Physics 312 Introduction to Astrophysics Lecture 7
|
|
- Milton Hamilton
- 6 years ago
- Views:
Transcription
1 Physics 312 Intoduction to Astophysics Lectue 7 James Buckley buckley@wuphys.wustl.edu Lectue 7 Eath/Moon System Tidal Foces Tides M= mass of moon o sun F 1 = GMm 2 F 2 = GMm ( + ) 2 Diffeence in gavitational foce on nea and fa side esults in oceans being pulled moe stongly than aveage gavitational foce on the igid body of the eath on nea side, moe weakly on fa side
2 Tides Note that the adius of the eath = 12, 742km is much smalle than the distance between the eath and moon moon = 384, 000km and the distance between the Eath and the sun sun = 149, 000, 000 km = F 2 = GM m 2 (1 + ) 2 2 =(0.03) 2 = GM m 0 = 2 ( ) GM m (1 + 2 ) 1 2 GM m GM m(1 2 ) 2 (define /) F 1 = GMm 2 F 2 = GMm ( + ) 2 Sum of foces F 1 + F 2 + F othe stu combines to keep Eath in cicula obit. Di eence, stetches oceans and makes tide Stetching, tidal foce = F 1 F 2 Tidal foce = 2GM m GMm Tidal foce = 2 [1 (1 2 )] = 2GM 3 2 Sping Tides Note that on the nea side, thee is a slightly lage foce than needed to keep the igid planet in obit aound the sun, but on the fa side slightly less - esulting in an effective stetching foce on both sides. So even when it is full moon, and it appeas that the foces of sun and moon wok against each othe, both povide a positive effective stetching foce, adding the tides. At full and new moon, we get stonge Sping tides
3 Neap Tides At fist and thid quate moon, effects of Sun and moon wok against each othe poducing weake neap tides Tidal Locking Nea Side (we always see this face fom Eath) Nea Side (we always see this face fom Eath) Moon is tidally locked to the Eath, we always see the same side (left) neve the fa side (ight). How did this come to be? If the moon wee not tidally locked, it would be compessed one way, then the next. All of this cunching dissipates enegy and the moon is only happy when it is locked in place!
4 Tidal Disuption Conside the tidal foce of a lage body of mass M on a smalle body, modeled vey oughly as two smalle masses m sepaated by a distance M m m Taylo seies expansion F () F ( 0 )+( 0 ) df ) d =0 F () = GMm df ) 2 dr = 2GMm 3 F = df d We can calculate the Roche limit the point at which the tidal foce ipping the two masses apat is geate than the self-gavity that pulls the masses togethe: 2GMm R 3 = Gmm 1/3 2M ( ) 2 ) R = m Rewiting in tems of density: M = 4 3 R3 M, m = 4 3 1/3 M m ) R 2.5 R 3 2 m 1/3 M Which is vey close to the moe caeful esult: Roche limit: R =2.44 R m Discussion Question Would you be less likely to find a Jovian (gas giant) planet o a teestial (ocky) planet vey close to anothe sta? If the adius of the event hoizon of a black hole is popotional to the mass of the black hole, would you be moe likely to suvive cossing the hoizon of a sola mass black hole o supemassive black hole?
5 Spaghettification { F ( + ) = GMm ( + ) 2 F () = GMm 2 F = GMm ( + ) 2 F 2GMm 3 At the event hoizon = sch = 2GM c 2 So the tidal foce at the event hoizon is : F lb 2 Msun M bh m astonaut 220 lb height 6 ft A black hole with the mass of the sun would snap you in half with a foce of half a tillion pounds at the event hoizon! Black Hole Oh Snap! of mass Mbh need to find a million-sola-mass black hole to suvive the jouney! Toques in Eath Moon system (1) Fiction in otating Eath pulls tidal bulge slightly ahead of moon (3) The Eath s bulge pulls the moon ahead, inceasing its obital distance (2) The moon gavity ties to pull the Eath s bulge back, slowing the otation Time out! How do we know that the tug of the eath doesn t incease the velocity, and decease the adius fom Keple s laws? If the adius inceases does the velocity decease?!
