Reformulated

NASA Astrophysics Data System (ADS)

Dehnen, H.

2018-01-01

With reference to MOND we propose a reformulation of Newton's theory of gravity in the sense of the static electrodynamics introducing a "material" quantity in analogy to the dielectric "constant". We propose that this quantity is induced by vacuum polarizations generated by the gravitational field itself. Herewith the flat rotation curves of the spiral galaxies can be explained as well as the observed high velocities near the center of the galaxy should be reconsidered.

Insect Flight: From Newton's Law to Neurons

NASA Astrophysics Data System (ADS)

Wang, Z. Jane

2016-03-01

Why do animals move the way they do? Bacteria, insects, birds, and fish share with us the necessity to move so as to live. Although each organism follows its own evolutionary course, it also obeys a set of common laws. At the very least, the movement of animals, like that of planets, is governed by Newton's law: All things fall. On Earth, most things fall in air or water, and their motions are thus subject to the laws of hydrodynamics. Through trial and error, animals have found ways to interact with fluid so they can float, drift, swim, sail, glide, soar, and fly. This elementary struggle to escape the fate of falling shapes the development of motors, sensors, and mind. Perhaps we can deduce parts of their neural computations by understanding what animals must do so as not to fall. Here I discuss recent developments along this line of inquiry in the case of insect flight. Asking how often a fly must sense its orientation in order to balance in air has shed new light on the role of motor neurons and steering muscles responsible for flight stability.

The physics of ice cream

NASA Astrophysics Data System (ADS)

Clarke, Chris

2003-05-01

Almost everybody likes ice cream, so it can provide an excellent vehicle for discussing and demonstrating a variety of physical phenomena, such as Newton's law of cooling, Boyle's law and the relationship between microstructure and macroscopic properties (e.g. Young's modulus). Furthermore, a demonstration of freezing point depression can be used to make ice cream in the classroom!

An Analysis of the Ontological Causal Relation in Physics and Its Educational Implications

ERIC Educational Resources Information Center

Cheong, Yong Wook

2016-01-01

An ontological causal relation is a quantified relation between certain interactions and changes in corresponding properties. Key ideas in physics, such as Newton's second law and the first law of thermodynamics, are representative examples of these relations. In connection with the teaching and learning of these relations, this study investigated…

76 FR 77950 - Approval and Promulgation of Implementation Plans and Designations of Areas for Air Quality...

Federal Register 2010, 2011, 2012, 2013, 2014

2011-12-15

..., Gwinnett, Hall, Henry, Newton, Paulding, Rockdale, Spalding and Walton Counties in Georgia. On June 23... additional requirements beyond those imposed by state law. For that reason, this proposed action: Is not a... tribal law. List of Subjects in 40 CFR Part 52 Environmental protection, Air pollution control...

Increasing the Drive of Your Physics Class

ERIC Educational Resources Information Center

Eisenstein, Stanley

2008-01-01

First-year physics students often have a difficult time grasping Newton's laws of motion and recognizing the forces that these laws depend on. The "Paper Car" project is an experiential activity that is rich in application of force principles. It is also simple enough that students are able to integrate straightforward but non-trivial physics…

77 FR 13491 - Approval and Promulgation of Implementation Plans and Designations of Areas for Air Quality...

Federal Register 2010, 2011, 2012, 2013, 2014

2012-03-07

..., Douglas, Fayette, Forsyth, Fulton, Gwinnett, Hall, Henry, Newton, Paulding, Rockdale, Spalding and Walton... would not impose additional requirements beyond those imposed by state law. For that reason, this action... substantial direct costs on tribal governments or preempt tribal law. The Congressional Review Act, 5 U.S.C...

Yes! We Are Rocket Scientists!

ERIC Educational Resources Information Center

Macduff, J. Trevor

2006-01-01

This article is an outline of what the author did in his classroom to incorporate the help of two volunteer engineers to create a powerful learning unit and cumulative review for his eighth-grade physical science students. This unit reviews what students have learned during the school year regarding force, motion, Newton's laws, gas laws, and…

Beyond Newton's law of cooling - estimation of time since death

NASA Astrophysics Data System (ADS)

Leinbach, Carl

2011-09-01

The estimate of the time since death and, thus, the time of death is strictly that, an estimate. However, the time of death can be an important piece of information in some coroner's cases, especially those that involve criminal or insurance investigations. It has been known almost from the beginning of time that bodies cool after the internal mechanisms such as circulation of the blood stop. A first attempt to link this phenomenon to the determination of the time of death used a crude linear relationship. Towards the end of the nineteenth century, Newton's law of cooling using body temperature data obtained by the coroner was used to make a more accurate estimate. While based on scientific principles and resulting in a better estimate, Newton's law does not really describe the cooling of a non-homogeneous human body. This article will discuss a more accurate model of the cooling process based on the theoretical work of Marshall and Hoare and the laboratory-based statistical work of Claus Henssge. Using DERIVE®6.10 and the statistical work of Henssge, the double exponential cooling formula developed by Marshall and Hoare will be explored. The end result is a tool that can be used in the field by coroner's scene investigators to determine a 95% confidence interval for the time since death and, thus, the time of death.

General-relativistic rotation: Self-gravitating fluid tori in motion around black holes

NASA Astrophysics Data System (ADS)

Karkowski, Janusz; Kulczycki, Wojciech; Mach, Patryk; Malec, Edward; Odrzywołek, Andrzej; Piróg, Michał

2018-05-01

We obtain from the first principles a general-relativistic Keplerian rotation law for self-gravitating disks around spinning black holes. This is an extension of a former rotation law that was designed mainly for toroids around spinless black holes. We integrate numerically axial stationary Einstein equations with self-gravitating disks around spinless or spinning black holes; that includes the first ever integration of the Keplerian selfgravitating tori. This construction can be used for the description of tight black hole-torus systems produced during coalescences of two neutron stars or modelling of compact active galactic nuclei.

Tests of the equivalence principle and gravitation theory using solar system bodies

NASA Technical Reports Server (NTRS)

Nordtvedt, K., Jr.

1971-01-01

The M sub g/M sub i ratio (ratio of body acceleration to gravitation field) of celestial bodies was measured. Deep probes of the post-Newtonian structure of gravitational theories are indicated. Kepler's third law is considered for the Sun-Jupiter system.

A WEAK LENSING STUDY OF X-RAY GROUPS IN THE COSMOS SURVEY: FORM AND EVOLUTION OF THE MASS-LUMINOSITY RELATION

DOE Office of Scientific and Technical Information (OSTI.GOV)

Leauthaud, Alexie; Finoguenov, Alexis; Cappelluti, Nico

2010-01-20

Measurements of X-ray scaling laws are critical for improving cosmological constraints derived with the halo mass function and for understanding the physical processes that govern the heating and cooling of the intracluster medium. In this paper, we use a sample of 206 X-ray-selected galaxy groups to investigate the scaling relation between X-ray luminosity (L{sub X}) and halo mass (M{sub 200}) where M{sub 200} is derived via stacked weak gravitational lensing. This work draws upon a broad array of multi-wavelength COSMOS observations including 1.64 degrees{sup 2} of contiguous imaging with the Advanced Camera for Surveys to a limiting magnitude of I{submore » F814W} = 26.5 and deep XMM-Newton/Chandra imaging to a limiting flux of 1.0 x 10{sup -15} erg cm{sup -2} s{sup -1} in the 0.5-2 keV band. The combined depth of these two data sets allows us to probe the lensing signals of X-ray-detected structures at both higher redshifts and lower masses than previously explored. Weak lensing profiles and halo masses are derived for nine sub-samples, narrowly binned in luminosity and redshift. The COSMOS data alone are well fit by a power law, M{sub 200} propor to (L{sub X}){sup a}lpha, with a slope of alpha = 0.66 +- 0.14. These results significantly extend the dynamic range for which the halo masses of X-ray-selected structures have been measured with weak gravitational lensing. As a result, tight constraints are obtained for the slope of the M-L{sub X} relation. The combination of our group data with previously published cluster data demonstrates that the M-L{sub X} relation is well described by a single power law, alpha = 0.64 +- 0.03, over two decades in mass, M{sub 200} approx 10{sup 13.5}-10{sup 15.5} h {sup -1}{sub 72} M{sub sun}. These results are inconsistent at the 3.7sigma level with the self-similar prediction of alpha = 0.75. We examine the redshift dependence of the M-L{sub X} relation and find little evidence for evolution beyond the rate predicted by self-similarity from z approx 0.25 to z approx 0.8.« less

Toying with Motion.

ERIC Educational Resources Information Center

Galus, Pamela J.

2002-01-01

Presents a variety of activities that support the development of an understanding of Newton's laws of motion. Activities use toy cars, mobile roads, and a seat-of-nails. Includes a scoring rubric. (DDR)

Molar distalization with the assistance of Temporary Anchorage Devices.

PubMed

Palencar, Adrian J

2015-01-01

This article describes efficient techniques for distalization of maxillary and mandibular molars with the assistance of Temporary Anchorage Devices (TADs). There are numerous occasions where the distalization of molars is required in lieu of the odontectomy of bicuspids. In the past, extra-oral force has been used, (i.e. Cervical or Combination Head Gear, or intra-oral force, i.e. Posterior Sagittal Appliance, Modified Greenfield Appliance, Williams DMJ 20001, CD Distalizer, Magill Sagittal, Pendulum Appliance, etc.). All the intra-oral appliances have a common denominator the orthodontic clinician has to deal with, the undesirable expression of the Third Law of Newton. The utilization of TADs allows us to circumvent this shortcoming, establishing an absolute anchorage, and thus completely negate the expression of the Third Law of Newton.

Kepler, the Ultimate Aristotelian

NASA Astrophysics Data System (ADS)

Davis, A. E. L.

A comparison is made between Aristotelian and Newtonian versions of Laws of Motion. Kepler was successful in proving the 2 laws of motion of a single planet - to the extent that agreement with a framework of theory constitutes a proof. Of course he invented his framework of causes after the event, to fit the motions that had been already been quantified - but it may seem to you that Kepler's mainly mechanistic way explanation could have been considered by his contemporaries just as reasonable as Newton's action at a distance. It could be now apprecated that there was a window of less than 50 years before Newton's total synthesis. No-one previously had had the motivation to create a system of "celestial physics" based on a judicious use of Aristotelian principles. Yet this is what Kepler achieved.

The cosmological Janus model: comparison with observational data

NASA Astrophysics Data System (ADS)

Petit, Jean-Pierre; Dagostini, Gilles

2017-01-01

In 2014 we presented a model based on a system of two coupled field equations to describe two populations of particles, one positive and the other mass of negative mass. The analysis of this system by Newtonian approximation show that the masses of the same signs attract according to Newton's law while the masses of opposite signs repel according to an anti-Newton law. This eliminates the runaway phenomenon. It uses the time-dependent exact solution of this system to build the bolometric magnitude distribution of the red-shift. Comparing the prediction of our model -which requires adjustment with a single parameter- with the data from 740 supernovae highlighting the acceleration of the universe gives an excellent agreement. The comparison is then made with the multi-parametric Λ CDM model.

Gauss-Bonnet chameleon mechanism of dark energy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ito, Yusaku; Nojiri, Shin'ichi

2009-05-15

As a model of the current accelerated expansion of the Universe, we consider a model of the scalar-Einstein-Gauss-Bonnet gravity. This model includes the propagating scalar modes, which might give a large correction to the Newton law. In order to avoid this problem, we propose an extension of the chameleon mechanism where the scalar mode becomes massive due to the coupling with the Gauss-Bonnet term. Since the Gauss-Bonnet invariant does not vanish near the Earth or in the Solar System, even in the vacuum, the scalar mode is massive even in the vacuum and the correction to the Newton law couldmore » be small. We also discuss the possibility that the model could describe simultaneously the inflation in the early Universe, in addition to the current accelerated expansion.« less

Precision Measurement of Distribution of Film Thickness on Pendulum for Experiment of G

NASA Astrophysics Data System (ADS)

Liu, Lin-Xia; Guan, Sheng-Guo; Liu, Qi; Zhang, Ya-Ting; Shao, Cheng-Gang; Luo, Jun

2009-09-01

Distribution of film thickness coated on the pendulum of measuring the Newton gravitational constant G is determined with a weighing method by means of a precision mass comparator. The experimental result shows that the gold film on the pendulum will contribute a correction of -24.3 ppm to our G measurement with an uncertainty of 4.3 ppm, which is significant for improving the G value with high precision.

Idea Bank.

ERIC Educational Resources Information Center

Science Teacher, 1990

1990-01-01

Eight activities for use in the science classroom are presented. Included are insect collecting, laboratory procedures and safety, recycling, current events, variable manipulation, scientific method, electricity, and mechanics (Newton's Second Law of Motion). (KR)

Modification of Schrödinger-Newton equation due to braneworld models with minimal length

NASA Astrophysics Data System (ADS)

Bhat, Anha; Dey, Sanjib; Faizal, Mir; Hou, Chenguang; Zhao, Qin

2017-07-01

We study the correction of the energy spectrum of a gravitational quantum well due to the combined effect of the braneworld model with infinite extra dimensions and generalized uncertainty principle. The correction terms arise from a natural deformation of a semiclassical theory of quantum gravity governed by the Schrödinger-Newton equation based on a minimal length framework. The two fold correction in the energy yields new values of the spectrum, which are closer to the values obtained in the GRANIT experiment. This raises the possibility that the combined theory of the semiclassical quantum gravity and the generalized uncertainty principle may provide an intermediate theory between the semiclassical and the full theory of quantum gravity. We also prepare a schematic experimental set-up which may guide to the understanding of the phenomena in the laboratory.

Another Look at Rocket Thrust

ERIC Educational Resources Information Center

Hester, Brooke; Burris, Jennifer

2012-01-01

Rocket propulsion is often introduced as an example of Newton's third law. The rocket exerts a force on the exhaust gas being ejected; the gas exerts an equal and opposite force--the thrust--on the rocket. Equivalently, in the absence of a net external force, the total momentum of the system, rocket plus ejected gas, remains constant. The law of…

Derivation of special relativity from Maxwell and Newton.

PubMed

Dunstan, D J

2008-05-28

Special relativity derives directly from the principle of relativity and from Newton's laws of motion with a single undetermined parameter, which is found from Faraday's and Ampère's experimental work and from Maxwell's own introduction of the displacement current to be the -c(-2) term in the Lorentz transformations. The axiom of the constancy of the speed of light is quite unnecessary. The behaviour and the mechanism of the propagation of light are not at the foundations of special relativity.

Mars Seasonal Polar Caps as a Test of the Equivalence Principle

NASA Technical Reports Server (NTRS)

Rubincam, Daivd Parry

2011-01-01

The seasonal polar caps of Mars can be used to test the equivalence principle in general relativity. The north and south caps, which are composed of carbon dioxide, wax and wane with the seasons. If the ratio of the inertial to gravitational masses of the caps differs from the same ratio for the rest of Mars, then the equivalence principle fails, Newton's third law fails, and the caps will pull Mars one way and then the other with a force aligned with the planet's spin axis. This leads to a secular change in Mars's along-track position in its orbit about the Sun, and to a secular change in the orbit's semimajor axis. The caps are a poor E6tv6s test of the equivalence principle, being 4 orders-of-magnitude weaker than laboratory tests and 7 orders-of-magnitude weaker than that found by lunar laser ranging; the reason is the small mass of the caps compared to Mars as a whole. The principal virtue of using Mars is that the caps contain carbon, an element not normally considered in such experiments. The Earth with its seasonal snow cover can also be used for a similar test.

Chaos in a dynamic model of traffic flows in an origin-destination network.

PubMed

Zhang, Xiaoyan; Jarrett, David F.

1998-06-01

In this paper we investigate the dynamic behavior of road traffic flows in an area represented by an origin-destination (O-D) network. Probably the most widely used model for estimating the distribution of O-D flows is the gravity model, [J. de D. Ortuzar and L. G. Willumsen, Modelling Transport (Wiley, New York, 1990)] which originated from an analogy with Newton's gravitational law. The conventional gravity model, however, is static. The investigation in this paper is based on a dynamic version of the gravity model proposed by Dendrinos and Sonis by modifying the conventional gravity model [D. S. Dendrinos and M. Sonis, Chaos and Social-Spatial Dynamics (Springer-Verlag, Berlin, 1990)]. The dynamic model describes the variations of O-D flows over discrete-time periods, such as each day, each week, and so on. It is shown that when the dimension of the system is one or two, the O-D flow pattern either approaches an equilibrium or oscillates. When the dimension is higher, the behavior found in the model includes equilibria, oscillations, periodic doubling, and chaos. Chaotic attractors are characterized by (positive) Liapunov exponents and fractal dimensions.(c) 1998 American Institute of Physics.

A Bridge Too Far

NASA Astrophysics Data System (ADS)

Halprin, L.

Manned space flight has stagnated for over forty years. No humans have travelled beyond LEO since 1972. This paper examines the historical reasons for this situation, postulates a possible explanation and proposes a potential way forward. The science required for manned space flight has existed for a very long time. The Chinese first developed rockets almost a millennium ago. The Laws of Universal Gravitation were described by Newton in the 17th century, and the rocket equation was formulated by Tsiolkovsky over a hundred years ago. Advances in chemical, electronic and materials technologies enabled manned space flight fifty years ago. But it still required the political will to authorise the enormous expense of the undertaking. Since the original political impetus for manned space flight evaporated after men reached the moon, the enterprise has stagnated. A three stage model linking (a) the science and technology, (b) the economic resources and (c) the will or motivation is presented as a possible explanation. A way for progressing the enterprise of manned space flight beyond this three-way nexus is proposed. By accepting the propositions put forward in this paper, it is plausible that stakeholders may be empowered to push beyond the excuses that have retarded manned space flight for so long.

Renormalization group scale-setting from the action—a road to modified gravity theories

NASA Astrophysics Data System (ADS)

Domazet, Silvije; Štefančić, Hrvoje

2012-12-01

The renormalization group (RG) corrected gravitational action in Einstein-Hilbert and other truncations is considered. The running scale of the RG is treated as a scalar field at the level of the action and determined in a scale-setting procedure recently introduced by Koch and Ramirez for the Einstein-Hilbert truncation. The scale-setting procedure is elaborated for other truncations of the gravitational action and applied to several phenomenologically interesting cases. It is shown how the logarithmic dependence of the Newton's coupling on the RG scale leads to exponentially suppressed effective cosmological constant and how the scale-setting in particular RG-corrected gravitational theories yields the effective f(R) modified gravity theories with negative powers of the Ricci scalar R. The scale-setting at the level of the action at the non-Gaussian fixed point in Einstein-Hilbert and more general truncations is shown to lead to universal effective action quadratic in the Ricci tensor.

Get a Kick Out of Physics.

ERIC Educational Resources Information Center

Hildreth, David P.; Matthews, Catherine E.

1997-01-01

Describes a number of demonstrations for physics that employ techniques of the martial arts to illustrate Newton's second law of motion. Demonstrations focus on the breaking of wooden boards using weights. (DDR)

Instrument development of causalitic thinking approach in physics learning to increase problem solving ability of pre-service teachers

NASA Astrophysics Data System (ADS)

Rokhmat, Joni; Marzuki, Hikmawati, Verawati, Ni Nyoman Sri Putu

2017-01-01

It has been developed instruments of Causalitic Thinking Approach (CTA) in Physics learning to increase Problem Solving Ability (PSA) of pre-service teachers (low and high groups). Causalitic means causality and analitic. Implementation of the CTA at kinematics and Newton's law about movement increased the PSA of students (significance 5%) and the increases were not different between the low and high groups. PSA includes abilities of understanding (IPSA-1), selecting (IPSA-2), differentiating (IPSA-3), determining (IPSA-4), applying (IPSA-5), and identifying (IPSA-6). The differences between pre-test (initial PSA) and post-test (final PSA), and between PSA-gain of low and high groups were tested using Wilcoxon signed-ranks test. Pairs of tcounted and ttable (tcount, ttable) at IPSA-1 to IPSA-6 for low group were (2,-), (0,5), (0,2), (0,0), (0,3), (0,0) at kinematics and (0,5), (0,5), (0,2), (0,5), (0,2), (0,0) at Newton's law. While, for high group, the pairs were (0,5), (0,5), (0,3), (0,3), (0,3), (0,0) at kinematics and (0,2), (0,5), (0,2), (0,3), (0,5), (0,2) at Newton's law. Finally, pairs of tcounted and ttable (tcounted, ttable) for the PSA gain differences were (0,3), (4,0), (5,2), (13.5,5), (5,2), (5,2) at kinematics and (3,2), (12,5), (10.5,5), (2,0), (8.5,5), (10.5,) at Newton's law. The value of ttable is related to the number of effective data pairs (for 6, 7, 8, and 9 pairs, the ttable respectively are 0, 2, 3, and 5). This first of three year research used mixed method of embedded experimental two-phase design and involved 49 students (39 females). The CTA facilitated students to develop ability of causality and analytic thinking. To solve phenomenon, students determined all causes and deductively predicted all of possible effects, and finally identified conditions of each causes which resulted in each effects. This paper will focus at three focus discussions, i.e. instruments of CTA, PSA increases, and responds of students to the instruments.

Physics that Textbook Writers Usually Get Wrong: III.

ERIC Educational Resources Information Center

Bauman, Robert P.

1992-01-01

Examines inconsistencies in science textbook discussions of vector quantities and force. Provides illustrations of textbook inconsistencies related to Newton's laws of motion and the concepts of centrifugal and coriolis force. (MDH)

A new electromagnetic NDI-technique based on the measurement of source-sample reaction forces

NASA Astrophysics Data System (ADS)

Fitzpatrick, G. L.; Skaugset, R. L.; Shih, W. C. L.

2001-04-01

Faraday's law of induction, Lenz's law, the Lorentz force law and Newton's third law, taken together, insure that sources (e.g., coil sources) of time-dependent electromagnetic fields, and nearby "nonmagnetic" electrical conductors (e.g., aluminum), always experience mutually repulsive (source-conductor) forces. This fact forms the basis for a new method for detecting cracks and corrosion in (aging) multi-layer airframes. The presence of cracks or corrosion (e.g., material thinning) in these structures is observed to reduce (second-harmonic) source-conductor reaction forces.

Lenz's Law Magic Trick

NASA Astrophysics Data System (ADS)

Ruiz, Michael J.

2006-02-01

The demonstration of Lenz's law by dropping a powerful magnet down a nonmagnetic metal pipe has become a classic lecture-hall demonstration.1,2 An inexpensive version is packaged as a professional magic trick3 called "Newton's Nightmare." Combining sleight-of-hand with a demonstration of Lenz's law is a surefire way to heighten student interest. The subsequent student discussion motivated by a desire to understand the magic trick can lead to a memorable physics lesson. This paper will discuss Lenz's law magic and review literature that reveals the subtlety of the physics.

Motional Mechanisms of Homopolar Motors & Rollers

NASA Astrophysics Data System (ADS)

Wong, H. K.

2009-10-01

The strong Nd2Fe14B permanent magnet has facilitated development of various fascinating yet simple homopolar motors However, the physics of these devices is often not explained, or is explained incorrectly. A major concern is that Newton's third law was overlooked in some of the earlier articles. In this paper, I will employ this law in explaining the motional mechanisms of these devices.

Tests of Gravity Using Lunar Laser Ranging.

PubMed

Merkowitz, Stephen M

2010-01-01

Lunar laser ranging (LLR) has been a workhorse for testing general relativity over the past four decades. The three retroreflector arrays put on the Moon by the Apollo astronauts and the French built arrays on the Soviet Lunokhod rovers continue to be useful targets, and have provided the most stringent tests of the Strong Equivalence Principle and the time variation of Newton's gravitational constant. The relatively new ranging system at the Apache Point 3.5 meter telescope now routinely makes millimeter level range measurements. Incredibly, it has taken 40 years for ground station technology to advance to the point where characteristics of the lunar retroreflectors are limiting the precision of the range measurements. In this article, we review the gravitational science and technology of lunar laser ranging and discuss prospects for the future.

