Chapter 13 Newton s s Universal Law of Gravity
|
|
- Justin Waters
- 6 years ago
- Views:
Transcription
1 Chapter 13 Newton s s Universal Law of Gravity F mm 1 rˆ 1 1 = G r G = 6.67x10 11 Nm kg
2
3 Sun at Center Orbits are Circular
4 Tycho Brahe Tycho was the greatest observational astronomer of his time. Tycho did not believe in the Copernican model because of the lack of observational parallax. He didn t believe that the Earth Moved.
5 The Rejection of the Copernican Heliocentric Model
6 Tycho Brahe Kepler worked for Tycho as his mathematician. Kepler derived his laws of planetary motion from Tycho s observational data. Kepler s Laws are thus empirical - based on observation and not Theory.
7 Kepler s 3 Laws of Planetary Motion 1: The orbit of each planet about the sun is an ellipse with the sun at one focus.. Each planet moves so that it sweeps out equal areas in equal times. 3. The square of the orbital period of any planet is proportional to the cube of the semimajor axis of the elliptical orbit. T r = constant
8 Planet Orbits are Elliptical
9 "The next question was - what makes planets go around the sun? At the time of Kepler some people answered this problem by saying that there were angels behind them beating their wings and pushing the planets around an orbit. As you will see, the answer is not very far from the truth. The only difference is that the angels sit in a different direction and their wings push inward." -Richard Feynman
10 Man of the Millennium Sir Issac Newton ( )
11 Gravitational Force is Universal The same force that makes the apple fall to Earth, causes the moon to fall around the Earth.
12 Universal Law of Gravity 1687 Every particle in the Universe attracts every other particle with a force along a line joining them. The force is directly proportional to the product to their masses and inversely proportional to the square of the distance between them. d M m F ~ mm d
13 How Does Newton s Universal Law of Gravity (ULG) Explain Kepler s Laws of Planetary Motion? Kepler s First Law (Orbits are ellipses) - Express F = ma as a second order differential equation in polar coordinates, substitute in F as an inverse square law and the radial solutions are ellipses! (See Wikipedia.com for a simple and elegant solution!) Kepler s Second Law (Equal Areas in Equal Time) - Conservation of Angular Momentum leads to it (See Book): da L = = constant dt M p Kepler s Third Law (T ~ r 3 ) Direct substitution into ULG of the centripetal acceleration (see book): T 4π = r GM Sun 3
14 G = F Measuring G: Cavendish 1798 ~ mm 6.67x10 d 11 Nm kg F = GmM d G is the same everywhere in the Universe. G s small size is a measure of relative strength of gravity. By comparison, the proportionality constant for the electric force is k~10 9!!
15 Universal Law of Gravity F mm 1 rˆ 1 1 = G r (Minus because of the direction of the unit vector. Attractive Central Forces are negative!) G = 6.67x10 11 Nm kg
16 Gravity: Inverse Square Law F = GmM d
17 Gravitational Force INSIDE the Earth How would the force of gravity and the acceleration due to gravity change as you fell through a hole in the Earth? What would your motion be? Assume you jump from rest. Ignore Air Resistance.
18 Gravitational Force INSIDE the Earth Inside the Earth the Gravitational Force is Linear. Acceleration decreases as you fall to the center (where your speed is the greatest) and then the acceleration increases but in the opposite direction, slowing you down to a stop at the other end but then you would fall back in again, bouncing back and forth forever!
19 Earth-Moon Gravity Calculate the magnitude of the force of gravity between the Earth and the Moon. The distance between the Earth and Moon centers is 3.84x10 8 m F EM = GmM d F EM = ( 11 )( 4 )( 6.673x10 Nm / kg 5.98x10 kg 7.35x10 kg ) ( x10 m) 0 F =.01x10 N EM
20 Earth-Moon Gravity Calculate the acceleration of the Earth due to the Earth-Moon gravitational interaction. a E = F m EM E =.01x x N kg a = 3.33x10 m/ s E 5
21 Earth-Moon Gravity Calculate the acceleration of the Moon due to the Earth-Moon gravitational interaction. a M = F m EM M =.01x x10 0 N kg a =.73x10 m/ s M 3
22 Earth-Moon Gravity The acceleration of gravity at the Moon due to the Earth is: a =.73x10 m/ s M 3 The acceleration of gravity at the Earth due to the moon is: a = 3.33x10 m/ s E 5 Why the difference? FORCE is the same. Acceleration is NOT!!! BECAUSE MASSES ARE DIFFERENT!
23 Force is not Acceleration! F Earth on Moon = F Moon on Earth The forces are equal but the accelerations are not!
24 Finding little g Calculate the acceleration of gravity acting on you at the surface of the Earth. What is g? F Source of the Force This is your WEIGHT! Gm M F = m a you E = you RE Gm you E R M E = m you a Response to the Force a = GM R E E Independent of your mass! This is why a rock and feather fall with the same acceleration!
25 Finding little g Calculate the acceleration of gravity acting on you at the surface of the Earth. What is g? F Source of the Force Gm M you E = you RE a = GM R E E F = m a Reaction to the Force a = ( 11 )( x10 Nm / kg 5.98x10 kg ) ( x10 m) a = 9.81 m/ s = g!
