Derivation of the Gravitational Red Shift from the Theorem of Orbits
|
|
- Alexis Waters
- 6 years ago
- Views:
Transcription
1 1 Deivation of the Gavitational Red Shift fom the Theoem of Obits by Myon W. Evans, Alpha Institute fo Advanced Study, Civil List Scientist. and Abstact The expeimentally obsevable gavitational ed shift is deived by otating the line element deived fom the Theoem of Obits. The latte is a simple special case of the Fobenius Theoem fo a spheically symmetic space-time. All known obits ae descibed by the geomety of the Theoem of Obits, and the gavitational ed shift is shown to be the pecession o phase shift caused by otating the line element of the Theoem of Obits. Keywods: ECE Theoy, gavitational ed shift, Theoem of Obits, line element otation. 1.1 Intoduction Recently in the ECE seies of papes [1 10] it has been shown that all known obits can be descibed diectly by the spheical symmety of space-time with tosion and cuvatue without having to use any field equation a pioi. The Theoem of Obits pape 111 has been deived fom the well known [11] Fobenius Theoem applied to a spheically symmetic space-time. Fom the Theoem of Obits the line element is deived, giving the obital equation. Theefoe the field of foce which becomes the Newtonian field of foce in the appopiate limit is deived diectly fom spheical space-time symmety. This pocedue is summaized in Section 1., and in Section 1.3 the well known gavitational ed shift is given a new meaning by deiving it fom otation of the line element of Section 1.. It is found that the gavitational ed
2 374 1 Deivation of the Gavitational Red Shift fom the Theoem of Obits shift is a pecession o phase shift - essentially a popety puely of spheical space-time and not of any field equation. In the standad model the gavitational ed shift is thought to be a wavelength change and incoectly deived fom a space-time that has no tosion. 1. Line Element and Obital Equation fom Theoem of Obits The Theoem of Obits is a simple example of the Fobenius Theoem [11] which defines the most geneal line element. The Theoem of Obits is: n = m = d = + µ 1.1 whee n and m ae functions of, the adial coodinate in spheical pola coodinates. The constant of integation is in geneal non-zeo, and goes to zeo in a Minkowski space-time. If the Fobenius Theoem is applied [11] to a spheically symmetic space-time the line element is: ds = nc dt + md + dω. 1. Fom the Theoem of Obits it is found that: n =1+ µ, 1.3 m = 1+ µ 1, 1.4 so that the line element becomes: ds = 1+ µ c dt + 1+ µ 1 d + dω 1.5 in spheical pola co-odinates. The obital equation is obtained by consideing the special case of obits in a plane, so the line element 1.5 educes to: ds = 1+ µ c dt + 1+ µ 1 d + dφ. 1.6
3 1. Line Element and Obital Equation fom Theoem of Obits 375 Define [1 11] the constant of motion: ds ɛ = = c dλ dλ = 1+ µ dt c dλ + 1+ µ 1 d dλ dφ dλ whee is the infinitesimal element of pope time. Now make the choice: to find: c = 1+ µ dt c + 1+ µ λ = τ d dφ To convet to S.I. units multiply thoughout by 1 m,wheemistobedetemined: 1 m dφ 1 1+ m µ dt c m µ 1 d = 1 mc Multiply though by 1+ µ : to find that: 1 m dφ 1+ µ 1 m 1+ µ c = 1 mc 1+ µ dt + 1 m d This is the obital equation: The total enegy in S.I. units is: 1 d m + V = E. 1.1 E = 1 mc 1+ µ dt. 1.13
4 376 1 Deivation of the Gavitational Red Shift fom the Theoem of Obits The potential enegy in S.I. units is: V = 1 m 1+ µ c + L 1.14 whee: L = dφ 1.15 is a constant of motion having the units of angula momentum pe unit mass. The facto 1 is intoduced [11] to wite the equation in standad dynamical fom. The potential enegy is theefoe: V = 1 mc + 1 µ mc + 1 ml + 1 ml µ and is made up of fou tems which ae identified below. Fo all obits excluding binay pulsas and the Cassini/Pionee anomaly it is found by expeimental obsevation that: Theefoe the potential enegy becomes: V = 1 mc m mg µ = mg c ml L mmg c Theefoe it becomes possible to identify the fou tems as follows. 1 A constant tem popotional to est enegy, 1 mc. The Newtonian potential of attaction, mm G/. 3 The centipetal epulsion, ml /. 4 The elativistic coection to the Newtonian attaction, L mmg/c 3. Theefoe the facto m is the mass of an object attacted by an object of mass M. The Theoem of Obits 1.1 is the geometical contol ove the way m and M inteact. The intoduction of m, M and G intoduces physics into pue geomety. The Newtonian limit is defined by: 1.19
