Astr 5465 Mar. 29, 2018 Galactic Dynamics I: Disks
|
|
- Percival Hudson
- 5 years ago
- Views:
Transcription
1 Galati Dynamis Overview Astr 5465 Mar. 29, 2018 Subjet is omplex but we will hit the highlights Our goal is to develop an appreiation of the subjet whih we an use to interpret observational data See Binney Tremaine and referenes therein for a full treatment of the subjet Distribution of mass determines gravitational aeleration on eah star Aeleration at eah 3d point and 3d veloity onstitutes 6 parameters in phase spae whih define the motion of eah star at one point in time We need to integrate these over time to determine stellar trajetory (orbit) Following stars via an N-body simulation is urrently impossible Instead let s onsider analyti models Distribution of stars reflets their orbital trajetories over a long time interval. So we assume a steady state for now Disk galaxies Key onepts inlude Cirular motion Deviations from irular motion Resonanes Density Waves Instabilities 1
2 Consider the properties of stellar orbits in the disk of the Milky Way Orbits are approximately irular but not preisely so let s see what information is available Jan Oort parameterized stellar orbits in the following way: Let the radial and tangential veloites of a star be: V r = Arsin2l V t = Br + Ar os2l where A and B are the Oort onstants given by: A = 1 " V 2 R dv dr B = 1 " V 2 R + dv dr = 1 2 R " dω dr = 1 2 R " dω dr + 2Ω R A is a measure of the loal radial gradient of the irular veloity, the shear B is a measure of the loal vortiity (url) Hipparos yields: A = km/s/kp, B = km/s/kp Combining them gives some insight into loal stellar orbits:! A + B = dv = +2.4 km/s/kp (flat rotation urve) " dr! A B = V = Ω( ) = 27.2 km/s/kp (P = 2π / Ω( ) = 230 Myr " R R o When ombined with a measure of = 8kp: V ( ) = 218 ( /8 kp) km/s 2
3 Consider small perturbations from irular orbits The veloity will be almost unhanged as star is perturbed radially but the small hange is signifiant Result is an elliptial orbit with a > R Angular momentum must be onserved: As r inreases, V must derease and vie versa Stars perturbed initially outward will fall behind those on irular orbit F grav > F ent so stars moves bak in Stars perturbed initially inward will lead those in irular orbit F grav < F ent so star moves bak out The yle repeats and so elliptial orbit an be modeled as an epiyle entered on the guiding (irular) orbit. We define and angular veloity for the epiyle k and it is retrograde. For a Keplerian potential (orbit about point mass) we have: W g = k g and so the orbit is a losed ellipse This is not true in general and so the orbits are not losed Unless we onsider a rotating frame with W = W g 1/2 k g then orbits are losed ellipses entered on galaxy If we have a phase shift of these orbits with radius we see a spiral-like pattern similar to that seen at the right. Now we have a dynamial method for produing spiral arms 3
4 Dynamial basis for epiyli motion of disk stars Consider the potential of a flattened, axisymmetri disk: F(R,z). Sine angular momentum is onserved (no azimuthal fores): r = Φ(R, z) and L z = R 2 φ = onst. For ylindrial oordinates (R, φ, z): R R φ 2 = Φ Φ and z = z with d dt (L z ) = 0 Note the entrifugal aeleration term. Consider z motions about the plane: Φ z ( = 0 sine the disk is ontinuous and symmetri about z = 0 If we expand the z-fore for small z (linear terms): z = Φ ( z z 2 Φ ( z 2 = z 2 Φ ( z 2 = ν 2 z where ν 2 = 2 Φ ( z 2 This is the equation of motion for symple harmoni motion with frequeny ν and the solution is: z(t) = Z os(νt +ψ 0 ) For the Milky Way near the sun, ν 2 = 4πGρ 0 or ν 0.096Myr 1 So the vertial osillation period (2π /ν) 6.5 x 10 7 yr 1/3 Ω 4
