Weber's gravitational force as static weak field approximation

NASA Astrophysics Data System (ADS)

Tiandho, Yuant

2016-02-01

Weber's gravitational force (WGF) is one of gravitational model that can accommodate a non-static system because it depends not only on the distance but also on the velocity and the acceleration. Unlike Newton's law of gravitation, WGF can predict the anomalous of Mercury and gravitational bending of light near massive object very well. Then, some researchers use WGF as an alternative model of gravitation and propose a new mechanics theory namely the relational mechanics theory. However, currently we have known that the theory of general relativity which proposed by Einstein can explain gravity with very accurate. Through the static weak field approximation for the non-relativistic object, we also have known that the theory of general relativity will reduce to Newton's law of gravity. In this work, we expand the static weak field approximation that compatible with relativistic object and we obtain a force equation which correspond to WGF. Therefore, WGF is more precise than Newton's gravitational law. The static-weak gravitational field that we used is a solution of the Einstein's equation in the vacuum that satisfy the linear field approximation. The expression of WGF with ξ = 1 and satisfy the requirement of energy conservation are obtained after resolving the geodesic equation. By this result, we can conclude that WGF can be derived from the general relativity.

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)

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.

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…

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.

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.

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.

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.

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)

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…

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.

Plausibility Arguments and Universal Gravitation

ERIC Educational Resources Information Center

Cunha, Ricardo F. F.; Tort, A. C.

2017-01-01

Newton's law of universal gravitation underpins our understanding of the dynamics of the Solar System and of a good portion of the observable universe. Generally, in the classroom or in textbooks, the law is presented initially in a qualitative way and at some point during the exposition its mathematical formulation is written on the blackboard…

How Spherical Is a Cube (Gravitationally)?

ERIC Educational Resources Information Center

Sanny, Jeff; Smith, David

2015-01-01

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. By integrating over ring elements of a spherical shell, we show that the…

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…

Teaching Universal Gravitation with Vector Games

ERIC Educational Resources Information Center

Lowry, Matthew

2008-01-01

Like many high school and college physics teachers, I have found playing vector games to be a useful way of illustrating the concepts of inertia, velocity, and acceleration. Like many, I have also had difficulty in trying to get students to understand Newton's law of universal gravitation, specifically the inverse-square law and its application to…

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…

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…

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…

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.

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)

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.

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)

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…

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…

From the Landgrave in Kassel to Isaac Newton

NASA Astrophysics Data System (ADS)

Høg, E.

2018-01-01

Landgrave Wilhelm IV established in 1560 the first permanent astronomical observatory in Europe. When he met the young Tycho Brahe in 1575 he recognized the genius and recommended him warmly to the Danish king Frederik II. Wilhelm and Tycho must share the credit for renewing astronomy with very accurate observations of positions of stars by new instrumentation and new methods. Tycho's observations of planets during 20 years enabled Johannes Kepler to derive the laws of planetary motion. These laws set Isaac Newton in a position to publish the laws of physical motion and universal gravitation in 1687 - the basis for the technical revolution.

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.

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.

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.

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)

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…

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.

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.

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),…

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)

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

Mass and Motion: Topics at the Interface of General Relativity and Newtonian Gravitation

NASA Astrophysics Data System (ADS)

Weatherall, James Owen

There is a long tradition, originating with Aristotle, of philosophers interested in the nature of unforced motion. How do bodies move in the absence of any external influence, and why? The modern answer to the "how'" half of this question is the subject of Newton's first law of motion, which states that in the absence of any external forces, a body traverses a straight line at constant velocity. Newton's first law, however, does not appear to provide an answer to the "why" half of the question. Indeed, many physicists and philosophers of physics, Einstein included, have held that this question cannot be answered until one moves to general relativity---and more, that general relativity is distinctive among spacetime theories precisely because it "explains" unforced motion, in the sense that the geodesic principle---the geometrical version of Newton's first law---can be proved as a theorem. In this dissertation, I argue that Newtonian gravitation provides an explanation of inertial motion almost identical to that of general relativity. However, the details of both cases are remarkably subtle, and considerable attention must be paid to the sense of "explain" being used. Four chapters of the dissertation are devoted to these considerations. The final chapter of the dissertation addresses a slightly different topic. In standard Newtonian gravitation, there are two distinct notions of mass: "inertial mass" and "(passive) gravitational mass". Yet it is an empirical fact that for any body, the values of these masses are always equal. Historically, many physicists have taken this fact to call for explanation. A natural place to look for an explanation of the coincidence of inertial and gravitational mass would be general relativity. In general relativity, however, there is no coherent notion of gravitational mass. This chapter shows how it is that gravitational mass arises as a distinct property of matter in the Newtonian limit of general relativity, and moreover, shows

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.

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…

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…

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.…

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)

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…

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.

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.

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.

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.

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…

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 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.

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.

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…

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.

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

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.

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.

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)

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,…

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…

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.

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…

Tornadogenesis Versus Newton's Third Law of Motion

NASA Astrophysics Data System (ADS)

Hardwig, R. B.

2015-12-01

For over 90 years scientists have tried to explain how tornadoes form and function. The present general consensus is that a tornado is just a function of the thunderstorm. Much research has been done to find the answer and numerous articles and papers have been written, all to no avail. This research explores the fact that a tornado cannot be just a function of a thunderstorm, as there is no opposite force within the thunderstorm to the air drawn up by the tornado, so there must be some external force involved in a tornado's formation. To have compliance with Newton's Third Law of Motion we must see an equal downforce or some other force within the thunderstorm, to that drawn up by the tornado. And if there was a downforce, that force would be virtually as damaging as the tornado itself. But we don't see this downforce or any other opposing force within the thunderstorm. Therefore, we must look for some other force that could cause a tornado's formation. And if that opposing force is not within the thunderstorm we need to be looking for some external force, outside the thunderstorm, that could cause a tornado. Also the fact that we have Waterspouts, Landspouts and Gustnadoes all without a thunderstorm, but since they all look and function just like a tornado, tells us that there must be some other force that is responsible for causing a tornado just like a Waterspout, Landspout or Gustnado. My research shows that there is one other force of energy that could cause all of these vortexes and is most likely the source of energy for a tornado's formation. That force is the High Velocity Overhead Jet Stream. My research shows a direct relationship between the High Velocity Overhead Jet Stream and Tornadogenesis as well as Waterspouts, Landspouts and Gustnadoes. Therefore, with the High Velocity Overhead Jet Stream providing the Action, at its interface with the tornado in the stratosphere, the Reaction is what we see on the ground as a tornado. With this explanation we

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.

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.

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…

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…

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…

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.

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

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.

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…

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.

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,…

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…

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

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).

The Generation Model of Particle Physics and Galactic Dark Matter

NASA Astrophysics Data System (ADS)

Robson, B. A.

2013-09-01

Galactic dark matter is matter hypothesized to account for the discrepancy of the mass of a galaxy determined from its gravitational effects, assuming the validity of Newton's law of universal gravitation, and the mass calculated from the "luminous matter", stars, gas, dust, etc. observed to be contained within the galaxy. The conclusive observation from the rotation curves of spiral galaxies that the mass discrepancy is greater, the larger the distance scales involved implies that either Newton's law of universal gravitation requires modification or considerably more mass (dark matter) is required to be present in each galaxy. Both the modification of Newton's law of gravitation and the hypothesis of the existence of considerable dark matter in a galaxy are discussed. It is shown that the Generation Model (GM) of particle physics, which leads to a modification of Newton's law of gravitation, is found to be essentially equivalent to that of Milgrom's modified Newtonian dynamics (MOND) theory, with the GM providing a physical understanding of the MOND theory. The continuing success of MOND theory in describing the extragalactic mass discrepancy problems constitutes a strong argument against the existence of undetected dark matter haloes, consisting of unknown nonbaryonic matter, surrounding spiral galaxies.

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.

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.

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.

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…

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)

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…

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.

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.

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.

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)

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.

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.

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.

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'of hydrostatic equilibrium, we measure gravitational mass and gas mass fraction to be M200=2.0 ± 0.3 × 1014 h70-1 M⊙ and fgas=0.20 ± 0.03 h-3/270 at r200=1.05 h-170 Mpc using the observed temperature profile. The complex structure in the core region is the key to explaining the discrepancy in gravitational mass determined from XMM-Newton X-ray observations and HST optical lensing measurements. This work is based on observations made with the XMM-Newton, an ESA science mission with instruments and contributions directly funded by ESA member states and the USA (NASA). Based on observations made with the European Southern Observatory telescopes obtained from the ESO/ST-ECF Science Archive Facility.

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…

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…

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.

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)

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)

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.

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

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.

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.

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.

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…

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.

Topological dynamics of gyroscopic and Floquet lattices from Newton's laws

NASA Astrophysics Data System (ADS)

Lee, Ching Hua; Li, Guangjie; Jin, Guliuxin; Liu, Yuhan; Zhang, Xiao

2018-02-01

Despite intense interest in realizing topological phases across a variety of electronic, photonic, and mechanical platforms, the detailed microscopic origin of topological behavior often remains elusive. To bridge this conceptual gap, we show how hallmarks of topological modes—boundary localization and chirality—emerge from Newton's laws in mechanical topological systems. We first construct a gyroscopic lattice with analytically solvable edge modes, and show how the Lorentz and spring restoring forces conspire to support very robust "dangling bond" boundary modes. The chirality and locality of these modes intuitively emerges from microscopic balancing of restoring forces and cyclotron tendencies. Next, we introduce the highlight of this work, an experimentally realistic mechanical nonequilibrium (Floquet) Chern lattice driven by ac electromagnets. Through appropriate synchronization of the ac driving protocol, the Floquet lattice is "pushed around" by a rotating potential analogous to an object washed ashore by water waves. Besides hosting "dangling bond" chiral modes analogous to the gyroscopic boundary modes, our Floquet Chern lattice also supports peculiar half-period chiral modes with no static analog, i.e., analogs of anomalous Floquet Chern insulators edge modes. With key parameters controlled electronically, our setup has the advantage of being dynamically tunable for applications involving arbitrary Floquet modulations. The physical intuition gleaned from our two prototypical topological systems is applicable not just to arbitrarily complicated mechanical systems, but also photonic and electrical topological setups.

The gravitational law of social interaction

NASA Astrophysics Data System (ADS)

Levy, Moshe; Goldenberg, Jacob

2014-01-01

While a great deal is known about the topology of social networks, there is much less agreement about the geographical structure of these networks. The fundamental question in this context is: how does the probability of a social link between two individuals depend on the physical distance between them? While it is clear that the probability decreases with the distance, various studies have found different functional forms for this dependence. The exact form of the distance dependence has crucial implications for network searchability and dynamics: Kleinberg (2000) [15] shows that the small-world property holds if the probability of a social link is a power-law function of the distance with power -2, but not with any other power. We investigate the distance dependence of link probability empirically by analyzing four very different sets of data: Facebook links, data from the electronic version of the Small-World experiment, email messages, and data from detailed personal interviews. All four datasets reveal the same empirical regularity: the probability of a social link is proportional to the inverse of the square of the distance between the two individuals, analogously to the distance dependence of the gravitational force. Thus, it seems that social networks spontaneously converge to the exact unique distance dependence that ensures the Small-World property.

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.

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

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

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.

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.

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.

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.

Statistical Diversions

ERIC Educational Resources Information Center

Petocz, Peter; Sowey, Eric

2008-01-01

When people speak of "the Law of Gravity" they are generally referring to what is more specifically known as "Newton's Law of Gravitation." This law states that the gravitational force (that is, the mutual attraction) between any two physical bodies is directly proportional to the product of their individual masses and inversely proportional to…

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

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.

Newton's method

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

More, J. J.; Sorensen, D. C.

1982-02-01

Newton's method plays a central role in the development of numerical techniques for optimization. In fact, most of the current practical methods for optimization can be viewed as variations on Newton's method. It is therefore important to understand Newton's method as an algorithm in its own right and as a key introduction to the most recent ideas in this area. One of the aims of this expository paper is to present and analyze two main approaches to Newton's method for unconstrained minimization: the line search approach and the trust region approach. The other aim is to present some of themore » recent developments in the optimization field which are related to Newton's method. In particular, we explore several variations on Newton's method which are appropriate for large scale problems, and we also show how quasi-Newton methods can be derived quite naturally from Newton's method.« less

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.

The Gravity Model for High School Students

ERIC Educational Resources Information Center

Tribble, Paul; Mitchell, William A.

1977-01-01

The authors suggest ways in which the gravity model can be used in high school geography classes. Based on Newton's Law of Molecular Gravitation, the law states that gravitation is in direct ratio to mass and inverse ratio to distance. One activity for students involves determination of zones of influence of cities of various sizes. (Author/AV)

Newtonian semiclassical gravity in three ontological quantum theories that solve the measurement problem: Formalisms and empirical predictions

NASA Astrophysics Data System (ADS)

Derakhshani, Maaneli

In this thesis, we consider the implications of solving the quantum measurement problem for the Newtonian description of semiclassical gravity. First we review the formalism of the Newtonian description of semiclassical gravity based on standard quantum mechanics---the Schroedinger-Newton theory---and two well-established predictions that come out of it, namely, gravitational 'cat states' and gravitationally-induced wavepacket collapse. Then we review three quantum theories with 'primitive ontologies' that are well-known known to solve the measurement problem---Schroedinger's many worlds theory, the GRW collapse theory with matter density ontology, and Nelson's stochastic mechanics. We extend the formalisms of these three quantum theories to Newtonian models of semiclassical gravity and evaluate their implications for gravitational cat states and gravitational wavepacket collapse. We find that (1) Newtonian semiclassical gravity based on Schroedinger's many worlds theory is mathematically equivalent to the Schroedinger-Newton theory and makes the same predictions; (2) Newtonian semiclassical gravity based on the GRW theory differs from Schroedinger-Newton only in the use of a stochastic collapse law, but this law allows it to suppress gravitational cat states so as not to be in contradiction with experiment, while allowing for gravitational wavepacket collapse to happen as well; (3) Newtonian semiclassical gravity based on Nelson's stochastic mechanics differs significantly from Schroedinger-Newton, and does not predict gravitational cat states nor gravitational wavepacket collapse. Considering that gravitational cat states are experimentally ruled out, but gravitational wavepacket collapse is testable in the near future, this implies that only the latter two are viable theories of Newtonian semiclassical gravity and that they can be experimentally tested against each other in future molecular interferometry experiments that are anticipated to be capable of testing

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

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.

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.

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.

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…

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.

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.

Relating constrained motion to force through Newton's second law

NASA Astrophysics Data System (ADS)

Roithmayr, Carlos M.