6 Angula Momentum Makes it Clea ~L = ~ ~p ~v ~L = ~ (m~v) ~L = ~ (m~v) =mv! ~ v 2 = GM GM v = p p L = GM m As inceases, the angula momentum inceases (fo a given mass m) So if angula momentum is conseved, and the Eath s angula momentum deceases, the angula momentum of the Moon s obit must incease, so inceases and v deceases! Equatoial Bulge In addition to tidal foces, the spin of the eath esults in an equatoial bulge (Kind of like the middle age spead o love handles fo planets)
7 Pecession 23.5 plane of the ecliptic F 1 = GMm 2 F 2 = GMm ( + ) 2 Diffeence in gavitational foce on nea and fa side bulge poduces toque, tying to twist the planet. But like a gyoscope, the toque doesn t twist the spinning planet the way we would expect, but instead changes the diection of the angula momentum in the diection of the toque (see demonstation) Pecession Angula Momentum L Gavitational Foce F Gavitational foce ties to twist the top, with a toque whose diection is pependicula to both the axis and the foce The angula momentum vecto changes its diection in the diection of the toque
8 Pecession Eath pecesses due to toque fom gavitational foces of the moon and sun on the equitoial bulge 26,000 yea peiod ove which pole sta changes, it will not always be Polais, o any sta fo that matte. Pecession Pecession is the slow (25,770 yea peiod) wobble of the eath s inclined obit. RA and DEC given in an epoch (e.g., 1950) and must be pecessed to cuent time. α = [m + n sin α tan δ] N δ = [n cos α] N N numbe of yeas fom efeence epoch m = s y 1 and n = "y 1 Physics Lectue 5 p.9/12
9 Spookily Simila - Moon and Sun The fact that the angula size of the moon and sun means that the effect of these two objects on the Eath. Stat with Newton s law of Gavity: The gavitational foce between two masses is popotional to the poduct of the masses and invesely popotional to the squae of the distances between the centes of the two masses M M 2 F = GM 1 M 2 2 Tidal Foces But the foce of gavity on the nea side of object M2 is lage than on the fa side. The diffeence in these foces is called the Tidal foce, and tuns out to be popotional to the poduct of the two masses and the atio of the length of mass M2 divided by the cube of the distance between the two objects + M M 2 F nea Stetching o tidal foce = F nea F fa 1 1 = GM 1 M 2 2 ( + ) 2 if is small compaed with, you can show that F tidal GM 1 M 2 3 F fa
10 Compae the Sun and the Moon Now, let s compae the effect of the Sun and the Moon on the tidal foces on the eath: Aveage density of the Sun is g/cm 3 and of the moon is 3.3 g/cm 3 - oddly simila! The sun and the moon have about the same angula size, 0.5 deg Tidal foces ae popotional to 1/d 3, The mass of the moon o sun is popotional to the poduct of the density times the volume. The volume of a sphee is popotional to the adius cubed, and mass is adius times volume so: Since the angula size of an object is oughly the atio of it s physical dimension (2 R) divided by the distance, and since the moon and the sun have the same angula size: So, compaing the tidal foces: M sun / 1.4 R 3 sun, M moon / 3.3 R 3 moon moon sun 0.5 =2R sun /d sun =2R moon /d moon F moon M eath (3.3 R 3 moon) d 3 moon F sun M eath (1.4 R 3 sun) d 3 sun so since R moon /d moon R sun /d sun we have : F moon (3.3/1.4)F sun The Sun and the Moon The sun and the moon have about the same angula size and close to the same aveage density. Thei impact on pecession and the tides ae quite simila! Because the moon just blocks the sun duing an eclipse, allowing humans to see the oute layes of the sun - coona and flaes! A fotuitous occuence! The moon doesn t shine on its own, but is eflected light fom the sun. Since it is petty gay, it is not eflecting all of the light (but it still looks white at night against the black sky)