5 Now onsider the radial motions about the irular guiding (referene) orbit: Φ ( = V 2 2 = Ω g For non-irular orbits the equation of motion is: R = R φ 2 Φ We an also write this interms of the angular momentum: R = Φ eff where Φ eff = Φ(R, z)+ L 2 z 2R sine L = 2 z φ R2 We an plot Φ eff to ilustrate the sharp rise at small r and the slow rise at large R. The minimum ours at the guiding orbit: Φ eff ( = 0 = Φ φ g (R 2 = Φ ( V g For some small perturbation x onsider the potential at R = R + x : R = x = Φ eff ( x 2 2 Φ eff ( 2 = x 2 2 Φ eff = κ 2 x ( One again this is the equation of simple harmoni motion about : x(t) = X os(κt +φ 0 ) where κ 2 = 2 Φ eff 2 ( = φ (( + 3L 2 z R g R or: 4 g κ 2 = R dω2 dr + 4Ω2 ( 5
6 Now onsider the azimuthal motions about the irular guiding (referene) orbit: Sine: L z = R 2 Ω g = onst., hanges in R yield hanges in Ω: Ω = φ = L z R = L z 2 ( + x) L z 1 2x 2 2 R g R ) = Ω 2x g 1 g ( R ) g ( Integrating yields: φ(t) = Ω g t 2Ω X g κr ) sin(κt +φ ) 0 g ( Thus, φ follows the guiding orbit with small amplitude SHM suprposed. If we let y be the azimuthal perturbations: Near the Sun we predit: κ 2 0 = 4B(A B) = 4BΩ 0 where κ 0 = 37 km/s/kp and Ω 0 = A B = 27 km/s/kp This orresponds to κ 0 / Ω (stars make 1.3 yles per orbit) and sine κ 0 / 2Ω then epiyles have radial/azimuthal 0.7 The observed veloity ellipsoid at = is: σ R /σ φ = κ 0 / 2Ω in good agreement, but: σ R /σ φ = 2Ω 0 /κ beause there are more stars at smaller R This results in about 1 kp exursions in R. Similarly, for z: σ z 30 km/s with ν Myr 1 with exursions of about 300 p. y(t) = 2Ω g κ X sin(κt +φ 0 ) and so the frequeny κ is that same as in x (radial diretion) but out of phase by 90 o. Together: x(t) = X os(κt) y(t) = 2Ω g κ X os(κt) assuming φ 0 = 0 Some properties are: elliptial epiyle with radial/azimuthal = κ /2Ω retrograde epiyli motion For a Keplerian potential: κ = Ω (losed ellipses) For flat rotation urve: κ = 2Ω For solid body rotation: κ = 2Ω (losed oval orbits) 6
Dr G. I. Ogilvie Lent Term 2005
Aretion Diss Mathematial Tripos, Part III Dr G. I. Ogilvie Lent Term 2005 1.4. Visous evolution of an aretion dis 1.4.1. Introdution The evolution of an aretion dis is regulated by two onservation laws:
More informationarxiv:gr-qc/ v2 6 Feb 2004
Hubble Red Shift and the Anomalous Aeleration of Pioneer 0 and arxiv:gr-q/0402024v2 6 Feb 2004 Kostadin Trenčevski Faulty of Natural Sienes and Mathematis, P.O.Box 62, 000 Skopje, Maedonia Abstrat It this
More informationECCENTRICITY SAMPLES: IMPLICATIONS ON THE POTENTIAL AND THE VELOCITY DISTRIBUTION
Serb. Astron. J. (017), OnLine-First UDC 54.6 34 + 54.6 33.8 DOI: https://doi.org/10.98/saj1701004c Original sientifi paper ECCENTRICITY SAMPLES: IMPLICATIONS ON THE POTENTIAL AND THE VELOCITY DISTRIBUTION
More informationLecture 6: The Orbits of Stars
Astr 509: Astrophysics III: Stellar Dynamics Winter Quarter 2005, University of Washington, Željko Ivezić Lecture 6: The Orbits of Stars Axisymmetric Potentials 1 Axisymmetric Potentials The problem: given
More informationSimple Considerations on the Cosmological Redshift
Apeiron, Vol. 5, No. 3, July 8 35 Simple Considerations on the Cosmologial Redshift José Franiso Garía Juliá C/ Dr. Maro Mereniano, 65, 5. 465 Valenia (Spain) E-mail: jose.garia@dival.es Generally, the
More informationPhysicsAndMathsTutor.com 1
PhysisAndMathsTutor.om. (a (i beam splitter [or semi-silvered mirror] (ii a ompensator [or a glass blok] allows for the thikness of the (semi-silvered mirror to obtain equal optial path lengths in the
More informationSpecial and General Relativity
9/16/009 Speial and General Relativity Inertial referene frame: a referene frame in whih an aeleration is the result of a fore. Examples of Inertial Referene Frames 1. This room. Experiment: Drop a ball.