26 In general, g for any Planet: g planet = GM R planet planet g field The gravitational field describes the effect that any object has on the empty space around itself in terms of the force that would be present if a second object were somewhere in that space F GM g = g = rˆ m r
27 Electric Field Two flavors of charge (+/-)
28 Problem 13.1 Find the magnitude of the Gravitational Field at O. Since the masses are static, just add the F F 3 fields due to each mass at O in a vector superposition.. Σ Σ = F m = Fiˆ+ F ˆj + ( F iˆ+ F ˆj ) g g 1 3x 3 Gm ˆ Gm ˆ Gm g = i+ j+ ˆi+ ˆj l l l ( cos 45.0 sin 45.0 ) F 1 GM 1 g = 1 ( ˆ ˆ) + i+ j Toward the F3. l
29
30 Curvature of Earth Curvature of the Earth: Every 8000 m, the Earth curves by 5 meters! If you threw the ball at 8000 m/s off the surface of the Earth (and there were no buildings or mountains in the way) how far would it travel in the vertical direction in 1 second? 1 Δ y = gt ~5 m/ s (1 s ) = 5m The ball will achieve orbit.
31 Orbital Velocity If you can throw a ball at 8000m/s, the Earth curves away from it so that the ball continually falls in free fall around the Earth it is in orbit around the Earth! Ignoring air resistance. Above the atmosphere
32 Projectile Motion/Orbital Motion Projectile Motion is Orbital motion that hits the Earth!
33 Orbital Motion & Escape Velocity 8km/s: Circular orbit Between 8 & 11. km/s: Elliptical orbit 11. km/s: Escape Earth 4.5 km/s: Escape Solar System!
34 Circular Orbits As the ball falls around the Earth in a circular orbit, does the acceleration due to gravity change its orbital speed? It only changes its direction! Ignoring air resistance. Above the atmosphere
35 Circular Orbital Velocity The force of gravity is perpendicular to the velocity of the ball so it doesn t speed it up it changes only the direction of the ball. Gravity provides a centripetal acceleration the keeps it in a circle! The PE and KE are the same throughout the orbit. Since F is parallel to r, angular momentum is also conserved. v
36 Elliptical Orbits As the satellite falls around the Earth in an elliptical orbit, does the acceleration due to gravity change its orbital speed? There is a component of force (and acceleration) in the direction of motion! Gravity changes the satellite s speed when in elliptical orbits. Mechanical Energy is conserved but KE and PE change throughout the orbit. Is angular momentum conserved? Why? Where is the speed greatest- A or B? B A
37 Orbits Circular Orbit Elliptical Orbit
38 Circular Orbit Speed With Increasing Altitude
39 g and v Above the Earth s Surface If an object is some distance h above the Earth s surface, r becomes R E + h g F = = GMm r GM E ( R + h) E The tangential speed of an object is its orbital speed and is given by the centripetal acceleration, g: E v v R + h r = = g GM E ( R + h) E Orbital speed decreases with increasing altitude! v = GM E ( R + h) E
40 Orbit Question Find the orbital speed of a satellite 00 km above the Earth. 4 6 Assume a circular orbit. M = 5.97x10 kg, R = 6.38x10 m F F mm G r F = m a s E = s mm G r s E = = m s v r E v = a = E E v r M EG R + h What is this? v = 4 11 (5.97x10 kg)(6.67x10 Nm / kg ) x10 m 3 v= 7.78x10 m/ s Notice that this is less 8km/s!
41 Τ= Orbit Question What is the period of a satellite orbiting 00 km above the Earth? 4 6 Assume a circular orbit. v π r = Τ = π r v 6 π (6.58x10 m) x10 m/ s Τ= 5314s = 88min M = 5.97x10 kg, R = 6.38x10 m E F E If you don t know the velocity: GMm = = r v m r ( π r / Τ) = m r 4π 3 Τ = GM r Kepler s 3 rd! Period increases with r!
42 Orbital Sum. with increasing altitude: g, acceleration decreases g = GM E r v, orbital speed decreases v = M EG r T, orbital period increases 4π 3 Τ = GM r
43 Satellite Orbits
44 Global Geostationary Satellite Coverage USA USA Euro Japan USSR China
45 Sun-Synchronous Near Polar Orbits With an orbital period of about 100 minutes, these satellites will complete slightly more than 14 orbits in a single day.
46
47 Grav. Potential Energy Work Since the Force is Conservative, the Work is independent of path. The work done by F along any radial segment is The work done by a force that is perpendicular to the displacement is 0 The total work is dw = F dr = F() r dr W = Recall that the work done by a conservative force on an object is: r r i f F() r dr W = Δ PE =ΔKE (As a rock falls, it loses PE but gains KE!!!)