Chapter 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 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 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 informationGravitation. Chapter 12. PowerPoint Lectures for University Physics, Twelfth Edition Hugh D. Young and Roger A. Freedman. Lectures by James Pazun
Chapte 12 Gavitation PowePoint Lectues fo Univesity Physics, Twelfth Edition Hugh D. Young and Roge A. Feedman Lectues by James Pazun Modified by P. Lam 5_31_2012 Goals fo Chapte 12 To study Newton s Law
More informationm1 m2 M 2 = M -1 L 3 T -2
GAVITATION Newton s Univesal law of gavitation. Evey paticle of matte in this univese attacts evey othe paticle with a foce which vaies diectly as the poduct of thei masses and invesely as the squae of
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 informationω = θ θ o = θ θ = s r v = rω
Unifom Cicula Motion Unifom cicula motion is the motion of an object taveling at a constant(unifom) speed in a cicula path. Fist we must define the angula displacement and angula velocity The angula displacement
More informationGravitation. AP/Honors Physics 1 Mr. Velazquez
Gavitation AP/Honos Physics 1 M. Velazquez Newton s Law of Gavitation Newton was the fist to make the connection between objects falling on Eath and the motion of the planets To illustate this connection
More informationUniform Circular Motion
Unifom Cicula Motion constant speed Pick a point in the objects motion... What diection is the velocity? HINT Think about what diection the object would tavel if the sting wee cut Unifom Cicula Motion
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 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 informationLecture 3. Basic Physics of Astrophysics - Force and Energy. Forces
Foces Lectue 3 Basic Physics of Astophysics - Foce and Enegy http://apod.nasa.gov/apod/ Momentum is the poduct of mass and velocity - a vecto p = mv (geneally m is taken to be constant) An unbalanced foce
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 informationEscape Velocity. GMm ] B
1 PHY2048 Mach 31, 2006 Escape Velocity Newton s law of gavity: F G = Gm 1m 2 2, whee G = 667 10 11 N m 2 /kg 2 2 3 10 10 N m 2 /kg 2 is Newton s Gavitational Constant Useful facts: R E = 6 10 6 m M E
More informationChap 5. Circular Motion: Gravitation
Chap 5. Cicula Motion: Gavitation Sec. 5.1 - Unifom Cicula Motion A body moves in unifom cicula motion, if the magnitude of the velocity vecto is constant and the diection changes at evey point and is
More informationPhysics: Work & Energy Beyond Earth Guided Inquiry
Physics: Wok & Enegy Beyond Eath Guided Inquiy Elliptical Obits Keple s Fist Law states that all planets move in an elliptical path aound the Sun. This concept can be extended to celestial bodies beyond
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 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 informationPHYSICS 220. Lecture 08. Textbook Sections Lecture 8 Purdue University, Physics 220 1
PHYSICS 0 Lectue 08 Cicula Motion Textbook Sections 5.3 5.5 Lectue 8 Pudue Univesity, Physics 0 1 Oveview Last Lectue Cicula Motion θ angula position adians ω angula velocity adians/second α angula acceleation
More informationRecap. Centripetal acceleration: v r. a = m/s 2 (towards center of curvature)
a = c v 2 Recap Centipetal acceleation: m/s 2 (towads cente of cuvatue) A centipetal foce F c is equied to keep a body in cicula motion: This foce poduces centipetal acceleation that continuously changes
More informationUniversal Gravitation
Chapte 1 Univesal Gavitation Pactice Poblem Solutions Student Textbook page 580 1. Conceptualize the Poblem - The law of univesal gavitation applies to this poblem. The gavitational foce, F g, between
More informationLecture 3. Basic Physics of Astrophysics - Force and Energy. Forces