More informationThe motions of stars in the Galaxy
The motions of stars in the Galaxy The stars in the Galaxy define various components, that do not only differ in their spatial distribution but also in their kinematics. The dominant motion of stars (and
More informationAccelerator Physics Particle Acceleration. G. A. Krafft Old Dominion University Jefferson Lab Lecture 4
Aelerator Physis Partile Aeleration G. A. Krafft Old Dominion University Jefferson Lab Leture 4 Graduate Aelerator Physis Fall 15 Clarifiations from Last Time On Crest, RI 1 RI a 1 1 Pg RL Pg L V Pg RL
More information(Newton s 2 nd Law for linear motion)
PHYSICS 3 Final Exaination ( Deeber Tie liit 3 hours Answer all 6 questions You and an assistant are holding the (opposite ends of a long plank when oops! the butterfingered assistant drops his end If
More informationClassical Diamagnetism and the Satellite Paradox
Classial Diamagnetism and the Satellite Paradox 1 Problem Kirk T. MDonald Joseph Henry Laboratories, Prineton University, Prineton, NJ 08544 (November 1, 008) In typial models of lassial diamagnetism (see,
More informationGravity from the Uncertainty Principle.
Gravity from the Unertainty Priniple. M.E. MCulloh Otober 29, 2013 Abstrat It is shown here that Newton's gravity law an be derived from the unertainty priniple. The idea is that as the distane between
More informationRadiation processes and mechanisms in astrophysics 3. R Subrahmanyan Notes on ATA lectures at UWA, Perth 22 May 2009
Radiation proesses and mehanisms in astrophysis R Subrahmanyan Notes on ATA letures at UWA, Perth May 009 Synhrotron radiation - 1 Synhrotron radiation emerges from eletrons moving with relativisti speeds
More informationExperiment 03: Work and Energy
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Physis Department Physis 8.01 Purpose of the Experiment: Experiment 03: Work and Energy In this experiment you allow a art to roll down an inlined ramp and run into
More informationPotential-Density pair: Worked Problem In a spherical galaxy, the density of matter varies with radius as. a r 2 (r+a) 2, ρ(r) = M 4π
15 Potential-Density pair: Worked Problem In a spherical galaxy, the density of matter varies with radius as where M and a are constants. ρ(r) = M 4π a r 2 (r+a) 2, (a) Verify that the total mass of the
More informationThe Milky Way Part 3 Stellar kinematics. Physics of Galaxies 2011 part 8
The Milky Way Part 3 Stellar kinematics Physics of Galaxies 2011 part 8 1 Stellar motions in the MW disk Let s continue with the rotation of the Galaxy, this time from the point of view of the stars First,
More informationNuclear Shell Structure Evolution Theory
Nulear Shell Struture Evolution Theory Zhengda Wang (1) Xiaobin Wang () Xiaodong Zhang () Xiaohun Wang () (1) Institute of Modern physis Chinese Aademy of SienesLan Zhou P. R. China 70000 () Seagate Tehnology
More informationThe Milky Way Part 2 Stellar kinematics. Physics of Galaxies 2012 part 7
The Milky Way Part 2 Stellar kinematics Physics of Galaxies 2012 part 7 1 Stellar motions in the MW disk Let s look at the rotation of the Galactic disk First, we need to introduce the concept of the Local
More informationEpicycles the short form.
Homework Set 3 Due Sept 9 CO 4.15 just part (a). (see CO pg. 908) CO 4.1 CO 4.36 (a),(b) CO 5.14 (assume that Sun currently has its max. u velocity.) CO 5.16 (Keplerian orbit = orbit around a point mass)
More informationThe Concept of Mass as Interfering Photons, and the Originating Mechanism of Gravitation D.T. Froedge
The Conept of Mass as Interfering Photons, and the Originating Mehanism of Gravitation D.T. Froedge V04 Formerly Auburn University Phys-dtfroedge@glasgow-ky.om Abstrat For most purposes in physis the onept
More informationMASSACHUSETTS INSTITUTE OF TECHNOLOGY Physics Department Physics 8.286: The Early Universe December 21, 2013 Prof. Alan Guth QUIZ 3 SOLUTIONS
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Physis Department Physis 8.286: The Early Universe Deember 2, 203 Prof. Alan Guth QUIZ 3 SOLUTIONS Quiz Date: Deember 5, 203 PROBLEM : DID YOU DO THE READING? (35
More informationCombined Electric and Magnetic Dipoles for Mesoband Radiation, Part 2
Sensor and Simulation Notes Note 53 3 May 8 Combined Eletri and Magneti Dipoles for Mesoband Radiation, Part Carl E. Baum University of New Mexio Department of Eletrial and Computer Engineering Albuquerque
More informationThe gravitational phenomena without the curved spacetime
The gravitational phenomena without the urved spaetime Mirosław J. Kubiak Abstrat: In this paper was presented a desription of the gravitational phenomena in the new medium, different than the urved spaetime,
More informationDensity Waves and Chaos in Spiral Galaxies. Frank Shu NTHU Physics Department 7 December 2005
Density Waves and Chaos in Spiral Galaxies Frank Shu NTHU Physics Department 7 December 2005 Outline of Talk Elements of Spiral Density-Wave Theory Theory of Spiral Substructure: Feather Formation by Gravitational
More informationThe Electromagnetic Radiation and Gravity
International Journal of Theoretial and Mathematial Physis 016, 6(3): 93-98 DOI: 10.593/j.ijtmp.0160603.01 The Eletromagneti Radiation and Gravity Bratianu Daniel Str. Teiului Nr. 16, Ploiesti, Romania
More informationParticle-wave symmetry in Quantum Mechanics And Special Relativity Theory
Partile-wave symmetry in Quantum Mehanis And Speial Relativity Theory Author one: XiaoLin Li,Chongqing,China,hidebrain@hotmail.om Corresponding author: XiaoLin Li, Chongqing,China,hidebrain@hotmail.om
More informationThe Gravitational Potential for a Moving Observer, Mercury s Perihelion, Photon Deflection and Time Delay of a Solar Grazing Photon
Albuquerque, NM 0 POCEEDINGS of the NPA 457 The Gravitational Potential for a Moving Observer, Merury s Perihelion, Photon Defletion and Time Delay of a Solar Grazing Photon Curtis E. enshaw Tele-Consultants,
More informationTHEORETICAL PROBLEM No. 3 WHY ARE STARS SO LARGE?