Tests of gravity Using Lunar Laser Ranging

NASA Technical Reports Server (NTRS)

Merkowitz, Stephen M.

2010-01-01

Lunar laser ranging (LLR) has been a workhorse for testing general relativity over the pat four decades. The three retrorefiector arrays put on the Moon by the Apollo astronauts and the French built array on the second Soviet Lunokhod rover continue to be useful targets, and have provided the most stringent tests of the Strong Equivalence Principle and the time variation of Newton's gravitational constant. The relatively new ranging system at the Apache Point :3.5 meter telescope now routinely makes millimeter level range measurements. Incredibly. it has taken 40 years for ground station technology to advance to the point where characteristics of the lunar retrorefiectors are limiting the precision of the range measurements. In this article. we review the gravitational science and technology of lunar laser ranging and discuss prospects for the future.

Non-minimally coupled varying constants quantum cosmologies

DOE Office of Scientific and Technical Information (OSTI.GOV)

Balcerzak, Adam, E-mail: abalcerz@wmf.univ.szczecin.pl

We consider gravity theory with varying speed of light and varying gravitational constant. Both constants are represented by non-minimally coupled scalar fields. We examine the cosmological evolution in the near curvature singularity regime. We find that at the curvature singularity the speed of light goes to infinity while the gravitational constant vanishes. This corresponds to the Newton's Mechanics limit represented by one of the vertex of the Bronshtein-Zelmanov-Okun cube [1,2]. The cosmological evolution includes both the pre-big-bang and post-big-bang phases separated by the curvature singularity. We also investigate the quantum counterpart of the considered theory and find the probability ofmore » transition of the universe from the collapsing pre-big-bang phase to the expanding post-big-bang phase.« less

Graphing Calculators, the CBL2[TM] and TI-Interactive[TM] in High School Science.

ERIC Educational Resources Information Center

Molnar, Bill

This collection of activities is designed to show how TI-Interactive[TM] and Calculator-based Laboratories (CBL) can be used to explore topics in high school science. The activities address such topics as specific heat, Boyle's Law, Newton's Law of Cooling, and Antarctic Ozone Levels. Teaching notes and calculator instructions are included as are…

Newton’s Rotating Water Bucket: A Simple Model

DTIC Science & Technology

2013-01-01

surface of the water must be an equipotential relative to the sum of the gravitational and centrifugal potential energies [9].) The value of z0 can be...twisted and the bucket is then released, it begins to spin and the surface of the water acquires a paraboloidal shape. In this paper, the parabolic...adopts a curved surface . Ernst Mach, for example, postulated that the parabolic shape must be due to the existence of matter in the universe

Celestial mechanics solutions that escape

NASA Astrophysics Data System (ADS)

Gingold, Harry; Solomon, Daniel

2017-08-01

We establish the existence of an open set of initial conditions through which pass solutions without singularities to Newton's gravitational equations in R3 on a semi-infinite interval in forward time, for which every pair of particles separates like At , A > 0, as t → ∞. The solutions are constructable as series with rapid uniform convergence and their asymptotic behavior to any order is prescribed. We show that this family of solutions depends on 6N parameters subject to certain constraints.

Applicability of Newton's law of cooling in monetary economics

NASA Astrophysics Data System (ADS)

Todorović, Jadranka Đurović; Tomić, Zoran; Denić, Nebojša; Petković, Dalibor; Kojić, Nenad; Petrović, Jelena; Petković, Biljana

2018-03-01

Inflation is a phenomenon which attracts the attention of many researchers. Inflation is not a recent date phenomenon, but it has existed ever since money emerged in world's first economies. With the development of economy and market, inflation developed as well. Today, even though there is a considerable number of research papers on inflation, there is still not enough knowledge about all factors which might cause inflation, and influence its evolution and dynamics. Regression analysis is a powerful statistical tool which might help analyse a vast amount of data on inflation, and provide an answer to the question about the factors of inflation, as well as the way those factors influence it. In this article Newton's Law of Cooling was applied to determine the long-term dynamics of monetary aggregates and inflation in Serbia and Croatia.

Fluctuations in Student Understanding of Newton's 3rd Law

NASA Astrophysics Data System (ADS)

Clark, Jessica W.; Sayre, Eleanor C.; Franklin, Scott V.

2010-10-01

We present data from a between-student study on student response to questions on Newton's Third Law given throughout the academic year. The study, conducted at Rochester Institute of Technology, involved students from the first and third of a three-quarter sequence. Construction of a response curve reveals subtle dynamics in student learning not captured by simple pre/post testing. We find a a significant positive effect from direct instruction, peaking at the end of instruction on forces, that diminishes by the end of the quarter. Two quarters later, in physics III, a significant dip in correct response occurs when instruction changes from the vector quantities of electric forces and fields to the scalar quantity of electric potential. Student response rebounds to its initial values, however, once instruction returns to the vector-based topics involving magnetic fields.

The Tablecloth Trick, Take II.

ERIC Educational Resources Information Center

Ringlein, James

2003-01-01

Explores the basic physics behind pulling a tablecloth out from under a set of dishes, glassware, and utensils without disturbing them. Discusses terminology of Newton's laws of motion and illustrates them using three simple examples. (NB)

String and Sticky Tape Experiments.

ERIC Educational Resources Information Center

Edge, R. D., Ed.

1979-01-01

Explains how to demonstrate the fundamentals of one dimensional kinematics such as Newton's third law of motion, and collision between bodies, using simple materials of marbles, strings, sticky tape, drinking straws, and rubber bands. (GA)

Texas Science Teacher Characteristics and Conceptual Understanding of Newton's Laws of Motion

NASA Astrophysics Data System (ADS)

Busby, Karin Burk

Misconceptions of Newtonian mechanics and other physical science concepts are well documented in primary and pre-service teacher populations (Burgoon, Heddle, & Duran, 2009; Allen & Coole, 2012; Kruger, Summers, & Palacio, 1990; Ginns & Watters, 1995; Trumper, 1999; Asikainen & Hirovonen, 2014). These misconceptions match the misconceptions held by students, leaving teachers ill-equipped to rectify these concepts in the classroom (Kind, 2014; Kruger et al., 1990; Cochran & Jones, 1998). Little research has been devoted to misconceptions held by in-service secondary teachers, the population responsible for teaching Newtonian mechanics. This study focuses on Texas in-service science teachers in middle school and high school science, specifically sixth grade science, seventh grade science, eighth grade science, integrated physics and chemistry, and physics teachers. This study utilizes two instruments to gauge conceptual understanding of Newton's laws of motion: the Force Concept Inventory [FCI] (Hestenes, Wells, & Swackhamer, 1992) and a custom instrument developed for the Texas Regional Collaboratives for Excellence in Science and Mathematics Teaching (Urquhart, M., e-mail, April 4, 2017). Use of each instrument had its strengths and limitations. In the initial work of this study, the FCI was given to middle and high school teacher volunteers in two urban school districts in the Dallas- Fort Worth area to assess current conceptual understanding of Newtonian mechanics. Along with the FCI, each participant was asked to complete a demographic survey. Demographic data collected included participant's sex, years of service in teaching position, current teaching position, degrees, certification type, and current certifications for science education. Correlations between variables and overall average on the FCI were determined by t-tests and ANOVA tests with a post-hoc Holm-Bonferroni correction test. Test questions pertaining to each of Newton's three laws of motion were extrapolated to determine any correlations. The sample size for this study was small (n=24), requiring a second study investigate potential correlations to teacher characteristics. The second study was conducted using the 2013-2014 school year participants in the Texas Regional Collaboratives for Excellence in Science and Mathematics Teaching [TRC] (Texas Regional Collaborative for Excellence in Science and Mathematics Teaching, 2013), a statewide program led by The University of Texas at Austin Center for STEM Education (Texas Regional Collaborative for Excellence in Science and Mathematics Teaching, 2013). Participants completed a demographic survey and took the TRC Physics Assessment instrument developed for the TRC to determine current conceptual understanding of Newtonian mechanics as defined by the Texas Essential Knowledge and Skills. The TRC also collected demographic data including Texas Educational Agency region, participant's sex, years of service in teaching, current teaching position, level of highest degree earned, whether or not the participant had a STEM degree, and certification type. Correlations were determined between overall average and conceptual force questions only. The sample size was substantial (n=368) but due to time constraints in its development, the TRC Physics Assessment was unable to undergo reliability or validity testing before implementation. Test question pertaining to each of Newton's three laws of motion were extrapolated to determine any correlations. A significance value of p= 0.05 was used for all tests. Both content assessments indicated that, on average, teacher-participants had a considerable misunderstanding of Newtonian mechanics with Newton's third law questions especially difficult for the populations. Teachers' current teaching assignment was statistically significant for most tests, suggesting that high school physics teachers have more conceptual understanding of Newtonian mechanics than middle school teachers but have not necessarily mastered Newtonian mechanics. STEM majors and participant's sex were significant only for the TRC Physics Assessment. One outcome of this study is a recommendation that the Texas teacher certification process for middle school science change to include a general science test that includes physical science. Also, in-service science teachers responsible for teaching Newton's laws of motion should participate in specific professional development from a physics content educational expert to address misconceptions. Additional recommendations include that physics teachers take a mentoring role to help other teachers in physical science concepts and that middle school curriculum provide assistance to teachers for addressing misconceptions of Newton's third law.

Theoretical astrophysics in the 19th century (Homage to Radó von Kövesligethy)

NASA Astrophysics Data System (ADS)

Balázs, Lajos G.

The nature of astronomical information is determined mostly by the incoming light. Theoretical astrophysics means basically the theory of light emission and its relation to the physical constitution of the emitting celestial bodies. The necessary physical disciplines include theory of gravitation, theory of radiation, thermodynamics, matter--radiation interaction. The most significant theoretical achievement in the 17th - 18th century was the axiomatic foundation of mechanics and the law of gravitation. In the context of the nature of light, there were two conceptions: Newton contra Huygens, i.e. particle versus wave phenomenon. Using the theory of gravitation, first speculations appeared on black holes (Michell, Laplace), cosmogony (Kant-Laplace theory), the structure of the Milky Way (Kant), and the explanation of motion of the celestial bodies. The Olbers Paradox, formulated in the 19th century, is still one of the most significant constraints on observational cosmology. The development of thermodynamics, matter-radiation interaction, development of the theory of electromagnetism became important milestones. Maxwell's theory was the classical framework of the interaction between matter and radiation. Kirchhoff and Bunsen's revolutionary discovery of spectral analysis (1859) showed that observation of spectra makes it possible to study the chemical composition of emitting bodies. Thermodynamics predicted the existence of the black body radiation. It did not succeed, however, to determine the functional form of the wavelength dependence. A combination of the thermodynamic equation of state with the equation of hydrostatics resulted in the first stellar models (Lane, Ritter, Schuster). The first successful spectral equation of black body radiation was the theory of continuous spectra of celestial bodies by Radó von Kövesligethy (published 1885 in Hungarian, 1890 in German). Kövesligethy made several assumptions on the matter-radiation interaction: radiating matter consists of interacting particles, the form of interaction is an inverse power law, the radiation field is represented by the aether, aether is made also from interacting particles, light is the propagation of the oscillation of the aether particles, there is an equipartition between the oscillations energy of material and aetheric particles. Based on these assumptions, he derived a spectral equation with the following properties: the spectral distribution of radiation depends only on the temperature, the total irradiated energy is finite (15 years before Planck!), the wavelength of the intensity maximum is inversely proportional to the temperature (eight years before Wien!). Using his spectral equation, he estimated the temperature of several celestial bodies, including the Sun.

The Effect of Using a Visual Representation Tool in a Teaching-Learning Sequence for Teaching Newton's Third Law

NASA Astrophysics Data System (ADS)

Savinainen, Antti; Mäkynen, Asko; Nieminen, Pasi; Viiri, Jouni

2017-02-01

This paper presents a research-based teaching-learning sequence (TLS) that focuses on the notion of interaction in teaching Newton's third law (N3 law) which is, as earlier studies have shown, a challenging topic for students to learn. The TLS made systematic use of a visual representation tool—an interaction diagram (ID)—highlighting interactions between objects and addressing the learning demand related to N3 law. This approach had been successful in enhancing students' understanding of N3 law in pilot studies conducted by teacher-researchers. However, it was unclear whether teachers, who have neither been involved with the research nor received intensive tutoring, could replicate the positive results in ordinary school settings. To address this question, we present an empirical study conducted in 10 Finnish upper secondary schools with students ( n = 261, aged 16) taking their mandatory physics course. The study design involved three groups: the heavy ID group (the TLS with seven to eight exercises on IDs), the light ID group (two to three exercises on IDs) and the no ID group (no exercises on IDs). The heavy and light ID groups answered eight ID questions, and all the students answered four questions on N3 law after teaching the force concept. The findings clearly suggest that systematic use of the IDs in teaching the force concept significantly fostered students' understanding of N3 law even with teachers who have no intensive tutoring or research background.

Finite entanglement entropy of black holes

NASA Astrophysics Data System (ADS)

Giaccari, Stefano; Modesto, Leonardo; Rachwał, Lesław; Zhu, Yiwei

2018-06-01

We compute the area term contribution to black holes' entanglement entropy (using the conical technique) for a class of local or weakly non-local super-renormalizable gravitational theories coupled to matter. For the first time, we explicitly prove that all the beta functions in the proposed theory, except for the cosmological constant, are identically zero in cut-off regularization scheme and not only in dimensional regularization scheme. In particular, we show that there is no divergence quadratic in cut-off and hence there is no contribution to the beta function of the Newton constant. As a consequence of this result, we argue that in these theories of gravity conical entropy is a sensible definition of physical entropy, in particular, it is positive-definite and gauge independent. On top of this the conical entropy, being expressed only in terms of the classical Newton constant, turns out to be finite and naturally coincides with Bekenstein-Hawking entropy. Finally, we propose a theory in which the renormalization of the Newton constant is entirely due to the Standard Model matter, arguing that such a contribution does not give the usual interpretational problems of conical entropy discussed in the literature.

Correlation between the Total Gravitating Mass of Groups and Clusters and the Supermassive Black Hole Mass of Brightest Galaxies

NASA Astrophysics Data System (ADS)

Bogdán, Ákos; Lovisari, Lorenzo; Volonteri, Marta; Dubois, Yohan

2018-01-01

Supermassive black holes (BHs) residing in the brightest cluster galaxies are over-massive relative to the stellar bulge mass or central stellar velocity dispersion of their host galaxies. As BHs residing at the bottom of the galaxy cluster’s potential well may undergo physical processes that are driven by the large-scale characteristics of the galaxy clusters, it is possible that the growth of these BHs is (indirectly) governed by the properties of their host clusters. In this work, we explore the connection between the mass of BHs residing in the brightest group/cluster galaxies (BGGs/BCGs) and the virial temperature, and hence total gravitating mass, of galaxy groups/clusters. To this end, we investigate a sample of 17 BGGs/BCGs with dynamical BH mass measurements and utilize XMM-Newton X-ray observations to measure the virial temperatures and infer the {M}500 mass of the galaxy groups/clusters. We find that the {M}{BH}{--}{kT} relation is significantly tighter and exhibits smaller scatter than the {M}{BH}{--}{M}{bulge} relations. The best-fitting power-law relations are {{log}}10({M}{BH}/{10}9 {M}ȯ )=0.20+1.74{{log}}10({kT}/1 {keV}) and {{log}}10({M}{BH}/{10}9 {M}ȯ ) = -0.80+1.72{{log}}10({M}{bulge}/{10}11 {M}ȯ ). Thus, the BH mass of BGGs/BCGs may be set by physical processes that are governed by the properties of the host galaxy group/cluster. These results are confronted with the Horizon-AGN simulation, which reproduces the observed relations well, albeit the simulated relations exhibit notably smaller scatter.

Theoretical physics implications of gravitational wave observation with future detectors

NASA Astrophysics Data System (ADS)

Chamberlain, Katie; Yunes, Nicolás

2017-10-01

Gravitational waves encode invaluable information about the nature of the relatively unexplored extreme gravity regime, where the gravitational interaction is strong, nonlinear and highly dynamical. Recent gravitational wave observations by advanced LIGO have provided the first glimpses into this regime, allowing for the extraction of new inferences on different aspects of theoretical physics. For example, these detections provide constraints on the mass of the graviton, Lorentz violation in the gravitational sector, the existence of large extra dimensions, the temporal variability of Newton's gravitational constant, and modified dispersion relations of gravitational waves. Many of these constraints, however, are not yet competitive with constraints obtained, for example, through Solar System observations or binary pulsar observations. In this paper, we study the degree to which theoretical physics inferences drawn from gravitational wave observations will strengthen with detections from future detectors. We consider future ground-based detectors, such as the LIGO-class expansions A + , Voyager, Cosmic Explorer and the Einstein Telescope, as well as space-based detectors, such as various configurations of eLISA and the recently proposed LISA mission. We find that space-based detectors will place constraints on general relativity up to 12 orders of magnitude more stringently than current aLIGO bounds, but these space-based constraints are comparable to those obtained with the ground-based Cosmic Explorer or the Einstein Telescope (A + and Voyager only lead to modest improvements in constraints). We also generically find that improvements in the instrument sensitivity band at low frequencies lead to large improvements in certain classes of constraints, while sensitivity improvements at high frequencies lead to more modest gains. These results strengthen the case for the development of future detectors, while providing additional information that could be useful in future design decisions.

A Weak Lensing Study of X-ray Groups in the Cosmos Survey: Form and Evolution of the Mass-Luminosity Relation

NASA Astrophysics Data System (ADS)

Leauthaud, Alexie; Finoguenov, Alexis; Kneib, Jean-Paul; Taylor, James E.; Massey, Richard; Rhodes, Jason; Ilbert, Olivier; Bundy, Kevin; Tinker, Jeremy; George, Matthew R.; Capak, Peter; Koekemoer, Anton M.; Johnston, David E.; Zhang, Yu-Ying; Cappelluti, Nico; Ellis, Richard S.; Elvis, Martin; Giodini, Stefania; Heymans, Catherine; Le Fèvre, Oliver; Lilly, Simon; McCracken, Henry J.; Mellier, Yannick; Réfrégier, Alexandre; Salvato, Mara; Scoville, Nick; Smoot, George; Tanaka, Masayuki; Van Waerbeke, Ludovic; Wolk, Melody

2010-01-01

Measurements of X-ray scaling laws are critical for improving cosmological constraints derived with the halo mass function and for understanding the physical processes that govern the heating and cooling of the intracluster medium. In this paper, we use a sample of 206 X-ray-selected galaxy groups to investigate the scaling relation between X-ray luminosity (L X) and halo mass (M 200) where M 200 is derived via stacked weak gravitational lensing. This work draws upon a broad array of multi-wavelength COSMOS observations including 1.64 degrees2 of contiguous imaging with the Advanced Camera for Surveys to a limiting magnitude of I F814W = 26.5 and deep XMM-Newton/Chandra imaging to a limiting flux of 1.0 × 10-15 erg cm-2 s-1 in the 0.5-2 keV band. The combined depth of these two data sets allows us to probe the lensing signals of X-ray-detected structures at both higher redshifts and lower masses than previously explored. Weak lensing profiles and halo masses are derived for nine sub-samples, narrowly binned in luminosity and redshift. The COSMOS data alone are well fit by a power law, M 200 vprop (L X)α, with a slope of α = 0.66 ± 0.14. These results significantly extend the dynamic range for which the halo masses of X-ray-selected structures have been measured with weak gravitational lensing. As a result, tight constraints are obtained for the slope of the M-L X relation. The combination of our group data with previously published cluster data demonstrates that the M-L X relation is well described by a single power law, α = 0.64 ± 0.03, over two decades in mass, M 200 ~ 1013.5-1015.5 h -1 72 M sun. These results are inconsistent at the 3.7σ level with the self-similar prediction of α = 0.75. We examine the redshift dependence of the M-L X relation and find little evidence for evolution beyond the rate predicted by self-similarity from z ~ 0.25 to z ~ 0.8. Based on observations with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by AURA Inc, under NASA contract NAS 5-26555; also based on data collected at the Subaru Telescope, which is operated by the National Astronomical Observatory of Japan; the XMM-Newton, an ESA science mission with instruments and contributions directly funded by ESA Member States and NASA; the European Southern Observatory under Large Program 175.A-0839, Chile; Kitt Peak National Observatory, Cerro Tololo Inter-American Observatory, and the National Optical Astronomy Observatory, which are operated by the Association of Universities for Research in Astronomy, Inc. (AURA) under cooperative agreement with the National Science Foundation; the National Radio Astronomy Observatory which is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc ; and the Canada-France-Hawaii Telescope with MegaPrime/MegaCam operated as a joint project by the Canada-France-Hawaii-Telescope Corporation, CEA/DAPNIA, the National Research Council of Canada, the Canadian Astronomy Data Centre, the Centre National de la Recherche Scientifique de France, TERAPIX and the University of Hawaii.

Two-ball Newton's cradle

NASA Astrophysics Data System (ADS)

Glendinning, Paul

2011-12-01

Newton's cradle for two balls with Hertzian interactions is considered as a hybrid system, and this makes it possible to derive return maps for the motion between collisions in an exact form despite the fact that the three-halves interaction law cannot be solved in closed form. The return maps depend on a constant whose value can only be determined numerically, but solutions can be written down explicitly in terms of this parameter, and we compare this with the results of simulations. The results are in fact independent of the details of the interaction potential.

Middle School Science Notes.

ERIC Educational Resources Information Center

School Science Review, 1984

1984-01-01

Presents (1) suggestions on teaching volume and density in the elementary school; (2) ideas for teaching about floating and sinking; (3) a simple computer program on color addition; and (4) an illustration of Newton's second law of motion. (JN)

A Multipurpose Experiment with an Electronic Balance

ERIC Educational Resources Information Center

Ganci, S.

2008-01-01

This short article describes some useful and quick applications of a cooking electronic balance. Newton's third law, Archimedes buoyancy and an estimate of relative density are accomplished in a very simple way. (Contains 1 figure.)

Labs That Are a Blast.

ERIC Educational Resources Information Center

Hendrix, Laura

1996-01-01

Presents activities that use a simple homemade apparatus called "the cannon" to demonstrate Newton's Third Law. Reviews the chemistry concepts behind the ignition of the cannon and presents the Momentum Lab and the Projectile Motion Lab. (JRH)

From Fears of Entropy to Comfort in Chaos: "Arcadia," "The Waste Land," "Numb3rs," and Man's Relationship with Science

ERIC Educational Resources Information Center

Miller, Kristen

2007-01-01

Through the use of some purposeful anachronisms, Tom Stoppard uses his 1993 play "Arcadia" to explore the effects on man's psyche of the transition from Newton's Laws to the laws of thermodynamics and from thermodynamics to chaos theory. However, remarkably similar reactions to these changes are also reflected in works from the actual time periods…

The gravitational wave contribution to cosmic microwave background anisotropies and the amplitude of mass fluctuations from COBE results

NASA Technical Reports Server (NTRS)

Lucchin, Francesco; Matarrese, Sabino; Mollerach, Silvia

1992-01-01

A stochastic background of primordial gravitational waves may substantially contribute, via the Sachs-Wolfe effect, to the large-scale cosmic microwave background (CMB) anisotropies recently detected by COBE. This implies a bias in any resulting determination of the primordial amplitude of density fluctuations. We consider the constraints imposed on n is less than 1 ('tilted') power-law fluctuation spectra, taking into account the contribution from both scalar and tensor waves, as predicted by power-law inflation. The gravitational wave contribution to CMB anisotropies generally reduces the required rms level of mass fluctuation, thereby increasing the linear bias parameter, even in models where the spectral index is close to the Harrison-Zel'dovich value n = 1. This 'gravitational wave bias' helps to reconcile the predictions of CDM models with observations on pairwise galaxy velocity dispersion on small scales.