5 1. Line Element and Obital Equation fom Theoem of Obits 377 when the familia Newtonian tems 1. and 1.3 dominate. The Newtonain foce of attaction is: F = V = mmg 1.0 which is the invese squae law of Newton. Fom Eqs 1.18 and 1.0 the total foce between m and M is: F = mmg + ml 3 3L mmg c This foce law descibes the vast majoity of known obits with geat accuacy. It descibes peihelion advance, deflection of light by gavity, fame dagging, Shapio time delay and all the phenomena incoectly attibuted in the standad model to the now obsolete [1 10] Einstein field equation. As agued, these phenomena ae due puely to the spheical symmety of space-time. The masses m and M ae intoduced following expeimental obsevation. The Newtonian foce is Eq Newton did not ealize the existence of the centipetal foce, and of couse did not ealize the existence of the elativistic coection. In binay pulsas pape 108 the obits decease by a few millimetes pe evolution. This effect is descibed by the addition of a vey small petubation as follows: mg µ = c + a which geneates an additional attaction potential: 1. and an additional foce of attaction: V = 1 c ma + L c 4 c F = ma 3 + L c which causes the two objects of a binay pulsa to spial in towads each othe fom a elativistic obit whose peihelion advance is a few degees pe evolution. This is a vey small effect, but epoducible and epeatable. The same type of phenomenon is found in the sola system in the well known Pionee/Cassini anomalies. Both spacecaft see a tiny additional foce of
6 378 1 Deivation of the Gavitational Red Shift fom the Theoem of Obits attaction not pesent in Eq The complete foce law fo binay pulsas and the Pionee Cassini obits is theefoe: F = mmg + m 3 L ac 3LmMG c 4 the Newtonian foce in this case being only one of five tems. aml c 5, The Gavitational Red Shift Conside the line element 1.5 in cylindical pola co-odinates: ds = 1+ µ c dt 1+ µ 1 d dφ dz. 1.6 Now otate it see pape 110 at an angula velocity ω as follows: The otated line element is theefoe: ds = φ = φ + ωt µ c dt 1+ µ 1 d dφ dz 1.8 whee: and It is found that: dφ = dφ + ωdt 1.9 dφ = dφ +ωdφdt + ω dt ds µ v = 1+ c c dt Ωdφdt 1+ µ d dφ dz whee the obital linea velocity of otation is defined by v = ω. 1.3
7 1.3 The Gavitational Red Shift 379 Identify the elativistic angula velocity compae pape 110 on as: Ω=ω 1+ 1 µ v c 1.33 and the infinitesimal of pope time by: = 1+ 1 µ v c dt The change of phase, o pecession, upon otating by π adians is: α =Ω ωdt =π 1+ µ 1 v c The limit 1.36 defines the Thomas pecession pape 110: αthomas = π 1 v c and the limit: v defines the gavitational ed shift: αgav = π 1+ µ Fo almost all obits, as agued in Section 1., it is found by expeimental obsevation that: µ = mg c 1.40
8 380 1 Deivation of the Gavitational Red Shift fom the Theoem of Obits so the gavitational ed shift is: αgav = π 1 mg 1 1 c πmg c as obseved expeimentally as is well known. The Thomas pecession is well obseved expeimentally in atomic and molecula specta in spin obit coupling. It is concluded that both the gavitational ed shift and the Thomas pecession ae due puely to the spheical symmety of space-time. The standad model s Einstein field equation is known to be geometically incoect because of its neglect of tosion, so the standad explanation of the gavitational ed shift cannot be coect. Similaly, the standad model s cosmological ed shift which is diffeent fom the gavitational ed shift is an atifact based on the Robeston Walke metic, which in pape 93 on was shown to violate basic geomety the Hodge dual of the Bianchi identity. Acknowledgments The Bitish Govenment is thanked fo the awad of a Civil List Pension and amoial ensigns fo pe-eminent contibutions to Bitain and the Commonwealth in science and the staffs of AIAS and many othe colleagues woldwide thanked fo inteesting discussions.
9 Refeences [1] M. W. Evans, Geneally Covaiant Unified Field Theoy Abamis 005 onwads, volumes one to fou, volumes five and six in pep. papes 71 onwads on [] L. Felke, The Evans Equations of Unified Field Theoy Abamis, 007. [3] K. Pendegast, Cystal Sphees pepint on [4] M. W. Evans, Omnia Opea section of fom 199 onwads. [5] M. W. Evans ed., Adv. Chem. Phys, vol ; M. W. Evans and S. Kielich eds., Adv. Chem. Phys., vol , 1993, [6] M. W. Evans and L. B. Cowell, Classical and Quantum Electodynamics and the B1.3 Field Wold Scientific, 001. [7] M. W. Evans and J.-P. Vigie, The Enigmatic Photon Kluwe, 1994 to 00, hadback and softback, in five volumes. [8] M. W. Evans, fifteen papes in Found. Phys. Lett., 003 to 005. [9] M. W. Evans. Acta Phys. Polon., 38B, ; Physica B, 403, [10] M. W. Evans and H. Eckadt, Physica B, 400, [11] S. P. Caoll, Space-time and Geomety: an Intoduction to Geneal Relativity Addison Wesley, New Yok, 004, and downloadable lectue notes, chapte 7.