THEORETICAL PROBLEM No. 3 WHY ARE STARS SO LARGE? The stars are spheres of hot gas. Most of them shine beause they are fusing hydrogen into helium in their entral parts. In this problem we use onepts of
More informationTHEORETICAL PROBLEM 2 SOLUTION DOPPLER LASER COOLING AND OPTICAL MOLASSES. v 1 c
THEOETICA POBEM SOUTION DOPPE ASE COOING AND OPTICA MOASSES The key to this problem is the Doppler effet (to be preise, the longitudinal Doppler effet): The frequeny of a monohromi beam of light deteted
More informationName Solutions to Test 1 September 23, 2016
Name Solutions to Test 1 September 3, 016 This test onsists of three parts. Please note that in parts II and III, you an skip one question of those offered. Possibly useful formulas: F qequb x xvt E Evpx
More informationElectromagnetic waves
Eletromagneti waves He predited eletromagneti wave propagation James Clerk Maxwell (1831-1879) Eletromagneti waves He predited eletromagneti wave propagation A singular theoretial ahievement of the 19
More informationFinal Review. A Puzzle... Special Relativity. Direction of the Force. Moving at the Speed of Light
Final Review A Puzzle... Diretion of the Fore A point harge q is loated a fixed height h above an infinite horizontal onduting plane. Another point harge q is loated a height z (with z > h) above the plane.
More informationGravitation is a Gradient in the Velocity of Light ABSTRACT
1 Gravitation is a Gradient in the Veloity of Light D.T. Froedge V5115 @ http://www.arxdtf.org Formerly Auburn University Phys-dtfroedge@glasgow-ky.om ABSTRACT It has long been known that a photon entering
More information13.Prandtl-Meyer Expansion Flow
3.Prandtl-eyer Expansion Flow This hapter will treat flow over a expansive orner, i.e., one that turns the flow outward. But before we onsider expansion flow, we will return to onsider the details of the
More informationGreen s function for the wave equation
Green s funtion for the wave equation Non-relativisti ase January 2019 1 The wave equations In the Lorentz Gauge, the wave equations for the potentials are (Notes 1 eqns 43 and 44): 1 2 A 2 2 2 A = µ 0
More informationBrazilian Journal of Physics, vol. 29, no. 3, September, Classical and Quantum Mechanics of a Charged Particle
Brazilian Journal of Physis, vol. 9, no. 3, September, 1999 51 Classial and Quantum Mehanis of a Charged Partile in Osillating Eletri and Magneti Fields V.L.B. de Jesus, A.P. Guimar~aes, and I.S. Oliveira
More informationClassical Trajectories in Rindler Space and Restricted Structure of Phase Space with PT-Symmetric Hamiltonian. Abstract
Classial Trajetories in Rindler Spae and Restrited Struture of Phase Spae with PT-Symmetri Hamiltonian Soma Mitra 1 and Somenath Chakrabarty 2 Department of Physis, Visva-Bharati, Santiniketan 731 235,
More informationStability Analysis of Orbital Motions around Uniformly Rotating Irregular Asteroids
Stability Analysis of Orbital Motions around Uniformly Rotating Irregular Asteroids By Xiyun HoU, ) Daniel J. SCHEERES, ) Xiaosheng XIN, ) Jinglang FENG, ) Jingshi TANG, ) Lin LIU, ) ) Shool of Astronomy
More informationEvaluation of effect of blade internal modes on sensitivity of Advanced LIGO
Evaluation of effet of blade internal modes on sensitivity of Advaned LIGO T0074-00-R Norna A Robertson 5 th Otober 00. Introdution The urrent model used to estimate the isolation ahieved by the quadruple
More informationThe homopolar generator: an analytical example
The homopolar generator: an analytial example Hendrik van Hees August 7, 214 1 Introdution It is surprising that the homopolar generator, invented in one of Faraday s ingenious experiments in 1831, still
More informationELECTROMAGNETIC RADIATION
LUCIANO BUGGIO ELECTROMAGNETIC RADIATION On the basis of the (unpreedented) dynami hypothesis that gives rise to yloidal motion a loal and deterministi model of eletromagneti radiation is onstruted, possessing
More information, an inverse square law.