When a mechanical system is subject to constraints its motion is in some way restricted. In accordance with Newton's second law, motion is a direct result of forces acting on a system; hence, constraint is inextricably linked to force. The presence of a constraint implies the application of particular forces needed to compel motion in accordance with the constraint; absence of a constraint implies the absence of such forces. The objective of this thesis is to formulate a comprehensive, consistent, and concise method for identifying a set of forces needed to constrain the behavior of a mechanical system modeled as a set of particles and rigid bodies. The goal is accomplished in large part by expressing constraint equations in vector form rather than entirely in terms of scalars. The method developed here can be applied whenever constraints can be described at the acceleration level by a set of independent equations that are linear in acceleration. Hence, the range of applicability extends to servo-constraints or program constraints described at the velocity level with relationships that are nonlinear in velocity. All configuration constraints, and an important class of classical motion constraints, can be expressed at the velocity level by using equations that are linear in velocity; therefore, the associated constraint equations are linear in acceleration when written at the acceleration level. Two new approaches are presented for deriving equations governing motion of a system subject to constraints expressed at the velocity level with equations that are nonlinear in velocity. By using partial accelerations instead of the partial velocities normally employed with Kane's method, it is possible to form dynamical equations that either do or do not contain evidence of the constraint forces, depending on the analyst's interests.

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)

Exact Descriptions of General Relativity Derived from Newtonian Mechanics within Curved Geometries

NASA Astrophysics Data System (ADS)

Savickas, David

2015-04-01

General relativity and Newtonian mechanics are shown to be exactly related when Newton's second law is written in a curved geometry by using the physical components of a vector as is defined in tensor calculus. By replacing length within the momentum's velocity by the vector metric in a curved geometry the second law can then be shown to be exactly identical to the geodesic equation of motion occurring in general relativity. When time's vector direction is constant, as similarly occurs in Newtonian mechanics, this equation can be reduced to a curved three-dimensional equation of motion that yields the the Schwarzschild equations of motion for an isolated particle. They can be used to describe gravitational behavior for any array of masses for which the Newtonian gravitational potential is known, and is shown to describe a mass particle's behavior in the gravitational field of a thin mass-rod. This use of Newton's laws allows relativistic behavior to be described in a physically comprehensible manner. D. Savickas, Int. J. Mod. Phys. D 23 1430018, (2014).

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.

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.

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.

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.

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.

Combining Newton's second law and de Broglie's particle-wave duality

NASA Astrophysics Data System (ADS)

Hill, James M.

2018-03-01

All matter can exhibit wave-like behaviour, and Louis de Broglie first predicted light to display the dual characteristics as both a collection of particles, called photons, or in some respects as a wave. The particle velocity is the group velocity of the wave, and if the particle velocity ug is subluminal then the associated wave or phase velocity up through the de Broglie relation ugup =c2 is necessarily superluminal. This is believed not to contradict the fact that information cannot be carried faster than the velocity of light c because the wave phase is supposed to carry no energy. However, the superluminal phase velocity may well be physically significant, and here we propose that the sub particle world and the super wave world might be equally important, and that each might exert an influence on the other, such that any mechanical equations must not only be Lorentz invariant but they must also be invariant under the transformation connecting the sub and super worlds. Following this approach, Einstein's equation E =mc2 becomes simply E = (m +m‧)c2 , where m and m‧ are masses given by Einstein expressions arising from the perceived sub and superluminal velocities ug and up respectively. This modification, although superficially simple, results from non-conventional physics and gives rise to an extension of Newton's second law, that might well account for the extra energy and mass that is known to exist in the universe, and referred to as dark energy and dark matter. An explicit solution for photons and light predicts a non-zero photon rest-mass m0 = hν / 2c2 , where h is Planck's constant and ν is the light frequency. Interestingly, the associated energy of this mass is the zero-point energy, believed to be the lowest energy that a quantum mechanical system may possess.

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

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.

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

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

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

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.

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.

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)

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.

Free Fall and the Equivalence Principle Revisited

ERIC Educational Resources Information Center

Pendrill, Ann-Marie

2017-01-01

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.…

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…

An Improved Newton's Method.

ERIC Educational Resources Information Center

Mathews, John H.

1989-01-01

Describes Newton's method to locate roots of an equation using the Newton-Raphson iteration formula. Develops an adaptive method overcoming limitations of the iteration method. Provides the algorithm and computer program of the adaptive Newton-Raphson method. (YP)

Dimensional Analysis and General Relativity

ERIC Educational Resources Information Center

Lovatt, Ian

2009-01-01

Newton's law of gravitation is a central topic in the first-year physics curriculum. A lecturer can go beyond the physical details and use the history of gravitation to discuss the development of scientific ideas; unfortunately, the most recent chapter in this history, general relativity, is not covered in first-year courses. This paper discusses…

Testing the gravitational inverse-square law at centimeter scales

NASA Astrophysics Data System (ADS)

Bonicalzi, Ricco

Many attempts to unify gravity with the Standard Model entail a gravitational inverse-square-law violation (ISLV) at some low level. This dissertation reports on the initial phase of a torsion-pendulum null experiment searching for such a violation in the interaction between two macroscopic bodies with a characteristic separation of 12 cm. Central to the experimental design is the special configuration of the mass distributions of both the pendulum and source mass to provide high-sensitivity to the horizontal gradient of the Laplacian of the interaction potential (a signature of ISLV), while strongly suppressing coupling through Newtonian gravity. Specifically, this design ensures that gravitational systematic effects arise only at second order in the fabrication errors of the pendulum and source mass. A key aspect of this work is the choice of the second-harmonic amplitude of pendulum oscillation as the torque observable, instead of the traditional oscillation frequency. This relatively recent torsion-pendulum method is markedly less sensitive to changes in torsion-fiber temperature and enables the ambient-temperature instrumentation of the initial phase to achieve necessary noise performance without heroic efforts to stabilize temperature. As details of the second-harmonic method have not yet been published, the presentation here dwells on a number of subtleties involved in analyzing the data. Experimental results are reported assuming a Yukawa-type interaction anomaly, where a is the strength of the Yukawa term relative to Newtonian gravity. A preliminary set of 34 data runs, each around a day in duration, produced a value of alpha = (-6.3 +/- 7.5) x 10-5. In the absence of significant systematic effects, even this interim result would have placed tighter bounds on ISLV than previously appearing in the literature. Unfortunately, an accelerated Department of Energy deadline for demolition of our Hanford laboratory facility compelled a shift of focus to the

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 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.

XMM-Newton publication statistics

NASA Astrophysics Data System (ADS)

Ness, J.-U.; Parmar, A. N.; Valencic, L. A.; Smith, R.; Loiseau, N.; Salama, A.; Ehle, M.; Schartel, N.

2014-02-01

We assessed the scientific productivity of XMM-Newton by examining XMM-Newton publications and data usage statistics. We analyse 3272 refereed papers, published until the end of 2012, that directly use XMM-Newton data. The SAO/NASA Astrophysics Data System (ADS) was used to provide additional information on each paper including the number of citations. For each paper, the XMM-Newton observation identifiers and instruments used to provide the scientific results were determined. The identifiers were used to access the XMM-{Newton} Science Archive (XSA) to provide detailed information on the observations themselves and on the original proposals. The information obtained from these sources was then combined to allow the scientific productivity of the mission to be assessed. Since around three years after the launch of XMM-Newton there have been around 300 refereed papers per year that directly use XMM-Newton data. After more than 13 years in operation, this rate shows no evidence that it is decreasing. Since 2002, around 100 scientists per year become lead authors for the first time on a refereed paper which directly uses XMM-Newton data. Each refereed XMM-Newton paper receives around four citations per year in the first few years with a long-term citation rate of three citations per year, more than five years after publication. About half of the articles citing XMM-Newton articles are not primarily X-ray observational papers. The distribution of elapsed time between observations taken under the Guest Observer programme and first article peaks at 2 years with a possible second peak at 3.25 years. Observations taken under the Target of Opportunity programme are published significantly faster, after one year on average. The fraction of science time taken until the end of 2009 that has been used in at least one article is {˜ 90} %. Most observations were used more than once, yielding on average a factor of two in usage on available observing time per year. About 20 % of

Isaac Newton: Eighteenth-century Perspectives

NASA Astrophysics Data System (ADS)

Hall, A. Rupert

1999-05-01

This new product of the ever-flourishing Newton industry seems a bit far-fetched at first sight: who but a few specialists would be interested in the historiography of Newton biography in the eighteenth century? On closer inspection, this book by one of the most important Newton scholars of our day turns out to be of interest to a wider audience as well. It contains several biographical sketches of Newton, written in the decades after his death. The two most important ones are the Eloge by the French mathematician Bernard de Fontenelle and the Italian scholar Paolo Frisi's Elogio. The latter piece was hitherto unavailable in English translation. Both articles are well-written, interesting and sometimes even entertaining. They give us new insights into the way Newton was revered throughout Europe and how not even the slightest blemish on his personality or work could be tolerated. An example is the way in which Newton's famous controversy with Leibniz is treated: Newton is without hesitation presented as the wronged party. Hall has provided very useful historical introductions to the memoirs as well as footnotes where needed. Among the other articles discussed is a well-known memoir by John Conduitt, who was married to Newton's niece. This memoir, substantial parts of which are included in this volume, has been a major source of personal information for Newton biographers up to this day. In a concluding chapter, Hall gives a very interesting overview of the later history of Newton biography, in which he describes the gradual change from adoration to a more critical approach in Newton's various biographers. In short, this is a very useful addition to the existing biographical literature on Newton. A J Kox

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.

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

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.

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.

Micro-orbits in a many-brane model and deviations from Newton's 1/r^2 law

NASA Astrophysics Data System (ADS)

Donini, A.; Marimón, S. G.

2016-12-01

We consider a five-dimensional model with geometry M = M_4 × S_1, with compactification radius R. The Standard Model particles are localized on a brane located at y=0, with identical branes localized at different points in the extra dimension. Objects located on our brane can orbit around objects located on a brane at a distance d=y/R, with an orbit and a period significantly different from the standard Newtonian ones. We study the kinematical properties of the orbits, finding that it is possible to distinguish one motion from the other in a large region of the initial conditions parameter space. This is a warm-up to study if a SM-like mass distribution on one (or more) distant brane(s) may represent a possible dark matter candidate. After using the same technique to the study of orbits of objects lying on the same brane (d=0), we apply this method to the detection of generic deviations from the inverse-square Newton law. We propose a possible experimental setup to look for departures from Newtonian motion in the micro-world, finding that an order of magnitude improvement on present bounds can be attained at the 95% CL under reasonable assumptions.

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.

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.

Newton's Apple

ERIC Educational Resources Information Center

Hendry, Archibald W.

2007-01-01

Isaac Newton may have seen an apple fall, but it was Robert Hooke who had a better idea of where it would land. No one really knows whether or not Isaac Newton actually saw an apple fall in his garden. Supposedly it took place in 1666, but it was a tale he told in his old age more than 60 years later, a time when his memory was failing and his…

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.

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.

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.;

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).

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…

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.

Evaluation of Optimal Formulas for Gravitational Tensors up to Gravitational Curvatures of a Tesseroid

NASA Astrophysics Data System (ADS)

Deng, Xiao-Le; Shen, Wen-Bin

2018-01-01

The forward modeling of the topographic effects of the gravitational parameters in the gravity field is a fundamental topic in geodesy and geophysics. Since the gravitational effects, including for instance the gravitational potential (GP), the gravity vector (GV) and the gravity gradient tensor (GGT), of the topographic (or isostatic) mass reduction have been expanded by adding the gravitational curvatures (GC) in geoscience, it is crucial to find efficient numerical approaches to evaluate these effects. In this paper, the GC formulas of a tesseroid in Cartesian integral kernels are derived in 3D/2D forms. Three generally used numerical approaches for computing the topographic effects (e.g., GP, GV, GGT, GC) of a tesseroid are studied, including the Taylor Series Expansion (TSE), Gauss-Legendre Quadrature (GLQ) and Newton-Cotes Quadrature (NCQ) approaches. Numerical investigations show that the GC formulas in Cartesian integral kernels are more efficient if compared to the previously given GC formulas in spherical integral kernels: by exploiting the 3D TSE second-order formulas, the computational burden associated with the former is 46%, as an average, of that associated with the latter. The GLQ behaves better than the 3D/2D TSE and NCQ in terms of accuracy and computational time. In addition, the effects of a spherical shell's thickness and large-scale geocentric distance on the GP, GV, GGT and GC functionals have been studied with the 3D TSE second-order formulas as well. The relative approximation errors of the GC functionals are larger with the thicker spherical shell, which are the same as those of the GP, GV and GGT. Finally, the very-near-area problem and polar singularity problem have been considered by the numerical methods of the 3D TSE, GLQ and NCQ. The relative approximation errors of the GC components are larger than those of the GP, GV and GGT, especially at the very near area. Compared to the GC formulas in spherical integral kernels, these new GC

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

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

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.

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.

Sometimes "Newton's Method" Always "Cycles"

ERIC Educational Resources Information Center

Latulippe, Joe; Switkes, Jennifer

2012-01-01

Are there functions for which Newton's method cycles for all non-trivial initial guesses? We construct and solve a differential equation whose solution is a real-valued function that two-cycles under Newton iteration. Higher-order cycles of Newton's method iterates are explored in the complex plane using complex powers of "x." We find a class of…

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.

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

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 Cosinusoidal Gravitational Potential, a Unique Alternative to Newton

NASA Astrophysics Data System (ADS)

Bartlett, D. F.

1997-04-01

Recently Bartlett & Su have shown that there are only three central potentials that allow a uniqueness theorem. (D.F. Bartlett & Y. Su, Am J. Phys. 62, 683 (1994)) Two of these, the newtonian and Yukawa, are familiar. The third, e^± ikr/r has hardly been studied at all. I consider the potential GM cos(kr)/r as an alternative to dark matter. The universal wavelength λ = 2π/k = 1800 lt-yrs comes from the only thoroughly catalogued system of galactic shells, those around the elliptical, NGC 3923. This λ is confirmed by the location of the gravitationally lensed images in the Einstein Cross. The potential can also explain several features of our Galaxy. The central bar is related dynamically to the spiral arms and, surprisingly, to the distant dwarf spheroidals. The radial oscillations of the potential provide the strong galactic tidal force that may be required to nudge distant comets into the inner solar system. The large, periodic oscillation of the sun within this radial pocket gives a unique mechanism for exposing the solar system to a periodic tidal force. The period of this oscillation and the period of cratering and mass extinctions agree, within errors.

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.

Isaac Newton: Man, Myth, and Mathematics.