REFUTATION OF GENERAL RELATIVITY: INCONSISTENCIES IN THE EINSTEINIAN THEORY OF PERIHELION PRECESSION
Jounal of Foundations of Physics and Chemisty () REFUTATION OF GENERAL RELATIVITY: INCONSISTENCIES IN THE EINSTEINIAN THEORY OF PERIHELION PRECESSION M. W. Evans and H. Eckadt Alpha Institute fo Advanced
More informationDevelopment of Spin Connection Resonance in the Coulomb Law
22 Development of Spin Connection Resonance in the Coulomb Law by Myon W. Evans, Alpha Institute fo Advanced Study, Civil List Scientist. (emyone@aol.com and www.aias.us) and H. Eckadt, Alpha Institute
More informationThe Schwartzchild Geometry
UNIVERSITY OF ROCHESTER The Schwatzchild Geomety Byon Osteweil Decembe 21, 2018 1 INTRODUCTION In ou study of geneal elativity, we ae inteested in the geomety of cuved spacetime in cetain special cases
More informationA New Approach to General Relativity
Apeion, Vol. 14, No. 3, July 7 7 A New Appoach to Geneal Relativity Ali Rıza Şahin Gaziosmanpaşa, Istanbul Tukey E-mail: aizasahin@gmail.com Hee we pesent a new point of view fo geneal elativity and/o
More informationClassical Mechanics Homework set 7, due Nov 8th: Solutions
Classical Mechanics Homewok set 7, due Nov 8th: Solutions 1. Do deivation 8.. It has been asked what effect does a total deivative as a function of q i, t have on the Hamiltonian. Thus, lets us begin with
More informationA NEW WAVE EQUATION FOR LAGRANGIAN DYNAMICS: THE PLANAR ORBIT FOR ANY FORCE LAW
Jounal of Foundations of Physics and Chemisty () A NEW WAVE EQUATION FOR AGRANGIAN DYNAMICS: THE PANAR ORBIT FOR ANY FORCE AW M. W. Evans, H. Eckat and B. Foltz Alpha Institute fo Advanced Studies www.aias.us,
More informationGENERAL RELATIVITY: THE GEODESICS OF THE SCHWARZSCHILD METRIC
GENERAL RELATIVITY: THE GEODESICS OF THE SCHWARZSCHILD METRIC GILBERT WEINSTEIN 1. Intoduction Recall that the exteio Schwazschild metic g defined on the 4-manifold M = R R 3 \B 2m ) = {t,, θ, φ): > 2m}
More informationAppendix B The Relativistic Transformation of Forces
Appendix B The Relativistic Tansfomation of oces B. The ou-foce We intoduced the idea of foces in Chapte 3 whee we saw that the change in the fou-momentum pe unit time is given by the expession d d w x
More informationd 2 x 0a d d =0. Relative to an arbitrary (accelerating frame) specified by x a = x a (x 0b ), the latter becomes: d 2 x a d 2 + a dx b dx c
Chapte 6 Geneal Relativity 6.1 Towads the Einstein equations Thee ae seveal ways of motivating the Einstein equations. The most natual is pehaps though consideations involving the Equivalence Pinciple.
More informationChapter 13 Gravitation
Chapte 13 Gavitation In this chapte we will exploe the following topics: -Newton s law of gavitation, which descibes the attactive foce between two point masses and its application to extended objects
More informationProblems with Mannheim s conformal gravity program
Poblems with Mannheim s confomal gavity pogam June 4, 18 Youngsub Yoon axiv:135.163v6 [g-qc] 7 Jul 13 Depatment of Physics and Astonomy Seoul National Univesity, Seoul 151-747, Koea Abstact We show that
More informationDoublet structure of Alkali spectra:
Doublet stuctue of : Caeful examination of the specta of alkali metals shows that each membe of some of the seies ae closed doublets. Fo example, sodium yellow line, coesponding to 3p 3s tansition, is
More informationPhysics 235 Chapter 5. Chapter 5 Gravitation
Chapte 5 Gavitation In this Chapte we will eview the popeties of the gavitational foce. The gavitational foce has been discussed in geat detail in you intoductoy physics couses, and we will pimaily focus
More informationFrom Gravitational Collapse to Black Holes
Fom Gavitational Collapse to Black Holes T. Nguyen PHY 391 Independent Study Tem Pape Pof. S.G. Rajeev Univesity of Rocheste Decembe 0, 018 1 Intoduction The pupose of this independent study is to familiaize
More informationDerivation of the Thomas Precession in Terms of the Infinitesimal Torsion Generator
17 Derivation of the Thomas Precession in Terms of the Infinitesimal Torsion Generator by Myron W. Evans, Alpha Institute for Advanced Study, Civil List Scientist. (emyrone@aol.com and www.aias.us) Abstract
More informationOSCILLATIONS AND GRAVITATION
1. SIMPLE HARMONIC MOTION Simple hamonic motion is any motion that is equivalent to a single component of unifom cicula motion. In this situation the velocity is always geatest in the middle of the motion,
More informationPhysics 161 Fall 2011 Extra Credit 2 Investigating Black Holes - Solutions The Following is Worth 50 Points!!!