48 Gravitational Potential Energy As a particle moves from A to B, its gravitational potential energy changes by f Δ U = U f Ui = W = F() r dr Choose the zero for the gravitational potential energy where the force is zero: U i = 0 where r i = GM Em Ur () = r r r i This is valid only for r R E and not valid for r < R E U is negative because of the choice of U i
49 Gravitational Potential Energy for the Earth Graph of the gravitational potential energy U versus r for an object above the Earth s surface The potential energy goes to zero as r approaches infinity. The potential energy is negative because the force is attractive and we chose the potential energy to be zero at infinite separation An external agent must do positive work to increase the separation between two objects The work done by the external agent produces an increase in the gravitational potential energy as the particles are separated U becomes less negative The absolute value of the potential energy can be thought of as the binding energy If an external agent applies a force larger than the binding energy, the excess energy will be in the form of kinetic energy of the particles when they are at infinite separation GM Em Ur () = r
50 Launch Problem How much energy is required to move a kg object from the Earth's surface to an altitude twice the Earth's radius? Mm U = G r 1 1 GMm Δ U = U f Ui = GMm = 3 R E R E 3 R E ( -11 ) ( 4 kg ) ( m) 6.67x10 Nm / kg (1000 ) kg 10 Δ U = = J
51 Problem 13.6 At the Earth's surface a projectile is launched straight up at a speed of 10.0 km/s. To what height will it rise? Ignore air resistance and the rotation of the Earth. The height attained is not small compared to the radius of the Earth, so U = mgh does not apply. Use: U = -GmM/r : K + U = K + U i i f f 1 p i M v GM M GM M = 0 R R + h E p E p E E 7 h =.5 10 m
52 Energy and Satellite Motion Circular Orbit Total energy E = K +U: 1 Mm E = mv G r Rewrite the Kinetic Energy: GMm F = = r Rewrite the Energy: GMm GMm E = r r v m r 1 GMm mv = r GMm E = r KE = ½ U In a bound system, E <0
53 i input f ri Orbit Question What minimum energy does it take to put a 00 kg satellite in orbit 00 km above the Earth? Assume a circular orbit. E i = E 1 GmM 1 GmM mv + E = mv r E 1 m v v GMm 1 1 = + R R h input ( f i ) ( ) E ( E + ) Substituting in the values: f f M = 5.98x10 kg, R = 6.38x10 m E v i 4 6 E v= x m s Τ= E = J input (from last time) /, 88min The minimum initial speed is just the rotational speed of the Earth: π RE = = m s s 9
54 Escape Speed from Earth An object of mass m is projected upward from the Earth s surface with an initial speed, v i.use energy considerations to find the minimum value of the initial speed needed to allow the object to move infinitely far away from the Earth: 1 GM m 1 GM Em mv = r E i mv f RE f 0 v esc = GM E R E r = v 11 4 (6.67x10 Nm / kg )(5.98x10 kg) = = 6.37x10 m esc km s
55 Solar System Escape Speeds In General: v esc = GM R Complete escape from an object is not really possible. The gravitational field is infinite and so some gravitational force will always be felt no matter how far away you can get.
56 Systems with Three or More Particles The total gravitational potential energy of the system is the sum over all pairs of particles Particles STATIC Gravitational potential energy obeys the superposition principle The absolute value of U total represents the work needed to separate the particles by an infinite distance Mm U = G r U = U + U + U total mm mm mm = G + + r 1 r 13 r
57 The 3-Body Problem Newton s Law of Gravity can solve orbits for two-body systems such as the Earth and Sun, resulting in elliptical orbits orbiting the CM of the system. The three-body problem (where more than one body is moving) is much more complicated and, in general, cannot be solved analytically. The orbits that result are chaotic. In fact, chaos theory evolved from attempts to solve the 3-Body Problem.
58
59 Lagrange Points Lagrange points are locations in space where gravitational forces and the orbital motion of a body balance each other. They were discovered by French mathematician Louis Lagrange in 177 in his gravitational studies of the 3-body problem: how a third, small body would orbit around two orbiting large ones. The L1 point of the Earth-Sun system affords an uninterrupted view of the sun and is currently home to the Solar and Heliospheric Observatory Satellite (SOHO). The L point of the Earth-Sun system is home to the Microwave Anisotropy Probe (MAP). The L1 and L points are unstable on a time scale of approximately 3 days, which requires satellites parked at these positions to undergo regular course and attitude corrections. The L4 and L5 points are stable and would be ideal locations for space habitats or solar power stations.
60 Interplanetary Super Highway Gravitational Potential Contour Map
61 L-5 Society
62
63 Orbiting Space Trash Man-made debris orbits at a speed of roughly 17,500 miles/hour (8,000 km/h)! More than 4,000 satellites have been launched into space since All that activity has led to large amounts of space trash. More than 13,000 objects that are at least three to four inches (seven to ten centimeters) wide. Of those objects, only 600 to 700 are still in use. 95 percent of everything up there that the United States is tracking is trash. There are millions of smaller parts that are too small to track.
64
65 Orbiting Space Trash Fast Trash Go Boom Australia, in 1979.
66
67 Orbiting Space Trash What Goes Up Must Come Down This is the main propellant tank of the second stage of a Delta launch vehicle which landed near Georgetown, TX, on January This approximately 50 kg tank is primarily a stainless steel structure and survived reentry relatively intact. Skylab crashed onto Australia in 1979.
68
69 Nuclear Power in Space
70
71
72
73 Our Spaceship Earth One island in one ocean...from space...we re all astronauts aboard a little spaceship called Earth - Bucky Fuller
74 Albert Einstein 1916 The Field Equation:
75
76
77
78 Mass WARPS Space-time
79 Mass grips space by telling it how to curve and space grips mass by telling it how to move! - John Wheeler
80 Precession of the Perihelion of Mercury
81 Gravity Probe B Gravitational Frame Dragging Space-Time Twist
82 Black Holes & Worm Holes
83 LISA Gravity Waves
84 Newton s 3 rd Law: Rocket Thrust p initial = p final = Mv mv 0 rocket gas p rocket = Mv rocket Mv rocket = mv gas Δ p =Δp rocket gas p gas = mv gas Rocket Pushes Gas Out. Gas Pushes Back on Rocket.