`Un-Darkening' the Cosmos: New laws of physics for an expanding universe

NASA Astrophysics Data System (ADS)

George, William

2017-11-01

Dark matter is believed to exist because Newton's Laws are inconsistent with the visible matter in galaxies. Dark energy is necessary to explain the universe expansion. (also available from www.turbulence-online.com) suggested that the equations themselves might be in error because they implicitly assume that time is measured in linear increments. This presentation couples the possible non-linearity of time with an expanding universe. Maxwell's equations for an expanding universe with constant speed of light are shown to be invariant only if time itself is non-linear. Both linear and exponential expansion rates are considered. A linearly expanding universe corresponds to logarithmic time, while exponential expansion corresponds to exponentially varying time. Revised Newton's laws using either leads to different definitions of mass and kinetic energy, both of which appear time-dependent if expressed in linear time. And provide the possibility of explaining the astronomical observations without either dark matter or dark energy. We would have never noticed the differences on earth, since the leading term in both expansions is linear in δ /to where to is the current age.

Similarity considerations and conservation laws for magneto-static atmospheres

NASA Technical Reports Server (NTRS)

Webb, G. M.

1986-01-01

The equations of magnetohydrostatic equilibria for a plasma in a gravitational field are investigated analytically. For equilibria with one ignorable spatial coordinate, the equations reduce to a single nonlinear elliptic equation for the magnetic potential. Similarity solutions of the elliptic equation are obtained for the case of an isothermal atmosphere in a uniform gravitational field. The solutions are obtained from a consideration of the invariance group of the elliptic equation. The importance of symmetries of the elliptic equation also appears in the determination of conservation laws. It turns out that the elliptic equation can be written as a variational principle, and the symmetries of the variational functional lead (via Noether's theorem) to conservation laws for the equation. As an example of the application of the similarity solutions, a model magnetostatic atmosphere is constructed in which the current density J is proportional to the cube of the magnetic potential, and falls off exponentially with distance vertical to the base, with an 'e-folding' distance equal to the gravitational scale height. The solutions show the interplay between the gravitational force, the J x B force (B, magnetic field induction) and the gas pressure gradient.

Another Look at Helmholtz's Model for the Gravitational Contraction of the Sun

ERIC Educational Resources Information Center

Tort, A. C.; Nogarol, F.

2011-01-01

We take another look at the Helmholtz model for the gravitational contraction of the Sun. We show that there are two other pedagogically useful ways of rederiving Helmholtz's main results that make use of Gauss's law, the concept of gravitational field energy and the work-kinetic energy theorem. An account of the energy balance involved in the…

Gravitational tension, spacetime pressure and black hole volume

NASA Astrophysics Data System (ADS)

Armas, Jay; Obers, Niels A.; Sanchioni, Marco

2016-09-01

We study the first law of black hole thermodynamics in the presence of surrounding gravitational fields and argue that variations of these fields are naturally incorporated in the first law by defining gravitational tension or gravitational binding energy. We demonstrate that this notion can also be applied in Anti-de Sitter spacetime, in which the surrounding gravitational field is sourced by a cosmological fluid, therefore showing that spacetime volume and gravitational tension encode the same physics as spacetime pressure and black hole volume. We furthermore show that it is possible to introduce a definition of spacetime pressure and black hole volume for any spacetime with characteristic length scales which does not necessarily require a cosmological constant sourcing Einstein equations. However, we show that black hole volume is non-universal in the flat spacetime limit, questioning its significance. We illustrate these ideas by studying the resulting black hole volume of Kaluza-Klein black holes and of a toy model for a black hole binary system in five spacetime dimensions (the black saturn solution) as well as of several novel perturbative black hole solutions. These include the higher-dimensional Kerr-Newman solution in Anti-de Sitter spacetime as well as other black holes in plane wave and Lifshitz spacetimes.

A Molecular Dynamics Simulation of the Turbulent Couette Minimal Flow Unit

NASA Astrophysics Data System (ADS)

Smith, Edward

2016-11-01

What happens to turbulent motions below the Kolmogorov length scale? In order to explore this question, a 300 million molecule Molecular Dynamics (MD) simulation is presented for the minimal Couette channel in which turbulence can be sustained. The regeneration cycle and turbulent statistics show excellent agreement to continuum based computational fluid dynamics (CFD) at Re=400. As MD requires only Newton's laws and a form of inter-molecular potential, it captures a much greater range of phenomena without requiring the assumptions of Newton's law of viscosity, thermodynamic equilibrium, fluid isotropy or the limitation of grid resolution. The fundamental nature of MD means it is uniquely placed to explore the nature of turbulent transport. A number of unique insights from MD are presented, including energy budgets, sub-grid turbulent energy spectra, probability density functions, Lagrangian statistics and fluid wall interactions. EPSRC Post Doctoral Prize Fellowship.

TEACHING PHYSICS: A computer-based revitalization of Atwood's machine

NASA Astrophysics Data System (ADS)

Trumper, Ricardo; Gelbman, Moshe

2000-09-01

Atwood's machine is used in a microcomputer-based experiment to demonstrate Newton's second law with considerable precision. The friction force on the masses and the moment of inertia of the pulley can also be estimated.

Experimentally Building a Qualitative Understanding of Newton's Second Law

NASA Astrophysics Data System (ADS)

Gates, Joshua

2014-12-01

Newton's second law is one of the cornerstones of the introductory physics curriculum, but it can still trouble a large number of students well after its introduction, hobbling their ability to apply the concept to problem solving1 and to related concepts, such as momentum, circular motion, and orbits. While there are several possibilities for lab activities addressing the functional relationship among net force, mass, and acceleration, the qualitative understanding of the connection between forces and acceleration can still be lacking,2 leading to poor performance in problem solving and in assessments such as the Force Concept Inventory3 and Force and Motion Conceptual Evaluation.4 There is a need for strong conceptual understanding of the relationships between net force and acceleration and between acceleration and velocity in order to effectively address common force-motion misconceptions;5 there is a large literature concerning student understanding of force and motion.6

Courseware Review.

ERIC Educational Resources Information Center

Risley, John S.

1984-01-01

Evaluates two computer programs for Apple II which provide drill and practice in Newton's laws of motion and in work-energy relationships. Student performance is recorded on the diskette allowing the teacher to view the number of questions completed and percentage correct. (JM)

Forensic Physics 101: Falls from a height

NASA Astrophysics Data System (ADS)

Cross, Rod

2008-09-01

The physics of falling from a height, a topic that could be included in a course on forensic physics or in an undergraduate class as an example of Newton's laws, is applied to a common forensic problem.

Equations of motion for train derailment dynamics

DOT National Transportation Integrated Search

2007-09-11

This paper describes a planar or two-dimensional model to : examine the gross motions of rail cars in a generalized train : derailment. Three coupled, second-order differential equations : are derived from Newton's Laws to calculate rigid-body car : ...

Reviews Book: George's Cosmic Treasure Hunt Book: 50 Physics Ideas You Really Need to Know Book: Head First Physics Book: Force and Motion—An illustrated Guide to Newton's Laws Book: Froth! The Science of Beer Equipment: SEP Charge Indicator Book: How Mathematics Happened—The First 50,000 Years Web Watch

NASA Astrophysics Data System (ADS)

2009-11-01

WE RECOMMEND George's Cosmic Treasure Hunt Another science-based kids' adventure from the Hawkings 50 Physics Ideas You Really Need to Know Brief, accessible descriptions of some complex physics Head First Physics Mechanics-focused non-traditional textbook Force and Motion—An illustrated Guide to Newton's Laws An original text aimed at students Froth! The Science of Beer A tongue-in-cheek physics-heavy guide to brewery science SEP Charge Indicator Classroom equipment that is affordable, usable and works How Mathematics Happened—The First 50,000 Years An enjoyable read suitable for student or teacher WEB WATCH Simulators can be useful teaching aids, as long as you remain aware of their flaws

Efficiency and its bounds for thermal engines at maximum power using Newton's law of cooling.

PubMed

Yan, H; Guo, Hao

2012-01-01

We study a thermal engine model for which Newton's cooling law is obeyed during heat transfer processes. The thermal efficiency and its bounds at maximum output power are derived and discussed. This model, though quite simple, can be applied not only to Carnot engines but also to four other types of engines. For the long thermal contact time limit, new bounds, tighter than what were known before, are obtained. In this case, this model can simulate Otto, Joule-Brayton, Diesel, and Atkinson engines. While in the short contact time limit, which corresponds to the Carnot cycle, the same efficiency bounds as that from Esposito et al. [Phys. Rev. Lett. 105, 150603 (2010)] are derived. In both cases, the thermal efficiency decreases as the ratio between the heat capacities of the working medium during heating and cooling stages increases. This might provide instructions for designing real engines. © 2012 American Physical Society

Quantum corrections to the gravitational potentials of a point source due to conformal fields in de Sitter

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fröb, Markus B.; Verdaguer, Enric, E-mail: mfroeb@itp.uni-leipzig.de, E-mail: enric.verdaguer@ub.edu

We derive the leading quantum corrections to the gravitational potentials in a de Sitter background, due to the vacuum polarization from loops of conformal fields. Our results are valid for arbitrary conformal theories, even strongly interacting ones, and are expressed using the coefficients b and b' appearing in the trace anomaly. Apart from the de Sitter generalization of the known flat-space results, we find two additional contributions: one which depends on the finite coefficients of terms quadratic in the curvature appearing in the renormalized effective action, and one which grows logarithmically with physical distance. While the first contribution corresponds tomore » a rescaling of the effective mass, the second contribution leads to a faster fall-off of the Newton potential at large distances, and is potentially measurable.« less

The 1.5 Ms observing campaign on IRAS 13224-3809 - I. X-ray spectral analysis

NASA Astrophysics Data System (ADS)

Jiang, J.; Parker, M. L.; Fabian, A. C.; Alston, W. N.; Buisson, D. J. K.; Cackett, E. M.; Chiang, C.-Y.; Dauser, T.; Gallo, L. C.; García, J. A.; Harrison, F. A.; Lohfink, A. M.; De Marco, B.; Kara, E.; Miller, J. M.; Miniutti, G.; Pinto, C.; Walton, D. J.; Wilkins, D. R.

2018-07-01

We present a detailed spectral analysis of the recent 1.5 Ms XMM-Newton observing campaign on the narrow-line Seyfert 1 galaxy IRAS 13224-3809, taken simultaneously with 500 ks of NuSTAR data. The X-ray light curve shows three flux peaks, registering at about 100 times the minimum flux seen during the campaign, and rapid variability with a time-scale of kiloseconds. The spectra are well fit with a primary power-law continuum, two relativistic-blurred reflection components from the inner accretion disc with very high iron abundance, and a simple blackbody-shaped model for the remaining soft excess. The spectral variability is dominated by the power-law continuum from a corona region within a few gravitational radii from the black hole. Additionally, blueshifted Ne X, Mg XII, Si XIV, and S XVI absorption lines are identified in the stacked low-flux spectrum, confirming the presence of a highly ionized outflow with velocity up to v = 0.267 and 0.225 c. We fit the absorption features with xstar models and find a relatively constant velocity outflow through the whole observation. Finally, we replace the bbody and supersolar abundance reflection models by fitting the soft excess successfully with the extended reflection model relxillD, which allows for higher densities than the standard relxill model. This returns a disc electron density ne > 1018.7 cm-3 and lowers the iron abundance from Z_Fe = 24^{+3}_{-4} Z_{⊙} with ne ≡ 1015 cm-3 to Z_Fe = 6.6^{+0.8}_{-2.1} Z_{⊙}.

Relativistic Transverse Gravitational Redshift

NASA Astrophysics Data System (ADS)

Mayer, A. F.

2012-12-01

The parametrized post-Newtonian (PPN) formalism is a tool for quantitative analysis of the weak gravitational field based on the field equations of general relativity. This formalism and its ten parameters provide the practical theoretical foundation for the evaluation of empirical data produced by space-based missions designed to map and better understand the gravitational field (e.g., GRAIL, GRACE, GOCE). Accordingly, mission data is interpreted in the context of the canonical PPN formalism; unexpected, anomalous data are explained as similarly unexpected but apparently real physical phenomena, which may be characterized as ``gravitational anomalies," or by various sources contributing to the total error budget. Another possibility, which is typically not considered, is a small modeling error in canonical general relativity. The concept of the idealized point-mass spherical equipotential surface, which originates with Newton's law of gravity, is preserved in Einstein's synthesis of special relativity with accelerated reference frames in the form of the field equations. It was not previously realized that the fundamental principles of relativity invalidate this concept and with it the idea that the gravitational field is conservative (i.e., zero net work is done on any closed path). The ideal radial free fall of a material body from arbitrarily-large range to a point on such an equipotential surface (S) determines a unique escape-velocity vector of magnitude v collinear to the acceleration vector of magnitude g at this point. For two such points on S separated by angle dφ , the Equivalence Principle implies distinct reference frames experiencing inertial acceleration of identical magnitude g in different directions in space. The complete equivalence of these inertially-accelerated frames to their analogous frames at rest on S requires evaluation at instantaneous velocity v relative to a local inertial observer. Because these velocity vectors are not parallel, a symmetric energy potential exists between the frames that is quantified by the instantaneous Δ {v} = v\\cdot{d}φ between them; in order for either frame to become indistinguishable from the other, such that their respective velocity and acceleration vectors are parallel, a change in velocity is required. While the qualitative features of general relativity imply this phenomenon (i.e., a symmetric potential difference between two points on a Newtonian `equipotential surface' that is similar to a friction effect), it is not predicted by the field equations due to a modeling error concerning time. This is an error of omission; time has fundamental geometric properties implied by the principles of relativity that are not reflected in the field equations. Where b is the radius and g is the gravitational acceleration characterizing a spherical geoid S of an ideal point-source gravitational field, an elegant derivation that rests on first principles shows that for two points at rest on S separated by a distance d << b, a symmetric relativistic redshift exists between these points of magnitude z = gd2/bc^2, which over 1 km at Earth sea level yields z ˜{10-17}. It can be tested with a variety of methods, in particular laser interferometry. A more sophisticated derivation yields a considerably more complex predictive formula for any two points in a gravitational field.

A Newton method for the magnetohydrodynamic equilibrium equations

NASA Astrophysics Data System (ADS)

Oliver, Hilary James

We have developed and implemented a (J, B) space Newton method to solve the full nonlinear three dimensional magnetohydrodynamic equilibrium equations in toroidal geometry. Various cases have been run successfully, demonstrating significant improvement over Picard iteration, including a 3D stellarator equilibrium at β = 2%. The algorithm first solves the equilibrium force balance equation for the current density J, given a guess for the magnetic field B. This step is taken from the Picard-iterative PIES 3D equilibrium code. Next, we apply Newton's method to Ampere's Law by expansion of the functional J(B), which is defined by the first step. An analytic calculation in magnetic coordinates, of how the Pfirsch-Schlüter currents vary in the plasma in response to a small change in the magnetic field, yields the Newton gradient term (analogous to ∇f . δx in Newton's method for f(x) = 0). The algorithm is computationally feasible because we do this analytically, and because the gradient term is flux surface local when expressed in terms of a vector potential in an Ar=0 gauge. The equations are discretized by a hybrid spectral/offset grid finite difference technique, and leading order radial dependence is factored from Fourier coefficients to improve finite- difference accuracy near the polar-like origin. After calculating the Newton gradient term we transfer the equation from the magnetic grid to a fixed background grid, which greatly improves the code's performance.

A Tilted Plane as a Gravitational Field Model.

ERIC Educational Resources Information Center

Hale, D. P.

1980-01-01

Describes an experiment for the use of a tilted plane as a two-dimensional uniform gravitational field to demonstrate the motion of projectiles, to determine the fundamental laws of mechanics, or to study the focusing properties of the uniform field. (SK)

Complex Teichmüller Space below the Planck Length for the Interpretation of Quantum Mechanics

NASA Astrophysics Data System (ADS)

Winterberg, Friedwardt

2014-03-01

As Newton's mysterious action at a distance law of gravity was explained as a Riemannian geometry by Einstein, it is proposed that the likewise mysterious non-local quantum mechanics is explained by the analytic continuation below the Planck length into a complex Teichmüller space. Newton's theory worked extremely well, as does quantum mechanics, but no satisfactory explanation has been given for quantum mechanics. In one space dimension, sufficient to explain the EPR paradox, the Teichmüller space is reduced to a space of complex Riemann surfaces. Einstein's curved space-time theory of gravity was confirmed by a tiny departure from Newton's theory in the motion of the planet Mercury, and an experiment is proposed to demonstrate the possible existence of a Teichmüller space below the Planck length.

Newton's Principia: Myth and Reality

NASA Astrophysics Data System (ADS)

Smith, George

2016-03-01

Myths about Newton's Principia abound. Some of them, such as the myth that the whole book was initially developed using the calculus and then transformed into a geometric mathematics, stem from remarks he made during the priority controversy with Leibniz over the calculus. Some of the most persistent, and misleading, arose from failures to read the book with care. Among the latter are the myth that he devised his theory of gravity in order to explain the already established ``laws'' of Kepler, and that in doing so he took himself to be establishing that Keplerian motion is ``absolute,'' if not with respect to ``absolute space,'' then at least with respect to the fixed stars taken as what came later to be known as an inertial frame. The talk will replace these two myths with the reality of what Newton took himself to have established.

Hematology: ATG and Newton's third law of motion.

PubMed

Brunstein, Claudio G

2010-01-01

Patients with hematological malignancies have a risk of developing graft-versus-host disease (GVHD) following allogeneic hematopoietic stem-cell transplantation. The addition of ATG to prophylaxis regimens decreases the incidence of GVHD without compromising overall survival in these patients.

Dipole Relaxation in an Electric Field.

ERIC Educational Resources Information Center

Neumann, Richard M.

1980-01-01

Derives an expression for the orientational entropy of a rigid rod (electric dipole) from Boltzmann's equation. Subsequent application of Newton's second law of motion produces Debye's classical expression for the relaxation of an electric dipole in a viscous medium. (Author/GS)

Numerical computation of gravitational field of general extended body and its application to rotation curve study of galaxies

NASA Astrophysics Data System (ADS)

Fukushima, Toshio

2017-06-01

Reviewed are recently developed methods of the numerical integration of the gravitational field of general two- or three-dimensional bodies with arbitrary shape and mass density distribution: (i) an axisymmetric infinitely-thin disc (Fukushima 2016a, MNRAS, 456, 3702), (ii) a general infinitely-thin plate (Fukushima 2016b, MNRAS, 459, 3825), (iii) a plane-symmetric and axisymmetric ring-like object (Fukushima 2016c, AJ, 152, 35), (iv) an axisymmetric thick disc (Fukushima 2016d, MNRAS, 462, 2138), and (v) a general three-dimensional body (Fukushima 2016e, MNRAS, 463, 1500). The key techniques employed are (a) the split quadrature method using the double exponential rule (Takahashi and Mori, 1973, Numer. Math., 21, 206), (b) the precise and fast computation of complete elliptic integrals (Fukushima 2015, J. Comp. Appl. Math., 282, 71), (c) Ridder's algorithm of numerical differentiaion (Ridder 1982, Adv. Eng. Softw., 4, 75), (d) the recursive computation of the zonal toroidal harmonics, and (e) the integration variable transformation to the local spherical polar coordinates. These devices succesfully regularize the Newton kernel in the integrands so as to provide accurate integral values. For example, the general 3D potential is regularly integrated as Φ (\\vec{x}) = - G \\int_0^∞ ( \\int_{-1}^1 ( \\int_0^{2π} ρ (\\vec{x}+\\vec{q}) dψ ) dγ ) q dq, where \\vec{q} = q (√{1-γ^2} cos ψ, √{1-γ^2} sin ψ, γ), is the relative position vector referred to \\vec{x}, the position vector at which the potential is evaluated. As a result, the new methods can compute the potential and acceleration vector very accurately. In fact, the axisymmetric integration reproduces the Miyamoto-Nagai potential with 14 correct digits. The developed methods are applied to the gravitational field study of galaxies and protoplanetary discs. Among them, the investigation on the rotation curve of M33 supports a disc-like structure of the dark matter with a double-power-law surface mass density distribution. Fortran 90 subroutines to execute these methods and their test programs and sample outputs are available from the author's WEB site: https://www.researchgate.net/profile/Toshio_Fukushima/

Accurate physical laws can permit new standard units: The two laws F→=ma→ and the proportionality of weight to mass

NASA Astrophysics Data System (ADS)

Saslow, Wayne M.

2014-04-01

Three common approaches to F→=ma→ are: (1) as an exactly true definition of force F→ in terms of measured inertial mass m and measured acceleration a→; (2) as an exactly true axiom relating measured values of a→, F→ and m; and (3) as an imperfect but accurately true physical law relating measured a→ to measured F→, with m an experimentally determined, matter-dependent constant, in the spirit of the resistance R in Ohm's law. In the third case, the natural units are those of a→ and F→, where a→ is normally specified using distance and time as standard units, and F→ from a spring scale as a standard unit; thus mass units are derived from force, distance, and time units such as newtons, meters, and seconds. The present work develops the third approach when one includes a second physical law (again, imperfect but accurate)—that balance-scale weight W is proportional to m—and the fact that balance-scale measurements of relative weight are more accurate than those of absolute force. When distance and time also are more accurately measurable than absolute force, this second physical law permits a shift to standards of mass, distance, and time units, such as kilograms, meters, and seconds, with the unit of force—the newton—a derived unit. However, were force and distance more accurately measurable than time (e.g., time measured with an hourglass), this second physical law would permit a shift to standards of force, mass, and distance units such as newtons, kilograms, and meters, with the unit of time—the second—a derived unit. Therefore, the choice of the most accurate standard units depends both on what is most accurately measurable and on the accuracy of physical law.

Antikythera Calculator advances modern science of 19 centuries

NASA Astrophysics Data System (ADS)

Pastore, Giovanni

2010-08-01

The Greek astronomic calculator, discovered in the depth of the sea in a naval wreckage of the 1st century B.C. in front of the island of Antikythera, is the most amazing among the archaeological discoveries of last century. The mechanism immediately appeared like a device out of its time. After years of study this devise is still provoking a discussion between scientists and archaeologists because of the complexity and the modernity of the scientific knowledge the work presupposes. Its epicyclical gearings show the high level of the scientific culture reached in that period of history. The knowledge of the planetary motion, necessary to the design of the epicyclic gearing of the Calculator of Antikythera, presumes that ancient Greek scientists knew the planetary motion of the celestial bodies and had already achieved the same results that have been attributed to scientists 19 centuries later. The scientific value of this gear mechanism is indisputable because the inventor of the Calculator of Antikythera had the knowledge that was "re-discovered" centuries later as the heliocentric theory proposed by Niccolò Copernicus in 1543 ( De revolutionibus orbium coelestium), the universal gravitation law formulated by Isaac Newton in 1687 ( Philosophiae Naturalis Principia Mathematica), and the kinematic study of the epicyclical gearings published by Robert Willis in 1841 ( Principles of mechanism).

The Influence of Planetary Mass on the Dynamical Lifetime of Planetary Systems

NASA Technical Reports Server (NTRS)

Lissauer, J. J.; Duncan, M. J.; Young, Richard E. (Technical Monitor)

1997-01-01

Recent numerical and analytic studies of planetary orbits have demonstrated the importance of resonances and chaos in destabilizing planetary systems. Newton's "clockwork" description of regular, predictable planetary orbits has been replaced by a view in which many systems can have long but finite lifetimes. This new knowledge has altered our perceptions of the later stages of planetary growth and of the stability of planetary systems. Stability criteria are inexact and time dependent. Most previous studies have focused on the effects in initial planetary orbits on the stability of the system. We are conducting an investigation which focuses on the dependence of stability criteria on planetary mass. Synthetic systems are created by increasing the masses of the planets in our Solar System or of the moons of a particular planet; these systems are then integrated until orbit crossing occurs. We have found that over some ranges, the time until orbit crossing varies to a good approximation as a power clothe factor by which the masses of the secondaries arc increased; some scatter occurs as a consequence of vie chaotic nature of orbital evolution. The slope of this power law varies substantially from system to system, and for moons it is mildly dependent on the inclusion of the planet's quadrupole moment in the gravitational potential.