Physics 161 Fall 011 Exta Cedit Investigating Black Holes - olutions The Following is Woth 50 Points!!! This exta cedit assignment will investigate vaious popeties of black holes that we didn t have time
More informationIntroduction to General Relativity 2
Intoduction to Geneal Relativity 2 Geneal Relativity Diffeential geomety Paallel tanspot How to compute metic? Deviation of geodesics Einstein equations Consequences Tests of Geneal Relativity Sola system
More informationMath Notes on Kepler s first law 1. r(t) kp(t)
Math 7 - Notes on Keple s fist law Planetay motion and Keple s Laws We conside the motion of a single planet about the sun; fo simplicity, we assign coodinates in R 3 so that the position of the sun is
More informationPhysics 2B Chapter 22 Notes - Magnetic Field Spring 2018
Physics B Chapte Notes - Magnetic Field Sping 018 Magnetic Field fom a Long Staight Cuent-Caying Wie In Chapte 11 we looked at Isaac Newton s Law of Gavitation, which established that a gavitational field
More informationSpherical Solutions due to the Exterior Geometry of a Charged Weyl Black Hole
Spheical Solutions due to the Exteio Geomety of a Chaged Weyl Black Hole Fain Payandeh 1, Mohsen Fathi Novembe 7, 018 axiv:10.415v [g-qc] 10 Oct 01 1 Depatment of Physics, Payame Noo Univesity, PO BOX
More informationAST 121S: The origin and evolution of the Universe. Introduction to Mathematical Handout 1
Please ead this fist... AST S: The oigin and evolution of the Univese Intoduction to Mathematical Handout This is an unusually long hand-out and one which uses in places mathematics that you may not be
More informationExtra notes for circular motion: Circular motion : v keeps changing, maybe both speed and
Exta notes fo cicula motion: Cicula motion : v keeps changing, maybe both speed and diection ae changing. At least v diection is changing. Hence a 0. Acceleation NEEDED to stay on cicula obit: a cp v /,
More informationPendulum in Orbit. Kirk T. McDonald Joseph Henry Laboratories, Princeton University, Princeton, NJ (December 1, 2017)
1 Poblem Pendulum in Obit Kik T. McDonald Joseph Heny Laboatoies, Pinceton Univesity, Pinceton, NJ 08544 (Decembe 1, 2017) Discuss the fequency of small oscillations of a simple pendulum in obit, say,
More informationEarth and Moon orbital anomalies
Eath and Moon obital anomalies Si non è veo, è ben tovato Ll. Bel axiv:1402.0788v2 [g-qc] 18 Feb 2014 Febuay 19, 2014 Abstact A time-dependent gavitational constant o mass would coectly descibe the suspected
More informationMASSACHUSETTS INSTITUTE OF TECHNOLOGY Physics Department. Problem Set 10 Solutions. r s
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Physics Depatment Physics 8.033 Decembe 5, 003 Poblem Set 10 Solutions Poblem 1 M s y x test paticle The figue above depicts the geomety of the poblem. The position
More informationProblems with Mannheim s conformal gravity program
Poblems with Mannheim s confomal gavity pogam Abstact We show that Mannheim s confomal gavity pogam, whose potential has a tem popotional to 1/ and anothe tem popotional to, does not educe to Newtonian
More informationThe Concept of the Effective Mass Tensor in GR. Clocks and Rods
The Concept of the Effective Mass Tenso in GR Clocks and Rods Miosław J. Kubiak Zespół Szkół Technicznych, Gudziądz, Poland Abstact: In the pape [] we pesented the concept of the effective ass tenso (EMT)
More information10. Force is inversely proportional to distance between the centers squared. R 4 = F 16 E 11.
NSWRS - P Physics Multiple hoice Pactice Gavitation Solution nswe 1. m mv Obital speed is found fom setting which gives v whee M is the object being obited. Notice that satellite mass does not affect obital
More informationThe Precession of Mercury s Perihelion
The Pecession of Mecuy s Peihelion Owen Biesel Januay 25, 2008 Contents 1 Intoduction 2 2 The Classical olution 2 3 Classical Calculation of the Peiod 4 4 The Relativistic olution 5 5 Remaks 9 1 1 Intoduction
More informationCircular Motion & Torque Test Review. The period is the amount of time it takes for an object to travel around a circular path once.