85 Rocket Propulsion The initial mass of the rocket plus all its fuel is M + Δm at time t i and velocity v The initial momentum of the system is p i = (M + Δm) v Final velocity given by Propulsion equation: M i vf vi = veln M f The force exerted on the rocket by the exhaust is given by the Thrust Equation: dv Thrust : M = v e dt dm dt
86 The first stage of a Saturn V space vehicle consumed fuel and oxidizer at the rate of kg/s, with an exhaust speed of m/s. Calculate the thrust produced by these engines. dv Thrust : M = v e dt dm dt
87 Rocket Problem A rocket for use in deep space is to be capable of boosting a total load (payload plus rocket frame and engine) of 3.00 metric tons to a speed of m/s. It has an engine and fuel designed to produce an exhaust speed of 000 m/s. How much fuel plus oxidizer is required? M i vf vi = veln M f M i v = ve ln M f i vv e M = e M f M i ( ) = e kg = kg ( ) 3 Δ M = M M = kg = 44 metric tons i f
88
"The next question was - what makes planets go around the sun? At the time of Kepler some people answered this problem by saying that there were
"The next question was - what makes planets go around the sun? At the time of Kepler some people answered this problem by saying that there were angels behind them beating their wings and pushing the planets
More informationChapter 13 Newton s Universal Law of Gravity
Chapter 13 Newton s Universal Law of Gravity F mm 1 rˆ 1 1 G r G 6.67x10 11 Nm kg Sun at Center Orbits are Circular Tycho Brahe 1546-1601 Tycho was the greatest observational astronomer of his time. Tycho
More informationUniversal Gravitation
Universal Gravitation Newton s Law of Universal Gravitation Every particle in the Universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely
More informationChapter 13. Universal Gravitation
Chapter 13 Universal Gravitation Planetary Motion A large amount of data had been collected by 1687. There was no clear understanding of the forces related to these motions. Isaac Newton provided the answer.
More informationPHYS 101 Previous Exam Problems. Gravitation
PHYS 101 Previous Exam Problems CHAPTER 13 Gravitation Newton s law of gravitation Shell theorem Variation of g Potential energy & work Escape speed Conservation of energy Kepler s laws - planets Orbits
More informationPhysics 12. Unit 5 Circular Motion and Gravitation Part 2
Physics 12 Unit 5 Circular Motion and Gravitation Part 2 1. Newton s law of gravitation We have seen in Physics 11 that the force acting on an object due to gravity is given by a well known formula: F
More informationChapter 13. Gravitation
Chapter 13 Gravitation 13.2 Newton s Law of Gravitation Here m 1 and m 2 are the masses of the particles, r is the distance between them, and G is the gravitational constant. G =6.67 x10 11 Nm 2 /kg 2
More informationChapter 13. Gravitation
Chapter 13 Gravitation e = c/a A note about eccentricity For a circle c = 0 à e = 0 a Orbit Examples Mercury has the highest eccentricity of any planet (a) e Mercury = 0.21 Halley s comet has an orbit
More information14.1 Earth Satellites. The path of an Earth satellite follows the curvature of the Earth.
The path of an Earth satellite follows the curvature of the Earth. A stone thrown fast enough to go a horizontal distance of 8 kilometers during the time (1 second) it takes to fall 5 meters, will orbit
More informationProjectile Motion. Conceptual Physics 11 th Edition. Projectile Motion. Projectile Motion. Projectile Motion. This lecture will help you understand:
Conceptual Physics 11 th Edition Projectile motion is a combination of a horizontal component, and Chapter 10: PROJECTILE AND SATELLITE MOTION a vertical component. This lecture will help you understand:
More informationConceptual Physics 11 th Edition
Conceptual Physics 11 th Edition Chapter 10: PROJECTILE AND SATELLITE MOTION This lecture will help you understand: Projectile Motion Fast-Moving Projectiles Satellites Circular Satellite Orbits Elliptical
More informationAP Physics Multiple Choice Practice Gravitation
AP Physics Multiple Choice Practice Gravitation 1. Each of five satellites makes a circular orbit about an object that is much more massive than any of the satellites. The mass and orbital radius of each
More informationGravitation & Kepler s Laws
Gravitation & Kepler s Laws What causes YOU to be pulled down to the surface of the earth? THE EARTH.or more specifically the EARTH S MASS. Anything that has MASS has a gravitational pull towards it. F
More informationPHYSICS 231 INTRODUCTORY PHYSICS I
PHYSICS 231 INTRODUCTORY PHYSICS I Lecture 11 Last Lecture Angular velocity, acceleration " = #$ #t = $ f %$ i t f % t i! = " f # " i t!" #!x $ 0 # v 0 Rotational/ Linear analogy "s = r"# v t = r" $ f
More informationWelcome back to Physics 215
Welcome back to Physics 215 Today s agenda: More rolling without slipping Newtonian gravity Planetary orbits Gravitational Potential Energy Physics 215 Spring 2018 Lecture 13-1 1 Rolling without slipping
More informationChapter 13: universal gravitation
Chapter 13: universal gravitation Newton s Law of Gravitation Weight Gravitational Potential Energy The Motion of Satellites Kepler s Laws and the Motion of Planets Spherical Mass Distributions Apparent
More informationConceptual Physics Fundamentals
Conceptual Physics Fundamentals Chapter 6: GRAVITY, PROJECTILES, AND SATELLITES This lecture will help you understand: The Universal Law of Gravity The Universal Gravitational Constant, G Gravity and Distance:
More informationPHYSICS. Chapter 13 Lecture FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E RANDALL D. KNIGHT Pearson Education, Inc.