Uniform irular motion Speed onstant, but eloity hanging. and a / t point to enter. s r θ > θ s/r t / r, also θ in small limit > t/r > a / r, entripetal aeleration Sine a points to enter of irle, F m a
More information20 Doppler shift and Doppler radars
20 Doppler shift and Doppler radars Doppler radars make a use of the Doppler shift phenomenon to detet the motion of EM wave refletors of interest e.g., a polie Doppler radar aims to identify the speed
More informationAdvanced Computational Fluid Dynamics AA215A Lecture 4
Advaned Computational Fluid Dynamis AA5A Leture 4 Antony Jameson Winter Quarter,, Stanford, CA Abstrat Leture 4 overs analysis of the equations of gas dynamis Contents Analysis of the equations of gas
More informationCritical Reflections on the Hafele and Keating Experiment
Critial Refletions on the Hafele and Keating Experiment W.Nawrot In 1971 Hafele and Keating performed their famous experiment whih onfirmed the time dilation predited by SRT by use of marosopi loks. As
More informationOn the Geometrical Conditions to Determine the Flat Behaviour of the Rotational Curves in Galaxies
On the Geometrial Conditions to Determine the Flat Behaviour of the Rotational Curves in Galaxies Departamento de Físia, Universidade Estadual de Londrina, Londrina, PR, Brazil E-mail: andrenaves@gmail.om
More informationPHYSICS 432/532: Cosmology Midterm Exam Solution Key (2018) 1. [40 points] Short answer (8 points each)
PHYSICS 432/532: Cosmology Midterm Exam Solution Key (2018) 1. [40 points] Short answer (8 points eah) (a) A galaxy is observed with a redshift of 0.02. How far away is the galaxy, and what is its lookbak
More informationThe Hanging Chain. John McCuan. January 19, 2006
The Hanging Chain John MCuan January 19, 2006 1 Introdution We onsider a hain of length L attahed to two points (a, u a and (b, u b in the plane. It is assumed that the hain hangs in the plane under a
More informationWhere as discussed previously we interpret solutions to this partial differential equation in the weak sense: b
Consider the pure initial value problem for a homogeneous system of onservation laws with no soure terms in one spae dimension: Where as disussed previously we interpret solutions to this partial differential
More informationphysics/ Nov 1999
Do Gravitational Fields Have Mass? Or on the Nature of Dark Matter Ernst Karl Kunst As has been shown before (a brief omment will be given in the text) relativisti mass and relativisti time dilation of
More informationPractice Exam 2 Solutions
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department o Physis Physis 801T Fall Term 004 Problem 1: stati equilibrium Pratie Exam Solutions You are able to hold out your arm in an outstrethed horizontal position
More informationEffect of magnetization process on levitation force between a superconducting. disk and a permanent magnet
Effet of magnetization proess on levitation fore between a superonduting disk and a permanent magnet L. Liu, Y. Hou, C.Y. He, Z.X. Gao Department of Physis, State Key Laboratory for Artifiial Mirostruture
More informationTowards an Absolute Cosmic Distance Gauge by using Redshift Spectra from Light Fatigue.