Honos Physics Fall, 2016 Cicula Motion & Toque Test Review Name: M. Leonad Instuctions: Complete the following woksheet. SHOW ALL OF YOUR WORK ON A SEPARATE SHEET OF PAPER. 1. Detemine whethe each statement
More informationHomework 7 Solutions
Homewok 7 olutions Phys 4 Octobe 3, 208. Let s talk about a space monkey. As the space monkey is oiginally obiting in a cicula obit and is massive, its tajectoy satisfies m mon 2 G m mon + L 2 2m mon 2
More informationGeometry of the homogeneous and isotropic spaces
Geomety of the homogeneous and isotopic spaces H. Sonoda Septembe 2000; last evised Octobe 2009 Abstact We summaize the aspects of the geomety of the homogeneous and isotopic spaces which ae most elevant
More informationBut for simplicity, we ll define significant as the time it takes a star to lose all memory of its original trajectory, i.e.,
Stella elaxation Time [Chandasekha 1960, Pinciples of Stella Dynamics, Chap II] [Ostike & Davidson 1968, Ap.J., 151, 679] Do stas eve collide? Ae inteactions between stas (as opposed to the geneal system
More informationRotational Motion. Lecture 6. Chapter 4. Physics I. Course website:
Lectue 6 Chapte 4 Physics I Rotational Motion Couse website: http://faculty.uml.edu/andiy_danylov/teaching/physicsi Today we ae going to discuss: Chapte 4: Unifom Cicula Motion: Section 4.4 Nonunifom Cicula
More informationNewton s Laws, Kepler s Laws, and Planetary Orbits
Newton s Laws, Keple s Laws, and Planetay Obits PROBLEM SET 4 DUE TUESDAY AT START OF LECTURE 28 Septembe 2017 ASTRONOMY 111 FALL 2017 1 Newton s & Keple s laws and planetay obits Unifom cicula motion
More informationThe Schwarzschild Solution
The Schwazschild Solution Johannes Schmude 1 Depatment of Physics Swansea Univesity, Swansea, SA2 8PP, United Kingdom Decembe 6, 2007 1 pyjs@swansea.ac.uk Intoduction We use the following conventions:
More informationF 12. = G m m 1 2 F 21 = F 12. = G m 1m 2. Review. Physics 201, Lecture 22. Newton s Law Of Universal Gravitation
Physics 201, Lectue 22 Review Today s Topics n Univesal Gavitation (Chapte 13.1-13.3) n Newton s Law of Univesal Gavitation n Popeties of Gavitational Foce n Planet Obits; Keple s Laws by Newton s Law
More information= 1. For a hyperbolic orbit with an attractive inverse square force, the polar equation with origin at the center of attraction is
15. Kepleian Obits Michael Fowle Peliminay: Pola Equations fo Conic Section Cuves As we shall find, Newton s equations fo paticle motion in an invese-squae cental foce give obits that ae conic section
More informationQuantum theory of angular momentum
Quantum theoy of angula momentum Igo Mazets igo.mazets+e141@tuwien.ac.at (Atominstitut TU Wien, Stadionallee 2, 1020 Wien Time: Fiday, 13:00 14:30 Place: Feihaus, Sem.R. DA gün 06B (exception date 18 Nov.:
More informationA Newtonian equivalent for the cosmological constant
A Newtonian equivalent fo the cosmological constant Mugu B. Răuţ We deduce fom Newtonian mechanics the cosmological constant, following some olde ideas. An equivalent to this constant in classical mechanics
More informationPhysics 181. Assignment 4
Physics 181 Assignment 4 Solutions 1. A sphee has within it a gavitational field given by g = g, whee g is constant and is the position vecto of the field point elative to the cente of the sphee. This
More information= 4 3 π( m) 3 (5480 kg m 3 ) = kg.
CHAPTER 11 THE GRAVITATIONAL FIELD Newton s Law of Gavitation m 1 m A foce of attaction occus between two masses given by Newton s Law of Gavitation Inetial mass and gavitational mass Gavitational potential
More informationPhysics 161: Black Holes: Lecture 5: 22 Jan 2013
Physics 161: Black Holes: Lectue 5: 22 Jan 2013 Pofesso: Kim Giest 5 Equivalence Pinciple, Gavitational Redshift and Geodesics of the Schwazschild Metic 5.1 Gavitational Redshift fom the Schwazschild metic
More informationDEVIL PHYSICS THE BADDEST CLASS ON CAMPUS IB PHYSICS
DEVIL PHYSICS THE BADDEST CLASS ON CAMPUS IB PHYSICS TSOKOS LESSON 6- THE LAW OF GRAVITATION Essential Idea: The Newtonian idea of gavitational foce acting between two spheical bodies and the laws of mechanics
More informationKEPLER S LAWS AND PLANETARY ORBITS
KEPE S AWS AND PANETAY OBITS 1. Selected popeties of pola coodinates and ellipses Pola coodinates: I take a some what extended view of pola coodinates in that I allow fo a z diection (cylindical coodinates
More informationPressure Calculation of a Constant Density Star in the Dynamic Theory of Gravity
Pessue Calculation of a Constant Density Sta in the Dynamic Theoy of Gavity Ioannis Iaklis Haanas Depatment of Physics and Astonomy Yok Univesity A Petie Science Building Yok Univesity Toonto Ontaio CANADA
More informationPhysics 221 Lecture 41 Nonlinear Absorption and Refraction
Physics 221 Lectue 41 Nonlinea Absoption and Refaction Refeences Meye-Aendt, pp. 97-98. Boyd, Nonlinea Optics, 1.4 Yaiv, Optical Waves in Cystals, p. 22 (Table of cystal symmeties) 1. Intoductoy Remaks.
More informationA thermodynamic degree of freedom solution to the galaxy cluster problem of MOND. Abstract
A themodynamic degee of feedom solution to the galaxy cluste poblem of MOND E.P.J. de Haas (Paul) Nijmegen, The Nethelands (Dated: Octobe 23, 2015) Abstact In this pape I discus the degee of feedom paamete
More informationIs there a magnification paradox in gravitational lensing?