ERIC Educational Resources Information Center

Rickey, V. Frederick

1987-01-01

This article was written in part to celebrate the anniversaries of landmark mathematical works by Newton and Descartes. It's other purpose is to dispel some myths about Sir Isaac Newton and to encourage readers to read Newton's works. (PK)

Newton's Metaphysics of Space as God's Emanative Effect

NASA Astrophysics Data System (ADS)

Jacquette, Dale

2014-09-01

In several of his writings, Isaac Newton proposed that physical space is God's "emanative effect" or "sensorium," revealing something interesting about the metaphysics underlying his mathematical physics. Newton's conjectures depart from Plato and Aristotle's metaphysics of space and from classical and Cambridge Neoplatonism. Present-day philosophical concepts of supervenience clarify Newton's ideas about space and offer a portrait of Newton not only as a mathematical physicist but an independent-minded rationalist philosopher.

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.

Inexact adaptive Newton methods

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

Bertiger, W.I.; Kelsey, F.J.

1985-02-01

The Inexact Adaptive Newton method (IAN) is a modification of the Adaptive Implicit Method/sup 1/ (AIM) with improved Newton convergence. Both methods simplify the Jacobian at each time step by zeroing coefficients in regions where saturations are changing slowly. The methods differ in how the diagonal block terms are treated. On test problems with up to 3,000 cells, IAN consistently saves approximately 30% of the CPU time when compared to the fully implicit method. AIM shows similar savings on some problems, but takes as much CPU time as fully implicit on other test problems due to poor Newton convergence.

Arakelian 564: An XMM-Newton View

NASA Technical Reports Server (NTRS)

Vignali, Cristian; Brandt, W. N.; Boller, Th.; Fabian, A. C.; Vaughan, Simon

2003-01-01

We report on two XMM-Newton observations of the bright narrow-line Seyfert 1 galaxy Ark 564 taken one year apart (2000 June and 2001 June). The 0.6-10 keV continuum is well described by a soft blackbody component (kTau approximately equal 140-150 eV) plus a steep power law (Tau approximately equal to 2.50-2.55). No significant spectral changes are observed between the two observations, although the X-ray flux in the second observation is approximately equal to 40-50 per cent lower. In both observations we detect a significant absorption edge at a rest-frame energy of approximately equal to 0.73 keV, corresponding to O VII. The presence of the absorption feature is confirmed by a simultaneous Chandra grating observation in 2000 June, although the best-fitting edge threshold is at a slightly lower energy in the Chandra data, possibly because of a different parameterization of the underlying X-ray continuum. We find tentative evidence for a broad iron emission line in the 2000 June observation. The results from an analysis of the power spectral density (PSD) function are also presented. The present XMM-Newton data support the idea that the PSD shown two breads, although the location of the high-frequency break requires further constraints.

"To Improve upon Hints of Things": Illustrating Isaac Newton.

PubMed

Schilt, Cornelis J

2016-01-01

When Isaac Newton died in 1727 he left a rich legacy in terms of draft manuscripts, encompassing a variety of topics: natural philosophy, mathematics, alchemy, theology, and chronology, as well as papers relating to his career at the Mint. One thing that immediately strikes us is the textuality of Newton's legacy: images are sparse. Regarding his scholarly endeavours we witness the same practice. Newton's extensive drafts on theology and chronology do not contain a single illustration or map. Today we have all of Newton's draft manuscripts as witnesses of his working methods, as well as access to a significant number of books from his own library. Drawing parallels between Newton's reading practices and his natural philosophical and scholarly work, this paper seeks to understand Newton's recondite writing and publishing politics.

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…

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.

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

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…

PEOPLE IN PHYSICS: Newton's apple

NASA Astrophysics Data System (ADS)

Sandford Smith, Daniel

1997-03-01

This essay has a long history. It was triggered at university by one of my tutors describing the dispute between Robert Hooke and Isaac Newton. He conjured up an image of Newton sitting at his desk doing calculations while Hooke went down mineshafts trying to detect a change in the strength of gravity. To someone who was finding the maths content of a physics degree somewhat challenging this was a symbolic image. I believe that the story of Newton and the apple illustrates the complex nature of scientific discovery.

The XMM-Newton serendipitous survey. VII. The third XMM-Newton serendipitous source catalogue

NASA Astrophysics Data System (ADS)

Rosen, S. R.; Webb, N. A.; Watson, M. G.; Ballet, J.; Barret, D.; Braito, V.; Carrera, F. J.; Ceballos, M. T.; Coriat, M.; Della Ceca, R.; Denkinson, G.; Esquej, P.; Farrell, S. A.; Freyberg, M.; Grisé, F.; Guillout, P.; Heil, L.; Koliopanos, F.; Law-Green, D.; Lamer, G.; Lin, D.; Martino, R.; Michel, L.; Motch, C.; Nebot Gomez-Moran, A.; Page, C. G.; Page, K.; Page, M.; Pakull, M. W.; Pye, J.; Read, A.; Rodriguez, P.; Sakano, M.; Saxton, R.; Schwope, A.; Scott, A. E.; Sturm, R.; Traulsen, I.; Yershov, V.; Zolotukhin, I.

2016-05-01

Context. Thanks to the large collecting area (3 ×~1500 cm2 at 1.5 keV) and wide field of view (30' across in full field mode) of the X-ray cameras on board the European Space Agency X-ray observatory XMM-Newton, each individual pointing can result in the detection of up to several hundred X-ray sources, most of which are newly discovered objects. Since XMM-Newton has now been in orbit for more than 15 yr, hundreds of thousands of sources have been detected. Aims: Recently, many improvements in the XMM-Newton data reduction algorithms have been made. These include enhanced source characterisation and reduced spurious source detections, refined astrometric precision of sources, greater net sensitivity for source detection, and the extraction of spectra and time series for fainter sources, both with better signal-to-noise. Thanks to these enhancements, the quality of the catalogue products has been much improved over earlier catalogues. Furthermore, almost 50% more observations are in the public domain compared to 2XMMi-DR3, allowing the XMM-Newton Survey Science Centre to produce a much larger and better quality X-ray source catalogue. Methods: The XMM-Newton Survey Science Centre has developed a pipeline to reduce the XMM-Newton data automatically. Using the latest version of this pipeline, along with better calibration, a new version of the catalogue has been produced, using XMM-Newton X-ray observations made public on or before 2013 December 31. Manual screening of all of the X-ray detections ensures the highest data quality. This catalogue is known as 3XMM. Results: In the latest release of the 3XMM catalogue, 3XMM-DR5, there are 565 962 X-ray detections comprising 396 910 unique X-ray sources. Spectra and lightcurves are provided for the 133 000 brightest sources. For all detections, the positions on the sky, a measure of the quality of the detection, and an evaluation of the X-ray variability is provided, along with the fluxes and count rates in 7 X-ray energy

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…

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.

Subsampled Hessian Newton Methods for Supervised Learning.

PubMed

Wang, Chien-Chih; Huang, Chun-Heng; Lin, Chih-Jen

2015-08-01

Newton methods can be applied in many supervised learning approaches. However, for large-scale data, the use of the whole Hessian matrix can be time-consuming. Recently, subsampled Newton methods have been proposed to reduce the computational time by using only a subset of data for calculating an approximation of the Hessian matrix. Unfortunately, we find that in some situations, the running speed is worse than the standard Newton method because cheaper but less accurate search directions are used. In this work, we propose some novel techniques to improve the existing subsampled Hessian Newton method. The main idea is to solve a two-dimensional subproblem per iteration to adjust the search direction to better minimize the second-order approximation of the function value. We prove the theoretical convergence of the proposed method. Experiments on logistic regression, linear SVM, maximum entropy, and deep networks indicate that our techniques significantly reduce the running time of the subsampled Hessian Newton method. The resulting algorithm becomes a compelling alternative to the standard Newton method for large-scale data classification.

Edme Mariotte and Newton's Cradle

ERIC Educational Resources Information Center

Cross, Rod

2012-01-01

The first recorded experiments describing the phenomena made popular by Newton's cradle appear to be those conducted by Edme Mariotte around 1670. He was quoted in Newton's "Principia," along with Wren, Wallis, and Huygens, as having conducted pioneering experiments on the collisions of pendulum balls. Each of these authors concluded that momentum…

Dispersion of gravitational waves in cold spherical interstellar medium

NASA Astrophysics Data System (ADS)

Barta, Dániel; Vasúth, Mátyás

We investigate the propagation of locally plane, small-amplitude, monochromatic gravitational waves (GWs) through cold compressible interstellar gas in order to provide a more accurate picture of expected waveforms for direct detection. The quasi-isothermal gas is concentrated in a spherical symmetric cloud held together by self-gravitation. Gravitational waves can be treated as linearized perturbations on the background inner Schwarzschild spacetime. The perturbed quantities lead to the field equations governing the gas dynamics and describe the interaction of gravitational waves with matter. We have shown that the transport equation of these amplitudes provides numerical solutions for the frequency-alteration. The decrease in frequency is driven by the energy dissipating process of GW-matter interactions. The decrease is significantly smaller than the magnitude of the original frequency and too small to be detectable by present second-generation and planned third-generation detectors. It exhibits a power-law relationship between original and decreased frequencies. The frequency deviation was examined particularly for the transient signal GW150914.

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.

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.

Eye-openers from XMM-Newton

NASA Astrophysics Data System (ADS)

2000-02-01

many years of work. They are all that we hoped they would be. In the LMC we can see the elements, which go to make up new stars and planets, being released in giant stellar explosions. We can even see the creation of new stars going on, using elements scattered through space by previous stellar explosions. This is what we built the EPIC cameras for and they are really fulfilling their promise" Multiwavelength views of Hickson Group 16 The HCG-16 viewed by EPIC and by the Optical Monitor in the visible and ultraviolet wavelengths is one of approximately a hundred compact galaxy clusters listed by Canadian astronomer Paul Hickson in the 1980s. The criteria for the Hickson cluster groups included their compactness, their isolation from other galaxies and a limited magnitude range between their members. Most Hicksons are very faint, but a few can be observed with modest aperture telescopes. Galaxies in Hickson groups have a high probability of interacting. Their study has shed light on the question of galactic evolution and the effects of interaction. Investigation into their gravitational behaviour has also significantly contributed to our understanding of "dark matter", the mysterious matter that most astronomers feel comprises well over 90% of our universe. Observation of celestial objects from space over a range of X-ray, ultraviolet and visible wavelengths, is a unique feature of the XMM-Newton mission. The EPIC-PN view of the Hickson 16 group shows a handful of bright X-sources and in the background more than a hundred faint X-ray sources that XMM-Newton is revealing for the first time. Juxtaposing the X-ray view of HCG 16 with that of the Optical Monitor reveals one of the great strengths of XMM-Newton in being able to routinely compare the optical, ultraviolet and X-ray properties of objects. Many of the X-ray sources are revealed as elongated "fuzzy blobs" coincident with some of the optical galaxies. Routine access to ultraviolet images is a first for the mission

Telecommunications Handbook: Connecting to Newton.

ERIC Educational Resources Information Center

Baker, Christopher; And Others

This handbook was written by the Argonne National Laboratory for use with their electronic bulletin board system (BBS) called Newton. Newton is an educational BBS for use by teachers, students, and parents. Topics range from discussions of science fair topics to online question and answer sessions with scientists. Future capabilities will include…

Newton's Cradle in Physics Education

ERIC Educational Resources Information Center

Gauld, Colin F.

2006-01-01

Newton's Cradle is a series of bifilar pendulums used in physics classrooms to demonstrate the role of the principles of conservation of momentum and kinetic energy in elastic collisions. The paper reviews the way in which textbooks use Newton's Cradle and points out the unsatisfactory nature of these treatments in almost all cases. The literature…

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.

High-order Newton-penalty algorithms

NASA Astrophysics Data System (ADS)

Dussault, Jean-Pierre

2005-10-01

Recent efforts in differentiable non-linear programming have been focused on interior point methods, akin to penalty and barrier algorithms. In this paper, we address the classical equality constrained program solved using the simple quadratic loss penalty function/algorithm. The suggestion to use extrapolations to track the differentiable trajectory associated with penalized subproblems goes back to the classic monograph of Fiacco & McCormick. This idea was further developed by Gould who obtained a two-steps quadratically convergent algorithm using prediction steps and Newton correction. Dussault interpreted the prediction step as a combined extrapolation with respect to the penalty parameter and the residual of the first order optimality conditions. Extrapolation with respect to the residual coincides with a Newton step.We explore here higher-order extrapolations, thus higher-order Newton-like methods. We first consider high-order variants of the Newton-Raphson method applied to non-linear systems of equations. Next, we obtain improved asymptotic convergence results for the quadratic loss penalty algorithm by using high-order extrapolation steps.

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

Toward milli-Newton electro- and magneto-static microactuators

NASA Technical Reports Server (NTRS)

Fan, Long-Sheng

1993-01-01

Microtechnologies can potentially push integrated electro- and magnetostatic actuators toward the regime where constant forces in the order of milli-Newton (or torques in the order of micro-Newton meter) can be generated with constant inputs within a volume of 1.0 x 1.0 x 0.02 mm with 'conventional' technology. 'Micro' actuators are, by definition, actuators with dimensions confined within a millimeter cube. Integrated microactuators based on electrostatics typically have force/torque in the order of sub-micro-Newton (sub-nano-Newton meter). These devices are capable of moving small objects at MHz frequencies. On the other hand, suppose we want to move a one cubic millimeter object around with 100 G acceleration; a few milli-Newton force will be required. Thus, milli-Newton microactuators are very desirable for some immediate applications, and it challenges micromechanical researchers to develop new process technologies, designs, and materials toward this goal.

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.

Keynes, Newton and the Royal Society: the events of 1942 and 1943

PubMed Central

Kuehn, Daniel

2013-01-01

Most discussions of John Maynard Keynes's activities in connection with Newton are restricted to the sale in 1936 at Sotheby's of Newton's Portsmouth Papers and to Keynes's 1946 essay ‘Newton, the Man’. This paper provides a history of Keynes's Newton-related work in the interim, highlighting especially the events of 1942 and 1943, which were particularly relevant to the Royal Society's role in the domestic and international promotion of Newton's legacy. During this period, Keynes lectured twice on Newton, leaving notes that would later be read by his brother Geoffrey in the famous commemoration of the Newton tercentenary in 1946. In 1943 Keynes assisted the Royal Society in its recognition of the Soviet celebrations and in the acquisition and preservation of more of the Newton library. In each instance Keynes took the opportunity to promote his interpretation of Newton as ‘the last of the magicians’: a scientist who had one foot in the pre-modern world and whose approach to understanding the world was as much intuitive as it was methodical. PMID:24686919

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.

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.

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.

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)

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.

Scale-covariant theory of gravitation and astrophysical applications

NASA Technical Reports Server (NTRS)

Canuto, V.; Adams, P. J.; Hsieh, S.-H.; Tsiang, E.