Lectue 3 Basic Physics of Astophysics - Foce and Enegy http://apod.nasa.gov/apod/ Foces Momentum is the poduct of mass and velocity - a vecto p = mv (geneally m is taken to be constant) An unbalanced foce
More informationMODULE 5 ADVANCED MECHANICS GRAVITATIONAL FIELD: MOTION OF PLANETS AND SATELLITES VISUAL PHYSICS ONLINE
VISUAL PHYSICS ONLIN MODUL 5 ADVANCD MCHANICS GRAVITATIONAL FILD: MOTION OF PLANTS AND SATLLITS SATLLITS: Obital motion of object of mass m about a massive object of mass M (m
More informationDetermining solar characteristics using planetary data
Detemining sola chaacteistics using planetay data Intoduction The Sun is a G-type main sequence sta at the cente of the Sola System aound which the planets, including ou Eath, obit. In this investigation
More informationCentral Force Motion
Cental Foce Motion Cental Foce Poblem Find the motion of two bodies inteacting via a cental foce. Examples: Gavitational foce (Keple poblem): m1m F 1, ( ) =! G ˆ Linea estoing foce: F 1, ( ) =! k ˆ Two
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 informationHistory of Astronomy - Part II. Tycho Brahe - An Observer. Johannes Kepler - A Theorist
Histoy of Astonomy - Pat II Afte the Copenican Revolution, astonomes stived fo moe obsevations to help bette explain the univese aound them Duing this time (600-750) many majo advances in science and astonomy
More informationChap13. Universal Gravitation
Chap13. Uniesal Gaitation Leel : AP Physics Instucto : Kim 13.1 Newton s Law of Uniesal Gaitation - Fomula fo Newton s Law of Gaitation F g = G m 1m 2 2 F21 m1 F12 12 m2 - m 1, m 2 is the mass of the object,
More informationF(r) = r f (r) 4.8. Central forces The most interesting problems in classical mechanics are about central forces.
4.8. Cental foces The most inteesting poblems in classical mechanics ae about cental foces. Definition of a cental foce: (i) the diection of the foce F() is paallel o antipaallel to ; in othe wods, fo
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 informationAP Physics - Coulomb's Law
AP Physics - oulomb's Law We ve leaned that electons have a minus one chage and potons have a positive one chage. This plus and minus one business doesn t wok vey well when we go in and ty to do the old
More informationExperiment 09: Angular momentum
Expeiment 09: Angula momentum Goals Investigate consevation of angula momentum and kinetic enegy in otational collisions. Measue and calculate moments of inetia. Measue and calculate non-consevative wok
More informationAP Physics 1 - Circular Motion and Gravitation Practice Test (Multiple Choice Section) Answer Section
AP Physics 1 - Cicula Motion and Gaitation Pactice est (Multiple Choice Section) Answe Section MULIPLE CHOICE 1. B he centipetal foce must be fiction since, lacking any fiction, the coin would slip off.
More informationRotational Motion. Every quantity that we have studied with translational motion has a rotational counterpart
Rotational Motion & Angula Momentum Rotational Motion Evey quantity that we have studied with tanslational motion has a otational countepat TRANSLATIONAL ROTATIONAL Displacement x Angula Position Velocity
More information20-9 ELECTRIC FIELD LINES 20-9 ELECTRIC POTENTIAL. Answers to the Conceptual Questions. Chapter 20 Electricity 241
Chapte 0 Electicity 41 0-9 ELECTRIC IELD LINES Goals Illustate the concept of electic field lines. Content The electic field can be symbolized by lines of foce thoughout space. The electic field is stonge
More informationGRAVITATION. Thus the magnitude of the gravitational force F that two particles of masses m1
GAVITATION 6.1 Newton s law of Gavitation Newton s law of gavitation states that evey body in this univese attacts evey othe body with a foce, which is diectly popotional to the poduct of thei masses and
More informationLecture 3. Basic Physics of Astrophysics - Force and Energy. Forces.