Is thee a magnification paadox in gavitational ing? Olaf Wucknitz wucknitz@asto.uni-bonn.de Astophysics semina/colloquium, Potsdam, 6 Novembe 7 Is thee a magnification paadox in gavitational ing? gavitational
More informationarxiv: v2 [gr-qc] 18 Aug 2014
Self-Consistent, Self-Coupled Scala Gavity J. Fanklin Depatment of Physics, Reed College, Potland, Oegon 970, USA Abstact A scala theoy of gavity extending Newtonian gavity to include field enegy as its
More informationLecture Series: The Spin of the Matter, Physics 4250, Fall Topic 8: Geometrodynamics of spinning particles First Draft.
Lectue Seies: The Spin of the Matte, Physics 450, Fall 00 Topic 8: Geometodynamics of spinning paticles Fist Daft D. Bill Pezzaglia CSUEB Physics Updated Nov 8, 00 Outline A. Maxwellian Gavity B. Gavitomagnetic
More informationarxiv: v1 [physics.pop-ph] 3 Jun 2013
A note on the electostatic enegy of two point chages axiv:1306.0401v1 [physics.pop-ph] 3 Jun 013 A C Tot Instituto de Física Univesidade Fedeal do io de Janeio Caixa Postal 68.58; CEP 1941-97 io de Janeio,
More informationMechanics Physics 151
Mechanics Physics 151 Lectue 5 Cental Foce Poblem (Chapte 3) What We Did Last Time Intoduced Hamilton s Pinciple Action integal is stationay fo the actual path Deived Lagange s Equations Used calculus
More informationChapter 5 Force and Motion
Chapte 5 Foce and Motion In Chaptes 2 and 4 we have studied kinematics, i.e., we descibed the motion of objects using paametes such as the position vecto, velocity, and acceleation without any insights
More informationDEVIL PHYSICS THE BADDEST CLASS ON CAMPUS IB PHYSICS
DEVIL PHYSICS THE BADDEST CLASS ON CAMPUS IB PHYSICS TSOKOS LESSON 10-1 DESCRIBING FIELDS Essential Idea: Electic chages and masses each influence the space aound them and that influence can be epesented
More information2 Lecture 2: The Bohr atom (1913) and the Schrödinger equation (1925)
1 Lectue 1: The beginnings of quantum physics 1. The Sten-Gelach expeiment. Atomic clocks 3. Planck 1900, blackbody adiation, and E ω 4. Photoelectic effect 5. Electon diffaction though cystals, de Boglie
More informationThe R-W Metric Has No Constant Curvature When Scalar Factor R(t) Changes with Time
Intenational Jounal of Astonomy and Astophysics,,, 77-8 doi:.436/ijaa..43 Published Online Decembe (http://www.scip.og/jounal/ijaa) The -W Metic Has No Constant Cuvatue When Scala Facto (t) Changes with
More informationChapter 13: Gravitation
v m m F G Chapte 13: Gavitation The foce that makes an apple fall is the same foce that holds moon in obit. Newton s law of gavitation: Evey paticle attacts any othe paticle with a gavitation foce given
More informationLecture 8 - Gauss s Law
Lectue 8 - Gauss s Law A Puzzle... Example Calculate the potential enegy, pe ion, fo an infinite 1D ionic cystal with sepaation a; that is, a ow of equally spaced chages of magnitude e and altenating sign.
More informationarxiv: v1 [physics.gen-ph] 29 Feb 2016
epl daft Pedicting Mecuy s Pecession using Simple Relativistic Newtonian Dynamics axiv:603.0560v [physics.gen-ph] 9 Feb 06 Y. Fiedman and J. M. Steine Jeusalem College of Technology Jeusalem, Isael PACS
More information2. Electrostatics. Dr. Rakhesh Singh Kshetrimayum 8/11/ Electromagnetic Field Theory by R. S. Kshetrimayum
2. Electostatics D. Rakhesh Singh Kshetimayum 1 2.1 Intoduction In this chapte, we will study how to find the electostatic fields fo vaious cases? fo symmetic known chage distibution fo un-symmetic known
More informationOrbital Angular Momentum Eigenfunctions
Obital Angula Moentu Eigenfunctions Michael Fowle 1/11/08 Intoduction In the last lectue we established that the opeatos J Jz have a coon set of eigenkets j J j = j( j+ 1 ) j Jz j = j whee j ae integes
More informationFoundations of Chemical Kinetics. Lecture 9: Generalizing collision theory