1977-01-01

A scale-covariant theory of gravitation is presented which is characterized by a set of equations that are complete only after a choice of the scale function is made. Special attention is given to gauge conditions and units which allow gravitational phenomena to be described in atomic units. The generalized gravitational-field equations are derived by performing a direct scale transformation, by extending Riemannian geometry to Weyl geometry through the introduction of the notion of cotensors, and from a variation principle. Modified conservation laws are provided, a set of dynamical equations is obtained, and astrophysical consequences are considered. The theory is applied to examine certain homogeneous cosmological solutions, perihelion shifts, light deflections, secular variations of planetary orbital elements, stellar structure equations for a star in quasi-static equilibrium, and the past thermal history of earth. The possible relation of the scale-covariant theory to gauge field theories and their predictions of cosmological constants is discussed.

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

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.

Newton-Cartan gravity and torsion

NASA Astrophysics Data System (ADS)

Bergshoeff, Eric; Chatzistavrakidis, Athanasios; Romano, Luca; Rosseel, Jan

2017-10-01

We compare the gauging of the Bargmann algebra, for the case of arbitrary torsion, with the result that one obtains from a null-reduction of General Relativity. Whereas the two procedures lead to the same result for Newton-Cartan geometry with arbitrary torsion, the null-reduction of the Einstein equations necessarily leads to Newton-Cartan gravity with zero torsion. We show, for three space-time dimensions, how Newton-Cartan gravity with arbitrary torsion can be obtained by starting from a Schrödinger field theory with dynamical exponent z = 2 for a complex compensating scalar and next coupling this field theory to a z = 2 Schrödinger geometry with arbitrary torsion. The latter theory can be obtained from either a gauging of the Schrödinger algebra, for arbitrary torsion, or from a null-reduction of conformal gravity.

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.

Semismooth Newton method for gradient constrained minimization problem

NASA Astrophysics Data System (ADS)

Anyyeva, Serbiniyaz; Kunisch, Karl

2012-08-01

In this paper we treat a gradient constrained minimization problem, particular case of which is the elasto-plastic torsion problem. In order to get the numerical approximation to the solution we have developed an algorithm in an infinite dimensional space framework using the concept of the generalized (Newton) differentiation. Regularization was done in order to approximate the problem with the unconstrained minimization problem and to make the pointwise maximum function Newton differentiable. Using semismooth Newton method, continuation method was developed in function space. For the numerical implementation the variational equations at Newton steps are discretized using finite elements method.

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.

How concept images affect students' interpretations of Newton's method

NASA Astrophysics Data System (ADS)

Engelke Infante, Nicole; Murphy, Kristen; Glenn, Celeste; Sealey, Vicki

2018-07-01

Knowing when students have the prerequisite knowledge to be able to read and understand a mathematical text is a perennial concern for instructors. Using text describing Newton's method and Vinner's notion of concept image, we exemplify how prerequisite knowledge influences understanding. Through clinical interviews with first-semester calculus students, we determined how evoked concept images of tangent lines and roots contributed to students' interpretation and application of Newton's method. Results show that some students' concept images of root and tangent line developed throughout the interview process, and most students were able to adequately interpret the text on Newton's method. However, students with insufficient concept images of tangent line and students who were unwilling or unable to modify their concept images of tangent line after reading the text were not successful in interpreting Newton's method.

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.

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)

There is grandeur in this view of Newton: Charles Darwin, Isaac Newton and Victorian conceptions of scientific virtue.

PubMed

Bellon, Richard

2014-01-01

For Victorian men of science, the scientific revolution of the seventeenth century represented a moral awakening. Great theoretical triumphs of inductive science flowed directly from a philosophical spirit that embraced the virtues of self-discipline, courage, patience and humility. Isaac Newton exemplified this union of moral and intellectual excellence. This, at least, was the story crafted by scientific leaders like David Brewster, Thomas Chalmers, John Herschel, Adam Sedgwick and William Whewell. Not everyone accepted this reading of history. Evangelicals who decried the 'materialism' of mainstream science assigned a different meaning to Newton's legacy on behalf of their 'scriptural' alternative. High-church critics of science like John Henry Newman, on the other hand, denied that Newton's secular achievements carried any moral significance at all. These debates over Newtonian standards of philosophical behavior had a decisive influence on Charles Darwin as he developed his theory of evolution by natural selection. Copyright © 2014 Elsevier Ltd. All rights reserved.

Newton-Cartan Gravity in Noninertial Reference Frames

NASA Astrophysics Data System (ADS)

Rodriguez, Leo; St. Germaine-Fuller, James; Wickramasekara, Sujeev

2015-03-01

We study Newton-Cartan gravity under transformations into all noninertial, nonrelativistic reference frames. These transformations form an infinite dimensional Lie group, called the Galilean line group, which contains as a subgroup the Galilei group. The fictitious forces of noninertial reference frames are encoded in the Cartan connection transformed under the Galilean line group. These fictitious forces, which are coordinate effects, do not contribute to the Ricci tensor. Only the 00-component of the Ricci tensor is non-zero and equals (4 π times) the matter density in all reference frames. While the Ricci field equation and Gauss' law are fulfilled by the physical matter density in inertial and linearly accelerating reference frames, in rotating reference frames Gauss' law holds for an effective mass density that differs from the physical matter density. This effective density has its origin in the simulated magnetic field of rotating frames, highlighting a striking difference between linearly and rotationally accelerating frames. The equations governing the simulated fields have the same form as Maxwell's equations, a surprising result given that these equations obey special relativity (and U (1) -gauge symmetry), rather than Galilean symmetry. This work was supported in part by the HHMI Undergraduate Science Education Award 52006298 and the Grinnell College Academic Affairs' CSFS and MAP programs.

Gravitation is Retarded:Theory and Evidence

NASA Astrophysics Data System (ADS)

Tang, K.

2009-12-01

Gravitation is Retarded:Theory and Evidence There were more than twenty times of observations about gravity anomalies during the solar eclipses since Maurice Allais’s pendulum test during the total solar eclipse of 1954 in Paris. All the theoretical modes are calculated according to Newton’s gravitation law. But due to the observation environments and conditions during above observations were not quite well, the platform for mounting the gravimeters were quite simple, so that the environment and human’s disturbance were unavoidable, therefore the data obtained from above observation where questionable. It is very hard to give a conclusion to say the gravity anomalies during the eclipses were really existing or not. The more important issue is that none of the suggested external factors could account for the magnitude and timing of observed anomalies, according to Chris Duif of University of Technology of Netherland. Since the total solar eclipse of Mohe, 1997, I have been working on a theory to explain the gravity anomalies. At Mohe, I was watching the image of the eclipse, and led a scientific term to conduct a comprehensive geophysical observation, including the gravity observation. The two kinds of observations were conducted at same location and same time. We noticed that solar light of the eclipse was emitted 500 seconds before the image reached to our eyes and cameras. It was reasonable to have similar idea that the gravitation emitted from the sun is also 500 seconds before our gravimeter received and recorded it; it means that gravitation is retarded. Based on either the Special Relativity or Leinard-Wiechert retarded potential, I have deduced the expressions for retarded gravitation; it is vector modification on Newton’s universal gravitation law. The retarded gravitation is gRT=-GM(R-Rβ)(1-β2)/R3(1-βr)3 For common cases, bodies move in a weak gravitation field along a quasi-straight light or with a slow speed, such as planets move around the

Family of spherical models with special gravitational properties

NASA Astrophysics Data System (ADS)

Kondratyev, B. P.

2015-03-01

A new method for studying the structural and gravitational properties of spherical systems based on an analysis of the ratio of the potentials for their subsystems and shells has been developed. It has been proven for the first time that the gravitational virial Z( r) of the subsystem without allowance for the influence of the outer shell is equal to twice the work done to disperce the subsystem's matter to infinity. A new class of spherical models has been constructed in which: (1) the ratio of the contribution to the potential at point r from the spherical subsystem to the contribution from the outer shell does not depend on radius and is equal to a constant γ; (2) the ratio of the gravitational energy W( r) to Z( r) for the spherical subsystem does not depend on r; and (3) the models are described by a power law of the density ρ = cr - κ and potential . Expressions for the gravitational energy W( r) and virial Z( r) have been found for the subsystem. The limiting case of ρ( r) ∝ r -5/2, where the subsystem's potential at any sampling point is exactly equal to the potential from the outer shell and Z( r) is equivalent to its gravitational energy W( r), is considered in detail. The results supplement the classical potential theory. The question about the application of the models to the superdense nuclear star cluster in the center of the Milky Way is discussed.

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.

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.

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.

Globally convergent techniques in nonlinear Newton-Krylov

NASA Technical Reports Server (NTRS)

Brown, Peter N.; Saad, Youcef

1989-01-01

Some convergence theory is presented for nonlinear Krylov subspace methods. The basic idea of these methods is to use variants of Newton's iteration in conjunction with a Krylov subspace method for solving the Jacobian linear systems. These methods are variants of inexact Newton methods where the approximate Newton direction is taken from a subspace of small dimensions. The main focus is to analyze these methods when they are combined with global strategies such as linesearch techniques and model trust region algorithms. Most of the convergence results are formulated for projection onto general subspaces rather than just Krylov subspaces.

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.

The "dark Side" of Gravitational Experiments

NASA Astrophysics Data System (ADS)

Hoyle, Charles D.

Theoretical speculations about the quantum nature of the gravitational interaction have motivated many recent experiments. But perhaps the most profound and puzzling questions that these investigations address surround the observed cosmic acceleration, or Dark Energy. This mysterious substance comprises roughly 2/3 of the energy density of the universe. Current gravitational experiments may soon have the sensitivity to detect subtle clues that will reveal the mechanism behind the cosmic acceleration. On the laboratory scale, short-range tests of the Newtonian inverse-square law (ISL) provide the most sensitive measurements of gravity at the Dark Energy length scale, λd = (ħc/ρd)1/4 ≈ 85 μm, where ρd ≈ 3.8 keV/cm3 is the observed Dark Energy density. This length scale may also have fundamental significance that could be related to the "size" of the graviton. At the University of Washington, we are conducting the world's most sensitive, short-range test of the Newtonian ISL.

Rate of convergence of k-step Newton estimators to efficient likelihood estimators

Treesearch

Steve Verrill

2007-01-01

We make use of Cramer conditions together with the well-known local quadratic convergence of Newton?s method to establish the asymptotic closeness of k-step Newton estimators to efficient likelihood estimators. In Verrill and Johnson [2007. Confidence bounds and hypothesis tests for normal distribution coefficients of variation. USDA Forest Products Laboratory Research...

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.

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.

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.

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…

Mass-sheet degeneracy, power-law models and external convergence: Impact on the determination of the Hubble constant from gravitational lensing

NASA Astrophysics Data System (ADS)

Schneider, Peter; Sluse, Dominique

2013-11-01

The light travel time differences in strong gravitational lensing systems allows an independent determination of the Hubble constant. This method has been successfully applied to several lens systems. The formally most precise measurements are, however, in tension with the recent determination of H0 from the Planck satellite for a spatially flat six-parameters ΛCDM cosmology. We reconsider the uncertainties of the method, concerning the mass profile of the lens galaxies, and show that the formal precision relies on the assumption that the mass profile is a perfect power law. Simple analytical arguments and numerical experiments reveal that mass-sheet like transformations yield significant freedom in choosing the mass profile, even when exquisite Einstein rings are observed. Furthermore, the characterization of the environment of the lens does not break that degeneracy which is not physically linked to extrinsic convergence. We present an illustrative example where the multiple imaging properties of a composite (baryons + dark matter) lens can be extremely well reproduced by a power-law model having the same velocity dispersion, but with predictions for the Hubble constant that deviate by ~20%. Hence we conclude that the impact of degeneracies between parametrized models have been underestimated in current H0 measurements from lensing, and need to be carefully reconsidered.

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.

Neural Generalized Predictive Control: A Newton-Raphson Implementation

NASA Technical Reports Server (NTRS)

Soloway, Donald; Haley, Pamela J.

1997-01-01

An efficient implementation of Generalized Predictive Control using a multi-layer feedforward neural network as the plant's nonlinear model is presented. In using Newton-Raphson as the optimization algorithm, the number of iterations needed for convergence is significantly reduced from other techniques. The main cost of the Newton-Raphson algorithm is in the calculation of the Hessian, but even with this overhead the low iteration numbers make Newton-Raphson faster than other techniques and a viable algorithm for real-time control. This paper presents a detailed derivation of the Neural Generalized Predictive Control algorithm with Newton-Raphson as the minimization algorithm. Simulation results show convergence to a good solution within two iterations and timing data show that real-time control is possible. Comments about the algorithm's implementation are also included.

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.

Isaac Newton and the astronomical refraction.

PubMed

Lehn, Waldemar H

2008-12-01

In a short interval toward the end of 1694, Isaac Newton developed two mathematical models for the theory of the astronomical refraction and calculated two refraction tables, but did not publish his theory. Much effort has been expended, starting with Biot in 1836, in the attempt to identify the methods and equations that Newton used. In contrast to previous work, a closed form solution is identified for the refraction integral that reproduces the table for his first model (in which density decays linearly with elevation). The parameters of his second model, which includes the exponential variation of pressure in an isothermal atmosphere, have also been identified by reproducing his results. The implication is clear that in each case Newton had derived exactly the correct equations for the astronomical refraction; furthermore, he was the first to do so.

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.;

Newton and Colour: The Complex Interplay of Theory and Experiment.

ERIC Educational Resources Information Center

Martins, Roberto De Andrade; Silva, Cibelle Celestino

2001-01-01

Elucidates some aspects of Newton's theory of light and colors, specifically as presented in his first optical paper in 1672. Analyzes Newton's main experiments intended to show that light is a mixture of rays with different refrangibilities. (SAH)

Isaac Newton Olympics.

ERIC Educational Resources Information Center

Cox, Carol

2001-01-01

Presents the Isaac Newton Olympics in which students complete a hands-on activity at seven stations and evaluate what they have learned in the activity and how it is related to real life. Includes both student and teacher instructions for three of the activities. (YDS)

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.

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.

27 CFR 9.152 - Malibu-Newton Canyon.

Code of Federal Regulations, 2010 CFR

2010-04-01

....” (2) Then south along Kanan Dume Road to the point where an unnamed, unimproved dirt road referred to... Canyon Road to an unnamed, unimproved dirt road referred to by the petitioner as Newton Mountain Way at... southeastern ridgeline of Newton Canyon, to an unnamed, unimproved dirt road referred to by the petitioner as...

XMM-Newton Observations of Four Millisecond Pulsars

NASA Technical Reports Server (NTRS)

Zavlin, Vyacheslav E.