Towards an Absolute Cosmi Distane Gauge by using Redshift Spetra from Light Fatigue. Desribed by using the Maxwell Analogy for Gravitation. T. De Mees - thierrydemees @ pandora.be Abstrat Light is an eletromagneti
More informationGeneration of EM waves
Generation of EM waves Susan Lea Spring 015 1 The Green s funtion In Lorentz gauge, we obtained the wave equation: A 4π J 1 The orresponding Green s funtion for the problem satisfies the simpler differential
More informationKinematics of the Solar Neighborhood
Chapter 15 Kinematics of the Solar Neighborhood Unlike an elliptical galaxy, the Milky Way rotates with a speed much larger than the random velocities of typical stars. Our position inside the disk of
More informationDYNAMICS OF GALAXIES
DYNAMICS OF GALAXIES 3. Piet van der Kruit Kapteyn Astronomical Institute University of Groningen the Netherlands Winter 2008/9 Contents Differential rotation Epicycle orbits Vertical motion Resonances
More informationRobust Flight Control Design for a Turn Coordination System with Parameter Uncertainties
Amerian Journal of Applied Sienes 4 (7): 496-501, 007 ISSN 1546-939 007 Siene Publiations Robust Flight ontrol Design for a urn oordination System with Parameter Unertainties 1 Ari Legowo and Hiroshi Okubo
More informationTORSION By Prof. Ahmed Amer
ORSION By Prof. Ahmed Amer orque wisting moments or torques are fores ating through distane so as to promote rotation. Example Using a wrenh to tighten a nut in a bolt. If the bolt, wrenh and fore are
More informationLecture #1: Quantum Mechanics Historical Background Photoelectric Effect. Compton Scattering
561 Fall 2017 Leture #1 page 1 Leture #1: Quantum Mehanis Historial Bakground Photoeletri Effet Compton Sattering Robert Field Experimental Spetrosopist = Quantum Mahinist TEXTBOOK: Quantum Chemistry,
More information4. (12) Write out an equation for Poynting s theorem in differential form. Explain in words what each term means physically.
Eletrodynamis I Exam 3 - Part A - Closed Book KSU 205/2/8 Name Eletrodynami Sore = 24 / 24 points Instrutions: Use SI units. Where appropriate, define all variables or symbols you use, in words. Try to
More informationAcoustic Waves in a Duct
Aousti Waves in a Dut 1 One-Dimensional Waves The one-dimensional wave approximation is valid when the wavelength λ is muh larger than the diameter of the dut D, λ D. The aousti pressure disturbane p is
More information). In accordance with the Lorentz transformations for the space-time coordinates of the same event, the space coordinates become
Relativity and quantum mehanis: Jorgensen 1 revisited 1. Introdution Bernhard Rothenstein, Politehnia University of Timisoara, Physis Department, Timisoara, Romania. brothenstein@gmail.om Abstrat. We first
More informationElectromagnetic radiation of the travelling spin wave propagating in an antiferromagnetic plate. Exact solution.
arxiv:physis/99536v1 [physis.lass-ph] 15 May 1999 Eletromagneti radiation of the travelling spin wave propagating in an antiferromagneti plate. Exat solution. A.A.Zhmudsky November 19, 16 Abstrat The exat
More information3 Tidal systems modelling: ASMITA model
3 Tidal systems modelling: ASMITA model 3.1 Introdution For many pratial appliations, simulation and predition of oastal behaviour (morphologial development of shorefae, beahes and dunes) at a ertain level
More informationPhysics 218, Spring February 2004
Physis 8 Spring 004 8 February 004 Today in Physis 8: dispersion Motion of bound eletrons in matter and the frequeny dependene of the dieletri onstant Dispersion relations Ordinary and anomalous dispersion
More informationShear Force and Bending Moment
Shear Fore and Bending oent Shear Fore: is the algebrai su of the vertial fores ating to the left or right of a ut setion along the span of the bea Bending oent: is the algebrai su of the oent of the fores
More informationWave Propagation through Random Media
Chapter 3. Wave Propagation through Random Media 3. Charateristis of Wave Behavior Sound propagation through random media is the entral part of this investigation. This hapter presents a frame of referene
More informationZero-energy space cancels the need for dark energy. Mathematics, Physics and Philosophy in the Interpretations of Relativity Theory
Zero-energy spae anels the need for dark energy Tuomo Suntola, www.si.fi/~suntola/, Finland Mathematis, Physis and Philosophy in the Interpretations of Relativity Theory 1 Latest PhysisWeb Summaries 20.7.2007:
More informationThe Special Theory of Relativity
The Speial Theory of Relatiity Galilean Newtonian Relatiity Galileo Galilei Isaa Newton Definition of an inertial referene frame: One in whih Newton s first law is alid. onstant if F0 Earth is rotating
More informationPhysical Laws, Absolutes, Relative Absolutes and Relativistic Time Phenomena
Page 1 of 10 Physial Laws, Absolutes, Relative Absolutes and Relativisti Time Phenomena Antonio Ruggeri modexp@iafria.om Sine in the field of knowledge we deal with absolutes, there are absolute laws that
More informationMillennium Relativity Acceleration Composition. The Relativistic Relationship between Acceleration and Uniform Motion
Millennium Relativity Aeleration Composition he Relativisti Relationship between Aeleration and niform Motion Copyright 003 Joseph A. Rybzyk Abstrat he relativisti priniples developed throughout the six
More informationCHAPTER 26 The Special Theory of Relativity
CHAPTER 6 The Speial Theory of Relativity Units Galilean-Newtonian Relativity Postulates of the Speial Theory of Relativity Simultaneity Time Dilation and the Twin Paradox Length Contration Four-Dimensional
More informationIntroduction to Quantum Chemistry
Chem. 140B Dr. J.A. Mak Introdution to Quantum Chemistry Without Quantum Mehanis, how would you explain: Periodi trends in properties of the elements Struture of ompounds e.g. Tetrahedral arbon in ethane,
More informationAharonov-Bohm effect. Dan Solomon.