Foundations of Chemical Kinetics Lectue 9: Genealizing collision theoy Mac R. Roussel Depatment of Chemisty and Biochemisty Spheical pola coodinates z θ φ y x Angles and solid angles θ a A Ω θ=a/ unit:
More informationPACS: c ; qd
1 FEEDBACK IN GRAVITATIONAL PROBLEM OF OLAR CYCLE AND PERIHELION PRECEION OF MERCURY by Jovan Djuic, etied UNM pofesso Balkanska 8, 11000 Belgade, ebia E-mail: olivedj@eunet.s PAC: 96.90.+c ; 96.60.qd
More informationAY 7A - Fall 2010 Section Worksheet 2 - Solutions Energy and Kepler s Law
AY 7A - Fall 00 Section Woksheet - Solutions Enegy and Keple s Law. Escape Velocity (a) A planet is obiting aound a sta. What is the total obital enegy of the planet? (i.e. Total Enegy = Potential Enegy
More informationTopic 7: Electrodynamics of spinning particles Revised Draft
Lectue Seies: The Spin of the Matte, Physics 4250, Fall 2010 1 Topic 7: Electodynamics of spinning paticles Revised Daft D. Bill Pezzaglia CSUEB Physics Updated Nov 28, 2010 Index: Rough Daft 2 A. Classical
More information3D-Central Force Problems I
5.73 Lectue #1 1-1 Roadmap 1. define adial momentum 3D-Cental Foce Poblems I Read: C-TDL, pages 643-660 fo next lectue. All -Body, 3-D poblems can be educed to * a -D angula pat that is exactly and univesally
More informationChapter 4. Newton s Laws of Motion
Chapte 4 Newton s Laws of Motion 4.1 Foces and Inteactions A foce is a push o a pull. It is that which causes an object to acceleate. The unit of foce in the metic system is the Newton. Foce is a vecto
More informationChapter 5 Force and Motion
Chapte 5 Foce and Motion In chaptes 2 and 4 we have studied kinematics i.e. descibed the motion of objects using paametes such as the position vecto, velocity and acceleation without any insights as to
More informationThis gives rise to the separable equation dr/r = 2 cot θ dθ which may be integrated to yield r(θ) = R sin 2 θ (3)
Physics 506 Winte 2008 Homewok Assignment #10 Solutions Textbook poblems: Ch. 12: 12.10, 12.13, 12.16, 12.19 12.10 A chaged paticle finds itself instantaneously in the equatoial plane of the eath s magnetic
More informationDeflection of light due to rotating mass a comparison among the results of different approaches
Jounal of Physics: Confeence Seies OPEN ACCESS Deflection of light due to otating mass a compaison among the esults of diffeent appoaches Recent citations - Gavitational Theoies nea the Galactic Cente
More informationProjection Gravitation, a Projection Force from 5-dimensional Space-time into 4-dimensional Space-time
Intenational Jounal of Physics, 17, Vol. 5, No. 5, 181-196 Available online at http://pubs.sciepub.com/ijp/5/5/6 Science and ducation Publishing DOI:1.1691/ijp-5-5-6 Pojection Gavitation, a Pojection Foce
More informationarxiv:gr-qc/ v1 29 Jan 1998
Gavitational Analog of the Electomagnetic Poynting Vecto L.M. de Menezes 1 axiv:g-qc/9801095v1 29 Jan 1998 Dept. of Physics and Astonomy, Univesity of Victoia, Victoia, B.C. Canada V8W 3P6 Abstact The
More information= e2. = 2e2. = 3e2. V = Ze2. where Z is the atomic numnber. Thus, we take as the Hamiltonian for a hydrogenic. H = p2 r. (19.4)
Chapte 9 Hydogen Atom I What is H int? That depends on the physical system and the accuacy with which it is descibed. A natual stating point is the fom H int = p + V, (9.) µ which descibes a two-paticle
More informationChapter 9 Dynamic stability analysis III Lateral motion (Lectures 33 and 34)
Pof. E.G. Tulapukaa Stability and contol Chapte 9 Dynamic stability analysis Lateal motion (Lectues 33 and 34) Keywods : Lateal dynamic stability - state vaiable fom of equations, chaacteistic equation
More informationQualifying Examination Electricity and Magnetism Solutions January 12, 2006
1 Qualifying Examination Electicity and Magnetism Solutions Januay 12, 2006 PROBLEM EA. a. Fist, we conside a unit length of cylinde to find the elationship between the total chage pe unit length λ and
More informationThe Spiral Structure of NGC 3198.