2005-01-01

I present an analysis of the XMM-Newton observations of four millisecond pulsars, J0437-4715, J2124-3358, J1024-0719, and J0034-0534. The new data provide strong evidence of thermal emission in the X-ray flux detected from the first three objects. This thermal component is best interpreted as radiation from pulsar polar caps covered with a nonmagnetic hydrogen atmosphere. A nonthermal power-law component, dominating at energies E greater than or equal to 3 keV, can also be present in the detected X-ray emission. For PSR J0437-4715, the timing analysis reveals that the shape and pulsed fraction of the pulsar light curves are energy dependent. This, together with the results obtained from the phase-resolved spectroscopy, supports the two-component (thermal plus nonthermal) interpretation of the pulsar's X-ray radiation. Highly significant pulsations have been found in the X-ray flux of PSRs 52124-3358 and 51024-0719. For PSR 50034-0534, a possible X-ray counterpart of the radio pulsar has been suggested. The inferred properties of the detected thermal emission are compared with predictions of radio pulsar models.

XMM-Newton Mobile Web Application

NASA Astrophysics Data System (ADS)

Ibarra, A.; Kennedy, M.; Rodríguez, P.; Hernández, C.; Saxton, R.; Gabriel, C.

2013-10-01

We present the first XMM-Newton web mobile application, coded using new web technologies such as HTML5, the Query mobile framework, and D3 JavaScript data-driven library. This new web mobile application focuses on re-formatted contents extracted directly from the XMM-Newton web, optimizing the contents for mobile devices. The main goals of this development were to reach all kind of handheld devices and operating systems, while minimizing software maintenance. The application therefore has been developed as a web mobile implementation rather than a more costly native application. New functionality will be added regularly.

Covariant theory of gravitation in the framework of special relativity

NASA Astrophysics Data System (ADS)

Vieira, R. S.; Brentan, H. B.

2018-04-01

In this work, we study the magnetic effects of gravity in the framework of special relativity. Imposing covariance of the gravitational force with respect to the Lorentz transformations, we show from a thought experiment that a magnetic-like force must be present whenever two or more bodies are in motion. The exact expression for this gravitomagnetic force is then derived purely from special relativity and the consequences of such a covariant theory are developed. For instance, we show that the gravitomagnetic fields satisfy a system of differential equations similar to the Maxwell equations of electrodynamics. This implies that the gravitational waves spread out with the speed of light in a flat spacetime, which is in agreement with the recent results concerning the gravitational waves detection. We also propose that the vector potential can be associated with the interaction momentum in the same way as the scalar potential is usually associated with the interaction energy. Other topics are also discussed, for example, the transformation laws for the fields, the energy and momentum stored in the gravitomagnetic fields, the invariance of the gravitational mass and so on. We remark that is not our intention here to propose an alternative theory of gravitation but, rather, only a first approximation for the gravitational phenomena, so that it can be applied whenever the gravitational force can be regarded as an ordinary effective force field and special relativity can be used with safety. To make this point clear we present briefly a comparison between our approach and that based on the (linearized) Einstein's theory. Finally, we remark that although we have assumed nothing from the electromagnetic theory, we found that gravity and electricity share many properties in common -these similarities, in fact, are just a requirement of special relativity that must apply to any physically acceptable force field.

Limits on the power-law mass and luminosity density profiles of elliptical galaxies from gravitational lensing systems

NASA Astrophysics Data System (ADS)

Cao, Shuo; Biesiada, Marek; Yao, Meng; Zhu, Zong-Hong

2016-09-01

We use 118 strong gravitational lenses observed by the SLACS, BOSS emission-line lens survey (BELLS), LSD and SL2S surveys to constrain the total mass profile and the profile of luminosity density of stars (light tracers) in elliptical galaxies up to redshift z ˜ 1. Assuming power-law density profiles for the total mass density, ρ = ρ0(r/r0)-α, and luminosity density, ν = ν0(r/r0)-δ, we investigate the power-law index and its first derivative with respect to the redshift. Using Monte Carlo simulations of the posterior likelihood taking the Planck's best-fitting cosmology as a prior, we find γ = 2.132 ± 0.055 with a mild trend ∂γ/∂zl = -0.067 ± 0.119 when α = δ = γ, suggesting that the total density profile of massive galaxies could have become slightly steeper over cosmic time. Furthermore, similar analyses performed on sub-samples defined by different lens redshifts and velocity dispersions indicate the need of treating low-, intermediate- and high-mass galaxies separately. Allowing δ to be a free parameter, we obtain α = 2.070 ± 0.031, ∂α/∂zl = -0.121 ± 0.078 and δ = 2.710 ± 0.143. The model in which mass traces light is rejected at >95 per cent confidence, and our analysis robustly indicates the presence of dark matter in the form of a mass component that is differently spatially extended than the light. In this case, intermediate-mass elliptical galaxies (200 km s-1 <σap ≤ 300 km s-1) show the best consistency with the singular isothermal sphere as an effective model of galactic lenses.

Newton-Krylov-Schwarz: An implicit solver for CFD

NASA Technical Reports Server (NTRS)

Cai, Xiao-Chuan; Keyes, David E.; Venkatakrishnan, V.

1995-01-01

Newton-Krylov methods and Krylov-Schwarz (domain decomposition) methods have begun to become established in computational fluid dynamics (CFD) over the past decade. The former employ a Krylov method inside of Newton's method in a Jacobian-free manner, through directional differencing. The latter employ an overlapping Schwarz domain decomposition to derive a preconditioner for the Krylov accelerator that relies primarily on local information, for data-parallel concurrency. They may be composed as Newton-Krylov-Schwarz (NKS) methods, which seem particularly well suited for solving nonlinear elliptic systems in high-latency, distributed-memory environments. We give a brief description of this family of algorithms, with an emphasis on domain decomposition iterative aspects. We then describe numerical simulations with Newton-Krylov-Schwarz methods on aerodynamics applications emphasizing comparisons with a standard defect-correction approach, subdomain preconditioner consistency, subdomain preconditioner quality, and the effect of a coarse grid.

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.

ARRIVAL TIME DIFFERENCES BETWEEN GRAVITATIONAL WAVES AND ELECTROMAGNETIC SIGNALS DUE TO GRAVITATIONAL LENSING

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

Takahashi, Ryuichi

In this study we demonstrate that general relativity predicts arrival time differences between gravitational wave (GW) and electromagnetic (EM) signals caused by the wave effects in gravitational lensing. The GW signals can arrive earlier than the EM signals in some cases if the GW/EM signals have passed through a lens, even if both signals were emitted simultaneously by a source. GW wavelengths are much larger than EM wavelengths; therefore, the propagation of the GWs does not follow the laws of geometrical optics, including the Shapiro time delay, if the lens mass is less than approximately 10{sup 5} M {sub ⊙}(more » f /Hz){sup −1}, where f is the GW frequency. The arrival time difference can reach ∼0.1 s ( f /Hz){sup −1} if the signals have passed by a lens of mass ∼8000 M {sub ⊙}( f /Hz){sup −1} with the impact parameter smaller than the Einstein radius; therefore, it is more prominent for lower GW frequencies. For example, when a distant supermassive black hole binary (SMBHB) in a galactic center is lensed by an intervening galaxy, the time lag becomes of the order of 10 days. Future pulsar timing arrays including the Square Kilometre Array and X-ray detectors may detect several time lags by measuring the orbital phase differences between the GW/EM signals in the SMBHBs. Gravitational lensing imprints a characteristic modulation on a chirp waveform; therefore, we can deduce whether a measured arrival time lag arises from intrinsic source properties or gravitational lensing. Determination of arrival time differences would be extremely useful in multimessenger observations and tests of general relativity.« less

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.

Chameleon scalar fields in relativistic gravitational backgrounds

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

Tsujikawa, Shinji; Tamaki, Takashi; Tavakol, Reza, E-mail: shinji@rs.kagu.tus.ac.jp, E-mail: tamaki@gravity.phys.waseda.ac.jp, E-mail: r.tavakol@qmul.ac.uk

2009-05-15

We study the field profile of a scalar field {phi} that couples to a matter fluid (dubbed a chameleon field) in the relativistic gravitational background of a spherically symmetric spacetime. Employing a linear expansion in terms of the gravitational potential {Phi}{sub c} at the surface of a compact object with a constant density, we derive the thin-shell field profile both inside and outside the object, as well as the resulting effective coupling with matter, analytically. We also carry out numerical simulations for the class of inverse power-law potentials V({phi}) = M{sup 4+n}{phi}{sup -n} by employing the information provided by ourmore » analytical solutions to set the boundary conditions around the centre of the object and show that thin-shell solutions in fact exist if the gravitational potential {Phi}{sub c} is smaller than 0.3, which marginally covers the case of neutron stars. Thus the chameleon mechanism is present in the relativistic gravitational backgrounds, capable of reducing the effective coupling. Since thin-shell solutions are sensitive to the choice of boundary conditions, our analytic field profile is very helpful to provide appropriate boundary conditions for {Phi}{sub c}{approx}« less

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.

Newton's Experimentum Crucis Reconsidered

ERIC Educational Resources Information Center

Holtsmark, Torger

1970-01-01

Certain terminological inconsistencies in the teaching of optical theory at the elementary level are traced back to Newton who derived them from Euclidean geometrical optics. Discusses this terminological ambiguity which influenced later textbooks. (LS)

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

XMM-Newton Remote Interface to Science Analysis Software: First Public Version

NASA Astrophysics Data System (ADS)

Ibarra, A.; Gabriel, C.

2011-07-01

We present the first public beta release of the XMM-Newton Remote Interface to Science Analysis (RISA) software, available through the official XMM-Newton web pages. In a nutshell, RISA is a web based application that encapsulates the XMM-Newton data analysis software. The client identifies observations and creates XMM-Newton workflows. The server processes the client request, creates job templates and sends the jobs to a computer. RISA has been designed to help, at the same time, non-expert and professional XMM-Newton users. Thanks to the predefined threads, non-expert users can easily produce light curves and spectra. And on the other hand, expert user can use the full parameter interface to tune their own analysis. In both cases, the VO compliant client/server design frees the users from having to install any specific software to analyze XMM-Newton data.

Why Did Newton See Indigo in the Spectrum?

ERIC Educational Resources Information Center

Biernson, George

1972-01-01

The arrangement of colors in Newton's color circle suggests that it was derived from paint mixtures, not light mixtures. If this is true it may be concluded that what Newton called indigo represents violet in modern terminology, and what he called violet represents purple. (Author/TS)

Newton gauge cosmological perturbations for static spherically symmetric modifications of the de Sitter metric

NASA Astrophysics Data System (ADS)

Santa Vélez, Camilo; Enea Romano, Antonio

2018-05-01

Static coordinates can be convenient to solve the vacuum Einstein's equations in presence of spherical symmetry, but for cosmological applications comoving coordinates are more suitable to describe an expanding Universe, especially in the framework of cosmological perturbation theory (CPT). Using CPT we develop a method to transform static spherically symmetric (SSS) modifications of the de Sitter solution from static coordinates to the Newton gauge. We test the method with the Schwarzschild de Sitter (SDS) metric and then derive general expressions for the Bardeen's potentials for a class of SSS metrics obtained by adding to the de Sitter metric a term linear in the mass and proportional to a general function of the radius. Using the gauge invariance of the Bardeen's potentials we then obtain a gauge invariant definition of the turn around radius. We apply the method to an SSS solution of the Brans-Dicke theory, confirming the results obtained independently by solving the perturbation equations in the Newton gauge. The Bardeen's potentials are then derived for new SSS metrics involving logarithmic, power law and exponential modifications of the de Sitter metric. We also apply the method to SSS metrics which give flat rotation curves, computing the radial energy density profile in comoving coordinates in presence of a cosmological constant.

An XMM-Newton Study of the Bright Narrow-Line Seyfert 1 Galaxy Arakelian 564

NASA Technical Reports Server (NTRS)

Brandt, Niel

2004-01-01

We report on two XMM-Newton observations of the bright Narrow-Line Seyfert 1 galaxy Ark 564 taken one year apart (2000 June and 2001 June). The 0.6-10 keV continuum is well described by a soft blackbody component (kT - 140-150 eV) plus a steep power law (Gamma - 2.50-2.55). No significant spectral changes are observed between the two observations, although the X-ray flux in the second observation is - 40-50 per cent lower. In both observations we detect a significant absorption edge at a rest-frame energy of - 0.73 keV, corresponding to 0 VII. The presence of the absorption feature is confirmed by a simultaneous Chandra grating observation in 2000 June, although the best-fitting edge threshold is at a slightly lower energy in the Chandra data, possibly because of a different parameterization of the underlying X-ray continuum. We find tentative evidence for a broad iron emission line in the 2000 June observation. The results from an analysis of the power spectral density (PSD) function are also presented. The present XMM-Newton data support the idea that the PSD shows two breaks, although the location of the high-frequency break requires further constraints.

`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.

XMM-Newton On-demand Reprocessing Using SaaS Technology

NASA Astrophysics Data System (ADS)

Ibarra, A.; Fajersztejn, N.; Loiseau, N.; Gabriel, C.

2014-05-01

We present here the architectural design of the new on-the-fly reprocessing capabilities that will be soon developed and implemented in the new XMM-Newton Science Operation Centre. The inclusion of processing capabilities into the archive, as we plan, will be possible thanks to the recent refurbishment of the XMM-Newton science archive, its alignment with the latest web technologies and the XMM-Newton Remote Interface for Science Analysis (RISA), a revolutionary idea of providing processing capabilities through internet services.

Self-gravitating axially symmetric disks in general-relativistic rotation

NASA Astrophysics Data System (ADS)

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

2018-05-01

We integrate numerically axially symmetric stationary Einstein equations describing self-gravitating disks around spinless black holes. The numerical scheme is based on a method developed by Shibata, but contains important new ingredients. We derive a new general-relativistic Keplerian rotation law for self-gravitating disks around spinning black holes. Former results concerning rotation around spinless black holes emerge in the limit of a vanishing spin parameter. These rotation curves might be used for the description of rotating stars, after appropriate modification around the symmetry axis. They can be applied to the description of compact torus-black hole configurations, including active galactic nuclei or products of coalescences of two neutron stars.