In praise of imperfection

NASA Astrophysics Data System (ADS)

White, Gary D.

2014-01-01

"I would never teach the Bohr model!" he exclaimed. "I don't believe in teaching things that are just wrong." He was a respected teacher, and I knew I should listen to what he had to say, but in the end I wasn't convinced that his view was right for me and my classes. In fact, I do believe in teaching things that are "just wrong"—selectively. For example, I like my introductory physics students to learn the planetary model of Hydrogen, and not only so that we can discuss why it is deficient. It's a great opportunity to "spiral back" to Newton's second law, circular motion, conservation of energy, and the origin of electromagnetic radiation—and it does get the ionization energy right if you assume an empirically determined radius for the atom! In addition, knowing specifically when, why, and how a model is wrong is one of the hallmarks that distinguishes science from other endeavors. Furthermore, one might argue that there really are no perfect models (models that successfully incorporate gravitational and quantum effects in one philosophically cohesive whole, for example), so every model is "just wrong" in some sense. Finally, even if there was a "perfect" model of the atom to teach, it does not follow that good pedagogy involves teaching it. Let me explain.

A cluster in a crowded environment: XMM-Newton and Chandra observations of A3558

NASA Astrophysics Data System (ADS)

Rossetti, M.; Ghizzardi, S.; Molendi, S.; Finoguenov, A.

2007-03-01

Combining XMM-Newton and Chandra data, we have performed a detailed study of Abell 3558. Our analysis shows that its dynamical history is more complicated than previously thought. We have found some traits typical of cool core clusters (surface brightness peaked at the center, peaked metal abundance profile) and others that are more common in merging clusters, like deviations from spherical symmetry in the thermodynamic quantities of the ICM. This last result has been achieved with a new technique for deriving temperature maps from images. We have also detected a cold front and, with the combined use of XMM-Newton and Chandra, we have characterized its properties, such as the speed and the metal abundance profile across the edge. This cold front is probably due to the sloshing of the core, induced by the perturbation of the gravitational potential associated with a past merger. The hydrodynamic processes related to this perturbation have presumably produced a tail of lower entropy, higher pressure and metal rich ICM, which extends behind the cold front for~500 kpc. The unique characteristics of A3558 are probably due to the very peculiar environment in which it is located: the core of the Shapley supercluster. Appendices A and B are only available in electronic form at http://www.aanda.org

Questions Students Ask: How Can a Downhill Skier Move Faster than a Sky Diver?

ERIC Educational Resources Information Center

Armenti, Angelo, Jr.

1984-01-01

Discusses the relationship of gravity, coefficient of friction, surface area, and Newton's second law to explain the physics involved in downhill skiers being able to move faster than sky divers in free fall. (JM)

Sci-Fi Science.

ERIC Educational Resources Information Center

Freudenrich, Craig C.

2000-01-01

Recommends using science fiction television episodes, novels, and films for teaching science and motivating students. Studies Newton's Law of Motion, principles of relativity, journey to Mars, interplanetary trajectories, artificial gravity, and Martian geology. Discusses science fiction's ability to capture student interest and the advantages of…

The Conveyor Belt Problem and Newton's Third Law.

ERIC Educational Resources Information Center

Stewart, Maurice Bruce

1989-01-01

Shows how the thermal power developed by friction is exactly half the supplied power in the general case of a variable force of friction. Investigates the mechanism whereby one-half the input energy is dissipated as heat using mathematical expressions. (YP)

An Alternative Way to Achieve Kepler's Laws of Equal Areas and Ellipses for the Earth

ERIC Educational Resources Information Center

Hsiang, W. Y.; Chang, H. C.; Yao, H.; Chen, P. J.

2011-01-01

Kepler's laws of planetary motion are acknowledged as highly significant to the construction of universal gravitation. This paper demonstrates different ways to derive the law of equal areas for the Earth by general geometrical and trigonometric methods, which are much simpler than the original derivation depicted by Kepler. The established law of…

Laser Interferometry for Gravitational Wave Observation: LISA and LISA Pathfinder

NASA Technical Reports Server (NTRS)

Guzman, Felipe

2010-01-01

The Laser Interferometer Space Antenna (LISA) is a planned NASA-ESA gravitational wave observatory in the frequency range of 0.1mHz-100mHz. This observation band is inaccessible to ground-based detectors due to the large ground motions of the Earth. Gravitational wave sources for LISA include galactic binaries, mergers of supermasive black-hole binaries, extreme-mass-ratio inspirals, and possibly from as yet unimagined sources. LISA is a constellation of three spacecraft separated by 5 million km in an equilateral triangle, whose center follows the Earth in a heliocentric orbit with an orbital phase offset oF 20 degrees. Challenging technology is required to ensure pure geodetic trajectories of the six onboard test masses, whose distance fluctuations will be measured by interspacecraft laser interferometers with picometer accuracy. LISA Pathfinder is an ESA-launched technology demonstration mission of key LISA subsystems such us spacecraft control with micro-newton thrusters, test mass drag-free control, and precision laser interferometry between free-flying test masses. Ground testing of flight hardware of the Gravitational Reference Sensor and Optical Metrology subsystems of LISA Pathfinder is currently ongoing. An introduction to laser interferometric gravitational wave detection, ground-based observatories, and a detailed description of the two missions together with an overview of current investigations conducted by the community will bc discussed. The current status in development and implementation of LISA Pathfinder pre-flight systems and latest results of the ongoing ground testing efforts will also be presented

Project Physics Handbook 1, Concepts of Motion.

ERIC Educational Resources Information Center

Harvard Univ., Cambridge, MA. Harvard Project Physics.

Thirteen experiments and 15 activities are presented in this unit handbook for student use. The experiment sections are concerned with naked-eye observation in astronomy, regularity and time, variations in data, uniform motion, gravitational acceleration, Galileo's experiments, Netson's laws, inertial and gravitational mass, trajectories, and…

A new detection of an UFO in the X-ray spectrum of a lensed QSO

NASA Astrophysics Data System (ADS)

Dadina, M.

2017-10-01

The discovery of the "M_{SMBH}-σ relation" indicated that a connection between the central black-hole and the hosting galaxies acted during the cosmic time. With the discovery in X-rays of the ultra-fast outflows in nearby AGN, we have most probably probed one of the ingredients that are needed to build-up this mechanism. At high-z, however, such measurements were possible only in an handful of objects and this was possible mainly for the presence of gravitational lenses that magnified otherwise X-ray weak QSO. Following this, we proposed a program to use XMM-Newton and gravitational lenses as telescopes to point bright, lensed and distant QSO to characterize in detail their X-ray spectrum and to detect blushifted absorption lines at E˜7-10 keV (rest frame). Here we present the preliminary results obtained for the z=2.64 QSO MG J0414+0534.

The Soft-X-Ray Emission of Ark 120. XMM-Newton, NuSTAR, and the Importance of Taking the Broad View

NASA Technical Reports Server (NTRS)

Matt, G.; Marinucci, A.; Guainazzi, M.; Brenneman, L. W.; Elvis, M.; Lohfink, A.; Arevalo, P.; Boggs, S. E.; Cappi, M.; Stern, D.;

General relativity with small cosmological constant from spontaneous compactification of Lovelock theory in vacuum

DOE Office of Scientific and Technical Information (OSTI.GOV)

Canfora, Fabrizio; Willison, Steven; Giacomini, Alex

2009-08-15

It is shown that Einstein gravity in four dimensions with small cosmological constant and small extra dimensions can be obtained by spontaneous compactification of Lovelock gravity in vacuum. Assuming that the extra dimensions are compact spaces of constant curvature, general relativity is recovered within a certain class of Lovelock theories possessing necessarily cubic or higher order terms in curvature. This bounds the higher dimension to at least 7. Remarkably, the effective gauge coupling and Newton constant in four dimensions are not proportional to the gravitational constant in higher dimensions, but are shifted with respect to their standard values. This effectmore » opens up new scenarios where a maximally symmetric solution in higher dimensions could decay into the compactified spacetime either by tunneling or through a gravitational analog of ghost condensation. Indeed, this is what occurs requiring both the extra dimensions and the four-dimensional cosmological constant to be small.« less

Pendulums, Pedagogy, and Matter: Lessons from the Editing of Newton's Principia

NASA Astrophysics Data System (ADS)

Biener, Zvi; Smeenk, Chris

Teaching Newtonian physics involves the replacement of students'' ideas about physical situations with precise concepts appropriate for mathematical applications. This paper focuses on the concepts of `matter'' and `mass''. We suggest that students, like some pre-Newtonian scientists we examine, use these terms in a way that conflicts with their Newtonian meaning. Specifically, `matter''and `mass'' indicate to them the sorts of things that are tangible,bulky, and take up space. In Newtonian mechanics, however, the terms are defined by Newton's Second Law: `mass'' is simply a measure of the acceleration generated by an impressed force. We examine the relationship between these conceptions as it was discussed by Newton and his editor, Roger Cotes, when analyzing a series of pendulum experiments. We suggest that these experiments, as well as more sophisticated computer simulations, can be used in the classroom to sufficiently differentiate the colloquial and precise meaning of these terms.

X-ray Luminosity and Absorption Column Fluctuations in the H2O Maser Galaxy NGC 4258 from Weeks to Years

DOE Office of Scientific and Technical Information (OSTI.GOV)

Argon, A.

2004-07-30

The authors report monitoring of the 0.3-10 keV spectrum of NGC 4258 with the XMM-Newton observatory at five epochs over 1.5 years. They also report reprocessing of an overlapping four epoch series of archival Chandra observations (0.5-10 keV). By including earlier ASCA and Beppo-SAX observations, they present a new, nine year time-series of models fit to the X-ray spectrum of NGC 4258. They model the Chandra and XMM-Newton data self-consistently with partially absorbed, hard power-law, soft thermal plasma, and soft power-law components. Over the nine years, the photo-electric absorbing column ({approx} 10{sup 23} cm{sup -2}) did not vary detectably, exceptmore » for a {approx} 40% drop between two ASCA epochs separated by 3 years (in 1993 and 1996) and a {approx} 60% rise between two XMM-Newton epochs separated by just 5 months (in 2001 and 2002). In contrast, factor of 2-3 changes are seen in absorbed flux on the timescale of years. These are uncorrelated with changes in absorbing column and indicative of central engine variability. The most rapid change in luminosity (5-10 keV) that the authors detect (with XMM-Newton and Chandra) is on the order of 30% over 19 days. The warped disk that is a known source of H{sub 2}O maser emission in NGC 4258 is believed to cross the line of sight to the central engine. They propose that the variations in absorbing column arise from inhomogeneities in the rotating disk, as they sweep across the line of sight. They estimate that the inhomogeneities are {approx} 10{sup 15} cm in size.« less

Animation, Incidental Learning, and Continuing Motivation.

ERIC Educational Resources Information Center

Rieber, Lloyd P.

1991-01-01

Effects of animated graphics presentations on incidental learning and the degree to which various computer practice activities contain intrinsically motivating characteristics were studied with 70 fourth graders learning about Newton's laws of motion. Incidental learning occurred without sacrifice of intentional learning. Students were highly…

Use of Force Platforms in Physics and Sport.

ERIC Educational Resources Information Center

Parker, Kerry

2001-01-01

The subject of biomechanics is growing as athletes turn to science to improve their performance, and biomechanics interests many students and is a good area in which to investigate forces and Newton's laws. Uses force platforms to quantify such studies. (Author/ASK)

Two Experimental Approaches of Looking at Buoyancy

ERIC Educational Resources Information Center

Moreira, J. Agostinho; Almeida, A.; Carvalho, P. Simeao

2013-01-01

In our teaching practice, we find that a large number of first-year university physics and chemistry students exhibit some difficulties with applying Newton's third law to fluids because they think fluids do not react to forces. (Contains 1 table and 3 figures.)

Levitating soliton of the Bose–Einstein condensate

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vysotina, N. V.; Rosanov, N. N., E-mail: nnrosanov@mail.ru

We have proposed a mechanical model that corresponds to the Newton equation for describing the dynamics of an oscillon, viz., a soliton-like cluster of the Bose–Einstein condensate (with atomic attraction) placed above an oscillating atomic mirror in a uniform gravitational field. The model describes the stochastic Fermi acceleration and periodic, quasi-periodic, and chaotic motion of the oscillon center, as well as hysteresis phenomena in the case of a slow variation of mirror oscillation frequency, which are in good agreement with the results obtained using the Gross–Pitaevskii equation.

Bernoulli's Principle

ERIC Educational Resources Information Center

Hewitt, Paul G.

2004-01-01

Some teachers have difficulty understanding Bernoulli's principle particularly when the principle is applied to the aerodynamic lift. Some teachers favor using Newton's laws instead of Bernoulli's principle to explain the physics behind lift. Some also consider Bernoulli's principle too difficult to explain to students and avoid teaching it…

Novel Third-Law Demonstration.

ERIC Educational Resources Information Center

Lonc, William

1995-01-01

Presents an easy method to demonstrate Third-Law interactions using identical button magnets sliding along a smooth (nonmagnetic) knitting needle. Explains the gravitational and magnetic interactions in the case of horizontal and vertical positions of the needle. (JRH)

Median statistics estimates of Hubble and Newton's constants

NASA Astrophysics Data System (ADS)

Bethapudi, Suryarao; Desai, Shantanu

2017-02-01

Robustness of any statistics depends upon the number of assumptions it makes about the measured data. We point out the advantages of median statistics using toy numerical experiments and demonstrate its robustness, when the number of assumptions we can make about the data are limited. We then apply the median statistics technique to obtain estimates of two constants of nature, Hubble constant (H0) and Newton's gravitational constant ( G , both of which show significant differences between different measurements. For H0, we update the analyses done by Chen and Ratra (2011) and Gott et al. (2001) using 576 measurements. We find after grouping the different results according to their primary type of measurement, the median estimates are given by H0 = 72.5^{+2.5}_{-8} km/sec/Mpc with errors corresponding to 95% c.l. (2 σ) and G=6.674702^{+0.0014}_{-0.0009} × 10^{-11} Nm2kg-2 corresponding to 68% c.l. (1σ).

Rowlands' Duality Principle: A Generalization of Noether's Theorem?

NASA Astrophysics Data System (ADS)

Karam, Sabah E.

This paper will examine a physical principle that has been used in making valid predictions and generalizes established conservation laws. In a previous paper it was shown how Rowlands' zero-totality condition could be viewed as a generalization of Newton's third law of motion. In this paper it will be argued that Rowlands' Duality Principle is a generalization of Noether's Theorem and that the two principles taken together are truly foundational principles that have tamed Metaphysics.

Advanced nursing practice and Newton's three laws of motion.

PubMed

Sturgeon, David

This article considers the reasons for the development of advanced practice roles among nurses and other healthcare professions. It explores the implications of financial constraints, consumer preferences and the development of new healthcare services on the reorganization of professional boundaries. It makes use of Sir Isaac Newton's three laws of motion to demonstrate how professional development in nursing has taken place in response to a number of external influences and demands. It also considers the significance of skill mix for the nursing profession, in particular the development and likely expansion of the physician assistant role. The application of different professionals and grades within a healthcare team or organization is central to the Government's Agenda for Change proposals and nurses have successfully adopted a number of roles traditionally performed by doctors. Nurses have demonstrated that they are capable of providing high quality care and contributing directly to positive patient outcome. Advanced nursing roles should not only reflect the changing nature of healthcare work, they should also be actively engaged in reconstructing healthcare boundaries.

Physics of Non-Inertial Reference Frames

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kamalov, Timur F.

2010-12-22

Physics of non-inertial reference frames is a generalizing of Newton's laws to any reference frames. It is the system of general axioms for classical and quantum mechanics. The first, Kinematics Principle reads: the kinematic state of a body free of forces conserves and equal in absolute value to an invariant of the observer's reference frame. The second, Dynamics Principle extended Newton's second law to non-inertial reference frames and also contains additional variables there are higher derivatives of coordinates. Dynamics Principle reads: a force induces a change in the kinematic state of the body and is proportional to the rate ofmore » its change. It is mean that if the kinematic invariant of the reference frame is n-th derivative with respect the time, then the dynamics of a body being affected by the force F is described by the 2n-th differential equation. The third, Statics Principle reads: the sum of all forces acting a body at rest is equal to zero.« less

A DEEP CHANDRA OBSERVATION OF THE WOLF-RAYET + BLACK HOLE BINARY NGC 300 X-1

DOE Office of Scientific and Technical Information (OSTI.GOV)

Binder, B.; Williams, B. F.; Anderson, S. F.

We have obtained a 63 ks Chandra ACIS-I observation of the Wolf-Rayet + black hole binary NGC 300 X-1. We measure rapid low-amplitude variability in the 0.35-8 keV light curve. The power density spectrum has a power-law index {gamma} = 1.02 {+-} 0.15 consistent with an accreting black hole in a steep power-law state. When compared to previous studies of NGC 300 X-1 performed with XMM-Newton, we find the source at the low end of the previously measured 0.3-10 keV luminosity. The spectrum of NGC 300 X-1 is dominated by a power law ({Gamma} = 2.0 {+-} 0.3) with amore » contribution at low energies by a thermal component. We estimate the 0.3-10 keV luminosity to be 2.6{sup +0.8}{sub -1.0} Multiplication-Sign 10{sup 38} erg s{sup -1}. The timing and spectroscopic properties of NGC 300 X-1 are consistent with being in a steep power-law state, similar to earlier observations performed with XMM-Newton. We additionally compare our observations to known high-mass X-ray binaries and ultraluminous X-ray sources, and find the properties of NGC 300 X-1 are most consistent with black hole high-mass X-ray binaries.« less

Water Rockets and Indirect Measurement.

ERIC Educational Resources Information Center

Inman, Duane

1997-01-01

Describes an activity that teaches a number of scientific concepts including indirect measurement, Newton's third law of motion, manipulating and controlling variables, and the scientific method of inquiry. Uses process skills such as observation, inference, prediction, mensuration, and communication as well as problem solving and higher-order…

Real-time Adaptive Control Using Neural Generalized Predictive Control

NASA Technical Reports Server (NTRS)

Haley, Pam; Soloway, Don; Gold, Brian

1999-01-01

The objective of this paper is to demonstrate the feasibility of a Nonlinear Generalized Predictive Control algorithm by showing real-time adaptive control on a plant with relatively fast time-constants. Generalized Predictive Control has classically been used in process control where linear control laws were formulated for plants with relatively slow time-constants. The plant of interest for this paper is a magnetic levitation device that is nonlinear and open-loop unstable. In this application, the reference model of the plant is a neural network that has an embedded nominal linear model in the network weights. The control based on the linear model provides initial stability at the beginning of network training. In using a neural network the control laws are nonlinear and online adaptation of the model is possible to capture unmodeled or time-varying dynamics. Newton-Raphson is the minimization algorithm. Newton-Raphson requires the calculation of the Hessian, but even with this computational expense the low iteration rate make this a viable algorithm for real-time control.

Control volume analyses of glottal flow using a fully-coupled numerical fluid-structure interaction model

NASA Astrophysics Data System (ADS)

Yang, Jubiao; Krane, Michael; Zhang, Lucy

2013-11-01

Vocal fold vibrations and the glottal jet are successfully simulated using the modified Immersed Finite Element method (mIFEM), a fully coupled dynamics approach to model fluid-structure interactions. A self-sustained and steady vocal fold vibration is captured given a constant pressure input at the glottal entrance. The flow rates at different axial locations in the glottis are calculated, showing small variations among them due to the vocal fold motion and deformation. To further facilitate the understanding of the phonation process, two control volume analyses, specifically with Bernoulli's equation and Newton's 2nd law, are carried out for the glottal flow based on the simulation results. A generalized Bernoulli's equation is derived to interpret the correlations between the velocity and pressure temporally and spatially along the center line which is a streamline using a half-space model with symmetry boundary condition. A specialized Newton's 2nd law equation is developed and divided into terms to help understand the driving mechanism of the glottal flow.

The anatomy of a launch vehicle : quarterly report topic

DOT National Transportation Integrated Search

2001-01-01

Conceptually, a rocket is a simple machine. Following Newton's law that every force has an equal and opposite reaction, a rocket pushes mass in one direction and moves in the other. However, a modern space launch vehicle is a finely tuned and very co...

Visualization of Kepler's Laws of Planetary Motion

ERIC Educational Resources Information Center

Lu, Meishu; Su, Jun; Wang, Weiguo; Lu, Jianlong

2017-01-01

For this article, we use a 3D printer to print a surface similar to universal gravitation for demonstrating and investigating Kepler's laws of planetary motion describing the motion of a small ball on the surface. This novel experimental method allows Kepler's laws of planetary motion to be visualized and will contribute to improving the…

Direct probe of the inner accretion flow around the supermassive black hole in NGC 2617

NASA Astrophysics Data System (ADS)

Giustini, M.; Costantini, E.; De Marco, B.; Svoboda, J.; Motta, S. E.; Proga, D.; Saxton, R.; Ferrigno, C.; Longinotti, A. L.; Miniutti, G.; Grupe, D.; Mathur, S.; Shappee, B. J.; Prieto, J. L.; Stanek, K.

2017-01-01

Aims: NGC 2617 is a nearby (z 0.01) active galaxy that recently switched from being a Seyfert 1.8 to be a Seyfert 1.0. At the same time, it underwent a strong increase of X-ray flux by one order of magnitude with respect to archival measurements. We characterise the X-ray spectral and timing properties of NGC 2617 with the aim of studying the physics of a changing-look active galactic nucleus (AGN). Methods: We performed a comprehensive timing and spectral analysis of two XMM-Newton pointed observations spaced by one month, complemented by archival quasi-simultaneous INTEGRAL observations. Results: We found that, to the first order, NGC 2617 looks like a type 1 AGN in the X-ray band and, with the addition of a modest reflection component, its continuum can be modelled well either with a power law plus a phenomenological blackbody, a partially covered power law, or a double Comptonisation model. Independent of the continuum adopted, in all three cases a column density of a few 1023 cm-2 of neutral gas covering 20-40% of the continuum source is required by the data. Most interestingly, absorption structures due to highly ionised iron have been detected in both observations with a redshift of about 0.1c with respect to the systemic redshift of the host galaxy. Conclusions: The redshifted absorber can be ascribed to a failed wind/aborted jets component, to gravitational redshift effects, and/or to matter directly falling towards the central supermassive black hole. In either case, we are probing the innermost accretion flow around the central supermassive black hole of NGC 2617 and might be even watching matter in a direct inflow towards the black hole itself.

Scale-Invariant Form of the Planck Law of Energy Distribution and its Connection to the Maxwell-Boltzmann Distribution

NASA Astrophysics Data System (ADS)

Sohrab, Siavash

2004-03-01

Scale-invariant form of the Planck law of energy distribution is introduced as belE:first fracɛ_νN_νV=ρ_νdν=frac8π m_β^2k fracν^3dνe^hν/kT-1 that at the chromodynamic scale β = γ for photon gas involves the gravitational mass of photon m_γ = (hk/c^3)^1/2. At a constant T, (1) describes the size spectrum of photon clusters of energy ɛ_cj = N_γ jhν_γ j = N_γ jɛ_γ j where N_γ j is the number of photons in cluster j (energy level j) per unit volume and ɛ_γ j is the energy of photon in cluster j. Similarly, at molecular-dynamic scale, Eq.(1) with m_β = M_β/No = M_βm_γc^2 gives the spectrum of size of molecular clusters acting as composite bosons with energy ɛ_cj = N_mjhν_mj = N_mjɛ_mj and matter wavelength and frequency given by h_β = p_βλ_β = h (de Broglie) and k_β = p_βν_β = k. Particles are suggested to oscillate in two directions (x^+, x^-) such that mm < u^2 > = 2mm < u^2_x^+ > = 3kT leading to calculated rms molecular speeds (1346, 336, 360, 300, 952, 287) m/s that are comparable with the observed velocity of sound (1286, 332, 337, 308, 972, 268) m/s for gases (H_2, O_2, N_2, Ar, He, CO_2) at s.t.p. as initially suspected by Newton.