Aharonov-Bohm effet. Dan Solomon. In the figure the magneti field is onfined to a solenoid of radius r 0 and is direted in the z- diretion, out of the paper. The solenoid is surrounded by a barrier that
More informationFiber Optic Cable Transmission Losses with Perturbation Effects
Fiber Opti Cable Transmission Losses with Perturbation Effets Kampanat Namngam 1*, Preeha Yupapin 2 and Pakkinee Chitsakul 1 1 Department of Mathematis and Computer Siene, Faulty of Siene, King Mongkut
More informationQ2. [40 points] Bishop-Hill Model: Calculation of Taylor Factors for Multiple Slip
27-750, A.D. Rollett Due: 20 th Ot., 2011. Homework 5, Volume Frations, Single and Multiple Slip Crystal Plastiity Note the 2 extra redit questions (at the end). Q1. [40 points] Single Slip: Calulating
More informationRelativity in Classical Physics
Relativity in Classial Physis Main Points Introdution Galilean (Newtonian) Relativity Relativity & Eletromagnetism Mihelson-Morley Experiment Introdution The theory of relativity deals with the study of
More informationTHE TWIN PARADOX A RELATIVISTIC DOMAIN RESOLUTION
THE TWIN PARADOX A RELATIVISTIC DOMAIN RESOLUTION Peter G.Bass P.G.Bass www.relativitydomains.om January 0 ABSTRACT This short paper shows that the so alled "Twin Paradox" of Speial Relativity, is in fat
More informationRelativistic Dynamics
Chapter 7 Relativisti Dynamis 7.1 General Priniples of Dynamis 7.2 Relativisti Ation As stated in Setion A.2, all of dynamis is derived from the priniple of least ation. Thus it is our hore to find a suitable
More informationdistribution of mass! The rotation curve of the Galaxy ! Stellar relaxation time! Virial theorem! Differential rotation of the stars in the disk
Today in Astronomy 142:! The local standard of rest the Milky Way, continued! Rotation curves and the! Stellar relaxation time! Virial theorem! Differential rotation of the stars in the disk distribution
More informationTorsion. Torsion is a moment that twists/deforms a member about its longitudinal axis
Mehanis of Solids I Torsion Torsional loads on Cirular Shafts Torsion is a moment that twists/deforms a member about its longitudinal axis 1 Shearing Stresses due to Torque o Net of the internal shearing
More informationMTH 142 Solution Practice for Exam 2
MTH 4 Solution Pratie for Eam Updated /7/4, 8: a.m.. (a) = 4/, hene MID() = ( + + ) +/ +6/ +/ ( 4 ) =. ( LEFT = ( 4..). =.7 and RIGHT = (.. ). =.7. Hene TRAP =.7.. (a) MID = (.49 +.48 +.9 +.98). = 4.96.
More informationProject 10.5C Circular Membrane Vibrations
Projet 1.5C Cirular Membrane Vibrations In problems involving regions that enjoy irular symmetry about the origin in the plane (or the vertial z-axis in spae), the use of polar (or ylindrial) oordinates
More informationPhysics for Scientists & Engineers 2
Review Maxwell s Equations Physis for Sientists & Engineers 2 Spring Semester 2005 Leture 32 Name Equation Desription Gauss Law for Eletri E d A = q en Fields " 0 Gauss Law for Magneti Fields Faraday s
More information19 Lecture 19: Cosmic Microwave Background Radiation
PHYS 652: Astrophysis 97 19 Leture 19: Cosmi Mirowave Bakground Radiation Observe the void its emptiness emits a pure light. Chuang-tzu The Big Piture: Today we are disussing the osmi mirowave bakground
More informationGreen s function for the wave equation
Green s funtion for the wave equation Non relativisti ase 1 The wave equations In the Lorentz Gauge, the wave equations for the potentials in Lorentz Gauge Gaussian units are: r 2 A 1 2 A 2 t = 4π 2 j
More informationTHE SOLAR SYSTEM. We begin with an inertial system and locate the planet and the sun with respect to it. Then. F m. Then
THE SOLAR SYSTEM We now want to apply what we have learned to the olar ytem. Hitorially thi wa the great teting ground for mehani and provided ome of it greatet triumph, uh a the diovery of the outer planet.