PHYSICS FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E Chapter 13 Lecture RANDALL D. KNIGHT Chapter 13 Newton s Theory of Gravity IN THIS CHAPTER, you will learn to understand the motion of satellites
More informationA SIMULATION OF THE MOTION OF AN EARTH BOUND SATELLITE
DOING PHYSICS WITH MATLAB A SIMULATION OF THE MOTION OF AN EARTH BOUND SATELLITE Download Directory: Matlab mscripts mec_satellite_gui.m The [2D] motion of a satellite around the Earth is computed from
More informationGravity. Newton s Law of Gravitation Kepler s Laws of Planetary Motion Gravitational Fields
Gravity Newton s Law of Gravitation Kepler s Laws of Planetary Motion Gravitational Fields Simulation Synchronous Rotation https://www.youtube.com/watch?v=ozib_l eg75q Sun-Earth-Moon System https://vimeo.com/16015937
More informationWelcome back to Physics 211. Physics 211 Spring 2014 Lecture Gravity
Welcome back to Physics 211 Today s agenda: Newtonian gravity Planetary orbits Gravitational Potential Energy Physics 211 Spring 2014 Lecture 14-1 1 Gravity Before 1687, large amount of data collected
More informationOutline for Today: Newton s Law of Universal Gravitation The Gravitational Field Orbital Motion Gravitational Potential Energy. Hello!
PHY131H1F - Class 13 Outline for Today: Newton s Law of Universal Gravitation The Gravitational Field Orbital Motion Gravitational Potential Energy Under the Flower of Kent apple tree in the Woolsthorpe
More informationChapter 4 Making Sense of the Universe: Understanding Motion, Energy, and Gravity. Copyright 2009 Pearson Education, Inc.
Chapter 4 Making Sense of the Universe: Understanding Motion, Energy, and Gravity How do we describe motion? Precise definitions to describe motion: Speed: Rate at which object moves speed = distance time
More informationGravitation. Luis Anchordoqui
Gravitation Kepler's law and Newton's Synthesis The nighttime sky with its myriad stars and shinning planets has always fascinated people on Earth. Towards the end of the XVI century the astronomer Tycho
More informationBasic Physics. What We Covered Last Class. Remaining Topics. Center of Gravity and Mass. Sun Earth System. PHYS 1411 Introduction to Astronomy
PHYS 1411 Introduction to Astronomy Basic Physics Chapter 5 What We Covered Last Class Recap of Newton s Laws Mass and Weight Work, Energy and Conservation of Energy Rotation, Angular velocity and acceleration
More informationOutline for Today: Newton s Law of Universal Gravitation The Gravitational Field Orbital Motion Gravitational Potential Energy
PHY131H1F - Class 13 Outline for Today: Newton s Law of Universal Gravitation The Gravitational Field Orbital Motion Gravitational Potential Energy Under the Flower of Kent apple tree in the Woolsthorpe
More informationPHYSICS CLASS XI CHAPTER 8 GRAVITATION
PHYSICS CLASS XI CHAPTER 8 GRAVITATION Q.1. Can we determine the mass of a satellite by measuring its time period? Ans. No, we cannot determine the mass of a satellite by measuring its time period. Q.2.
More informationWelcome back to Physics 215
Welcome back to Physics 215 Today s agenda: Gravity 15-2 1 Current assignments HW#15 due Monday, 12/12 Final Exam, Thursday, Dec. 15 th, 3-5pm in 104N. Two sheets of handwritten notes and a calculator
More informationChapter 14 Satellite Motion
1 Academic Physics Mechanics Chapter 14 Satellite Motion The Mechanical Universe Kepler's Three Laws (Episode 21) The Kepler Problem (Episode 22) Energy and Eccentricity (Episode 23) Navigating in Space
More informationPHYSICS 12 NAME: Gravitation
NAME: Gravitation 1. The gravitational force of attraction between the Sun and an asteroid travelling in an orbit of radius 4.14x10 11 m is 4.62 x 10 17 N. What is the mass of the asteroid? 2. A certain
More informationHW Chapter 5 Q 7,8,18,21 P 4,6,8. Chapter 5. The Law of Universal Gravitation Gravity
HW Chapter 5 Q 7,8,18,21 P 4,6,8 Chapter 5 The Law of Universal Gravitation Gravity Newton s Law of Universal Gravitation Every particle in the Universe attracts every other particle with a force that
More informationWeightlessness and satellites in orbit. Orbital energies
Weightlessness and satellites in orbit Orbital energies Review PE = - GMm R v escape = 2GM E R = 2gR E Keppler s law: R3 = GM s T 2 4π 2 Orbital Motion Orbital velocity escape velocity In orbital motion
More informationGravitational Potential Energy. The Gravitational Field. Grav. Potential Energy Work. Grav. Potential Energy Work
The Gravitational Field Exists at every point in space The gravitational force experienced by a test particle placed at that point divided by the mass of the test particle magnitude of the freefall acceleration
More informationDownloaded from
Chapter 8 (Gravitation) Multiple Choice Questions Single Correct Answer Type Q1. The earth is an approximate sphere. If the interior contained matter which is not of the same density everywhere, then on
More informationAP Physics-B Universal Gravitation Introduction: Kepler s Laws of Planetary Motion: Newton s Law of Universal Gravitation: Performance Objectives:
AP Physics-B Universal Gravitation Introduction: Astronomy is the oldest science. Practical needs and imagination acted together to give astronomy an early importance. For thousands of years, the motions
More informationLecture 16. Gravitation
Lecture 16 Gravitation Today s Topics: The Gravitational Force Satellites in Circular Orbits Apparent Weightlessness lliptical Orbits and angular momentum Kepler s Laws of Orbital Motion Gravitational
More informationINTRODUCTION: Ptolemy geo-centric theory Nicolas Copernicus Helio-centric theory TychoBrahe Johannes Kepler
INTRODUCTION: Ptolemy in second century gave geo-centric theory of planetary motion in which the Earth is considered stationary at the centre of the universe and all the stars and the planets including
More information5. Universal Laws of Motion
5. Universal Laws of Motion If I have seen farther than others, it is because I have stood on the shoulders of giants. Sir Isaac Newton (164 177) Physicist Image courtesy of NASA/JPL Sir Isaac Newton (164-177)
More informationChapter 9 Lecture. Pearson Physics. Gravity and Circular Motion. Prepared by Chris Chiaverina Pearson Education, Inc.