Gravitation. [Book on general relativity

NASA Technical Reports Server (NTRS)

Misner, C. W.; Thorne, K. S.; Wheeler, J. A.

1973-01-01

This textbook on gravitation physics (Einstein's general relativity or geometrodynamics) is designed for a rigorous full-year course at the graduate level. The material is presented in two parallel tracks in an attempt to divide key physical ideas from more complex enrichment material to be selected at the discretion of the reader or teacher. The full book is intended to provide competence relative to the laws of physics in flat space-time, Einstein's geometric framework for physics, applications with pulsars and neutron stars, cosmology, the Schwarzschild geometry and gravitational collapse, gravitational waves, experimental tests of Einstein's theory, and mathematical concepts of differential geometry.

Lower limit to the scale of an effective quantum theory of gravitation.

PubMed

Caldwell, R R; Grin, Daniel

2008-01-25

An effective quantum theory of gravitation in which gravity weakens at energies higher than approximately 10(-3) eV is one way to accommodate the apparent smallness of the cosmological constant. Such a theory predicts departures from the Newtonian inverse-square force law on distances below approximately 0.05 mm. However, it is shown that this modification also leads to changes in the long-range behavior of gravity and is inconsistent with observed gravitational lenses.

XMM-Newton X-ray and HST weak gravitational lensing study of the extremely X-ray luminous galaxy cluster Cl J120958.9+495352 (z = 0.902)

NASA Astrophysics Data System (ADS)

Thölken, Sophia; Schrabback, Tim; Reiprich, Thomas H.; Lovisari, Lorenzo; Allen, Steven W.; Hoekstra, Henk; Applegate, Douglas; Buddendiek, Axel; Hicks, Amalia

2018-03-01

Context. Observations of relaxed, massive, and distant clusters can provide important tests of standard cosmological models, for example by using the gas mass fraction. To perform this test, the dynamical state of the cluster and its gas properties have to be investigated. X-ray analyses provide one of the best opportunities to access this information and to determine important properties such as temperature profiles, gas mass, and the total X-ray hydrostatic mass. For the last of these, weak gravitational lensing analyses are complementary independent probes that are essential in order to test whether X-ray masses could be biased. Aims: We study the very luminous, high redshift (z = 0.902) galaxy cluster Cl J120958.9+495352 using XMM-Newton data. We measure global cluster properties and study the temperature profile and the cooling time to investigate the dynamical status with respect to the presence of a cool core. We use Hubble Space Telescope (HST) weak lensing data to estimate its total mass and determine the gas mass fraction. Methods: We perform a spectral analysis using an XMM-Newton observation of 15 ks cleaned exposure time. As the treatment of the background is crucial, we use two different approaches to account for the background emission to verify our results. We account for point spread function effects and deproject our results to estimate the gas mass fraction of the cluster. We measure weak lensing galaxy shapes from mosaic HST imaging and select background galaxies photometrically in combination with imaging data from the William Herschel Telescope. Results: The X-ray luminosity of Cl J120958.9+495352 in the 0.1-2.4 keV band estimated from our XMM-Newton data is LX = (13.4+1.2-1.0) × 1044 erg/s and thus it is one of the most X-ray luminous clusters known at similarly high redshift. We find clear indications for the presence of a cool core from the temperature profile and the central cooling time, which is very rare at such high redshifts. Based on the weak lensing analysis, we estimate a cluster mass of M500/1014 M⊙ = 4.4+2.2-2.0 (stat.) + 0.6 (sys.) and a gas mass fraction of fgas,2500 = 0.11-0.03+0.06 in good agreement with previous findings for high redshift and local clusters.

High-energy gravitational scattering and the general relativistic two-body problem

NASA Astrophysics Data System (ADS)

Damour, Thibault

2018-02-01

A technique for translating the classical scattering function of two gravitationally interacting bodies into a corresponding (effective one-body) Hamiltonian description has been recently introduced [Phys. Rev. D 94, 104015 (2016), 10.1103/PhysRevD.94.104015]. Using this technique, we derive, for the first time, to second-order in Newton's constant (i.e. one classical loop) the Hamiltonian of two point masses having an arbitrary (possibly relativistic) relative velocity. The resulting (second post-Minkowskian) Hamiltonian is found to have a tame high-energy structure which we relate both to gravitational self-force studies of large mass-ratio binary systems, and to the ultra high-energy quantum scattering results of Amati, Ciafaloni and Veneziano. We derive several consequences of our second post-Minkowskian Hamiltonian: (i) the need to use special phase-space gauges to get a tame high-energy limit; and (ii) predictions about a (rest-mass independent) linear Regge trajectory behavior of high-angular-momenta, high-energy circular orbits. Ways of testing these predictions by dedicated numerical simulations are indicated. We finally indicate a way to connect our classical results to the quantum gravitational scattering amplitude of two particles, and we urge amplitude experts to use their novel techniques to compute the two-loop scattering amplitude of scalar masses, from which one could deduce the third post-Minkowskian effective one-body Hamiltonian.

Self similar flow behind an exponential shock wave in a self-gravitating, rotating, axisymmetric dusty gas with heat conduction and radiation heat flux

NASA Astrophysics Data System (ADS)

Bajargaan, Ruchi; Patel, Arvind

2018-04-01

One-dimensional unsteady adiabatic flow behind an exponential shock wave propagating in a self-gravitating, rotating, axisymmetric dusty gas with heat conduction and radiation heat flux, which has exponentially varying azimuthal and axial fluid velocities, is investigated. The shock wave is driven out by a piston moving with time according to an exponential law. The dusty gas is taken to be a mixture of a non-ideal gas and small solid particles. The density of the ambient medium is assumed to be constant. The equilibrium flow conditions are maintained and energy is varying exponentially, which is continuously supplied by the piston. The heat conduction is expressed in the terms of Fourier's law, and the radiation is assumed of diffusion type for an optically thick grey gas model. The thermal conductivity and the absorption coefficient are assumed to vary with temperature and density according to a power law. The effects of the variation of heat transfer parameters, gravitation parameter and dusty gas parameters on the shock strength, the distance between the piston and the shock front, and on the flow variables are studied out in detail. It is interesting to note that the similarity solution exists under the constant initial angular velocity, and the shock strength is independent from the self gravitation, heat conduction and radiation heat flux.

On pendulums and air resistance. The mathematics and physics of Denis Diderot

NASA Astrophysics Data System (ADS)

Dahmen, Sílvio R.

2015-09-01

In this article Denis Diderot's Fifth Memoir of 1748 on the problem of a pendulum damped by air resistance is discussed in its historical as well as mathematical aspects. Diderot wrote the Memoir in order to clarify an assumption Newton made without further justification in the first pages of the Principia in connection with an experiment to verify the Third Law of Motion using colliding pendulums. To explain the differences between experimental and theoretical values, Newton assumed the bob was traversed. By giving Newton's arguments a mathematical scaffolding and recasting his geometrical reasoning in the language of differential calculus, Diderot provided a step-by-step solution guide to the problem. He also showed that Newton's assumption was equivalent to having assumed F R proportional the bob's velocity v, when in fact he believed it should be replaced by F R ˜ v 2. His solution is presented in full detail and his results are compared to those obtained from a Lindstedt-Poincaré approximation for an oscillator with quadratic damping. It is shown that, up to a prefactor, both results coincide. Some results that follow from his approach are presented and discussed for the first time. Experimental evidence to support Diderot's or Newton's claims is discussed together with the limitations of their solutions. Some misprints in the original memoir are pointed out.

Non-Lipschitz Approach to Quantum Mechnics

NASA Technical Reports Server (NTRS)

Zak, Michail

1997-01-01

An attempt to reconcile quantum mechanics with Newton's laws represented by the non-Lipschitz formalism has been made. As a Proof-of-concept, a line of equally spaced atoms was studied. It appeared that enforcement of atom incompressibility required relaxation of the lipschitz condition at the points of contact.

Retraining Teachers in Physics.

ERIC Educational Resources Information Center

McGervey, John D.; Heckathorn, Dick

1990-01-01

Provides an inservice workshop experience for underprepared physics or physical science teachers. Describes a demonstration showing conservation of momentum using an air track, gliders, and a model railway train. Includes a brief introduction to demonstrations of Newton's second law, scattering of laser light, and the effect of a telescope on…

Self-acceleration in scalar-bimetric theories

NASA Astrophysics Data System (ADS)

Brax, Philippe; Valageas, Patrick

2018-05-01

We describe scalar-bimetric theories where the dynamics of the Universe are governed by two separate metrics, each with an Einstein-Hilbert term. In this setting, the baryonic and dark matter components of the Universe couple to metrics which are constructed as functions of these two gravitational metrics. More precisely, the two metrics coupled to matter are obtained by a linear combination of their vierbeins, with scalar-dependent coefficients. The scalar field, contrary to dark-energy models, does not have a potential of which the role is to mimic a late-time cosmological constant. The late-time acceleration of the expansion of the Universe can be easily obtained at the background level in these models by appropriately choosing the coupling functions appearing in the decomposition of the vierbeins for the baryonic and dark matter metrics. We explicitly show how the concordance model can be retrieved with negligible scalar kinetic energy. This requires the scalar coupling functions to show variations of order unity during the accelerated expansion era. This leads in turn to deviations of order unity for the effective Newton constants and a fifth force that is of the same order as Newtonian gravity, with peculiar features. The baryonic and dark matter self-gravities are amplified although the gravitational force between baryons and dark matter is reduced and even becomes repulsive at low redshift. This slows down the growth of baryonic density perturbations on cosmological scales, while dark matter perturbations are enhanced. These scalar-bimetric theories have a perturbative cutoff scale of the order of 1 AU, which prevents a precise comparison with Solar System data. On the other hand, we can deduce strong requirements on putative UV completions by analyzing the stringent constraints in the Solar System. Hence, in our local environment, the upper bound on the time evolution of Newton's constant requires an efficient screening mechanism that both damps the fifth force on small scales and decouples the local value of Newton constant from its cosmological value. This cannot be achieved by a quasistatic chameleon mechanism and requires going beyond the quasistatic regime and probably using derivative screenings, such as Kmouflage or Vainshtein screening, on small scales.

Semantics in Teaching Introductory Physics.

ERIC Educational Resources Information Center

Williams, H. Thomas

1999-01-01

Contends that the large vocabulary used for precise purposes in physics contains many words that have related but potentially confusing meanings in everyday usage. Analyzes the treatment of Newton's Laws of Motion in several well-known introductory textbooks for evidence of inconsistent language use. Makes teaching suggestions. (Contains 11…

Modeling the Mousetrap Car

ERIC Educational Resources Information Center

Jumper, William D.

2012-01-01

Many high school and introductory college physics courses make use of mousetrap car projects and competitions as a way of providing an engaging hands-on learning experience incorporating Newton's laws, conversion of potential to kinetic energy, dissipative forces, and rotational mechanics. Presented here is a simple analytical and finite element…

Comparing Three Methods for Teaching Newton's Third Law

ERIC Educational Resources Information Center

Smith, Trevor I.; Wittman, Michael C.

2007-01-01

Although guided-inquiry methods for teaching introductory physics have been individually shown to be more effective at improving conceptual understanding than traditional lecture-style instruction, researchers in physics education have not studied differences among reform-based curricula in much detail. Several researchers have developed…

What's in a Symbol?

ERIC Educational Resources Information Center

Leadstone, Stuart

2013-01-01

This "Science Note" explores the new adaptation of Newton's Second Law of Motion, "F = ma." In older physics and applied mathematics textbooks this expression appears as "P = mf." The author examines why "f" is now favored over "a" and why practitioners write "P = mf" rather than…

Self-Paced Physics, Segment 18.

ERIC Educational Resources Information Center

New York Inst. of Tech., Old Westbury.

Eighty-seven problems are included in this volume which is arranged to match study segments 2 through 14. The subject matter is related to projectiles, simple harmonic motion, kinetic friction, multiple pulley arrangements, motion on inclined planes, circular motion, potential energy, kinetic energy, center of mass, Newton's laws, elastic and…

Mechanics, Waves and Thermodynamics

NASA Astrophysics Data System (ADS)

Ranjan Jain, Sudhir

2016-05-01

Figures; Preface; Acknowledgement; 1. Energy, mass, momentum; 2. Kinematics, Newton's laws of motion; 3. Circular motion; 4. The principle of least action; 5. Work and energy; 6. Mechanics of a system of particles; 7. Friction; 8. Impulse and collisions; 9. Central forces; 10. Dimensional analysis; 11. Oscillations; 12. Waves; 13. Sound of music; 14. Fluid mechanics; 15. Water waves; 16. The kinetic theory of gases; 17. Concepts and laws of thermodynamics; 18. Some applications of thermodynamics; 19. Basic ideas of statistical mechanics; Bibliography; Index.

Gravitational waves produced by compressible MHD turbulence from cosmological phase transitions

NASA Astrophysics Data System (ADS)

Peter, Niksa; Martin, Schlederer; Günter, Sigl

2018-07-01

We calculate the gravitational wave spectrum produced by magneto-hydrodynamic turbulence in a first order phase transitions. We focus in particular on the role of decorrelation of incompressible (solenoidal) homogeneous isotropic turbulence, which is dominated by the sweeping effect. The sweeping effect describes that turbulent decorrelation is primarily due to the small scale eddies being swept with by large scale eddies in a stochastic manner. This effect reduces the gravitational wave signal produced by incompressible MHD turbulence by around an order of magnitude compared to previous studies. Additionally, we find a more complicated dependence for the spectral shape of the gravitational wave spectrum on the energy density sourced by solenoidal modes (magnetic and kinetic). The high frequency tail follows either a k ‑5/3 or a k ‑8/3 power law for large and small solenoidal turbulence density parameter, respectively. Further, magnetic helicity tends to increase the gravitational wave energy at low frequencies. Moreover, we show how solenoidal modes might impact the gravitational wave spectrum from dilatational modes e.g. sound waves. We find that solenoidal modes greatly affect the shape of the gravitational wave spectrum due to the sweeping effect on the dilatational modes. For a high velocity flow, one expects a k ‑2 high frequency tail, due to sweeping. In contrast, for a low velocity flow and a sound wave dominated flow, we expect a k ‑3 high frequency tail. If neither of these limiting cases is realized, the gravitational wave spectrum may be a broken power law with index between  ‑2 and  ‑3, extending up to the frequency at which the source is damped by viscous dissipation.

Introducing Conservation of Momentum

ERIC Educational Resources Information Center

Brunt, Marjorie; Brunt, Geoff

2013-01-01

The teaching of the principle of conservation of linear momentum is considered (ages 15 + ). From the principle, the momenta of two masses in an isolated system are considered. Sketch graphs of the momenta make Newton's laws appear obvious. Examples using different collision conditions are considered. Conservation of momentum is considered…

Investigating Comfort Temperatures and Heat Transfer in Sleeping Bags

ERIC Educational Resources Information Center

Hill, Trevor; Hill, Lara

2017-01-01

After many years of confusion, thermal performance of sleeping bags has now been quantified and unified using expensive test techniques. Based on Newton's law of cooling, we present a simple inexpensive test and model to check manufacturers' claims on the temperature performance of a range of modern sleeping bags.

The Art of Physics

ERIC Educational Resources Information Center

Spevak, Arlene

2008-01-01

The algebraic concepts and major ideas that govern Newton's laws of motion can often be a challenge for the majority of ninth-grade students. Therefore, to make learning these concepts less task-oriented and more enjoyable, the author developed lessons that allow students to construct and express their understanding of these ideas through…

A Qualitative Approach to Electricity.

ERIC Educational Resources Information Center

Haertel, Hermann

In the teaching of physics, the study of electricity and magnetism typically follows the introduction of the basic concepts of mechanics. However, there are some new concepts associated with electromagnetic fields that seem at first to the student to be unrelated to, or even incompatible with, Newton's third law as learned in mechanics.…

Project Physics Text 3, The Triumph of Mechanics.

ERIC Educational Resources Information Center

Harvard Univ., Cambridge, MA. Harvard Project Physics.

Mechanical theories are presented in this unit of the Project Physics text for senior high students. Collisions, Newton's laws, isolated systems, and Leibniz' concept are discussed, leading to conservation of mass and momentum. Energy conservation is analyzed in terms of mechanical energy, heat energy, steam engines, Watt's engine, Joule's…

Project Physics Tests 1, Concepts of Motion.

ERIC Educational Resources Information Center

Harvard Univ., Cambridge, MA. Harvard Project Physics.

Test items relating to Project Physics Unit 1 are presented in this booklet, consisting of 70 multiple-choice and 20 problem-and-essay questions. Concepts of motion are examined with respect to velocities, acceleration, forces, vectors, Newton's laws, and circular motion. Suggestions are made for time consumption in answering some items. Besides…

Learning Activity Package, Physical Science. LAP Numbers 8, 9, 10, and 11.

ERIC Educational Resources Information Center

Williams, G. J.

These four units of the Learning Activity Packages (LAPs) for individualized instruction in physical science cover nuclear reactions, alpha and beta particles, atomic radiation, medical use of nuclear energy, fission, fusion, simple machines, Newton's laws of motion, electricity, currents, electromagnetism, Oersted's experiment, sound, light,…

Paradigms and Postmodernism in Science and Science Education.

ERIC Educational Resources Information Center

Pushkin, David B.

Science, particularly the physical sciences, has undergone several paradigm shifts during history. The modernistic and mechanistic world that was viewed through the lens of Newton's laws no longer offers valid answers to present-day questions. This paper examines four themes: the evolution of physics, the evolution of chemistry, the evolution of…

Animation as a Distractor to Learning.

ERIC Educational Resources Information Center

Rieber, Lloyd P.

1996-01-01

A study of 364 fifth graders investigated distractibility of animated graphics in a computer-based tutorial about Newton's Laws of Motion. Found no difference in post-test performance for those with high, medium, or no distraction graphics. Students in the two distraction conditions took less time to process instructional frames than students in…

Have a Blast, Safely!

ERIC Educational Resources Information Center

Roy, Ken

2005-01-01

Model rocketry is one of the best ways to get students interested in the physical sciences. Following safety guidelines, rocketry can really turn students on to science and also help them understand the applications of theories and scientific principles (Newton's laws of motion, force, mass, projectile motion, etc.) they are learning. The study…

Fan Cart: The Next Generation

ERIC Educational Resources Information Center

Lamore, Brian

2016-01-01

For years the fan cart has provided physics students with an excellent resource for exploring fundamental mechanics concepts such as acceleration, Newton's laws, impulse, momentum, work-energy, and energy conversions. "The Physics Teacher" has even seen some excellent do-it-yourself (DIY) fan carts and activities. If you are interested…

Multiple Teaching Approaches, Teaching Sequence and Concept Retention in High School Physics Education

ERIC Educational Resources Information Center

Fogarty, Ian; Geelan, David

2013-01-01

Students in 4 Canadian high school physics classes completed instructional sequences in two key physics topics related to motion--Straight Line Motion and Newton's First Law. Different sequences of laboratory investigation, teacher explanation (lecture) and the use of computer-based scientific visualizations (animations and simulations) were…

Magneto-hydrodynamical model for plasma

NASA Astrophysics Data System (ADS)

Liu, Ruikuan; Yang, Jiayan

2017-10-01

Based on the Newton's second law and the Maxwell equations for the electromagnetic field, we establish a new 3-D incompressible magneto-hydrodynamics model for the motion of plasma under the standard Coulomb gauge. By using the Galerkin method, we prove the existence of a global weak solution for this new 3-D model.

How Stable Is Stable?

ERIC Educational Resources Information Center

Baehr, Marie

1994-01-01

Provides a problem where students are asked to find the point at which a soda can floating in some liquid changes its equilibrium between stable and unstable as the soda is removed from the can. Requires use of Newton's first law, center of mass, Archimedes' principle, stable and unstable equilibrium, and buoyant force position. (MVL)

Earth Day at Union Station

NASA Image and Video Library

2013-04-22

Students assemble balloon race cars and Alka-Seltzer film canister rockets to demonstrate Newton's third Law of motion at the NASA Science Gallery at Union Station, Monday, April 22, 2013 in Washington. The NASA Science Gallery exhibits are being sponsored by NASA in honor of Earth Day. (Photo Credit: NASA/Carla Cioffi)

The foundations of space biology and medicine. Volume 2: Ecological and physiological bases of space biology and medicine. Part 3: Effect on the organism of dynamic flight factors. Chapter 1: Principles of gravitational biology

NASA Technical Reports Server (NTRS)

Smith, A. H.

1972-01-01

The physical principles of gravitation are discussed, such as gravitational and intertial forces, weight and mass, weightlessness, size and scale effects, scale limits of gravitational effects, and gravity as a biogenic factor. The behavior of the accelerative force gravitation, is described. This law proposes and quantifies the mutual gravitational attraction existing between all bodies of matter, the force being proportional to the product of masses, and inversely related to the square of the distance separating them. Gravity orientation, chronic acceleration, and hematology are examined. Systematic responses, such as circulation and renal functions, are also considered, along with animal response to a decreased acceleration field and physiology of hyper- and hypodynamic fields.

Playing Newtonian Games with Modellus

ERIC Educational Resources Information Center

Teodoro, Vitor Duarte

2004-01-01

This article is a short introduction on how to use Modellus (a computer package that is freely available on the Internet and used in the IOP "Advancing Physics" course) to build physics games using Newton's laws, expressed as differential equations. Solving systems of differential equations is beyond most secondary-school or first-year college…

A Project-Based Course on Newton's Laws for Talented Junior High-School Students

ERIC Educational Resources Information Center

Langbeheim, Elon

2015-01-01

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…

Entropic forces in Brownian motion

NASA Astrophysics Data System (ADS)

Roos, Nico

2014-12-01

Interest in the concept of entropic forces has risen considerably since Verlinde proposed in 2011 to interpret the force in Newton's second law and gravity as entropic forces. Brownian motion—the motion of a small particle (pollen) driven by random impulses from the surrounding molecules—may be the first example of a stochastic process in which such forces are expected to emerge. In this article, it is shown that at least two types of entropic force can be identified in three-dimensional Brownian motion. This analysis yields simple derivations of known results of Brownian motion, Hooke's law, and—applying an external (non-radial) force—Curie's law and the Langevin-Debye equation.

Flux-vector splitting algorithm for chain-rule conservation-law form

NASA Technical Reports Server (NTRS)

Shih, T. I.-P.; Nguyen, H. L.; Willis, E. A.; Steinthorsson, E.; Li, Z.

1991-01-01

A flux-vector splitting algorithm with Newton-Raphson iteration was developed for the 'full compressible' Navier-Stokes equations cast in chain-rule conservation-law form. The algorithm is intended for problems with deforming spatial domains and for problems whose governing equations cannot be cast in strong conservation-law form. The usefulness of the algorithm for such problems was demonstrated by applying it to analyze the unsteady, two- and three-dimensional flows inside one combustion chamber of a Wankel engine under nonfiring conditions. Solutions were obtained to examine the algorithm in terms of conservation error, robustness, and ability to handle complex flows on time-dependent grid systems.