More informationSpiral Structure in Galaxies
Department of Physics Seminar - 4 th year Spiral Structure in Galaxies Author: Maruška Žerjal Adviser: prof. dr. Tomaž Zwitter Ljubljana, April 2010 Abstract The most numerous among bright galaxies and
More informationLecture XIX: Particle motion exterior to a spherical star
Lecture XIX: Particle motion exterior to a spherical star Christopher M. Hirata Caltech M/C 350-7, Pasadena CA 95, USA Dated: January 8, 0 I. OVERVIEW Our next objective is to consider the motion of test
More informationIN-PLANE VIBRATIONS OF CURVED BEAMS WITH VARIABLE CROSS-SECTIONS CARRYING ADDITIONAL MASS
11 th International Conferene on Vibration Problems Z. Dimitrovová et al. (eds.) Lisbon, Portugal, 9-1 September 013 IN-PLANE VIBRATIONS OF CURVED BEAMS WITH VARIABLE CROSS-SECTIONS CARRYING ADDITIONAL
More informationPhysics 2D Lecture Slides Lecture 7: Jan 14th 2004
Quiz is This Friday Quiz will over Setions.-.6 (inlusive) Remaining material will be arried over to Quiz Bring Blue Book, hek alulator battery Write all answers in indelible ink else no grade! Write answers
More informationMetric of Universe The Causes of Red Shift.
Metri of Universe The Causes of Red Shift. ELKIN IGOR. ielkin@yande.ru Annotation Poinare and Einstein supposed that it is pratially impossible to determine one-way speed of light, that s why speed of
More informationLecture 15 (Nov. 1, 2017)
Leture 5 8.3 Quantum Theor I, Fall 07 74 Leture 5 (Nov., 07 5. Charged Partile in a Uniform Magneti Field Last time, we disussed the quantum mehanis of a harged partile moving in a uniform magneti field
More informationDYNAMICS OF CAPILLARY FLOW AND TRANSPORT PROPERTIES IN CARBONATE SEDIMENTARY FORMATION BY TIME-CONTROLLED POROSIMETRY
SCA4-44 /5 DYNAMICS OF CAPILLARY FLOW AND TRANSPORT PROPERTIES IN CARBONATE SEDIMENTARY FORMATION BY TIME-CONTROLLED POROSIMETRY A. Cerepi, Institut EGID-Bordeaux 3, Université Mihel de Montaigne,, allée
More informationAnswers to Coursebook questions Chapter J2
Answers to Courseook questions Chapter J 1 a Partiles are produed in ollisions one example out of many is: a ollision of an eletron with a positron in a synhrotron. If we produe a pair of a partile and
More informationCavity flow with surface tension past a flat plate
Proeedings of the 7 th International Symposium on Cavitation CAV9 Paper No. ## August 7-, 9, Ann Arbor, Mihigan, USA Cavity flow with surfae tension past a flat plate Yuriy Savhenko Institute of Hydromehanis
More informationMath 2374: Multivariable Calculus and Vector Analysis
Math 2374: Multivariable Calulus and Vetor Analysis Part 26 Fall 2012 The integrals of multivariable alulus line integral of salar-valued funtion line integral of vetor fields surfae integral of salar-valued
More informationThe Corpuscular Structure of Matter, the Interaction of Material Particles, and Quantum Phenomena as a Consequence of Selfvariations.
The Corpusular Struture of Matter, the Interation of Material Partiles, and Quantum Phenomena as a Consequene of Selfvariations. Emmanuil Manousos APM Institute for the Advanement of Physis and Mathematis,
More informationSpiral and Bar Pattern Time-Dependence in Galaxies
Spiral and Bar Pattern Time-Dependence in Galaxies M95 Daniel Pfenniger Geneva Observatory, University of Geneva, Switzerland Collaborators: Kanak Saha (Pune), Yu-Ting Wu & Ron Taam (Taipei) NASA/JPL-Caltech/ESO/R.
More information(a) We desribe physics as a sequence of events labelled by their space time coordinates: x µ = (x 0, x 1, x 2 x 3 ) = (c t, x) (12.
2 Relativity Postulates (a) All inertial observers have the same equations of motion and the same physial laws. Relativity explains how to translate the measurements and events aording to one inertial
More information