Nonstandard gravitational waves imply gravitational slip: On the difficulty of partially hiding new gravitational degrees of freedom

NASA Astrophysics Data System (ADS)

Sawicki, Ignacy; Saltas, Ippocratis D.; Motta, Mariele; Amendola, Luca; Kunz, Martin

2017-04-01

In many generalized models of gravity, perfect fluids in cosmology give rise to gravitational slip. Simultaneously, in very broad classes of such models, the propagation of gravitational waves is altered. We investigate the extent to which there is a one-to-one relationship between these two properties in three classes of models with one extra degree of freedom: scalar (Horndeski and beyond), vector (Einstein-aether), and tensor (bimetric). We prove that in bimetric gravity and Einstein-aether, it is impossible to dynamically hide the gravitational slip on all scales whenever the propagation of gravitational waves is modified. Horndeski models are much more flexible, but it is nonetheless only possible to hide gravitational slip dynamically when the action for perturbations is tuned to evolve in time toward a divergent kinetic term. These results provide an explicit, theoretical argument for the interpretation of future observations if they disfavored the presence of gravitational slip.

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.

The Arithmetic of events and a new theory of Gravitation

NASA Astrophysics Data System (ADS)

Abbasi, Malek

2012-04-01

Of fundamental importance in physics is the concept of event. This study tries; first, to provide a mathematical background showing how must deal with these events and based on what laws the watches, another important concept used frequently in this research, record them. Armed, then, with this mathematical background, the Gravitational Clouds Theory, a novel theory of gravitation concerning the role of the matter and energy in the universe, is proposed. This completely new theory leads to miscellanies results some of which are: the second Einstein's postulate; the well known identity E = mc2; the time-dilation phenomenon and Fitzgerald-Lorentz contraction. This theory will also explain why indeed we never feel the speed of the Earth, what is the origin of Dark matter-energy and many other extraordinary results associated with cosmology.

The Arithmetic of Events and a New Theory of Gravitation

NASA Astrophysics Data System (ADS)

Abbasi, Malek

2012-10-01

Of fundamental importance in physics is the concept of event. This study tries, first, to provide a mathematical background showing how must deal with these events and based on what laws the watches, another important concept used frequently in this research, record them. Armed, then, with this mathematical background, the Gravitational Clouds Theory, a novel theory of gravitation concerning the role of the matter and energy in the universe, is proposed. This completely new theory leads to miscellanies results some of which are: the second Einstein's postulate; the well known identity E = mc2; the time-dilation phenomenon and Fitzgerald-Lorentz contraction. This theory will also explain why indeed we never feel the speed of the Earth, what is the origin of Dark matter-energy and many other extraordinary results associated with cosmology.

How to test gravitation theories by means of gravitational-wave measurements

NASA Technical Reports Server (NTRS)

Thorne, K. S.

1974-01-01

Gravitational-wave experiments are a potentially powerful tool for testing gravitation theories. Most theories in the literature predict rather different polarization properties for gravitational waves than are predicted by general relativity; and many theories predict anomalies in the propagation speeds of gravitational waves.

Mass hierarchy, mass gap and corrections to Newton's law on thick branes with Poincaré symmetry

NASA Astrophysics Data System (ADS)

Barbosa-Cendejas, Nandinii; Herrera-Aguilar, Alfredo; Kanakoglou, Konstantinos; Nucamendi, Ulises; Quiros, Israel

2014-01-01

We consider a scalar thick brane configuration arising in a 5D theory of gravity coupled to a self-interacting scalar field in a Riemannian manifold. We start from known classical solutions of the corresponding field equations and elaborate on the physics of the transverse traceless modes of linear fluctuations of the classical background, which obey a Schrödinger-like equation. We further consider two special cases in which this equation can be solved analytically for any massive mode with , in contrast with numerical approaches, allowing us to study in closed form the massive spectrum of Kaluza-Klein (KK) excitations and to analytically compute the corrections to Newton's law in the thin brane limit. In the first case we consider a novel solution with a mass gap in the spectrum of KK fluctuations with two bound states—the massless 4D graviton free of tachyonic instabilities and a massive KK excitation—as well as a tower of continuous massive KK modes which obey a Legendre equation. The mass gap is defined by the inverse of the brane thickness, allowing us to get rid of the potentially dangerous multiplicity of arbitrarily light KK modes. It is shown that due to this lucky circumstance, the solution of the mass hierarchy problem is much simpler and transparent than in the thin Randall-Sundrum (RS) two-brane configuration. In the second case we present a smooth version of the RS model with a single massless bound state, which accounts for the 4D graviton, and a sector of continuous fluctuation modes with no mass gap, which obey a confluent Heun equation in the Ince limit. (The latter seems to have physical applications for the first time within braneworld models). For this solution the mass hierarchy problem is solved with positive branes as in the Lykken-Randall (LR) model and the model is completely free of naked singularities. We also show that the scalar-tensor system is stable under scalar perturbations with no scalar modes localized on the braneworld

Gravitational Waves from Gravitational Collapse.

PubMed

Fryer, Chris L; New, Kimberly C B

2011-01-01

Gravitational-wave emission from stellar collapse has been studied for nearly four decades. Current state-of-the-art numerical investigations of collapse include those that use progenitors with more realistic angular momentum profiles, properly treat microphysics issues, account for general relativity, and examine non-axisymmetric effects in three dimensions. Such simulations predict that gravitational waves from various phenomena associated with gravitational collapse could be detectable with ground-based and space-based interferometric observatories. This review covers the entire range of stellar collapse sources of gravitational waves: from the accretion-induced collapse of a white dwarf through the collapse down to neutron stars or black holes of massive stars to the collapse of supermassive stars. Supplementary material is available for this article at 10.12942/lrr-2011-1.

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.

Unsteady Newton-Busemann flow theory. Part 2: Bodies of revolution

NASA Technical Reports Server (NTRS)

Hui, W. H.; Tobak, M.

1981-01-01

Newtonian flow theory for unsteady flow past oscillating bodies of revolution at very high Mach numbers is completed by adding a centrifugal force correction to the impact pressures. Exact formulas for the unsteady pressure and the stability derivatives are obtained in closed form and are applicable to bodies of revolution that have arbitrary shapes, arbitrary thicknesses, and either sharp or blunt noses. The centrifugal force correction arising from the curved trajectories followed by the fluid particles in unsteady flow cannot be neglected even for the case of a circular cone. With this correction, the present theory is in excellent agreement with experimental results for sharp cones and for cones with small nose bluntness; gives poor agreement with the results of experiments in air for bodies with moderate or large nose bluntness. The pitching motions of slender power-law bodies of revulution are shown to be always dynamically stable according to Newton-Busemann theory.

NuSTAR and XMM-Newton Observations of the Hard X- Ray Spectrum of Centaurus A

NASA Technical Reports Server (NTRS)

Furst, F.; Muller, C.; Madsen, K. K.; Lanz, L.; Rivers, E.; Brightman, M.; Arevalo, P.; Balokovic, M.; Beuchert, T.; Zhang, W.

2016-01-01

We present simultaneous XMM-Newton and Nuclear Spectroscopic Telescope Array (NuSTAR) observations spanning 3-78 keV of the nearest radio galaxy, Centaurus A (Cen A). The accretion geometry around the central engine in Cen A is still debated, and we investigate possible configurations using detailed X-ray spectral modeling. NuSTAR imaged the central region of Cen A with subarcminute resolution at X-ray energies above 10 keV for the first time, but found no evidence for an extended source or other off-nuclear point sources. The XMM-Newton and NuSTAR spectra agree well and can be described with an absorbed power law with a photon index Gamma = 1.8150 +/- 0.005 and a fluorescent Fe Kaline in good agreement with literature values. The spectrum is greater than 1 MeV. A thermal Comptonization continuum describes the data well, with parameters that agree with values measured by INTEGRAL, in particular an electron temperature kTe between approximately 100-300 keV and seed photon input temperatures between 5 and 50 eV. We do not find evidence for reflection or a broad iron line and put stringent upper limits of R is less than 0.01 on the reflection fraction and accretion disk illumination. We use archival Chandra data to estimate the contribution from diffuse emission, extra-nuclear point sources, and the outer X-ray jet to the observed NuSTAR and XMM-Newton X-ray spectra and find the contribution to be negligible. We discuss different scenarios for the physical origin of the observed hard X-ray spectrum and conclude that the inner disk is replaced by an advection-dominated accretion flow or that the X-rays are dominated by synchrotron self-Compton emission from the inner regions of the radio jet or a combination thereof.

Regional recovery of the disturbing gravitational potential by inverting satellite gravitational gradients

NASA Astrophysics Data System (ADS)

Pitoňák, Martin; Šprlák, Michal; Hamáčková, Eliška; Novák, Pavel

2016-04-01

Regional recovery of the disturbing gravitational potential in the area of Central Europe from satellite gravitational gradients data is discussed in this contribution. The disturbing gravitational potential is obtained by inverting surface integral formulas which transform the disturbing gravitational potential onto disturbing gravitational gradients in the spherical local north-oriented frame. Two numerical approaches that solve the inverse problem are considered. In the first approach, the integral formulas are rigorously decomposed into two parts, that is, the effects of the gradient data within near and distant zones. While the effect of the near zone data is sought as an inverse problem, the effect of the distant zone data is synthesized from the global gravitational model GGM05S using spectral weights given by truncation error coefficients up to the degree 150. In the second approach, a reference gravitational field up to the degree 180 is applied to reduce and smooth measured gravitational gradients. In both cases we recovered the disturbing gravitational potential from each of the four well-measured gravitational gradients of the GOCE satellite separately as well as from their combination. Obtained results are compared with the EGM2008, DIR-r2, TIM-r2 and SPW-r2 global gravitational models. The best fit was achieved for EGM2008 and the second approach combining all four well-measured gravitational gradients with rms of 1.231 m2 s-2.

On the Shoulders of Sir Isaac Newton and Arthur Storer

ERIC Educational Resources Information Center

Martin, Helen E.; Evans-Gondo, Bonita

2013-01-01

Helen E. Martin, the author of this article, is a retired National Board Certified Teacher who has been researching Sir Isaac Newton's unpublished manuscripts for over three decades. While researching the work of Newton, a teacher she was mentoring asked for some hands-on activities to study planetary motion. The description of the activity…

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.

Lectures on gravitation

NASA Astrophysics Data System (ADS)

Das, Ashok

1. Basics of geometry and relativity. 1.1. Two dimensional geometry. 1.2. Inertial and gravitational masses. 1.3. Relativity -- 2. Relativistic dynamics. 2.1. Relativistic point particle. 2.2. Current and charge densities. 2.3. Maxwell's equations in the presence of sources. 2.4. Motion of a charged particle in EM field. 2.5. Energy-momentum tensor. 2.6. Angular momentum -- 3. Principle of general covariance. 3.1. Principle of equivalence. 3.2. Principle of general covariance. 3.3. Tensor densities -- 4. Affine connection and covariant derivative. 4.1. Parallel transport of a vector. 4.2. Christoffel symbol. 4.3. Covariant derivative of contravariant tensors. 4.4. Metric compatibility. 4.5. Covariant derivative of covariant and mixed tensors. 4.6. Electromagnetic analogy. 4.7. Gradient, divergence and curl -- 5. Geodesic equation. 5.1. Covariant differentiation along a curve. 5.2. Curvature from derivatives. 5.3. Parallel transport along a closed curve. 5.4. Geodesic equation. 5.5. Derivation of geodesic equation from a Lagrangian -- 6. Applications of the geodesic equation. 6.1. Geodesic as representing gravitational effect. 6.2. Rotating coordinate system and the Coriolis force. 6.3. Gravitational red shift. 6.4. Twin paradox and general covariance. 6.5. Other equations in the presence of gravitation -- 7. Curvature tensor and Einstein's equation. 7.1. Curvilinear coordinates versus gravitational field. 7.2. Definition of an inertial coordinate frame. 7.3. Geodesic deviation. 7.4. Properties of the curvature tensor. 7.5. Einstein's equation. 7.6. Cosmological constant. 7.7. Initial value problem. 7.8. Einstein's equation from an action -- 8. Schwarzschild solution. 8.1. Line element. 8.2. Connection. 8.3. Solution of the Einstein equation. 8.4. Properties of the Schwarzschild solution. 8.5. Isotropic coordinates -- 9. Tests of general relativity. 9.1. Radar echo experiment. 9.2. Motion of a particle in a Schwarzschild background. 9.3. Motion of light rays in a

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.

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…

(BNL/DoE-hyped) ``Self-Organized-Criticality'' (SOC) is Merely Newton's(1687) Third Law of Motion F = ma REdiscovery: LONG PRE-``Bak''!!!

NASA Astrophysics Data System (ADS)

Bak, P. R. E.; Newton, I.; Siegel, Edward Carl-Ludwig

2011-03-01

"Bak"/BNL/DoE "self-organized-criticality"(SOC) usual BNL/DoE media-hype P.R spin-doctoring "show-biz" "Bush-waaa-...-aaah!!!" is manifestly-demonstrated in two distinct ways to be nothing but Newton's Third Law of Motion F = ma REdiscovery!!! PHYSICS: (1687) cross-multiplied F = ma rewritten as 1/m = a/F = OUTPUT/INPUT = EFFECT/ CAUSE = inverse-mass mechanical-susceptibility = X ("w "); X ("w ") (F.-D. theorem-equivalence /proportionality) P("w ") "noise" power-spectrum; E w ; and E (any/all media upper-limiting-speeds) m. Thus: w E m; inversion yields: 1/w 1 /E 1 /m a/F = X ("w ") P("w "); hence: F = ma dual/inverse-integral-transform is "'SOC"'s" P(w) 1 / w (1) !!! ; "PURE"-MATHS: F = ma double-integral time-series s(t) = [vot + (1/2) at (2) ] inverse/dual-integral-transform formally defines power-spectrum: P (w) = S { s (t) e [ - (iORnoi) wt ] } dt = S { [ vot + (1 / 2) at 2) ] e [ - (iORnoi) wt ] } dt = voS { te [ - (iORnoi) wt ] } dt + (1 / 2) S { [ a = / = a (t) ] e [ - (iORnoi) wt) } dt = vo (d / dw) Delta (w) + (1 / 2) [ a = / = a (t) ] (d / dw) (2) Delta (w) = vo / w (0) + (1 / 2) [ a = / = a (t) ] / w 1 : ifa = 0 , then P(w) 1 / w 0 , VS . ifa = / = a (t) = / = 0 , then P(w) 1 /w; = by physics: ``SOC'' RE-expresses F = ma!!!: ``just `a tad' late/tardy'' REdiscovery of F=ma: LONG PRE-"Bak"!!!

Newtons's Thermometry: The Role of Radiation.

ERIC Educational Resources Information Center

French, A. P.