Chapter 9 Lecture Pearson Physics Gravity and Circular Motion Prepared by Chris Chiaverina Chapter Contents Newton's Law of Universal Gravity Applications of Gravity Circular Motion Planetary Motion and
More informationLecture 9 Chapter 13 Gravitation. Gravitation
Lecture 9 Chapter 13 Gravitation Gravitation UNIVERSAL GRAVITATION For any two masses in the universe: F = Gm 1m 2 r 2 G = a constant evaluated by Henry Cavendish +F -F m 1 m 2 r Two people pass in a hall.
More informationName: Earth 110 Exploration of the Solar System Assignment 1: Celestial Motions and Forces Due on Tuesday, Jan. 19, 2016
Name: Earth 110 Exploration of the Solar System Assignment 1: Celestial Motions and Forces Due on Tuesday, Jan. 19, 2016 Why are celestial motions and forces important? They explain the world around us.
More informationChapter 8 - Gravity Tuesday, March 24 th
Chapter 8 - Gravity Tuesday, March 24 th Newton s law of gravitation Gravitational potential energy Escape velocity Kepler s laws Demonstration, iclicker and example problems We are jumping backwards to
More informationChapter 5 Lecture Notes
Formulas: a C = v 2 /r a = a C + a T F = Gm 1 m 2 /r 2 Chapter 5 Lecture Notes Physics 2414 - Strauss Constants: G = 6.67 10-11 N-m 2 /kg 2. Main Ideas: 1. Uniform circular motion 2. Nonuniform circular
More informationGeneral Physics I. Lecture 7: The Law of Gravity. Prof. WAN, Xin 万歆.
General Physics I Lecture 7: The Law of Gravity Prof. WAN, Xin 万歆 xinwan@zju.edu.cn http://zimp.zju.edu.cn/~xinwan/ Outline Newton's law of universal gravitation Motion of the planets; Kepler's laws Measuring
More informationChapter 7. Preview. Objectives Tangential Speed Centripetal Acceleration Centripetal Force Describing a Rotating System. Section 1 Circular Motion
Section 1 Circular Motion Preview Objectives Tangential Speed Centripetal Acceleration Centripetal Force Describing a Rotating System Section 1 Circular Motion Objectives Solve problems involving centripetal
More informationNewton s Gravitational Law
1 Newton s Gravitational Law Gravity exists because bodies have masses. Newton s Gravitational Law states that the force of attraction between two point masses is directly proportional to the product of
More informationMidterm 3 Thursday April 13th
Welcome back to Physics 215 Today s agenda: rolling friction & review Newtonian gravity Planetary orbits Gravitational Potential Energy Physics 215 Spring 2017 Lecture 13-1 1 Midterm 3 Thursday April 13th
More informationAP Physics C Textbook Problems
AP Physics C Textbook Problems Chapter 13 Pages 412 416 HW-16: 03. A 200-kg object and a 500-kg object are separated by 0.400 m. Find the net gravitational force exerted by these objects on a 50.0-kg object
More informationCircular Motion. Gravitation
Circular Motion Gravitation Circular Motion Uniform circular motion is motion in a circle at constant speed. Centripetal force is the force that keeps an object moving in a circle. Centripetal acceleration,
More informationVISUAL PHYSICS ONLINE
VISUAL PHYSICS ONLINE EXCEL SIMULATION MOTION OF SATELLITES DOWNLOAD the MS EXCEL program PA50satellite.xlsx and view the worksheet Display as shown in the figure below. One of the most important questions
More informationGravitational Fields Review
Gravitational Fields Review 2.1 Exploration of Space Be able to: o describe planetary motion using Kepler s Laws o solve problems using Kepler s Laws o describe Newton s Law of Universal Gravitation o
More informationChapter 10. Projectile and Satellite Motion
Chapter 10 Projectile and Satellite Motion Which of these expresses a vector quantity? a. 10 kg b. 10 kg to the north c. 10 m/s d. 10 m/s to the north Which of these expresses a vector quantity? a. 10
More informationChapter 12 Gravity. Copyright 2010 Pearson Education, Inc.
Chapter 12 Gravity Units of Chapter 12 Newton s Law of Universal Gravitation Gravitational Attraction of Spherical Bodies Kepler s Laws of Orbital Motion Gravitational Potential Energy Energy Conservation
More informationChapter 12 Gravity. Copyright 2010 Pearson Education, Inc.