Cosmology and the Sinusoidal Potential

NASA Astrophysics Data System (ADS)

Bartlett, David F.

2006-06-01

The nature of dark matter (and dark energy) remains a mystery. An alternative is being explored by several scientists: changing Newton's (and Einstein's) field equations. The sinusoidal potential is the latest attempt[1]. Here the gravitational law is alternately attractive and repulsive:φ = -GM cos(kor)/r, where λo=2π/ko = 1/20 of the distance from the sun to the center of the Milky Way. The proposal accommodates several structural features of the Milky Way including, paradoxically, its spiral shape and flat rotation curve. The sinusoidal potential's unique feature is strong galactic tidal forces (dg/dr). These may explain why the new planetoid Sedna is securely between the Kuiper Belt and the Oort cloud and why distant comets are more influenced by galactic tides that are in the r, rather than the z-direction.At this meeting I discuss the consequences of the sinusoidal potential for cosmology. Here the alternation of attraction and repulsion gives (i) an open universe, and (ii) gravitational lensing which is usually weak, but occasionally very strong. An open universe is one that, asymptotically, has a size R which varies directly as time t. The open universe conflicts both with the old Einstein-deSitter model (R α t2/3} and the new accelerating one. The evidence for an accelerating universe decisively rejects the Einstein-deSitter model. The rejection of an open (or empty) universe is less secure. This rejection is influenced by the different ways the groups studying the brightness of supernovae use the HST. Surprising additional inputs include neutrino masses, the equivalence principle, LSB galaxies, and "over-luminous" Sn1a. I thank Mostafa Jon Dadras and Patrick Motl for early help and John Cumalat for continual support. [1] D.F. Bartlett, "Analogies between electricity and gravity", Metrologia 41, S115-S124 (2004).

XMM-Newton observations of the non-thermal supernova remnant HESS J1731-347 (G353.6-0.7)

NASA Astrophysics Data System (ADS)

Doroshenko, V.; Pühlhofer, G.; Bamba, A.; Acero, F.; Tian, W. W.; Klochkov, D.; Santangelo, A.

2017-12-01

We report on the analysis of XMM-Newton observations of the non-thermal shell-type supernova remnant HESS J1731-347 (G353.6-0.7). For the first time the complete remnant shell has been covered in X-rays, which allowed direct comparison with radio and TeV observations. We carried out a spatially resolved spectral analysis of XMM-Newton data and confirmed the previously reported non-thermal power-law X-ray spectrum of the source with negligible variations of spectral index across the shell. On the other hand, the X-ray absorption column is strongly variable and correlates with the CO emission thus confirming that the absorbing material must be in the foreground and reinforcing the previously suggested lower limit on distance. Finally, we find that the X-ray emission of the remnant is suppressed towards the Galactic plane, which points to lower shock velocities in this region, likely due to the interaction of the shock with the nearby molecular cloud.

Testing General Relativity with the Reflection Spectrum of the Supermassive Black Hole in 1H0707-495.

PubMed

Cao, Zheng; Nampalliwar, Sourabh; Bambi, Cosimo; Dauser, Thomas; García, Javier A

2018-02-02

Recently, we have extended the x-ray reflection model relxill to test the spacetime metric in the strong gravitational field of astrophysical black holes. In the present Letter, we employ this extended model to analyze XMM-Newton, NuSTAR, and Swift data of the supermassive black hole in 1H0707-495 and test deviations from a Kerr metric parametrized by the Johannsen deformation parameter α_{13}. Our results are consistent with the hypothesis that the spacetime metric around the black hole in 1H0707-495 is described by the Kerr solution.

Erratum: Erratum to: Thermodynamic implications of the gravitationally induced particle creation scenario

NASA Astrophysics Data System (ADS)

Saha, Subhajit; Mondal, Anindita

2018-04-01

We would like to rectify an error regarding the validity of the first law of thermodynamics (FLT) on the apparent horizon of a spatially flat Friedmann-Lemaitre-Robertson-Walker (FLRW) universe for the gravitationally induced particle creation scenario with constant specific entropy and an arbitrary particle creation rate (see Sect. 3.1 of original article)

Titius-Bode laws in the solar system. 2: Build your own law from disk models

NASA Astrophysics Data System (ADS)

Dubrulle, B.; Graner, F.

1994-02-01

Simply respecting both scale and rotational invariance, it is easy to construct an endless collection of theoretical models predicting a Titius-Bode law, irrespective to their physical content. Due to the numerous ways to get the law and its intrinsic arbitrariness, it is not a useful constraint on theories of solar system formation. To illustrate the simple elegance of scale-invariant methods, we explicitly cook up one of the simplest examples, an infinitely thin cold gaseous disk rotating around a central object. In that academic case, the Titius-Bode law holds during the linear stage of the gravitational instability. The time scale of the instability is of the order of a self-gravitating time scale, (G rhod)-1/2, where rhod is the disk density. This model links the separation between different density maxima with the ratio MD/MC of the masses of the disk and the central object; for instance, MD/MC of the order of 0.18 roughly leads to the observed separation between the planets. We discuss the boundary conditions and the limit of the Wentzel-Kramer-Brillouin (WKB) approximation.

Bianchi type-II String Cosmological Model with Magnetic Field in Scale-Covariant Theory of Gravitation

NASA Astrophysics Data System (ADS)

Sharma, N. K.; Singh, J. K.

2014-12-01

The spatially homogeneous and totally anisotropic Bianchi type-II cosmological solutions of massive strings have been investigated in the presence of the magnetic field in the framework of scale-covariant theory of gravitation formulated by Canuto et al. (Phys. Rev. Lett. 39, 429, 1977). With the help of special law of variation for Hubble's parameter proposed by Berman (Nuovo Cimento 74, 182, 1983) string cosmological model is obtained in this theory. We use the power law relation between scalar field ϕ and scale factor R to find the solutions. Some physical and kinematical properties of the model are also discussed.

The Origin of Gravitation

NASA Astrophysics Data System (ADS)

Zheng, Sheng Ming

2012-10-01

In the natural world, people have discovered four kinds of forces: electromagnetic force, gravitation, weak force, and strong force. Although the gravitation has been discovered more than three hundred years, its mechanism of origin is unclear until today. While investigating the origin of gravitation, I do some experiments discover the moving photons produce gravitation. This discovery shows the origin of gravitation. Meanwhile I do some experiments discover the light interference fringes are produced by the gravitation: my discovery demonstrate light is a particle, but is not a wave-particle duality. Furthermore, applications of this discovery to other moving particles show a similar effect. In a word: the micro particle moving produce gravitation and electromagnetic force. Then I do quantity experiment get a general formula: Reveal the essence of gravitational mass and the essence of electric charge; reveal the origin of gravitation and the essence of matter wave. Along this way, I unify the gravitation and electromagnetic force. Namely I find a natural law that from atomic world to star world play in moving track. See website: https://www.lap-publishing.com/catalog/details/store/gb/book/978-3-8473-2658-8/mechanism-of-interaction-in-moving-matter

A-Posteriori Error Estimation for Hyperbolic Conservation Laws with Constraint

NASA Technical Reports Server (NTRS)

Barth, Timothy

2004-01-01

This lecture considers a-posteriori error estimates for the numerical solution of conservation laws with time invariant constraints such as those arising in magnetohydrodynamics (MHD) and gravitational physics. Using standard duality arguments, a-posteriori error estimates for the discontinuous Galerkin finite element method are then presented for MHD with solenoidal constraint. From these estimates, a procedure for adaptive discretization is outlined. A taxonomy of Green's functions for the linearized MHD operator is given which characterizes the domain of dependence for pointwise errors. The extension to other constrained systems such as the Einstein equations of gravitational physics are then considered. Finally, future directions and open problems are discussed.

A New Characterization of the Compton Process in the ULX Spectra

NASA Astrophysics Data System (ADS)

Kobayashi, S.; Nakazawa, K.; Makishima, K.

2015-07-01

Ultra Luminous X-ray sources (ULXs) are unusually luminous point sources located at arms of spiral galaxies, and are candidates for the intermediate mass black holes (Makishima+2000). Their spectra make transition betweens power-law shapes (PL state) and convex shapes (disk-like state). The latter state can be explained with either the multi-color disk (MCD)+thermal Comptonization (THC) model or a Slim disk model (Watari+2000). We adopt the former modeling, because it generally gives physically more reasonable parameters (Miyawaki+2009). To characterize the ULXs spectra with a unified way, we applied the MCD+THC model to several datasets of ULXs obtained by Suzaku, XMM-Newton, and Nu-Star. The model well explains all the spectra, in terms of cool disk (T_{in}˜0.2 keV), and a cool thick (T_{e}˜2 keV, τ ˜10) corona. The derived parameters can be characterized by two new parameters. One is Q≡ T_{e}/T_{in} which describes balance between the Compton cooling and gravitational heating of the corona, while the other is f≡ L_{raw}/L_{tot}, namely, the directly-visible (without Comptonization) MCD luminosity. Then, the PL state spectra have been found to show Q˜10 and f˜0.7, while those of the disk-like state Q˜ 3 and f≤0.01. Thus, the two states are clearly separated in terms of Q and f.

A solution to the Navier-Stokes equations based upon the Newton Kantorovich method

NASA Technical Reports Server (NTRS)

Davis, J. E.; Gabrielsen, R. E.; Mehta, U. B.

1977-01-01

An implicit finite difference scheme based on the Newton-Kantorovich technique was developed for the numerical solution of the nonsteady, incompressible, two-dimensional Navier-Stokes equations in conservation-law form. The algorithm was second-order-time accurate, noniterative with regard to the nonlinear terms in the vorticity transport equation except at the earliest few time steps, and spatially factored. Numerical results were obtained with the technique for a circular cylinder at Reynolds number 15. Results indicate that the technique is in excellent agreement with other numerical techniques for all geometries and Reynolds numbers investigated, and indicates a potential for significant reduction in computation time over current iterative techniques.

Notions of Physical Laws in Childhood.

ERIC Educational Resources Information Center

Von Pfuhl Rodrigues, Dulce Madalena Autran

1980-01-01

Presented is an experiment investigating children's awareness of regularities in physical phenomena and their capacity for expressing these regularities. Hypothesized and confirmed is that children can use statements with the form and purpose of a physical law. Cartoons related to Archimedes' principle (and connected gravitation and fluid…

Beyond Descartes and Newton: Recovering life and humanity.

PubMed

Kauffman, Stuart A; Gare, Arran

2015-12-01

Attempts to 'naturalize' phenomenology challenge both traditional phenomenology and traditional approaches to cognitive science. They challenge Edmund Husserl's rejection of naturalism and his attempt to establish phenomenology as a foundational transcendental discipline, and they challenge efforts to explain cognition through mainstream science. While appearing to be a retreat from the bold claims made for phenomenology, it is really its triumph. Naturalized phenomenology is spearheading a successful challenge to the heritage of Cartesian dualism. This converges with the reaction against Cartesian thought within science itself. Descartes divided the universe between res cogitans, thinking substances, and res extensa, the mechanical world. The latter won with Newton and we have, in most of objective science since, literally lost our mind, hence our humanity. Despite Darwin, biologists remain children of Newton, and dream of a grand theory that is epistemologically complete and would allow lawful entailment of the evolution of the biosphere. This dream is no longer tenable. We now have to recognize that science and scientists are within and part of the world we are striving to comprehend, as proponents of endophysics have argued, and that physics, biology and mathematics have to be reconceived accordingly. Interpreting quantum mechanics from this perspective is shown to both illuminate conscious experience and reveal new paths for its further development. In biology we must now justify the use of the word "function". As we shall see, we cannot prestate the ever new biological functions that arise and constitute the very phase space of evolution. Hence, we cannot mathematize the detailed becoming of the biosphere, nor write differential equations for functional variables we do not know ahead of time, nor integrate those equations, so no laws "entail" evolution. The dream of a grand theory fails. In place of entailing laws, a post-entailing law explanatory framework is proposed in which Actuals arise in evolution that constitute new boundary conditions that are enabling constraints that create new, typically unprestatable, Adjacent Possible opportunities for further evolution, in which new Actuals arise, in a persistent becoming. Evolution flows into a typically unprestatable succession of Adjacent Possibles. Given the concept of function, the concept of functional closure of an organism making a living in its world, becomes central. Implications for patterns in evolution include historical reconstruction, and statistical laws such as the distribution of extinction events, or species per genus, and the use of formal cause, not efficient cause, laws. Copyright © 2015. Published by Elsevier Ltd.

Simultaneous solution of the geoid and the surface density anomalies

NASA Astrophysics Data System (ADS)

Ardalan, A. A.; Safari, A.; Karimi, R.; AllahTavakoli, Y.

2012-04-01

The main application of the land gravity data in geodesy is "local geoid" or "local gravity field" modeling, whereas the same data could play a vital role for the anomalous mass-density modeling in geophysical explorations. In the realm of local geoid computations based on Geodetic Boundary Value Problems (GBVP), it is needed that the effect of the topographic (or residual terrain) masses be removed via application of the Newton integral in order to perform the downward continuation in a harmonic space. However, harmonization of the downward continuation domain may not be perfectly possible unless accurate information about the mass-density of the topographic masses be available. On the other hand, from the exploration point of view the unwanted topographical masses within the aforementioned procedure could be regarded as the signal. In order to overcome the effect of the remaining masses within the remove step of the GBVP, which cause uncertainties in mathematical modeling of the problem, here we are proposing a methodology for simultaneous solution of the geoid and residual surface density modeling In other words, a new mathematical model will be offered which both provides the needed harmonic space for downward continuation and at the same time accounts for the non-harmonic terms of gravitational field and makes use of it for residual mass density modeling within the topographic region. The presented new model enjoys from uniqueness of the solution, opposite to the inverse application of the Newton integral for mass density modeling which is non-unique, and only needs regularization to remove its instability problem. In this way, the solution of the model provides both the incremental harmonic gravitational potential on surface of the reference ellipsoid as the gravity field model and the lateral surface mass-density variations via the second derivatives of the non harmonic terms of gravitational field. As the case study and accuracy verification, the proposed methodology is applied for identification of the salt geological structures as well as geoid computations within the northern coasts of Persian Gulf.

Cosmic growth signatures of modified gravitational strength

DOE Office of Scientific and Technical Information (OSTI.GOV)

Denissenya, Mikhail; Linder, Eric V., E-mail: mikhail.denissenya@nu.edu.kz, E-mail: evlinder@lbl.gov

2017-06-01

Cosmic growth of large scale structure probes the entire history of cosmic expansion and gravitational coupling. To get a clear picture of the effects of modification of gravity we consider a deviation in the coupling strength (effective Newton's constant) at different redshifts, with different durations and amplitudes. We derive, analytically and numerically, the impact on the growth rate and growth amplitude. Galaxy redshift surveys can measure a product of these through redshift space distortions and we connect the modified gravity to the observable in a way that may provide a useful parametrization of the ability of future surveys to testmore » gravity. In particular, modifications during the matter dominated era can be treated by a single parameter, the ''area'' of the modification, to an accuracy of ∼0.3% in the observables. We project constraints on both early and late time gravity for the Dark Energy Spectroscopic Instrument and discuss what is needed for tightening tests of gravity to better than 5% uncertainty.« less

Impact of topology in foliated quantum Einstein gravity.

PubMed

Houthoff, W B; Kurov, A; Saueressig, F

2017-01-01

We use a functional renormalization group equation tailored to the Arnowitt-Deser-Misner formulation of gravity to study the scale dependence of Newton's coupling and the cosmological constant on a background spacetime with topology [Formula: see text]. The resulting beta functions possess a non-trivial renormalization group fixed point, which may provide the high-energy completion of the theory through the asymptotic safety mechanism. The fixed point is robust with respect to changing the parametrization of the metric fluctuations and regulator scheme. The phase diagrams show that this fixed point is connected to a classical regime through a crossover. In addition the flow may exhibit a regime of "gravitational instability", modifying the theory in the deep infrared. Our work complements earlier studies of the gravitational renormalization group flow on a background topology [Formula: see text] (Biemans et al. Phys Rev D 95:086013, 2017, Biemans et al. arXiv:1702.06539, 2017) and establishes that the flow is essentially independent of the background topology.

Project Physics Reader 1, Concepts of Motion.

ERIC Educational Resources Information Center

Harvard Univ., Cambridge, MA. Harvard Project Physics.

As a supplement to Project Physics Unit 1, 21 articles are presented in this reader. Concepts of motion are discussed under headings: motion, motion in words, representation of movement, introducing vectors, Galileo's discussion of projectile motion, Newton's laws of dynamics, the dynamics of a golf club, report on Tait's lecture on force, and bad…

Interpreting Recoil for Undergraduate Students

ERIC Educational Resources Information Center

Elsayed, Tarek A.

2012-01-01

The phenomenon of recoil is usually explained to students in the context of Newton's third law. Typically, when a projectile is fired, the recoil of the launch mechanism is interpreted as a reaction to the ejection of the smaller projectile. The same phenomenon is also interpreted in the context of the conservation of linear momentum, which is…

Essential Shift: Scientific Revolution in the 20th Century

DTIC Science & Technology

1993-05-17

be one of the most successful in the history of science . Its explanation of experimental results and observations was comparable to that with which...Newton’s laws of force and gravity had achieved three centuries before.5 3 Bohr wrote, "in the history of science there are few events which, in the

Simulation of the Physics of Flight

ERIC Educational Resources Information Center

Lane, W. Brian

2013-01-01

Computer simulations continue to prove to be a valuable tool in physics education. Based on the needs of an Aviation Physics course, we developed the PHYSics of FLIght Simulator (PhysFliS), which numerically solves Newton's second law for an airplane in flight based on standard aerodynamics relationships. The simulation can be used to pique…

Motional Mechanisms of Homopolar Motors & Rollers

ERIC Educational Resources Information Center

Wong, H. K.

2009-01-01

The strong Nd[subscript 2]Fe[subscript 14]B permanent magnet has facilitated development of various fascinating yet simple homopolar motors. However, the physics of these devices is often not explained, or is explained incorrectly. A major concern is that Newton's third law was overlooked in some of the earlier articles. In this paper, I will…

Second Differences: A Mathematical Bridge between Two Projects

ERIC Educational Resources Information Center

Fischer, Joyce; Wayment, Stanley; Johnson, Christopher

2010-01-01

Making connections is one of the most important foundations involved in learning mathematics. Two projects are presented in this article: one involving Newton's Second Law of Motion and the other involving the determination of star numbers, a type of figurate number. The two invoke seemingly different modalities for students at different levels of…

Probing the Nature of Short Swift Bursts via Deep INTEGRAL Monitoring of GRB 050925

NASA Technical Reports Server (NTRS)

Sakamoto, T.; Barbier, L.; Barthelmy, S. D.; Cummings, J. R.; Fenimore, E. E.; Gehrels, N.; Krimm, H. A.; Markwardt, C. B.; Palmer, D. M.; Parsons, A. M.;

Integrating Gender and Group Differences into Bridging Strategy

ERIC Educational Resources Information Center

Yilmaz, Serkan; Eryilmaz, Ali

2010-01-01

The main goal of this study was to integrate gender and group effect into bridging strategy in order to assess the effect of bridging analogy-based instruction on sophomore students' misconceptions in Newton's Third Law. Specifically, the authors developed and benefited from anchoring analogy diagnostic test to merge the effect of group and gender…

The Physics of Bird Flight: An Experiment

ERIC Educational Resources Information Center

Mihail, Michael D.; George, Thomas F.; Feldman, Bernard J.

2008-01-01

This article describes an experiment that measures the forces acting on a flying bird during takeoff. The experiment uses a minimum of equipment and only an elementary knowledge of kinematics and Newton's second law. The experiment involves first digitally videotaping a bird during takeoff, analyzing the video to determine the bird's position as a…

Origins of Newton's First Law

ERIC Educational Resources Information Center

Hecht, Eugene

2015-01-01

Anyone who has taught introductory physics should know that roughly a third of the students initially believe that any object at rest will remain at rest, whereas any moving body not propelled by applied forces will promptly come to rest. Likewise, about half of those uninitiated students believe that any object moving at a constant speed must be…

Saying the Wrong Thing: Improving Learning with Multimedia by Including Misconceptions

ERIC Educational Resources Information Center

Muller, D. A.; Bewes, J.; Sharma, M. D.; Reimann, P.

2008-01-01

In this study, 364 first-year physics students were randomly assigned to one of four online multimedia treatments on Newton's First and Second Laws of Motion: (1) the "Exposition", a concise lecture-style presentation; (2) the "Extended Exposition", the Exposition with additional interesting information; (3) the "Refutation", the Exposition with…

Flight Physics for Beginners: Simple Examples of Applying Newton's Laws

ERIC Educational Resources Information Center

Spathopoulos, Vassilis

2011-01-01

Educators are constantly trying to find new ways of motivating their students. In subjects such as mechanics with a strong mathematical component, it is particularly important to devise real-life examples that can increase interest and student excitement. Aircraft flight is a topic that most young people find exciting. It therefore would seem…

Physical Analysis of an Electric Resistor Heating

ERIC Educational Resources Information Center

Perea Martins, J. E. M.

2018-01-01

This work describes a simple experiment to measure the resistor temperature as a function of the applied power and proves that it is an efficient way to introduce some important physical concepts in classroom, including the Joule's first law, hot-spot temperature, thermal resistance, thermal dissipation constant, time constant and the Newton's law…

How Fast Does a Building Fall?

ERIC Educational Resources Information Center

Denny, Mark

2010-01-01

In this paper, the time required for a tower block to collapse is calculated. The tower collapses progressively, with one floor falling onto the floor below, causing it to fall. The rate of collapse is found to be not much slower than freefall. The calculation is an engaging and relevant application of Newton's laws, suitable for undergraduate…

Newton's Third Law on a Scale Balance

ERIC Educational Resources Information Center

Nopparatjamjomras, Suchai; Panijpan, Bhinyo; Huntula, Jiradawan

2009-01-01

We propose a series of experiments involving balance readings of an object naturally floating or forced to be partially or fully immersed in water contained in a beaker sitting on an electronic scale balance. Students were asked to predict, observe and explain each case. The teacher facilitated the learning by asking probing questions, giving…

Promoting Vicarious Learning of Physics Using Deep Questions with Explanations

ERIC Educational Resources Information Center

Craig, Scotty D.; Gholson, Barry; Brittingham, Joshua K.; Williams, Joah L.; Shubeck, Keith T.

2012-01-01

Two experiments explored the role of vicarious "self" explanations in facilitating student learning gains during computer-presented instruction. In Exp. 1, college students with low or high knowledge on Newton's laws were tested in four conditions: (a) monologue (M), (b) questions (Q), (c) explanation (E), and (d) question + explanation (Q + E).…

The Foundations of Einstein's Theory of Gravitation

NASA Astrophysics Data System (ADS)

Freundlich, Erwin; Brose, Translated by Henry L.; Einstein, Preface by Albert; Turner, Introduction by H. H.

2011-06-01

Introduction; 1. The special theory of relativity as a stepping-stone to the general theory of relativity; 2. Two fundamental postulates in the mathematical formulation of physical laws; 3. Concerning the fulfilment of the two postulates; 4. The difficulties in the principles of classical mechanics; 5. Einstein's theory of gravitation; 6. The verification of the new theory by actual experience; Appendix; Index.

Hanging an Airplane: A Case Study in Static Equilibrium

ERIC Educational Resources Information Center

Katz, Debora M.

2009-01-01

Our classrooms are filled with engineering majors who take a semester-long course in static equilibrium. Many students find this class too challenging and drop their engineering major. In our introductory physics class, we often breeze through static equilibrium; to physicists equilibrium is just a special case of Newton's second law. While it is…

Connecting in Space: Docking with the International Space Station. Educational Brief.

ERIC Educational Resources Information Center

National Aeronautics and Space Administration, Washington, DC.