The Spial Stuctue of NGC 3198. Buce Rout Novembe 8, 2009 Abstact Obsevations of NGC 3198 show a discepancy between the otational velocity and its appaent geomety which defies the pedicted behaviou of Kepleian
More informationAnalytic Evaluation of two-electron Atomic Integrals involving Extended Hylleraas-CI functions with STO basis
Analytic Evaluation of two-electon Atomic Integals involving Extended Hylleaas-CI functions with STO basis B PADHY (Retd.) Faculty Membe Depatment of Physics, Khalikote (Autonomous) College, Behampu-760001,
More informationm 1 r = r 1 - r 2 m 2 r 2 m1 r1
Topic 4: Two-Body Cental Foce Motion Reading Assignment: Hand & Finch Chap. 4 This will be the last topic coveed on the midtem exam. I will pass out homewok this week but not next week.. Eliminating the
More informationThe Origin of Orbits in Spherically Symmetric Space-Time
18 The Origin of Orbits in Spherically Symmetric Space-Time by Myron W. Evans, Alpha Institute for Advanced Study, Civil List Scientist. (emyrone@aol.com and www.aias.us) and Horst Eckardt, Alpha Institute
More informationA Relativistic Electron in a Coulomb Potential
A Relativistic Electon in a Coulomb Potential Alfed Whitehead Physics 518, Fall 009 The Poblem Solve the Diac Equation fo an electon in a Coulomb potential. Identify the conseved quantum numbes. Specify
More informationBLACK HOLES IN STRING THEORY
Black holes in sting theoy N Sadikaj & A Duka Pape pesented in 1 -st Intenational Scientific Confeence on Pofessional Sciences, Alexande Moisiu Univesity, Dues Novembe 016 BLACK OLES IN STRING TEORY NDRIÇIM
More information2 Governing Equations
2 Govening Equations This chapte develops the govening equations of motion fo a homogeneous isotopic elastic solid, using the linea thee-dimensional theoy of elasticity in cylindical coodinates. At fist,
More information2. Plane Elasticity Problems
S0 Solid Mechanics Fall 009. Plane lasticity Poblems Main Refeence: Theoy of lasticity by S.P. Timoshenko and J.N. Goodie McGaw-Hill New Yok. Chaptes 3..1 The plane-stess poblem A thin sheet of an isotopic
More informationis the instantaneous position vector of any grid point or fluid
Absolute inetial, elative inetial and non-inetial coodinates fo a moving but non-defoming contol volume Tao Xing, Pablo Caica, and Fed Sten bjective Deive and coelate the govening equations of motion in
More information7.2. Coulomb s Law. The Electric Force
Coulomb s aw Recall that chaged objects attact some objects and epel othes at a distance, without making any contact with those objects Electic foce,, o the foce acting between two chaged objects, is somewhat
More informationyou of a spring. The potential energy for a spring is given by the parabola U( x)
Small oscillations The theoy of small oscillations is an extemely impotant topic in mechanics. Conside a system that has a potential enegy diagam as below: U B C A x Thee ae thee points of stable equilibium,
More informationBetween any two masses, there exists a mutual attractive force.
YEAR 12 PHYSICS: GRAVITATION PAST EXAM QUESTIONS Name: QUESTION 1 (1995 EXAM) (a) State Newton s Univesal Law of Gavitation in wods Between any two masses, thee exists a mutual attactive foce. This foce
More informationThe Strain Compatibility Equations in Polar Coordinates RAWB, Last Update 27/12/07
The Stain Compatibility Equations in Pola Coodinates RAWB Last Update 7//7 In D thee is just one compatibility equation. In D polas it is (Equ.) whee denotes the enineein shea (twice the tensoial shea)
More informationLecture 3.7 ELECTRICITY. Electric charge Coulomb s law Electric field
Lectue 3.7 ELECTRICITY Electic chage Coulomb s law Electic field ELECTRICITY Inteaction between electically chages objects Many impotant uses Light Heat Rail tavel Computes Cental nevous system Human body
More informationForce between two parallel current wires and Newton s. third law
Foce between two paallel cuent wies and Newton s thid law Yannan Yang (Shanghai Jinjuan Infomation Science and Technology Co., Ltd.) Abstact: In this pape, the essence of the inteaction between two paallel
More informationLight Time Delay and Apparent Position
Light Time Delay and ppaent Position nalytical Gaphics, Inc. www.agi.com info@agi.com 610.981.8000 800.220.4785 Contents Intoduction... 3 Computing Light Time Delay... 3 Tansmission fom to... 4 Reception
More informationI. CONSTRUCTION OF THE GREEN S FUNCTION
I. CONSTRUCTION OF THE GREEN S FUNCTION The Helmohltz equation in 4 dimensions is 4 + k G 4 x, x = δ 4 x x. In this equation, G is the Geen s function and 4 efes to the dimensionality. In the vey end,
More informationOur Universe: GRAVITATION
Ou Univese: GRAVITATION Fom Ancient times many scientists had shown geat inteest towads the sky. Most of the scientist studied the motion of celestial bodies. One of the most influential geek astonomes
More informationNuclear size corrections to the energy levels of single-electron atoms
Nuclea size coections to the enegy levels of single-electon atoms Babak Nadii Nii a eseach Institute fo Astonomy and Astophysics of Maagha (IAAM IAN P. O. Box: 554-44. Abstact A study is made of nuclea
More informationS7: Classical mechanics problem set 2
J. Magoian MT 9, boowing fom J. J. Binney s 6 couse S7: Classical mechanics poblem set. Show that if the Hamiltonian is indepdent of a genealized co-odinate q, then the conjugate momentum p is a constant
More informationCh 13 Universal Gravitation
Ch 13 Univesal Gavitation Ch 13 Univesal Gavitation Why do celestial objects move the way they do? Keple (1561-1630) Tycho Bahe s assistant, analyzed celestial motion mathematically Galileo (1564-1642)
More informationThe main paradox of KAM-theory for restricted three-body problem (R3BP, celestial mechanics)
The main paadox of KAM-theoy fo esticted thee-body poblem (R3BP celestial mechanics) Segey V. Eshkov Institute fo Time Natue Exploations M.V. Lomonosov's Moscow State Univesity Leninskie goy 1-1 Moscow
More information