Chapter 12 Gravity Units of Chapter 12 Newton s Law of Universal Gravitation Gravitational Attraction of Spherical Bodies Kepler s Laws of Orbital Motion Gravitational Potential Energy Energy Conservation
More informationClassical mechanics: conservation laws and gravity
Classical mechanics: conservation laws and gravity The homework that would ordinarily have been due today is now due Thursday at midnight. There will be a normal assignment due next Tuesday You should
More informationGravitation and Newton s Synthesis
Lecture 10 Chapter 6 Physics I 0.4.014 Gravitation and Newton s Synthesis Course website: http://faculty.uml.edu/andriy_danylov/teaching/physicsi Lecture Capture: http://echo360.uml.edu/danylov013/physics1spring.html
More informationGravitation and Newton s Synthesis
Lecture 10 Chapter 6 Physics I 0.4.014 Gravitation and Newton s Synthesis Course website: http://faculty.uml.edu/andriy_danylov/teaching/physicsi Lecture Capture: http://echo360.uml.edu/danylov013/physics1spring.html
More informationSatellite Orbital Maneuvers and Transfers. Dr Ugur GUVEN
Satellite Orbital Maneuvers and Transfers Dr Ugur GUVEN Orbit Maneuvers At some point during the lifetime of most space vehicles or satellites, we must change one or more of the orbital elements. For example,
More informationGravitational Potential Energy and Total Energy *
OpenStax-CNX module: m58347 Gravitational Potential Energy and Total Energy * OpenStax This work is produced by OpenStax-CNX and licensed under the Creative Commons Attribution License 4.0 By the end of
More informationAP Physics QUIZ Gravitation
AP Physics QUIZ Gravitation Name: 1. If F1 is the magnitude of the force exerted by the Earth on a satellite in orbit about the Earth and F2 is the magnitude of the force exerted by the satellite on the
More informationLecture 15 - Orbit Problems
Lecture 15 - Orbit Problems A Puzzle... The ellipse shown below has one focus at the origin and its major axis lies along the x-axis. The ellipse has a semimajor axis of length a and a semi-minor axis
More informationPSI AP Physics C Universal Gravity Multiple Choice Questions
PSI AP Physics C Universal Gravity Multiple Choice Questions 1. Who determined the value of the gravitational constant (G)? (A) Newton (B) Galileo (C) Einstein (D) Schrödinger (E) Cavendish 2. Who came
More informationChapter: The Laws of Motion
Chapter 4 Table of Contents Chapter: The Laws of Motion Section 1: Newton s Second Law Section 2: Gravity Section 3: The Third Law of Motion 3 Motion and Forces Newton s Laws of Motion The British scientist
More informationGravity and Orbits. Objectives. Clarify a number of basic concepts. Gravity
Gravity and Orbits Objectives Clarify a number of basic concepts Speed vs. velocity Acceleration, and its relation to force Momentum and angular momentum Gravity Understand its basic workings Understand
More information6. Summarize Newton s Law of gravity and the inverse square concept. Write out the equation
HW due Today. 1. Read p. 175 180. 2. Summarize the historical account of Brahe and Kepler 3. Write out Kepler s 3 laws. 1) Planets in orbit follow an elliptical path, the Sun is located at a focus of the
More information7.4 Universal Gravitation
Circular Motion Velocity is a vector quantity, which means that it involves both speed (magnitude) and direction. Therefore an object traveling at a constant speed can still accelerate if the direction
More informationPlanetary Mechanics:
Planetary Mechanics: Satellites A satellite is an object or a body that revolves around another body due to the gravitational attraction to the greater mass. Ex: The planets are natural satellites of the
More informationLecture Outline. Chapter 13 Gravity Pearson Education, Inc. Slide 13-1
Lecture Outline Chapter 13 Gravity Slide 13-1 The plan Lab this week: exam problems will put problems on mastering for chapters without HW; will also go over exam 2 Final coverage: now posted; some sections/chapters
More information7 Study Guide. Gravitation Vocabulary Review
Date Period Name CHAPTER 7 Study Guide Gravitation Vocabulary Review Write the term that correctly completes the statement. Use each term once. Kepler s second law Newton s law of universal gravitation
More informationSteve Smith Tuition: Physics Notes
Steve Smith Tuition: Physics Notes E = mc 2 F = GMm sin θ m = mλ d hν = φ + 1 2 mv2 Static Fields IV: Gravity Examples Contents 1 Gravitational Field Equations 3 1.1 adial Gravitational Field Equations.................................