Tue Wed Thu Thu Lectue 3 Basic Physics of Astophysics - Foce and Enegy ISB 165 Wed 5 Thu 4 http://apod.nasa.gov/apod/ Foces Momentum is the poduct of mass and velocity - a vecto p = mv (geneally m is taken
More informationSIO 229 Gravity and Geomagnetism. Lecture 6. J 2 for Earth. J 2 in the solar system. A first look at the geoid.
SIO 229 Gavity and Geomagnetism Lectue 6. J 2 fo Eath. J 2 in the sola system. A fist look at the geoid. The Thee Big Themes of the Gavity Lectues 1.) An ellipsoidal otating Eath Refeence body (mass +
More informationPHYSICS NOTES GRAVITATION
GRAVITATION Newton s law of gavitation The law states that evey paticle of matte in the univese attacts evey othe paticle with a foce which is diectly popotional to the poduct of thei masses and invesely
More information10. Universal Gravitation
10. Univesal Gavitation Hee it is folks, the end of the echanics section of the couse! This is an appopiate place to complete the study of mechanics, because with his Law of Univesal Gavitation, Newton
More informationForce of gravity and its potential function
F. W. Phs0 E:\Ecel files\ch gavitational foce and potential.doc page of 6 0/0/005 8:9 PM Last pinted 0/0/005 8:9:00 PM Foce of gavit and its potential function (.) Let us calculate the potential function
More informationHW Solutions # MIT - Prof. Please study example 12.5 "from the earth to the moon". 2GmA v esc
HW Solutions # 11-8.01 MIT - Pof. Kowalski Univesal Gavity. 1) 12.23 Escaping Fom Asteoid Please study example 12.5 "fom the eath to the moon". a) The escape velocity deived in the example (fom enegy consevation)
More informationDEVIL PHYSICS THE BADDEST CLASS ON CAMPUS IB PHYSICS
DEVIL PHYSICS THE BADDEST CLASS ON CAMPUS IB PHYSICS LSN 10-: MOTION IN A GRAVITATIONAL FIELD Questions Fom Reading Activity? Gavity Waves? Essential Idea: Simila appoaches can be taken in analyzing electical
More informationPhysics 231 Lecture 21
Physics 3 Lectue Main points o today s lectue: Angula momentum: L Newton s law o univesal gavitation: GMm F PE GMm Keple s laws and the elation between the obital peiod and obital adius. T π GM 4 3 Rolling
More informationFrom Newton to Einstein. Mid-Term Test, 12a.m. Thur. 13 th Nov Duration: 50 minutes. There are 20 marks in Section A and 30 in Section B.
Fom Newton to Einstein Mid-Tem Test, a.m. Thu. 3 th Nov. 008 Duation: 50 minutes. Thee ae 0 maks in Section A and 30 in Section B. Use g = 0 ms in numeical calculations. You ma use the following epessions
More informationPaths of planet Mars in sky
Section 4 Gavity and the Sola System The oldest common-sense view is that the eath is stationay (and flat?) and the stas, sun and planets evolve aound it. This GEOCENTRIC MODEL was poposed explicitly by
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 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 informationRadius of the Moon is 1700 km and the mass is 7.3x 10^22 kg Stone. Moon
xample: A 1-kg stone is thown vetically up fom the suface of the Moon by Supeman. The maximum height fom the suface eached by the stone is the same as the adius of the moon. Assuming no ai esistance and
More informationb) (5) What is the magnitude of the force on the 6.0-kg block due to the contact with the 12.0-kg block?