1993-01-01

Discusses Newton's idea of predicting very high temperatures of objects by observing the time needed for the object to cool to some standard reference temperature. This article discusses experimental deviations from this idea and provides explanations for the observed results. (MVL)

Reheating signature in the gravitational wave spectrum from self-ordering scalar fields

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

Kuroyanagi, Sachiko; Hiramatsu, Takashi; Yokoyama, Jun'ichi, E-mail: skuro@nagoya-u.jp, E-mail: hiramatz@yukawa.kyoto-u.ac.jp, E-mail: yokoyama@resceu.s.u-tokyo.ac.jp

2016-02-01

We investigate the imprint of reheating on the gravitational wave spectrum produced by self-ordering of multi-component scalar fields after a global phase transition. The equation of state of the Universe during reheating, which usually has different behaviour from that of a radiation-dominated Universe, affects the evolution of gravitational waves through the Hubble expansion term in the equations of motion. This gives rise to a different power-law behavior of frequency in the gravitational wave spectrum. The reheating history is therefore imprinted in the shape of the spectrum. We perform 512{sup 3} lattice simulations to investigate how the ordering scalar field reactsmore » to the change of the Hubble expansion and how the reheating effect arises in the spectrum. We also compare the result with inflation-produced gravitational waves, which has a similar spectral shape, and discuss whether it is possible to distinguish the origin between inflation and global phase transition by detecting the shape with future direct detection gravitational wave experiments such as DECIGO.« less

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)

Gravitational domain walls and the dynamics of the gravitational constant G

NASA Astrophysics Data System (ADS)

Bunster, Claudio; Gomberoff, Andrés

2017-07-01

From the point of view of elementary particle physics, the gravitational constant G is extraordinarily small. This has led to asking whether it could have decayed to its present value from an initial one commensurate with microscopical units. A mechanism that leads to such a decay is proposed herein. It is based on assuming that G may take different values within regions of the universe separated by a novel kind of domain wall, a "G -wall." The idea is implemented by introducing a gauge potential Aμ ν ρ, and its conjugate D , which determines the value of G as an integration constant rather than a fundamental constant. The value of G jumps when one goes through a G -wall. The procedure extends one previously developed for the cosmological constant, but the generalization is far from straightforward: (i) The intrinsic geometry of a G -wall is not the same as seen from its two sides because the second law of black hole thermodynamics mandates that the jump in G must cause a discontinuity in the scale of length. (ii) The size of the decay step in G is controlled by a function G (D ) which may be chosen so as to diminish the value of G towards the asymptote G =0 . It is shown that: (i) The dynamics of the gravitational field with G treated as a dynamical variable, coupled to G -walls and matter, follows from an action principle, which is given. (ii) A particle that impinges on a G -wall may be refracted or reflected. (iii) The various forces between two particles change when a G -wall is inserted in between them. (iv) G -walls may be nucleated trough tunneling and thermal effects, whose semiclassical probabilities are evaluated. (v) If the action principle is constructed properly, the entropy of a black hole increases when the value of the gravitational constant is changed through the absorption of a G-wall by the hole.

Optimized formulas for the gravitational field of a tesseroid

NASA Astrophysics Data System (ADS)

Grombein, Thomas; Seitz, Kurt; Heck, Bernhard

2013-07-01

Various tasks in geodesy, geophysics, and related geosciences require precise information on the impact of mass distributions on gravity field-related quantities, such as the gravitational potential and its partial derivatives. Using forward modeling based on Newton's integral, mass distributions are generally decomposed into regular elementary bodies. In classical approaches, prisms or point mass approximations are mostly utilized. Considering the effect of the sphericity of the Earth, alternative mass modeling methods based on tesseroid bodies (spherical prisms) should be taken into account, particularly in regional and global applications. Expressions for the gravitational field of a point mass are relatively simple when formulated in Cartesian coordinates. In the case of integrating over a tesseroid volume bounded by geocentric spherical coordinates, it will be shown that it is also beneficial to represent the integral kernel in terms of Cartesian coordinates. This considerably simplifies the determination of the tesseroid's potential derivatives in comparison with previously published methodologies that make use of integral kernels expressed in spherical coordinates. Based on this idea, optimized formulas for the gravitational potential of a homogeneous tesseroid and its derivatives up to second-order are elaborated in this paper. These new formulas do not suffer from the polar singularity of the spherical coordinate system and can, therefore, be evaluated for any position on the globe. Since integrals over tesseroid volumes cannot be solved analytically, the numerical evaluation is achieved by means of expanding the integral kernel in a Taylor series with fourth-order error in the spatial coordinates of the integration point. As the structure of the Cartesian integral kernel is substantially simplified, Taylor coefficients can be represented in a compact and computationally attractive form. Thus, the use of the optimized tesseroid formulas particularly

Swift, XMM-Newton, and NuSTAR Observations of PSR J2032+4127/MT91 213

NASA Astrophysics Data System (ADS)

Li, K. L.; Kong, A. K. H.; Tam, P. H. T.; Hou, X.; Takata, J.; Hui, C. Y.

2017-07-01

We report our recent Swift, NuSTAR, and XMM-Newton X-ray and Lijiang optical observations on PSR J2032+4127/MT91 213, the γ-ray binary candidate with a period of 45-50 years. The coming periastron of the system was predicted to be in 2017 November, around which high-energy flares from keV to TeV are expected. Recent studies with Chandra and Swift X-ray observations taken in 2015/2016 showed that its X-ray emission has been brighter by a factors of ˜10 than that before 2013, probably revealing some ongoing activities between the pulsar wind and the stellar wind. Our new Swift/XRT lightcurve shows no strong evidence of a single vigorous brightening trend, but rather several strong X-ray flares on weekly to monthly timescales with a slowly brightening baseline, namely the low state. The NuSTAR and XMM-Newton observations taken during the flaring and the low states, respectively, show a denser environment and a softer power-law index during the flaring state, implying that the pulsar wind interacted with the stronger stellar winds of the companion to produce the flares. These precursors would be crucial in studying the predicted giant outburst from this extreme γ-ray binary during the periastron passage in late 2017.

The gravitational Schwinger effect and attenuation of gravitational waves

NASA Astrophysics Data System (ADS)

McDougall, Patrick Guarneri

This paper will discuss the possible production of photons from gravitational waves. This process is shown to be possible by examining Feynman diagrams, the Schwinger Effect, and Hawking Radiation. The end goal of this project is to find the decay length of a gravitational wave and assert that this decay is due to photons being created at the expense of the gravitational wave. To do this, we first find the state function using the Klein Gordon equation, then find the current due to this state function. We then take the current to be directly proportional to the production rate per volume. This is then used to find the decay length that this kind of production would produce, gives a prediction of how this effect will change the distance an event creating a gravitational wave will be located, and shows that this effect is small but can be significant near the source of a gravitational wave.

Power-law versus log-law in wall-bounded turbulence: A large-eddy simulation perspective

NASA Astrophysics Data System (ADS)

Cheng, W.; Samtaney, R.

2014-01-01

The debate whether the mean streamwise velocity in wall-bounded turbulent flows obeys a log-law or a power-law scaling originated over two decades ago, and continues to ferment in recent years. As experiments and direct numerical simulation can not provide sufficient clues, in this study we present an insight into this debate from a large-eddy simulation (LES) viewpoint. The LES organically combines state-of-the-art models (the stretched-vortex model and inflow rescaling method) with a virtual-wall model derived under different scaling law assumptions (the log-law or the power-law by George and Castillo ["Zero-pressure-gradient turbulent boundary layer," Appl. Mech. Rev. 50, 689 (1997)]). Comparison of LES results for Reθ ranging from 105 to 1011 for zero-pressure-gradient turbulent boundary layer flows are carried out for the mean streamwise velocity, its gradient and its scaled gradient. Our results provide strong evidence that for both sets of modeling assumption (log law or power law), the turbulence gravitates naturally towards the log-law scaling at extremely large Reynolds numbers.

Comparing three methods for teaching Newton's third law

NASA Astrophysics Data System (ADS)

Smith, Trevor I.; Wittmann, Michael C.

2007-12-01

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 University of Washington style tutorial materials, but the different curricula have not been compared against each other. Our study examines three tutorials designed to improve student understanding of Newton’s third law: the University of Washington’s Tutorials in Introductory Physics (TIP), the University of Maryland’s Activity-Based Tutorials (ABT), and the Open Source Tutorials (OST) also developed at the University of Maryland. Each tutorial was designed with different goals and agendas, and each employs different methods to help students understand the physics. We analyzed pretest and post-test data, including course examinations and data from the Force and Motion Conceptual Evaluation (FMCE). Using both FMCE and course data, we find that students using the OST version of the tutorial perform better than students using either of the other two.

The architecture of Newton, a general-purpose dynamics simulator

NASA Technical Reports Server (NTRS)

Cremer, James F.; Stewart, A. James

1989-01-01

The architecture for Newton, a general-purpose system for simulating the dynamics of complex physical objects, is described. The system automatically formulates and analyzes equations of motion, and performs automatic modification of this system equations when necessitated by changes in kinematic relationships between objects. Impact and temporary contact are handled, although only using simple models. User-directed influence of simulations is achieved using Newton's module, which can be used to experiment with the control of many-degree-of-freedom articulated objects.

On a class of Newton-like methods for solving nonlinear equations

NASA Astrophysics Data System (ADS)

Argyros, Ioannis K.

2009-06-01

We provide a semilocal convergence analysis for a certain class of Newton-like methods considered also in [I.K. Argyros, A unifying local-semilocal convergence analysis and applications for two-point Newton-like methods in Banach space, J. Math. Anal. Appl. 298 (2004) 374-397; I.K. Argyros, Computational theory of iterative methods, in: C.K. Chui, L. Wuytack (Eds.), Series: Studies in Computational Mathematics, vol. 15, Elsevier Publ. Co, New York, USA, 2007; J.E. Dennis, Toward a unified convergence theory for Newton-like methods, in: L.B. Rall (Ed.), Nonlinear Functional Analysis and Applications, Academic Press, New York, 1971], in order to approximate a locally unique solution of an equation in a Banach space. Using a combination of Lipschitz and center-Lipschitz conditions, instead of only Lipschitz conditions [F.A. Potra, Sharp error bounds for a class of Newton-like methods, Libertas Math. 5 (1985) 71-84], we provide an analysis with the following advantages over the work in [F.A. Potra, Sharp error bounds for a class of Newton-like methods, Libertas Math. 5 (1985) 71-84] which improved the works in [W.E. Bosarge, P.L. Falb, A multipoint method of third order, J. Optimiz. Theory Appl. 4 (1969) 156-166; W.E. Bosarge, P.L. Falb, Infinite dimensional multipoint methods and the solution of two point boundary value problems, Numer. Math. 14 (1970) 264-286; J.E. Dennis, On the Kantorovich hypothesis for Newton's method, SIAM J. Numer. Anal. 6 (3) (1969) 493-507; J.E. Dennis, Toward a unified convergence theory for Newton-like methods, in: L.B. Rall (Ed.), Nonlinear Functional Analysis and Applications, Academic Press, New York, 1971; H.J. Kornstaedt, Ein allgemeiner Konvergenzstaz fü r verschä rfte Newton-Verfahrem, in: ISNM, vol. 28, Birkhaü ser Verlag, Basel and Stuttgart, 1975, pp. 53-69; P. Laasonen, Ein überquadratisch konvergenter iterativer algorithmus, Ann. Acad. Sci. Fenn. Ser I 450 (1969) 1-10; F.A. Potra, On a modified secant method, L'analyse num

Accuracy of gravitational physics tests using ranges to the inner planets

NASA Technical Reports Server (NTRS)

Ashby, N.; Bender, P.

1981-01-01

A number of different types of deviations from Kepler's laws for planetary orbits can occur in nonNewtonian metric gravitational theories. These include secular changes in all of the orbital elements and in the mean motion, plus additional periodic perturbations in the coordinates. The first order corrections to the Keplerian motion of a single planet around the Sun due to the parameterized post Newtonian theory parameters were calculated as well as the corrections due to the solar quadrupole moment and a possible secular change in the gravitational constant. The results were applied to the case of proposed high accuracy ranging experiments from the Earth to a Mercury orbiting spacecraft in order to see how well the various parameters can be determined.

First law of entanglement entropy in topologically massive gravity

NASA Astrophysics Data System (ADS)

Cheng, Long; Hung, Ling-Yan; Liu, Si-Nong; Zhou, Hong-Zhe

2016-09-01

In this paper we explore the validity of the first law of entanglement entropy in the context of topologically massive gravity (TMG). We find that the variation of the holographic entanglement entropy under perturbation from the pure anti-de Sitter background satisfies the first law upon imposing the bulk equations of motion in a given time slice, despite the appearance of instabilities in the bulk for generic gravitational Chern-Simons coupling μ . The Noether-Wald entropy is different from the holographic entanglement entropy in a general boosted frame. However, this discrepancy does not affect the entanglement first law.

XMM-Newton and INTEGRAL view of the hard state of EXO 1745-248 during its 2015 outburst

NASA Astrophysics Data System (ADS)

Matranga, M.; Papitto, A.; Di Salvo, T.; Bozzo, E.; Torres, D. F.; Iaria, R.; Burderi, L.; Rea, N.; de Martino, D.; Sanchez-Fernandez, C.; Gambino, A. F.; Ferrigno, C.; Stella, L.

2017-07-01

Context. Transient low-mass X-ray binaries (LMXBs) often show outbursts that typically last a few weeks and are characterized by a high X-ray luminosity (Lx ≈ 1036-1038 erg s-1), while most of the time they are found in X-ray quiescence (LX ≈ 1031-1033 erg s-1). The source EXO 1745-248 is one of them. Aims: The broad-band coverage and sensitivity of the instrument on board XMM-Newton and INTEGRAL offers the opportunity of characterizing the hard X-ray spectrum during the outburst of EXO 1745-248. Methods: We report on quasi-simultaneous XMM-Newton and INTEGRAL observations of the X-ray transient EXO 1745-248 located in the globular cluster Terzan 5, performed ten days after the beginning of the outburst (on 2015 March 16) of the source between March and June 2015. The source was caught in a hard state, emitting a 0.8-100 keV luminosity of ≃ 1037 erg s-1. Results: The spectral continuum was dominated by thermal Comptonization of seed photons with temperature kTin ≃ 1.3 keV, by a cloud with a moderate optical depth τ ≃ 2, and with an electron temperature of kTe ≃ 40 keV. A weaker soft thermal component at temperature kTth ≃ 0.6-0.7 keV and compatible with a fraction of the neutron star radius was also detected. A rich emission line spectrum was observed by the EPIC-pn on board XMM-Newton; features at energies compatible with K-α transitions of ionized sulfur, argon, calcium, and iron were detected, with a broadness compatible with either thermal Compton broadening or Doppler broadening in the inner parts of an accretion disk truncated at 20 ± 6 gravitational radii from the neutron star. Strikingly, at least one narrow emission line ascribed to neutral or mildly ionized iron is needed to model the prominent emission complex detected between 5.5 and 7.5 keV. The different ionization state and broadness suggest an origin in a region located farther from the neutron star than where the other emission lines are produced. Seven consecutive type I bursts

Asymptotic solutions for the case of nearly symmetric gravitational lens systems

NASA Astrophysics Data System (ADS)

Wertz, O.; Pelgrims, V.; Surdej, J.