This brief discusses the space shuttle and the docking procedures used with the International Space Station (ISS). Using this activity designed for grades 5-12, students demonstrate and identify procedures for determining the best method for completing the docking activity. Students will also study and identify Newton's Laws of Motion. A mockup…

Explanation of relativistic phenomena on the basis of interactions of particle energy, applied energy, and field energy

NASA Astrophysics Data System (ADS)

Fernando, Viraj

2011-09-01

This paper formulates a coherent theory of occurrence of relativistic phenomena in their interconnection in a feedback loop, unlike other theories, by tracing back concepts that Newton held but suppressed, when he developed his mechanics in his Principia. Despite Newtonian mechanics being based on a closed system, Newton in the General Scholium has indicated that in reality thee is in an open system, where 'a certain most subtle spirit' participates and directs all interactions from motion of bodies, to motion of light, to how the human brain operates. We have identified this 'most subtle spirit' as the non-empirical 'universal governing field' and that no empirical interaction in this universe can occur without exchange of energy between the empirical interactants and the governing field. By analyzing the energy momentum equation, we have demonstrated that everything empirical has a non-empirical substratum, identified with Spinoza's primitive substance, which binds everything in the universe to the field and through it to one another. Algorithm of Motion is founded on the Pythagorean character of the energy-momentum equation, which is applicable to all velocities 0

Flow of sand and a variable mass Atwood machine

NASA Astrophysics Data System (ADS)

Flores, José; Solovey, Guillermo; Gil, Salvador

2003-07-01

We discuss a simple and inexpensive apparatus that lets us measure the instantaneous flow rate of granular media, such as sand, in real time. The measurements allow us to elucidate the phenomenological laws that govern the flow of granular media through an aperture. We use this apparatus to construct a variable mass system and study the motion of an Atwood machine with one weight changing in time in a controlled manner. The study illustrates Newton's second law for variable mass systems and lets us investigate the dependence of the flow rate on acceleration.

Applying the Socratic Method to Physics Education

NASA Astrophysics Data System (ADS)

Corcoran, Ed

2005-04-01

We have restructured University Physics I and II in accordance with methods that PER has shown to be effective, including a more interactive discussion- and activity-based curriculum based on the premise that developing understanding requires an interactive process in which students have the opportunity to talk through and think through ideas with both other students and the teacher. Studies have shown that in classes implementing this approach to teaching as compared to classes using a traditional approach, students have significantly higher gains on the Force Concept Inventory (FCI). This has been true in UPI. However, UPI FCI results seem to suggest that there is a significant conceptual hole in students' understanding of Newton's Second Law. Two labs in UPI which teach Newton's Second Law will be redesigned replacing more activity with students as a group talking through, thinking through, and answering conceptual questions asked by the TA. The results will be measured by comparing FCI results to those from previous semesters, coupled with interviews. The results will be analyzed, and we will attempt to understand why gains were or were not made.

Thermoregulation in endotherms: physiological principles and ecological consequences.

PubMed

Rezende, Enrico L; Bacigalupe, Leonardo D

2015-10-01

In a seminal study published nearly 70 years ago, Scholander et al. (Biol Bull 99:259-271, 1950) employed Newton's law of cooling to describe how metabolic rates (MR) in birds and mammals vary predictably with ambient temperature (T a). Here, we explore the theoretical consequences of Newton's law of cooling and show that a thermoregulatory polygon provides an intuitively simple and yet useful description of thermoregulatory responses in endothermic organisms. This polygon encapsulates the region in which heat production and dissipation are in equilibrium and, therefore, the range of conditions in which thermoregulation is possible. Whereas the typical U-shaped curve describes the relationship between T a and MR at rest, thermoregulatory polygons expand this framework to incorporate the impact of activity, other behaviors and environmental conditions on thermoregulation and energy balance. We discuss how this framework can be employed to study the limits to effective thermoregulation and their ecological repercussions, allometric effects and residual variation in MR and thermal insulation, and how thermoregulatory requirements might constrain locomotor or reproductive performance (as proposed, for instance, by the heat dissipation limit theory). In many systems the limited empirical knowledge on how organismal traits may respond to environmental changes prevents physiological ecology from becoming a fully developed predictive science. In endotherms, however, we contend that the lack of theoretical developments that translate current physiological understanding into formal mechanistic models remains the main impediment to study the ecological and evolutionary repercussions of thermoregulation. In spite of the inherent limitations of Newton's law of cooling as an oversimplified description of the mechanics of heat transfer, we argue that understanding how systems that obey this approximation work can be enlightening on conceptual grounds and relevant as an analytical and predictive tool to study ecological phenomena. As such, the proposed approach may constitute a powerful tool to study the impact of thermoregulatory constraints on variables related to fitness, such as survival and reproductive output, and help elucidating how species will be affected by ongoing climate change.

Optimizing the inner loop of the gravitational force interaction on modern processors

DOE Office of Scientific and Technical Information (OSTI.GOV)

Warren, Michael S

2010-12-08

We have achieved superior performance on multiple generations of the fastest supercomputers in the world with our hashed oct-tree N-body code (HOT), spanning almost two decades and garnering multiple Gordon Bell Prizes for significant achievement in parallel processing. Execution time for our N-body code is largely influenced by the force calculation in the inner loop. Improvements to the inner loop using SSE3 instructions has enabled the calculation of over 200 million gravitational interactions per second per processor on a 2.6 GHz Opteron, for a computational rate of over 7 Gflops in single precision (700/0 of peak). We obtain optimal performancemore » some processors (including the Cell) by decomposing the reciprocal square root function required for a gravitational interaction into a table lookup, Chebychev polynomial interpolation, and Newton-Raphson iteration, using the algorithm of Karp. By unrolling the loop by a factor of six, and using SPU intrinsics to compute on vectors, we obtain performance of over 16 Gflops on a single Cell SPE. Aggregated over the 8 SPEs on a Cell processor, the overall performance is roughly 130 Gflops. In comparison, the ordinary C version of our inner loop only obtains 1.6 Gflops per SPE with the spuxlc compiler.« less

At Odds: Reconciling Experimental and Theoretical Results in High School Physics

ERIC Educational Resources Information Center

Gates, Joshua

2009-01-01

For this experiment, students are divided into 2 groups and presented with a static equilibrium force-balance problem to solve. One group works entirely experimentally and the other group theoretically, using Newton's laws. The groups present their seemingly dissimilar results and must reconcile them through discussion. (Contains 3 figures.)

Transforming Common-Sense Beliefs into Newtonian Thinking through Just-in-Time Teaching

ERIC Educational Resources Information Center

Formica, Sarah P.; Easley, Jessica L.; Spraker, Mark C.

2010-01-01

To determine whether teaching an introductory physics course with a traditional lecture style or with Just-in-Time teaching (a student-centered, interactive-engagement style) will help students to better understand Newtonian concepts, such as Newton's Third Law, 222 students in introductory physics courses taught by traditional lecture styles and…

N-body dynamics on closed surfaces: the axioms of mechanics

PubMed Central

Dritschel, David G.; Schaefer, Rodrigo G.

2016-01-01

A major challenge for our understanding of the mathematical basis of particle dynamics is the formulation of N-body and N-vortex dynamics on Riemann surfaces. In this paper, we show how the two problems are, in fact, closely related when considering the role played by the intrinsic geometry of the surface. This enables a straightforward deduction of the dynamics of point masses, using recently derived results for point vortices on general closed differentiable surfaces M endowed with a metric g. We find, generally, that Kepler's Laws do not hold. What is more, even Newton's First Law (the law of inertia) fails on closed surfaces with variable curvature (e.g. the ellipsoid). PMID:27616915

Speed, Acceleration, and Velocity: Level II, Unit 9, Lesson 1; Force, Mass, and Distance: Lesson 2; Types of Motion and Rest: Lesson 3; Electricity and Magnetism: Lesson 4; Electrical, Magnetic, and Gravitational Fields: Lesson 5; The Conservation and Conversion of Matter and Energy: Lesson 6; Simple Machines and Work: Lesson 7; Gas Laws: Lesson 8; Principles of Heat Engines: Lesson 9; Sound and Sound Waves: Lesson 10; Light Waves and Particles: Lesson 11; Program. A High.....

ERIC Educational Resources Information Center

Manpower Administration (DOL), Washington, DC. Job Corps.

This self-study program for high-school level contains lessons on: Speed, Acceleration, and Velocity; Force, Mass, and Distance; Types of Motion and Rest; Electricity and Magnetism; Electrical, Magnetic, and Gravitational Fields; The Conservation and Conversion of Matter and Energy; Simple Machines and Work; Gas Laws; Principles of Heat Engines;…

Nonrelativistic fluids on scale covariant Newton-Cartan backgrounds

NASA Astrophysics Data System (ADS)

Mitra, Arpita

2017-12-01

The nonrelativistic covariant framework for fields is extended to investigate fields and fluids on scale covariant curved backgrounds. The scale covariant Newton-Cartan background is constructed using the localization of space-time symmetries of nonrelativistic fields in flat space. Following this, we provide a Weyl covariant formalism which can be used to study scale invariant fluids. By considering ideal fluids as an example, we describe its thermodynamic and hydrodynamic properties and explicitly demonstrate that it satisfies the local second law of thermodynamics. As a further application, we consider the low energy description of Hall fluids. Specifically, we find that the gauge fields for scale transformations lead to corrections of the Wen-Zee and Berry phase terms contained in the effective action.

Free fall and the equivalence principle revisited

NASA Astrophysics Data System (ADS)

Pendrill, Ann-Marie

2017-11-01

Free fall is commonly discussed as an example of the equivalence principle, in the context of a homogeneous gravitational field, which is a reasonable approximation for small test masses falling moderate distances. Newton’s law of gravity provides a generalisation to larger distances, and also brings in an inhomogeneity in the gravitational field. In addition, Newton’s third law of action and reaction causes the Earth to accelerate towards the falling object, bringing in a mass dependence in the time required for an object to reach ground—in spite of the equivalence between inertial and gravitational mass. These aspects are rarely discussed in textbooks when the motion of everyday objects are discussed. Although these effects are extremely small, it may still be important for teachers to make assumptions and approximations explicit, to be aware of small corrections, and also to be prepared to estimate their size. Even if the corrections are not part of regular teaching, some students may reflect on them, and their questions deserve to be taken seriously.

Sensitivity curves for searches for gravitational-wave backgrounds

NASA Astrophysics Data System (ADS)

Thrane, Eric; Romano, Joseph D.

2013-12-01

We propose a graphical representation of detector sensitivity curves for stochastic gravitational-wave backgrounds that takes into account the increase in sensitivity that comes from integrating over frequency in addition to integrating over time. This method is valid for backgrounds that have a power-law spectrum in the analysis band. We call these graphs “power-law integrated curves.” For simplicity, we consider cross-correlation searches for unpolarized and isotropic stochastic backgrounds using two or more detectors. We apply our method to construct power-law integrated sensitivity curves for second-generation ground-based detectors such as Advanced LIGO, space-based detectors such as LISA and the Big Bang Observer, and timing residuals from a pulsar timing array. The code used to produce these plots is available at https://dcc.ligo.org/LIGO-P1300115/public for researchers interested in constructing similar sensitivity curves.

Corrections to Newton’s law of gravitation - application to hybrid Bloch brane

NASA Astrophysics Data System (ADS)

Almeida, C. A. S.; Veras, D. F. S.; Dantas, D. M.

2018-02-01

We present in this work, the calculations of corrections in the Newton’s law of gravitation due to Kaluza-Klein gravitons in five-dimensional warped thick braneworld scenarios. We consider here a recently proposed model, namely, the hybrid Bloch brane. This model couples two scalar fields to gravity and is engendered from a domain wall-like defect. Also, two other models the so-called asymmetric hybrid brane and compact brane are considered. Such models are deformations of the ϕ 4 and sine-Gordon topological defects, respectively. Therefore we consider the branes engendered by such defects and we also compute the corrections in their cases. In order to attain the mass spectrum and its corresponding eigenfunctions which are the essential quantities for computing the correction to the Newtonian potential, we develop a suitable numerical technique. The calculation of slight deviations in the gravitational potential may be used as a selection tool for braneworld scenarios matching with future experimental measurements in high energy collisions

XMM-Newton Archival Study of the ULX Population in Nearby Galaxies

NASA Technical Reports Server (NTRS)

Winter, Lisa M.; Mushotzky, Richard; Reynolds, Christopher S.

2005-01-01

We have conducted an archival XMM-Newton study of the bright X-ray point sources in 32 nearby galaxies. From our list of approximately 100 point sources, we attempt to determine if there is a low-state counterpart to the Ultraluminous X-ray (ULX) population. Indeed, 16 sources in our sample match the criteria we set for a low-state ULX, namely, L(sub X) greater than 10(exp 38 ergs per second) and a spectrum best fit with an absorbed power law. Further, we find evidence for 26 high-state ULXs which are best fit by a combined blackbody and a power law. As in Galactic black hole systems, the spectral indices, GAMMA, of the low-state objects, as well a s the luminosities, tend to be lower than those of the high-state objects. The observed range of blackbody temperatures is 0.1-1 keV with the most luminous systems tending toward the lowest temperatures. We also find a class of object whose properties (luminosity, blackbody temperature, and power law slopes) are very similar to those of galactic stellar mass black holes. In addition, we find a subset of these objects that can be best fit by a Comptonized spectrum similar to that used for Galactic black holes in the very high state, when they are radiating near the Eddington limit.

Evidence for Orbital Decay of RX J1914.4+2456: Gravitational Radiation and the Nature of the X-Ray Emission

NASA Technical Reports Server (NTRS)

Strohmayer, Tod E.; White, Nicholas E. (Technical Monitor)

2002-01-01

RX J1914.4+2456 is a candidate double-degenerate binary (AM CVn) with a putative 569 s orbital period. If this identification is correct, then it has one of the shortest binary orbital periods known, and gravitational radiation should drive the orbital evolution and mass transfer if the binary is semi-detached. Here we report the results of a coherent timing study of the archival ROSAT data for RX J1914.4+2456. We performed a phase coherent timing analysis using all five ROSAT observations spanning a four-year period. We demonstrate that all the data can be phase connected, and we show that the 1.756 mHz orbital frequency is increasing at a rate of 1.5 +/- 0.4 x 10(exp -17) Hz/s consistent with the expected loss of angular momentum from the binary system via gravitational radiation. In addition to providing evidence for the emission of gravitational waves, our measurement of the orbital v(dot) constrains models for the X-ray emission and the nature of the secondary. If stable mass accretion drives the X-ray flux, then a positive v(dot) is inconsistent with a degenerate donor. A helium burning dwarf is compatible if indeed such systems can have periods as short as that of RX J1914.4+2456, an open theoretical question. Our measurement of a positive v(dot) is consistent with the unipolar induction model of Wu et al. which does not require accretion to drive the X-ray flux. We discuss how future timing measurements of RX J1914.4+2456 (and systems like it) with for example, Chandra and XMM-Newton, can provide a unique probe of the interaction between mass loss and gravitational radiation. We also discuss the importance of such measurements in the context of gravitational wave detection from space, such as is expected in the future with the LISA mission.

Accurate Determination of Comet and Asteroid Orbits Leading to Collision With Earth

NASA Technical Reports Server (NTRS)

Roithmayr, Carlos M.; Kay-Bunnell, Linda; Mazanek, Daniel D.; Kumar, Renjith R.; Seywald, Hans; Hausman, Matthew A.

2005-01-01

Movements of the celestial bodies in our solar system inspired Isaac Newton to work out his profound laws of gravitation and motion; with one or two notable exceptions, all of those objects move as Newton said they would. But normally harmonious orbital motion is accompanied by the risk of collision, which can be cataclysmic. The Earth s moon is thought to have been produced by such an event, and we recently witnessed magnificent bombardments of Jupiter by several pieces of what was once Comet Shoemaker-Levy 9. Other comets or asteroids may have met the Earth with such violence that dinosaurs and other forms of life became extinct; it is this possibility that causes us to ask how the human species might avoid a similar catastrophe, and the answer requires a thorough understanding of orbital motion. The two red square flags with black square centers displayed are internationally recognized as a warning of an impending hurricane. Mariners and coastal residents who know the meaning of this symbol and the signs evident in the sky and ocean can act in advance to try to protect lives and property; someone who is unfamiliar with the warning signs or chooses to ignore them is in much greater jeopardy. Although collisions between Earth and large comets or asteroids occur much less frequently than landfall of a hurricane, it is imperative that we learn to identify the harbingers of such collisions by careful examination of an object s path. An accurate determination of the orbit of a comet or asteroid is necessary in order to know if, when, and where on the Earth s surface a collision will occur. Generally speaking, the longer the warning time, the better the chance of being able to plan and execute action to prevent a collision. The more accurate the determination of an orbit, the less likely such action will be wasted effort or, what is worse, an effort that increases rather than decreases the probability of a collision. Conditions necessary for a collision to occur are discussed, and warning times for long-period comets and near-Earth asteroids are presented.

Correcting Geophysical Fallacies

NASA Astrophysics Data System (ADS)

Barbat, W. N.

2013-12-01

The escape velocity from a Big Bang explosion would greatly exceed the speed of light, which is impossible; William Tifft's (1976-77) observations of a common stepwise decline in photon size of 72.5 km/sec replaces a universal Doppler Red Shift, so the universe is not expanding; and the idea that all the mass and energy of the universe were instantly created is unscientific. Joseph Larmor's 1897 equation relates the radiation of photons from a moving electric charge to the square of a change of the acceleration of the charge. Hence the continual centripetal acceleration of orbiting electrons continually radiates low grade photon heat (Zero Point Energy). Shpenkov and Kreidik (2008) found that the heat source which sustains the Cosmic Background Energy at the measured peak blackbody temperature of 2.725+/-0.002K must be due to radiation from the orbital electron motion of hydrogen at its fundamental period, which they calculated to be 2.7289K. Cosmic Background Energy is not left over from a Big Bang 13 billion years ago. Of course, if nature can create energy, then it is reasonable to expect that man can create energy too. Importantly, the creation of photons by orbiting electrons and spinning protons also creates mass. Isaac Newton showed in Book 3 of Opticks that light rays bend as they pass closely over a sharp knife edge, and that the closer the ray is to the knife edge, the more the light path bends. Newton thus showed that corpuscles of light (photons) obey the law of gravitation, so photons possess mass. Photon creation inside stars builds up intense heat and pressure, splitting photons into electrons and positrons. A large positron and photon can apparently combine into a three lump particle with a charge of plus one, making a new proton. Hollow electrons can apparently surround a proton, making a neutron for fission. A small spun-off star advances up the main sequence until a buildup of iron cools and shrinks the core from its hydrogen envelope, leaving a planet. Over eons, planets increase to 70-90% of older galaxies to comprise Dark Matter. Radiation from orbiting electrons and spinning protons would comprise Dark Energy.

The New Interpretation of the Laws of Air Resistance

NASA Technical Reports Server (NTRS)

Prandtl, L

1923-01-01

A closer examination of Newton's formula for air resistance shows that it is well to consider the air as an ordinary fluid, and, indeed for most of the velocities considered, as a non-compressible fluid, so long as the dimensions of the moving body are large in comparison with the mean free path of the particles of air.

Visualization of Kepler’s laws of planetary motion

NASA Astrophysics Data System (ADS)

Lu, Meishu; Su, Jun; Wang, Weiguo; Lu, Jianlong

2017-03-01

For this article, we use a 3D printer to print a surface similar to universal gravitation for demonstrating and investigating Kepler’s laws of planetary motion describing the motion of a small ball on the surface. This novel experimental method allows Kepler’s laws of planetary motion to be visualized and will contribute to improving the manipulative ability of middle school students and the accessibility of classroom education.

Measuring the Specific Heat of Metals by Cooling

ERIC Educational Resources Information Center

Dittrich, William; Minkin, Leonid; Shapovalov, Alexander S.

2010-01-01

Three in one? Yes, three standard undergraduate thermodynamics experiments in one, not an oval can of lubricating oil. Previously it has been shown that the PASCO scientific apparatus for measuring coefficients of thermal expansion of metals can also be used to illustrate Newton's law of cooling in the same experiment. Now it will be shown that by…

The Effect of Concept Cartoon-Embedded Worksheets on Grade 9 Students' Conceptual Understanding of Newton's Laws of Motion

ERIC Educational Resources Information Center

Atasoy, Sengül; Ergin, Serap

2017-01-01

Background: A substantial review study of concept cartoons reports that few studies have indicated their functions. For this reason, the present study illuminates the extent to which concept cartoon-embedded worksheets (through constructivist context) accomplish these functions in conceptual learning. Purpose: The purpose of the study is to…

A Simple Apparatus for Demonstrating Fluid Forces and Newton's Third Law

ERIC Educational Resources Information Center

Mohazzabi, Pirooz; James, Mark C.

2012-01-01

Over 2200 years ago, in order to determine the purity of a golden crown of the king of Syracuse, Archimedes submerged the crown in water and determined its volume by measuring the volume of the displaced water. This simple experiment became the foundation of what eventually became known as Archimedes' principle: An object fully or partially…

Introducing Gyroscopes Quantitatively without Putting Students into a Spin

ERIC Educational Resources Information Center

McGlynn, Enda

2007-01-01

The uniform precession of a simple form of gyroscope is analysed via a direct application of Newton's laws, using only concepts generally taught to physics and engineering students in the first two years of an undergraduate programme, with an emphasis on understanding the forces and torques acting on the system. This type of approach, in the…

How Can "Weightless" Astronauts Be Weighed?

ERIC Educational Resources Information Center

Carnicer, Jesus; Reyes, Francisco; Guisasola, Jenaro

2012-01-01

In introductory physics courses, within the context of studying Newton's laws, it is common to consider the problem of a body's "weight" when it is in free fall. The solution shows that the "weight" is zero and this leads to a discussion of the concept of weight. There are permanent free-fall situations such as astronauts in a spacecraft orbiting…

Work-Energy Theorem and Friction Forces: Two Experiments

ERIC Educational Resources Information Center

Bonanno, A.; Bozzo, G.; Grandinetti, M.; Sapia, P.

2016-01-01

Several studies have showed the subsistence, even in students enrolled in scientific degree courses, of spontaneous ideas regarding the motion of bodies that conflict with Newton's laws. One of the causes is related to the intuitive preconceptions that students have about the role of friction as a force. In fact, in real world novices do not…

The Use of Force Notation to Detect Students' Misconceptions: Mutual Interactions Case

ERIC Educational Resources Information Center

Serhane, Ahcene; Zeghdaoui, Abdelhamid; Debiache, Mehdi

2017-01-01

Using a conventional notation for representing forces on diagrams, students were presented with questions on the interaction between two objects. The results show that complete understanding of Newton's Third Law of Motion is quite rare, and that some problems relate to misunderstanding which force acts on each body. The use of the terms…

Swept Away: Exploring the Physics of Curling

ERIC Educational Resources Information Center

Esser, Liza

2011-01-01

Studying the Olympic sport of curling is a fun and engaging way to learn about the concepts of friction, forces, momentum, and Newton's laws. Each winter, the author takes her eighth-grade physical science class on a field trip to experience curling firsthand. This field trip has become a favorite of the eighth graders at Capitol Hill Day School…

Explaining Newton's Laws of Motion: Using Student Reasoning through Representations to Develop Conceptual Understanding

ERIC Educational Resources Information Center

Waldrip, Bruce; Prain, Vaughan; Sellings, Peter

2013-01-01

The development of students' reasoning and argumentation skills in school science is currently attracting strong research interest. In this paper we report on a study where we aimed to investigate student learning on the topic of motion when students, guided by their teacher, responded to a sequence of representational challenges in which their…

Modeling the Motion of an Increasing Mass System

ERIC Educational Resources Information Center

Kunkel, William; Harrington, Randal

2010-01-01

Problems on the dynamics of changing mass systems often call for the more general form of Newton's second law Fnet = dp/dt. These problems usually involve situations where the mass of the system decreases, such as in rocket propulsion. In contrast, this experiment examines a system where the mass "increases" at a constant rate and the net force…

Application of Newtonian Physics to Predict the Speed of a Gravity Racer

ERIC Educational Resources Information Center

Driscoll, H. F.; Bullas, A. M.; King, C. E.; Senior, T.; Haake, S. J.; Hart, J.