Geneal Physics I Exam 2 - Chs. 4,5,6 - Foces, Cicula Motion, Enegy Oct. 13, 2010 Name Rec. Inst. Rec. Time Fo full cedit, make you wok clea to the gade. Show fomulas used, essential steps, and esults with
More informationDYNAMICS OF UNIFORM CIRCULAR MOTION
Chapte 5 Dynamics of Unifom Cicula Motion Chapte 5 DYNAMICS OF UNIFOM CICULA MOTION PEVIEW An object which is moing in a cicula path with a constant speed is said to be in unifom cicula motion. Fo an object
More informationCircular-Rotational Motion Mock Exam. Instructions: (92 points) Answer the following questions. SHOW ALL OF YOUR WORK.
AP Physics C Sping, 2017 Cicula-Rotational Motion Mock Exam Name: Answe Key M. Leonad Instuctions: (92 points) Answe the following questions. SHOW ALL OF YOUR WORK. ( ) 1. A stuntman dives a motocycle
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 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 informationSpring 2001 Physics 2048 Test 3 solutions
Sping 001 Physics 048 Test 3 solutions Poblem 1. (Shot Answe: 15 points) a. 1 b. 3 c. 4* d. 9 e. 8 f. 9 *emembe that since KE = ½ mv, KE must be positive Poblem (Estimation Poblem: 15 points) Use momentum-impulse
More informationGaia s Place in Space
Gaia s Place in Space The impotance of obital positions fo satellites Obits and Lagange Points Satellites can be launched into a numbe of diffeent obits depending on thei objectives and what they ae obseving.
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 informationWhen a mass moves because of a force, we can define several types of problem.
Mechanics Lectue 4 3D Foces, gadient opeato, momentum 3D Foces When a mass moves because of a foce, we can define seveal types of poblem. ) When we know the foce F as a function of time t, F=F(t). ) When
More informationF g. = G mm. m 1. = 7.0 kg m 2. = 5.5 kg r = 0.60 m G = N m 2 kg 2 = = N
Chapte answes Heinemann Physics 4e Section. Woked example: Ty youself.. GRAVITATIONAL ATTRACTION BETWEEN SMALL OBJECTS Two bowling balls ae sitting next to each othe on a shelf so that the centes of the
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 informationLecture 1a: Satellite Orbits
Lectue 1a: Satellite Obits Outline 1. Newton s Laws of Motion 2. Newton s Law of Univesal Gavitation 3. Calculating satellite obital paametes (assuming cicula motion) Scala & Vectos Scala: a physical quantity
More informationPotential Energy and Conservation of Energy
Potential Enegy and Consevation of Enegy Consevative Foces Definition: Consevative Foce If the wok done by a foce in moving an object fom an initial point to a final point is independent of the path (A
More informationKEPLER S LAWS OF PLANETARY MOTION
EPER S AWS OF PANETARY MOTION 1. Intoduction We ae now in a position to apply what we have leaned about the coss poduct and vecto valued functions to deive eple s aws of planetay motion. These laws wee
More information1. A stone falls from a platform 18 m high. When will it hit the ground? (a) 1.74 s (b) 1.83 s (c) 1.92 s (d) 2.01 s
1. A stone falls fom a platfom 18 m high. When will it hit the gound? (a) 1.74 s (b) 1.83 s (c) 1.9 s (d).01 s Constant acceleation D = v 0 t + ½ a t. Which, if any, of these foces causes the otation of
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 informationPhysics 111. Ch 12: Gravity. Newton s Universal Gravity. R - hat. the equation. = Gm 1 m 2. F g 2 1. ˆr 2 1. Gravity G =
ics Announcements day, embe 9, 004 Ch 1: Gavity Univesal Law Potential Enegy Keple s Laws Ch 15: Fluids density hydostatic equilibium Pascal s Pinciple This week s lab will be anothe physics wokshop -
More informationSection 26 The Laws of Rotational Motion
Physics 24A Class Notes Section 26 The Laws of otational Motion What do objects do and why do they do it? They otate and we have established the quantities needed to descibe this motion. We now need to
More informationMidterm Exam #2, Part A
Physics 151 Mach 17, 2006 Midtem Exam #2, Pat A Roste No.: Scoe: Exam time limit: 50 minutes. You may use calculatos and both sides of ONE sheet of notes, handwitten only. Closed book; no collaboation.