2012-08-01

Gravitational lensing provides a powerful tool to determine the Hubble parameter H0 from the measurement of the time delay Δt between two lensed images of a background variable source. Nevertheless, knowledge of the deflector mass distribution constitutes a hurdle. We propose in the present work interesting solutions for the case of nearly symmetric gravitational lens systems. For the case of a small misalignment between the source, the deflector and the observer, we first consider power-law (ɛ) axially symmetric models for which we derive an analytical relation between the amplification ratio and source position which is independent of the power-law slope ɛ. According to this relation, we deduce an expression for H0 also irrespective of the value ɛ. Secondly, we consider the power-law axially symmetric lens models with an external large-scale gravitational field, the shear γ, resulting in the so-called ɛ-γ models, for which we deduce simple first-order equations linking the model parameters and the lensed image positions, the latter being observable quantities. We also deduce simple relations between H0 and observables quantities only. From these equations, we may estimate the value of the Hubble parameter in a robust way. Nevertheless, comparison between the ɛ-γ and singular isothermal ellipsoid (SIE) models leads to the conclusion that these models remain most often distinct. Therefore, even for the case of a small misalignment, use of the first-order equations and precise astrometric measurements of the positions of the lensed images with respect to the centre of the deflector enables one to discriminate between these two families of models. Finally, we confront the models with numerical simulations to evaluate the intrinsic error of the first-order expressions used when deriving the model parameters under the assumption of a quasi-alignment between the source, the deflector and the observer. From these same simulations, we estimate for the case of the

Higher symmetries of the Schrödinger operator in Newton-Cartan geometry

NASA Astrophysics Data System (ADS)

Gundry, James

2017-03-01

We establish several relationships between the non-relativistic conformal symmetries of Newton-Cartan geometry and the Schrödinger equation. In particular we discuss the algebra sch(d) of vector fields conformally-preserving a flat Newton-Cartan spacetime, and we prove that its curved generalisation generates the symmetry group of the covariant Schrödinger equation coupled to a Newtonian potential and generalised Coriolis force. We provide intrinsic Newton-Cartan definitions of Killing tensors and conformal Schrödinger-Killing tensors, and we discuss their respective links to conserved quantities and to the higher symmetries of the Schrödinger equation. Finally we consider the role of conformal symmetries in Newtonian twistor theory, where the infinite-dimensional algebra of holomorphic vector fields on twistor space corresponds to the symmetry algebra cnc(3) on the Newton-Cartan spacetime.

How Two Differing Portraits of Newton Can Teach Us about the Cultural Context of Science

ERIC Educational Resources Information Center

Tucci, Pasquale

2015-01-01

Like several scientists, Isaac Newton has been represented many times over many different periods, and portraits of Newton were often commissioned by the scientist himself. These portraits tell us a lot about the scientist, the artist and the cultural context. This article examines two very different portraits of Newton that were realized more…

Variational nature, integration, and properties of Newton reaction path

NASA Astrophysics Data System (ADS)

Bofill, Josep Maria; Quapp, Wolfgang

2011-02-01

The distinguished coordinate path and the reduced gradient following path or its equivalent formulation, the Newton trajectory, are analyzed and unified using the theory of calculus of variations. It is shown that their minimum character is related to the fact that the curve is located in a valley region. In this case, we say that the Newton trajectory is a reaction path with the category of minimum energy path. In addition to these findings a Runge-Kutta-Fehlberg algorithm to integrate these curves is also proposed.

Variational nature, integration, and properties of Newton reaction path.

PubMed

Bofill, Josep Maria; Quapp, Wolfgang

2011-02-21

The distinguished coordinate path and the reduced gradient following path or its equivalent formulation, the Newton trajectory, are analyzed and unified using the theory of calculus of variations. It is shown that their minimum character is related to the fact that the curve is located in a valley region. In this case, we say that the Newton trajectory is a reaction path with the category of minimum energy path. In addition to these findings a Runge-Kutta-Fehlberg algorithm to integrate these curves is also proposed.

A New Newton-Like Iterative Method for Roots of Analytic Functions

ERIC Educational Resources Information Center

Otolorin, Olayiwola

2005-01-01

A new Newton-like iterative formula for the solution of non-linear equations is proposed. To derive the formula, the convergence criteria of the one-parameter iteration formula, and also the quasilinearization in the derivation of Newton's formula are reviewed. The result is a new formula which eliminates the limitations of other methods. There is…

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.

Gravitational Waves

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

Miller, Jonah Maxwell

This report has slides on Gravitational Waves; Pound and Rebka: A Shocking Fact; Light is a Ruler; Gravity is the Curvature of Spacetime; Gravitational Waves Made Simple; How a Gravitational Wave Affects Stuff Here; LIGO; This Detection: Neutron Stars; What the Gravitational Wave Looks Like; The Sound of Merging Neutron Stars; Neutron Star Mergers: More than GWs; The Radioactive Cloud; The Kilonova; and finally Summary, Multimessenger Astronomy.

Newton shows the light: a commentary on Newton (1672) 'A letter … containing his new theory about light and colours…'.

PubMed

Fara, Patricia

2015-04-13

Isaac Newton's reputation was initially established by his 1672 paper on the refraction of light through a prism; this is now seen as a ground-breaking account and the foundation of modern optics. In it, he claimed to refute Cartesian ideas of light modification by definitively demonstrating that the refrangibility of a ray is linked to its colour, hence arguing that colour is an intrinsic property of light and does not arise from passing through a medium. Newton's later significance as a world-famous scientific genius and the apparent confirmation of his experimental results have tended to obscure the realities of his reception at the time. This paper explores the rhetorical strategies Newton deployed to convince his audience that his conclusions were certain and unchallengeable. This commentary was written to celebrate the 350th anniversary of the journal Philosophical Transactions of the Royal Society.

Hyperunified field theory and gravitational gauge-geometry duality

NASA Astrophysics Data System (ADS)

Wu, Yue-Liang

2018-01-01

A hyperunified field theory is built in detail based on the postulates of gauge invariance and coordinate independence along with the conformal scaling symmetry. All elementary particles are merged into a single hyper-spinor field and all basic forces are unified into a fundamental interaction governed by the hyper-spin gauge symmetry SP(1, D_h-1). The dimension D_h of hyper-spacetime is conjectured to have a physical origin in correlation with the hyper-spin charge of elementary particles. The hyper-gravifield fiber bundle structure of biframe hyper-spacetime appears naturally with the globally flat Minkowski hyper-spacetime as a base spacetime and the locally flat hyper-gravifield spacetime as a fiber that is viewed as a dynamically emerged hyper-spacetime characterized by a non-commutative geometry. The gravitational origin of gauge symmetry is revealed with the hyper-gravifield that plays an essential role as a Goldstone-like field. The gauge-gravity and gravity-geometry correspondences bring about the gravitational gauge-geometry duality. The basic properties of hyperunified field theory and the issue on the fundamental scale are analyzed within the framework of quantum field theory, which allows us to describe the laws of nature in deriving the gauge gravitational equation with the conserved current and the geometric gravitational equations of Einstein-like type and beyond.

Convergence of Newton's method for a single real equation

NASA Technical Reports Server (NTRS)

Campbell, C. W.

1985-01-01

Newton's method for finding the zeroes of a single real function is investigated in some detail. Convergence is generally checked using the Contraction Mapping Theorem which yields sufficient but not necessary conditions for convergence of the general single point iteration method. The resulting convergence intervals are frequently considerably smaller than actual convergence zones. For a specific single point iteration method, such as Newton's method, better estimates of regions of convergence should be possible. A technique is described which, under certain conditions (frequently satisfied by well behaved functions) gives much larger zones where convergence is guaranteed.

Gauss's law test of gravity at short range

NASA Technical Reports Server (NTRS)

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

1993-01-01

A null test of the gravitational inverse-square law can be performed by testing Gauss's law for the field. We have constructed a three-axis superconducting gravity gradiometer and carried out such a test. A lead pendulum weighing 1500 kg was used to produce a time-varying field. This experiment places a new (2-sigma) limit of alpha = (0.9 + or - 4.6) x 10 exp -4 at lambda of 1.5 m, where alpha and lambda are parameters for the generalized potential phi = -(GM/r)(l + alpha e exp -r/lambda).

The fourth law of black-hole thermodynamics

NASA Astrophysics Data System (ADS)

Lousto, C. O.

1993-12-01

We show that black holes fulfill the scaling laws arising in critical transitions. In particular, we find that in the transition from negative to positive values the heat capacities CJQ, CΩQ and CJΦ give rise to critical exponents satisfying the scaling laws. The three transitions have the same critical exponents as predicted by the universality hypothesis. We also briefly discuss the implications of this result with regards to the connections among gravitation, quantum mechanics and statistical physics. Permanent address: Instituto de Astronomía y Física del Espacio, Casilla de Correo 67-Sucursal 28, 1428 Buenos Aires, Argentina.

Space and motion in nature and Scripture: Galileo, Descartes, Newton.

PubMed

Janiak, Andrew

2015-06-01

In the Scholium to the Definitions in Principia mathematica, Newton departs from his main task of discussing space, time and motion by suddenly mentioning the proper method for interpreting Scripture. This is surprising, and it has long been ignored by scholars. In this paper, I argue that the Scripture passage in the Scholium is actually far from incidental: it reflects Newton's substantive concern, one evident in correspondence and manuscripts from the 1680s, that any general understanding of space, time and motion must enable readers to recognize the veracity of Biblical claims about natural phenomena, including the motion of the earth. This substantive concern sheds new light on an aspect of Newton's project in the Scholium. It also underscores Newton's originality in dealing with the famous problem of reconciling theological and philosophical conceptions of nature in the seventeenth century. Copyright © 2015 Elsevier Ltd. All rights reserved.

Gravitational waves — A review on the theoretical foundations of gravitational radiation

NASA Astrophysics Data System (ADS)

Dirkes, Alain

2018-05-01

In this paper, we review the theoretical foundations of gravitational waves in the framework of Albert Einstein’s theory of general relativity. Following Einstein’s early efforts, we first derive the linearized Einstein field equations and work out the corresponding gravitational wave equation. Moreover, we present the gravitational potentials in the far away wave zone field point approximation obtained from the relaxed Einstein field equations. We close this review by taking a closer look on the radiative losses of gravitating n-body systems and present some aspects of the current interferometric gravitational waves detectors. Each section has a separate appendix contribution where further computational details are displayed. To conclude, we summarize the main results and present a brief outlook in terms of current ongoing efforts to build a spaced-based gravitational wave observatory.

Planetesimal formation in self-gravitating discs

NASA Astrophysics Data System (ADS)

Gibbons, P. G.; Rice, W. K. M.; Mamatsashvili, G. R.

2012-10-01

We study particle dynamics in local two-dimensional simulations of self-gravitating accretion discs with a simple cooling law. It is well known that the structure which arises in the gaseous component of the disc due to a gravitational instability can have a significant effect on the evolution of dust particles. Previous results using global simulations indicate that spiral density waves are highly efficient at collecting dust particles, creating significant local overdensities which may be able to undergo gravitational collapse. We expand on these findings using a range of cooling times to mimic the conditions at a large range of radii within the disc. Here we use the PENCIL code to solve the 2D local shearing sheet equations for gas on a fixed grid together with the equations of motion for solids coupled to the gas solely through aerodynamic drag force. We find that spiral density waves can create significant enhancements in the surface density of solids, equivalent to 1-10 cm sized particles in a disc following the profiles of Clarke around an ˜1 M⊙ star, causing it to reach concentrations several orders of magnitude larger than the particles mean surface density. We also study the velocity dispersion of the particles, finding that the spiral structure can result in the particle velocities becoming highly ordered, having a narrow velocity dispersion. This implies low relative velocities between particles, which in turn suggest that collisions are typically low energy, lessening the likelihood of grain destruction. Both these findings suggest that the density waves that arise due to gravitational instabilities in the early stages of star formation provide excellent sites for the formation of large, planetesimal-sized objects.

Newton's method: A link between continuous and discrete solutions of nonlinear problems

NASA Technical Reports Server (NTRS)

Thurston, G. A.

1980-01-01

Newton's method for nonlinear mechanics problems replaces the governing nonlinear equations by an iterative sequence of linear equations. When the linear equations are linear differential equations, the equations are usually solved by numerical methods. The iterative sequence in Newton's method can exhibit poor convergence properties when the nonlinear problem has multiple solutions for a fixed set of parameters, unless the iterative sequences are aimed at solving for each solution separately. The theory of the linear differential operators is often a better guide for solution strategies in applying Newton's method than the theory of linear algebra associated with the numerical analogs of the differential operators. In fact, the theory for the differential operators can suggest the choice of numerical linear operators. In this paper the method of variation of parameters from the theory of linear ordinary differential equations is examined in detail in the context of Newton's method to demonstrate how it might be used as a guide for numerical solutions.

The importance of being equivalent: Newton's two models of one-body motion

NASA Astrophysics Data System (ADS)

Pourciau, Bruce

2004-05-01

As an undergraduate at Cambridge, Newton entered into his "Waste Book" an assumption that we have named the Equivalence Assumption (The Younger): "If a body move progressively in some crooked line [about a center of motion] ..., [then this] crooked line may bee conceived to consist of an infinite number of streight lines. Or else in any point of the croked line the motion may bee conceived to be on in the tangent". In this assumption, Newton somewhat imprecisely describes two mathematical models, a "polygonal limit model" and a "tangent deflected model", for "one-body motion", that is, for the motion of a "body in orbit about a fixed center", and then claims that these two models are equivalent. In the first part of this paper, we study the Principia to determine how the elder Newton would more carefully describe the polygonal limit and tangent deflected models. From these more careful descriptions, we then create Equivalence Assumption (The Elder), a precise interpretation of Equivalence Assumption (The Younger) as it might have been restated by Newton, after say 1687. We then review certain portions of the Waste Book and the Principia to make the case that, although Newton never restates nor even alludes to the Equivalence Assumption after his youthful Waste Book entry, still the polygonal limit and tangent deflected models, as well as an unspoken belief in their equivalence, infuse Newton's work on orbital motion. In particular, we show that the persuasiveness of the argument for the Area Property in Proposition 1 of the Principia depends crucially on the validity of Equivalence Assumption (The Elder). After this case is made, we present the mathematical analysis required to establish the validity of the Equivalence Assumption (The Elder). Finally, to illustrate the fundamental nature of the resulting theorem, the Equivalence Theorem as we call it, we present three significant applications: we use the Equivalence Theorem first to clarify and resolve questions