2016-01-01

Gravity racing can be studied using numerical solutions to the equations of motion derived from Newton's second law. This allows students to explore the physics of gravity racing and to understand how design and course selection influences vehicle speed. Using Euler's method, we have developed a spreadsheet application that can be used to predict…

The Step to Rationality: The Efficacy of Thought Experiments in Science, Ethics, and Free Will

ERIC Educational Resources Information Center

Shepard, Roger N.

2008-01-01

Examples from Archimedes, Galileo, Newton, Einstein, and others suggest that fundamental laws of physics were--or, at least, could have been--discovered by experiments performed not in the physical world but only in the mind. Although problematic for a strict empiricist, the evolutionary emergence in humans of deeply internalized implicit…

What Supports an Aeroplane? Force, Momentum, Energy and Power in Flight

ERIC Educational Resources Information Center

Robertson, David

2014-01-01

Some apparently confusing aspects of Newton's laws as applied to an aircraft in normal horizontal flight are neatly resolved by a careful analysis of force, momentum, energy and power. A number of related phenomena are explained at the same time, including the lift and induced drag coefficients, used empirically in the aviation industry.

Computer Solution of the Two-Dimensional Tether Ball: Problem to Illustrate Newton's Second Law.

ERIC Educational Resources Information Center

Zimmerman, W. Bruce

Force diagrams involving angular velocity, linear velocity, centripetal force, work, and kinetic energy are given with related equations of motion expressed in polar coordinates. The computer is used to solve differential equations, thus reducing the mathematical requirements of the students. An experiment is conducted using an air table to check…

Misconceptions on Classical Mechanics by Freshman University Students: A Case Study in a Physics Department in Greece

ERIC Educational Resources Information Center

Stylos, George; Evangelakis, George A.; Kotsis, Konstantinos T.

2008-01-01

This paper presents results of an empirical research study on Newton's laws classical mechanics and its perceptions on freshman students at the Physics Department, University of Ioannina, Greece. Results and outcome measures reveal misconceptions on students' perceptions in consideration of the fundamental concepts in freshman Physics education.…

Problem Solving of Newton's Second Law through a System of Total Mass Motion

ERIC Educational Resources Information Center

Abdullah, Helmi

2014-01-01

Nowadays, many researchers discovered various effective strategies in teaching physics, from traditional to modern strategy. However, research on physics problem solving is still inadequate. Physics problem is an integral part of physics learning and requires strategy to solve it. Besides that, problem solving is the best way to convey principle,…

Wren, Sir Christopher (1632-1723)

NASA Astrophysics Data System (ADS)

Murdin, P.

2000-11-01

Architect and astronomer, born in East Knoyle, Wiltshire, became professor of astronomy at Gresham College, and Savilian Professor of Astronomy at Oxford. He rebuilt London after the fire of 1666, planning the entire city and rebuilding 51 churches, including St Paul's Cathedral. Newton acknowledges Wren as a mathematician in the Principia. Wren independently proved KEPLER's third law and formula...

The Physics of a Walking Robot

ERIC Educational Resources Information Center

Guemez, J.; Fiolhais, M.

2013-01-01

The physics of walking is explored, using a toy as a concrete example and a "toy model" applied to it. Besides using Newton's second law, the problem is also discussed from the thermodynamical perspective. Once the steady state (constant velocity) is achieved, we show that the internal energy of the toy is dissipated as heat in the…

Thermal conductivity as influenced by the temperature and apparent viscosity of dairy products.

PubMed

Gonçalves, B J; Pereira, C G; Lago, A M T; Gonçalves, C S; Giarola, T M O; Abreu, L R; Resende, J V

2017-05-01

This study aimed to evaluate the rheological behavior and thermal conductivity of dairy products, composed of the same chemical components but with different formulations, as a function of temperature. Subsequently, thermal conductivity was related to the apparent viscosity of yogurt, fermented dairy beverage, and fermented milk. Thermal conductivity measures and rheological tests were performed at 5, 10, 15, 20, and 25°C using linear probe heating and an oscillatory rheometer with concentric cylinder geometry, respectively. The results were compared with those calculated using the parallel, series, and Maxwell-Eucken models as a function of temperature, and the discrepancies in the results are discussed. Linear equations were fitted to evaluate the influence of temperature on the thermal conductivity of the dairy products. The rheological behavior, specifically apparent viscosity versus shear rate, was influenced by temperature. Herschel-Bulkley, power law, and Newton's law models were used to fit the experimental data. The Herschel-Bulkley model best described the adjustments for yogurt, the power law model did so for fermented dairy beverages, and Newton's law model did so for fermented milk and was then used to determine the rheological parameters. Fermented milk showed a Newtonian trend, whereas yogurt and fermented dairy beverage were shear thinning. Apparent viscosity was correlated with temperature by the Arrhenius equation. The formulation influenced the effective thermal conductivity. The relationship between the 2 properties was established by fixing the temperature and expressing conductivity as a function of apparent viscosity. Thermal conductivity increased with viscosity and decreased with increasing temperature. Copyright © 2017 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.

Drawing and Using Free Body Diagrams: Why It May Be Better Not to Decompose Forces

ERIC Educational Resources Information Center

Aviani, Ivica; Erceg, Nataša; Mešic, Vanes

2015-01-01

In this study we investigated how two different approaches to drawing free body diagrams influence the development of students' understanding of Newton's laws, including their ability to identify real forces. For this purpose we developed a 12-item two-tier multiple choice survey and conducted a quasiexperiment. This experiment included two groups…

Teaching Notes

NASA Astrophysics Data System (ADS)

2001-03-01

If you would like to contribute a teaching note for any of these sections please contact ped@iop.org. Contents: PHYSICS ON A SHOESTRING: Demonstrating resolution Magnetic tea patterns LET'S INVESTIGATE: Conducting foam TECHNICAL TRIMMINGS: Polarimeter Old experiments on air-tracks gain new fans MY WAY: Newton's laws ON THE MAP: The International School of Lusaka CURIOSITY: Inflation theory PHYSICS ON A SHOESTRING

The NANOGrav Nine-Year Data Set: Limits on the Isotropic Stochastic Gravitational Wave Background

NASA Technical Reports Server (NTRS)

Arzoumanian, Z.; Brazier, A.; Burke-Spolaor, S.; Chamberlin, S. J.; Chatterjee, S.; Christy, B.; Cordes, J. M.; Cornish, N. J.; Crowter, K.; Demorest, P. B.;

Einstein’s Legacy to Astronomy: From Black Holes to the Expanding Universe

NASA Astrophysics Data System (ADS)

Bartusiak, Marcia

2006-12-01

Albert Einstein placed a formidable imprint on astronomy. Not since the time of Isaac Newton, three centuries ago, has a single individual so influenced the field. Many of the great astronomical findings of the 20th century--the expanding universe, compact stars, origin of the Sun’s power, black holes, gravitational lensing, dark energy, gravity waves--are rooted in the physics that Einstein so brilliantly deduced. This illustrated presentation, the Gemant Award Lecture sponsored by the American Institute of Physics, will provide a guided tour through the cosmos and explain how our understanding of the universe was transformed by Einstein’s theories of special and general relativity.

Eddington's theory of gravity and its progeny.

PubMed

Bañados, Máximo; Ferreira, Pedro G

2010-07-02

We resurrect Eddington's proposal for the gravitational action in the presence of a cosmological constant and extend it to include matter fields. We show that the Newton-Poisson equation is modified in the presence of sources and that charged black holes show great similarities with those arising in Born-Infeld electrodynamics coupled to gravity. When we consider homogeneous and isotropic space-times, we find that there is a minimum length (and maximum density) at early times, clearly pointing to an alternative theory of the big bang. We thus argue that the modern formulation of Eddington's theory, Born-Infeld gravity, presents us with a novel, nonsingular description of the Universe.

Quantum-corrected Geometry of Horizon Vicinity

NASA Astrophysics Data System (ADS)

Park, I. Y.

2017-12-01

We study the deformation of the horizon-vicinity geometry caused by quantum gravitational effects. Departure from the semi-classical picture is noted, and the fact that the matter part of the action comes at a higher order in Newton's constant than does the Einstein-Hilbert term is crucial for the departure. The analysis leads to a Firewall-type energy measured by an infalling observer for which quantum generation of the cosmological constant is critical. The analysis seems to suggest that the Firewall should be a part of such deformation and that the information be stored both in the horizon-vicinity and asymptotic boundary region. We also examine the behavior near the cosmological horizon.

That gravity thing

NASA Astrophysics Data System (ADS)

Jewess, Mike

2009-05-01

Your news article "New probe plots Earth's gravity field" (March p11) reports on the European Space Agency's Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) - a satellite that will measure the Earth's gravitational field. It describes the way that g, the acceleration of free fall at the Earth's surface, varies with latitude; this variation is great enough to require adjustment of pendulum clocks between latitudes and also the recalibration of all balances that do not directly compare one mass with a reference mass. The article also notes that the spin of the (effectively fluid) Earth causes it to bulge at the equator, a realization that goes back to Newton's Principia.

Statolith action by the numbers: Physics and feasbility

NASA Astrophysics Data System (ADS)

Todd, Paul; Yoder, Thomas; Staehelin, L. Andrew

2016-07-01

All modern (and ancient) studies make it clear that statolith motion is required for gravisensing, and some evidence indicates a role for statolith-microfilament interaction. In this study two components of statolith action are considered quantitatively: (1) the movement of statoliths through the columella cell cytoplasm and (2) forces at the site of action of the statolith. (1) Statoliths move through the cytoplasm in the presence of viscous and elastic forces that may be considered separately. The viscous component may be characterized as a solution with a viscosity of approximately 40 centiPoise. Statoliths are deflected from perfectly vertical trajectories by various obstacles, including actin filaments, and their velocities are influenced by interactions between statoliths. Channeling flow is commonly observed, but this cannot be due to the breaking of actin filaments by the force of the sedimenting statolith, as about 600 pN force is required to break a filament, and the force due to gravity on the amyloplast is about 0.07 pN. Under least viscous conditions the randomly-directed Brownian diffusion velocity of the amyloplast is about 10% the sedimentation velocity. (2) Intimate association of statoliths with the cortical ER region requiring gravitational force is postulated. Thin-section micrographs clearly show an interface between the cortex and the central cytoplasm of the columella cell in vascular plant species that have been studied. Whether or not an exchange of chemical components is required, experiments, including observations in low gravity, have demonstrated that the statolith is shallowly embedded in this cortical region to the extent that deformation occurs consistent with Newton's third law. Relieving the gravitational force results in instantaneous motion of the amyloplast away from the cortex. The following inquiry was made concerning the physics at the interface between the statolith and the material of the cortical ER region. How much force does the statolith exert on the interface between the ER cortex and inner cytoplasm? What is the origin of the elastic force that opposes the penetration of the statolith and that causes it to rebound when the gravitational force is relieved? Candidates considered included actin filaments, endoplasmic membrane, an immiscible-phase interface, and a miscible-phase interface. Forces estimated to produce a 300nm indentation in such interfaces were 100, 30, 0.3, and <1 pN, respectively. The gravitational force on a single statolith is typically 0.1 pN or less. These numbers suggest that the statolith is interacting with an aqueous-aqueous interface with low interfacial tension (<1 μN/m). Further quantitative testing of these notions should be performed on forthcoming low-gravity sub-orbital crewed flights on which dynamic microscopy can be performed during several seconds of increased g-loading followed by some ten minutes of reduced gravity.

Pressure-Volume Work Exercises Illustrating the First and Second Laws.

ERIC Educational Resources Information Center

Hoover, William G.; Moran, Bill

1979-01-01

Presented are two problem exercises involving rapid compression and expansion of ideal gases which illustrate the first and second laws of thermodynamics. The first problem involves the conversion of gravitational energy into heat through mechanical work. The second involves the mutual interaction of two gases through an adiabatic piston. (BT)

Resolving the Large Scale Spectral Variability of the Luminous Seyfert 1 Galaxy 1H 0419-577

NASA Technical Reports Server (NTRS)

Pounds, K. A.; Reeves, J. N.; Page, K. L.; OBrien, P. T.

2004-01-01

An XMM-Newton observation of the luminous Seyfert 1 galaxy 1H 0419-577 in September 2002, when the source was in an extreme low-flux state, found a very hard X-ray spectrum at 1-10 keV with a strong soft excess below approximately 1 keV. Comparison with an earlier XMM-Newton observation when 1H 0419-577 was X-ray bright indicated the dominant spectral variability was due to a steep power law or cool Comptonized thermal emission. Four further XMM-Newton observations, with 1H 0419-577 in intermediate flux states, now support that conclusion, while we also find the variable emission component in intermediate state difference spectra to be strongly modified by absorption in low ionisation matter. The variable soft excess is seen to be an artefact of absorption of the underlying continuum while the core soft emission is attributed to recombination in an extended region of more highly ionised gas. This new analysis underlines the importance of fully accounting for absorption in characterizing AGN X-ray spectra.

Noether's stars in f (R) gravity

NASA Astrophysics Data System (ADS)

De Laurentis, Mariafelicia

2018-05-01

The Noether Symmetry Approach can be used to construct spherically symmetric solutions in f (R) gravity. Specifically, the Noether conserved quantity is related to the gravitational mass and a gravitational radius that reduces to the Schwarzschild radius in the limit f (R) → R. We show that it is possible to construct the M- R relation for neutron stars depending on the Noether conserved quantity and the associated gravitational radius. This approach enables the recovery of extreme massive stars that could not be stable in the standard Tolman-Oppenheimer-Volkoff based on General Relativity. Examples are given for some power law f (R) gravity models.

Gravitationally confined relativistic neutrinos

NASA Astrophysics Data System (ADS)

Vayenas, C. G.; Fokas, A. S.; Grigoriou, D.

2017-09-01

Combining special relativity, the equivalence principle, and Newton’s universal gravitational law with gravitational rather than rest masses, one finds that gravitational interactions between relativistic neutrinos with kinetic energies above 50 MeV are very strong and can lead to the formation of gravitationally confined composite structures with the mass and other properties of hadrons. One may model such structures by considering three neutrinos moving symmetrically on a circular orbit under the influence of their gravitational attraction, and by assuming quantization of their angular momentum, as in the Bohr model of the H atom. The model contains no adjustable parameters and its solution, using a neutrino rest mass of 0.05 eV/c2, leads to composite state radii close to 1 fm and composite state masses close to 1 GeV/c2. Similar models of relativistic rotating electron - neutrino pairs give a mass of 81 GeV/c2, close to that of W bosons. This novel mechanism of generating mass suggests that the Higgs mass generation mechanism can be modeled as a latent gravitational field which gets activated by relativistic neutrinos.

Dynamical evolution of dense star clusters in galactic nuclei

NASA Astrophysics Data System (ADS)

Haas, Jaroslav; Šubr, Ladislav

2014-05-01

By means of direct numerical N-body modeling, we investigate the orbital evolution of an initially thin, central mass dominated stellar disk. We include the perturbative gravitational influence of an extended spherically symmetric star cluster and the mutual gravitational interaction of the stars within the disk. Our results show that the two-body relaxation of the disk leads to significant changes of its radial density profile. In particular, the disk naturally evolves, for a variety of initial configurations, a similar broken power-law surface density profile. Hence, it appears that the single power-law surface density profile ∝R -2 suggested by various authors to describe the young stellar disk observed in the Sgr A* region does not match theoretical expectations.

Safety management of an underground-based gravitational wave telescope: KAGRA

NASA Astrophysics Data System (ADS)

Ohishi, Naoko; Miyoki, Shinji; Uchiyama, Takashi; Miyakawa, Osamu; Ohashi, Masatake

2014-08-01

KAGRA is a unique gravitational wave telescope with its location underground and use of cryogenic mirrors. Safety management plays an important role for secure development and operation of such a unique and large facility. Based on relevant law in Japan, Labor Standard Act and Industrial Safety and Health Law, various countermeasures are mandated to avoid foreseeable accidents and diseases. In addition to the usual safety management of hazardous materials, such as cranes, organic solvents, lasers, there are specific safety issues in the tunnel. Prevention of collapse, flood, and fire accidents are the most critical issues for the underground facility. Ventilation is also important for prevention of air pollution by carbon monoxide, carbon dioxide, organic solvents and radon. Oxygen deficiency should also be prevented.

Geometric optics for a coupling model of electromagnetic and gravitational fields

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jing, Jiliang, E-mail: jljing@hunnu.edu.cn; Chen, Songbai; Pan, Qiyuan

2016-04-15

The coupling between the electromagnetic and gravitational fields results in “faster than light” photons, and then the first and third laws of geometric optics are invalid in usual spacetime. By introducing an effective spacetime, we find that the wave vector can be casted into null and then it obeys the geodesic equation, the polarization vector is perpendicular to the rays, and the number of photons is conserved. That is to say, the laws of geometric optics are valid for the modified theory in the effective spacetime. We also show that the focusing theorem of light rays for the modified theorymore » in the effective spacetime can be cast into the usual form.« less

Kepler unbound: Some elegant curiosities of classical mechanics

NASA Astrophysics Data System (ADS)

MacKay, Niall J.; Salour, Sam

2015-01-01

We explain two exotic systems of classical mechanics: the McIntosh-Cisneros-Zwanziger ("MICZ") Kepler system, of motion of a charged particle in the presence of a modified dyon; and Gibbons and Manton's description of the slow motion of well-separated solitonic ("BPS") monopoles using Taub-NUT space. Each system is characterized by the conservation of a Laplace-Runge-Lenz vector, and we use elementary vector techniques to show that each obeys a subtly different variation on Kepler's three laws for the Newton-Coulomb two-body problem, including a new modified Kepler third law for BPS monopoles.

Fifth dimension of life and the 4/5 allometric scaling law for human brain.

PubMed

He, Ji-Huan; Zhang, Juan

2004-01-01

Brain cells are not spherical. The basal metabolic rate (B) of a spherical cell scales as B approximately r2, where r is the radius of the cell; that of a brain cell scales as B approximately r(d), where r is the characteristic radius of the cell and d is the fractal dimensionality of its contour. The fractal geometry of the cell leads to a 4/5 allometric scaling law for human brain, uniquely endowing humans with a 5th dimension and successfully explains why the scaling exponent varies during rest and exercise. A striking analogy between Kleiber's 3/4 law and Newton's second law is heuristically illustrated. A physical explanation is given for the 4th dimension of life for three-dimensional organisms and the 5th dimension for human brain.

INTEGRAL and XMM-Newton Spectral Studies of NGC 4388

NASA Technical Reports Server (NTRS)

Beckmann, V.; Gehrels, N.; Favre, P.; Walter, R.; Courvoisier, T. J.-L.; Petrucci, P.-O.; Malzac, J.

2004-01-01

We present first INTEGRAL and XMM-Newton observations of a Seyfert galaxy, the type 2 AGN NGC 4388. Several INTEGRAL observations performed in 2003 allow us to study the spectrum in the 20 - 300 keV range. In addition two XMM-Newton observations give detailed insight into the 0.2 - 10 keV emission. Comparison with previous observations by BeppoSAX, SIGMA and CGRO/OSSE show that the overall spectrum for soft X-rays up to the gamma-rays can be described by a highly absorbed (N(sub H approx. = 2.7 x 10(exp 23)/sq cm) and variable non-thermal component in addition to constant non-absorbed thermal emission (T approx. = 0.8 keV) of low abundance (Z approx. 5% Z (solar)), plus a constant Fe K a line. The hard X-ray component is well described by a simple power law with a mean photon index of Gamma = 1.7. During the INTEGRAL observations the flux at 100 keV increased by a factor of 1.5. The analysis of XMM-Newton data implies that the emission below 3 keV is decoupled from the AGN and probably due to extended emission as seen in Chandra observations. The constant iron line emission is apparently also decoupled from the direct emission of the central engine and likely to be generated in the obscuring material, e.g. in the molecular torus.

Duality of force laws and conformal transformations

NASA Astrophysics Data System (ADS)

Kothawala, Dawood

2011-06-01

As was first noted by Isaac Newton, the two most famous ellipses of classical mechanics, arising from the force laws F ∝r and F ∝1/r2, can be mapped onto each other by changing the location of the center of force. Less well known is that this mapping can also be achieved by the complex transformation, z →z2. We derive this result and its generalization by writing the Gaussian curvature in its covariant form, and then changing the metric by a conformal transformation which mimics this mapping of the curves. We indicate how the conserved Laplace-Runge-Lenz vector for the 1/r2 force law transforms under this transformation, and compare it with the corresponding quantities for the linear force law. Our main aim is to present this duality by introducing concepts from differential geometry.

Thermal analysis of a reactive generalized Couette flow of power law fluids between concentric cylindrical pipes

NASA Astrophysics Data System (ADS)

Makinde, O. D.

2014-12-01

In this paper, the steady generalized axial Couette flow of Ostwald-de Waele power law reactive fluids between concentric cylindrical pipes is investigated. It is assumed that the outer cylinder is stationary and exchanges heat with the ambient surrounding following Newton's law of cooling, while the inner cylinder with isothermal surface is set in motion in the axial direction. The model nonlinear differential equations for the momentum and energy balance are obtained and tackled numerically using the shooting method coupled with the Runge-Kutta-Fehlberg integration technique. The effects of various embedded thermophysical parameters on the velocity and temperature fields including skin friction, Nusselt number and thermal criticality conditions are presented graphically and discussed quantitatively.

Beyond Newton's Law of Cooling--Estimation of Time since Death

ERIC Educational Resources Information Center

Leinbach, Carl

2011-01-01

The estimate of the time since death and, thus, the time of death is strictly that, an estimate. However, the time of death can be an important piece of information in some coroner's cases, especially those that involve criminal or insurance investigations. It has been known almost from the beginning of time that bodies cool after the internal…

The Motion of a Leaking Oscillator: A Study for the Physics Class

ERIC Educational Resources Information Center

Rodrigues, Hilário; Panza, Nelson; Portes, Dirceu; Soares, Alexandre

2014-01-01

This paper is essentially about the general form of Newton's second law for variable mass problems. We develop a model for describing the motion of the one-dimensional oscillator with a variable mass within the framework of classroom physics. We present a simple numerical procedure for the solution of the equation of motion of the system to…

Discovery Learning, Representation, and Explanation within a Computer-Based Simulation: Finding the Right Mix

ERIC Educational Resources Information Center

Rieber, Lloyd P.; Tzeng, Shyh-Chii; Tribble, Kelly

2004-01-01

The purpose of this research was to explore how adult users interact and learn during an interactive computer-based simulation supplemented with brief multimedia explanations of the content. A total of 52 college students interacted with a computer-based simulation of Newton's laws of motion in which they had control over the motion of a simple…

Feedback and Elaboration within a Computer-Based Simulation: A Dual Coding Perspective.

ERIC Educational Resources Information Center

Rieber, Lloyd P.; And Others

The purpose of this study was to explore how adult users interact and learn during a computer-based simulation given visual and verbal forms of feedback coupled with embedded elaborations of the content. A total of 52 college students interacted with a computer-based simulation of Newton's laws of motion in which they had control over the motion…

Acceleration in One, Two, and Three Dimensions in Launched Roller Coasters

ERIC Educational Resources Information Center

Pendrill, Ann-Marie

2008-01-01

During a roller coaster ride, the body experiences acceleration in three dimensions. An accelerometer can measure and provide a graph of the forces on the body during different parts of a ride. To couple the experience of the body to pictures of the ride and an analysis of data can contribute to a deeper understanding of Newton's laws. This…