More informationPractice. Understanding Concepts. Answers J 2. (a) J (b) 2% m/s. Gravitation and Celestial Mechanics 287
Pactice Undestanding Concepts 1. Detemine the gavitational potential enegy of the Eath Moon system, given that the aveage distance between thei centes is 3.84 10 5 km, and the mass of the Moon is 0.0123
More informationUniform Circular Motion
Unifom Cicula Motion Intoduction Ealie we defined acceleation as being the change in velocity with time: a = v t Until now we have only talked about changes in the magnitude of the acceleation: the speeding
More information1) Consider a particle moving with constant speed that experiences no net force. What path must this particle be taking?
Chapte 5 Test Cicula Motion and Gavitation 1) Conside a paticle moving with constant speed that expeiences no net foce. What path must this paticle be taking? A) It is moving in a paabola. B) It is moving
More informationChapter. s r. check whether your calculator is in all other parts of the body. When a rigid body rotates through a given angle, all
conveted to adians. Also, be sue to vanced to a new position (Fig. 7.2b). In this inteval, the line OP has moved check whethe you calculato is in all othe pats of the body. When a igid body otates though
More informationBasic oces an Keple s Laws 1. Two ientical sphees of gol ae in contact with each othe. The gavitational foce of attaction between them is Diectly popotional to the squae of thei aius ) Diectly popotional
More informationCentral Force Problem. Central Force Motion. Two Body Problem: Center of Mass Coordinates. Reduction of Two Body Problem 8.01 W14D1. + m 2. m 2.
Cental oce Poblem ind the motion of two bodies inteacting via a cental foce. Cental oce Motion 8.01 W14D1 Examples: Gavitational foce (Keple poblem): 1 1, ( ) G mm Linea estoing foce: ( ) k 1, Two Body
More informationUniversity Physics Volume I Unit 1: Mechanics Chapter 13: Gravitation Conceptual Questions
OpenStax Univesity Physics Volume I Univesity Physics Volume I Conceptual Questions 1. Action at a distance, such as is the case fo gavity, was once thought to be illogical and theefoe untue. What is the
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 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 informationb) (5) What average force magnitude was applied by the students working together?
Geneal Physics I Exam 3 - Chs. 7,8,9 - Momentum, Rotation, Equilibium Nov. 3, 2010 Name Rec. Inst. Rec. Time Fo full cedit, make you wok clea to the gade. Show fomulas used, essential steps, and esults
More informationLecture 22. PE = GMm r TE = GMm 2a. T 2 = 4π 2 GM. Main points of today s lecture: Gravitational potential energy: Total energy of orbit:
Lectue Main points of today s lectue: Gavitational potential enegy: Total enegy of obit: PE = GMm TE = GMm a Keple s laws and the elation between the obital peiod and obital adius. T = 4π GM a3 Midtem
More informationPhysics C Rotational Motion Name: ANSWER KEY_ AP Review Packet
Linea and angula analogs Linea Rotation x position x displacement v velocity a T tangential acceleation Vectos in otational motion Use the ight hand ule to detemine diection of the vecto! Don t foget centipetal
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 informationPS113 Chapter 5 Dynamics of Uniform Circular Motion
PS113 Chapte 5 Dynamics of Unifom Cicula Motion 1 Unifom cicula motion Unifom cicula motion is the motion of an object taveling at a constant (unifom) speed on a cicula path. The peiod T is the time equied
More informationOrbits. Newton suggested that an object could be put into orbit if it were launched from a high hill at a high speed
Satellites & Obits Obits Newton suggested that an object could be put into obit if it wee launched fom a high hill at a high speed If the launch speed was high enough, the object would fall aound Eath
More informationPhysics 1114: Unit 5 Hand-out Homework (Answers)
Physics 1114: Unit 5 Hand-out Homewok (Answes) Poblem set 1 1. The flywheel on an expeimental bus is otating at 420 RPM (evolutions pe minute). To find (a) the angula velocity in ad/s (adians/second),
More information15 B1 1. Figure 1. At what speed would the car have to travel for resonant oscillations to occur? Comment on your answer.
Kiangsu-Chekiang College (Shatin) F:EasteHolidaysAssignmentAns.doc Easte Holidays Assignment Answe Fom 6B Subject: Physics. (a) State the conditions fo a body to undego simple hamonic motion. ( mak) (a)
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 informationRevision Guide for Chapter 11
Revision Guide fo Chapte 11 Contents Revision Checklist Revision Notes Momentum... 4 Newton's laws of motion... 4 Wok... 5 Gavitational field... 5 Potential enegy... 7 Kinetic enegy... 8 Pojectile... 9
More informationTo Feel a Force Chapter 7 Static equilibrium - torque and friction
To eel a oce Chapte 7 Chapte 7: Static fiction, toque and static equilibium A. Review of foce vectos Between the eath and a small mass, gavitational foces of equal magnitude and opposite diection act on
More information- 5 - TEST 1R. This is the repeat version of TEST 1, which was held during Session.
- 5 - TEST 1R This is the epeat vesion of TEST 1, which was held duing Session. This epeat test should be attempted by those students who missed Test 1, o who wish to impove thei mak in Test 1. IF YOU
More informationKepler's 1 st Law by Newton
Astonom 10 Section 1 MWF 1500-1550 134 Astonom Building This Class (Lectue 7): Gavitation Net Class: Theo of Planeta Motion HW # Due Fida! Missed nd planetaium date. (onl 5 left), including tonight Stadial
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 informationGraphs of Sine and Cosine Functions
Gaphs of Sine and Cosine Functions In pevious sections, we defined the tigonometic o cicula functions in tems of the movement of a point aound the cicumfeence of a unit cicle, o the angle fomed by the
More informationChapter 5. Uniform Circular Motion. a c =v 2 /r
Chapte 5 Unifom Cicula Motion a c =v 2 / Unifom cicula motion: Motion in a cicula path with constant speed s v 1) Speed and peiod Peiod, T: time fo one evolution Speed is elated to peiod: Path fo one evolution:
More informationChapter 5: Uniform Circular Motion
Chapte 5: Unifom Cicula Motion Motion at constant speed in a cicle Centipetal acceleation Banked cuves Obital motion Weightlessness, atificial gavity Vetical cicula motion Centipetal Foce Acceleation towad
More informationGravitational Potential Energy in General
Gavitational Potential Enegy in Geneal 6.3 To exploe such concepts as how much enegy a space pobe needs to escape fom Eath s gavity, we must expand on the topic of gavitational potential enegy, which we
More information1 Dark Cloud Hanging over Twentieth Century Physics
We ae Looking fo Moden Newton by Caol He, Bo He, and Jin He http://www.galaxyanatomy.com/ Wuhan FutueSpace Scientific Copoation Limited, Wuhan, Hubei 430074, China E-mail: mathnob@yahoo.com Abstact Newton
More informationGravity Notes for PHYS Joe Wolfe, UNSW
Gavity Notes fo PHYS 111-1131. Joe Wolfe, UNSW 1 Gavity: whee does it fit in? Gavity [geneal elativity] Electic foce* gavitons photons Weak nuclea foce intemediate vecto bosons Stong nuclea foce Colou
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 informationr cos, and y r sin with the origin of coordinate system located at
Lectue 3-3 Kinematics of Rotation Duing ou peious lectues we hae consideed diffeent examples of motion in one and seeal dimensions. But in each case the moing object was consideed as a paticle-like object,
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 information