More informationForces, Momentum, & Gravity. Force and Motion Cause and Effect. Student Learning Objectives 2/16/2016
Forces, Momentum, & Gravity (Chapter 3) Force and Motion Cause and Effect In chapter 2 we studied motion but not its cause. In this chapter we will look at both force and motion the cause and effect. We
More informationGRAVITATION CONCEPTUAL PROBLEMS
GRAVITATION CONCEPTUAL PROBLEMS Q-01 Gravitational force is a weak force but still it is considered the most important force. Why? Ans Gravitational force plays an important role for initiating the birth
More informationCopyright 2010 Pearson Education, Inc. GRAVITY. Chapter 12
GRAVITY Chapter 12 Units of Chapter 12 Newton s Law of Universal Gravitation Gravitational Attraction of Spherical Bodies Kepler s Laws of Orbital Motion Gravitational Potential Energy Energy Conservation
More informationChapter: The Laws of Motion
Table of Contents Chapter: The Laws of Motion Section 1: Newton s Second Law Section 2: Gravity Section 3: The Third Law of Motion 1 Newton s Second Law Force, Mass, and Acceleration Newton s first law
More information(b) The period T and the angular frequency ω of uniform rotation are related to the cyclic frequency f as. , ω = 2πf =
PHY 302 K. Solutions for problem set #9. Non-textbook problem #1: (a) Rotation frequency of 1 Hz means one revolution per second, or 60 revolutions per minute (RPM). The pre-lp vinyl disks rotated at 78
More informationCH 8. Universal Gravitation Planetary and Satellite Motion
CH 8 Universal Gravitation Planetary and Satellite Motion Sir Isaac Newton UNIVERSAL GRAVITATION Newton: Universal Gravitation Newton concluded that earthly objects and heavenly objects obey the same physical
More informationAP Physics 1 Chapter 7 Circular Motion and Gravitation
AP Physics 1 Chapter 7 Circular Motion and Gravitation Chapter 7: Circular Motion and Angular Measure Gravitation Angular Speed and Velocity Uniform Circular Motion and Centripetal Acceleration Angular
More informationToday. Laws of Motion. Conservation Laws. Gravity. tides
Today Laws of Motion Conservation Laws Gravity tides Newton s Laws of Motion Our goals for learning: Newton s three laws of motion Universal Gravity How did Newton change our view of the universe? He realized
More informationCopyright 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
Chapter 13. Newton s Theory of Gravity The beautiful rings of Saturn consist of countless centimeter-sized ice crystals, all orbiting the planet under the influence of gravity. Chapter Goal: To use Newton
More informationLesson 9. Luis Anchordoqui. Physics 168. Tuesday, October 24, 17
Lesson 9 Physics 168 1 Static Equilibrium 2 Conditions for Equilibrium An object with forces acting on it but that is not moving is said to be in equilibrium 3 Conditions for Equilibrium (cont d) First
More informationUnit 5: Gravity and Rotational Motion. Brent Royuk Phys-109 Concordia University
Unit 5: Gravity and Rotational Motion Brent Royuk Phys-109 Concordia University Rotational Concepts There s a whole branch of mechanics devoted to rotational motion, with angular equivalents for distance,
More information18. Kepler as a young man became the assistant to A) Nicolaus Copernicus. B) Ptolemy. C) Tycho Brahe. D) Sir Isaac Newton.
Name: Date: 1. The word planet is derived from a Greek term meaning A) bright nighttime object. B) astrological sign. C) wanderer. D) nontwinkling star. 2. The planets that were known before the telescope
More informationEpisode 403: Orbital motion
Episode 40: Orbital motion In this episode, students will learn how to combine concepts learned in the study of circular motion with Newton s Law of Universal Gravitation to understand the (circular) motion
More informationF 12. = G m m 1 2 F 21. = G m 1m 2 = F 12. Review: Newton s Law Of Universal Gravitation. Physics 201, Lecture 23. g As Function of Height
Physics 01, Lecture Today s Topics n Universal Gravitation (Chapter 1 n Review: Newton s Law of Universal Gravitation n Properties of Gravitational Field (1.4 n Gravitational Potential Energy (1.5 n Escape
More informationChapter 8. Dynamics II: Motion in a Plane
Chapter 8. Dynamics II: Motion in a Plane Chapter Goal: To learn how to solve problems about motion in a plane. Slide 8-2 Chapter 8 Preview Slide 8-3 Chapter 8 Preview Slide 8-4 Chapter 8 Preview Slide
More informationPhys 2101 Gabriela González
Phys 2101 Gabriela González Newton s law : F = Gm 1 m 2 /r 2 Explains why apples fall, why the planets move around the Sun, sciencebulletins.amnh.org And in YouTube! Explains just as well as Newtons why
More informationGravitation. chapter 9
chapter 9 Gravitation Circular orbits (Section 9.3) 1, 2, and 3 are simple exercises to supplement the quantitative calculations of Examples 4, 5, and 6 in Section 9.3. 1. Satellite near Earth s surface
More informationISSUED BY K V - DOWNLOADED FROM GRAVITATION
CONCEPTS GRAVITATION Kepler's law of planetry motion (a) Kepler's first law (law of orbit): Every planet revolves around the sun in an elliptical orbit with the sun is situated at one focus of the ellipse.
More informationRotational Motion and the Law of Gravity 1
Rotational Motion and the Law of Gravity 1 Linear motion is described by position, velocity, and acceleration. Circular motion repeats itself in circles around the axis of rotation Ex. Planets in orbit,
More informationKepler, Newton, and laws of motion
Kepler, Newton, and laws of motion First: A Little History Geocentric vs. heliocentric model for solar system (sec. 2.2-2.4)! The only history in this course is this progression: Aristotle (~350 BC) Ptolemy
More informationSpecial Relativity: The laws of physics must be the same in all inertial reference frames.
Special Relativity: The laws of physics must be the same in all inertial reference frames. Inertial Reference Frame: One in which an object is observed to have zero acceleration when no forces act on it
More informationGRAVITATION. F = GmM R 2
GRAVITATION Name: Partner: Section: Date: PURPOSE: To explore the gravitational force and Kepler s Laws of Planetary motion. INTRODUCTION: Newton s law of Universal Gravitation tells us that the gravitational
More informationQuestions Chapter 13 Gravitation
Questions Chapter 13 Gravitation 13-1 Newton's Law of Gravitation 13-2 Gravitation and Principle of Superposition 13-3 Gravitation Near Earth's Surface 13-4 Gravitation Inside Earth 13-5 Gravitational
More informationChapter 13 Gravity Pearson Education, Inc. Slide 13-1
Chapter 13 Gravity Slide 13-1 The plan Lab this week: there will be time for exam problems Final exam: sections posted today; some left out Final format: all multiple choice, almost all short problems,
More informationv lim a t = d v dt a n = v2 R curvature
PHY 02 K. Solutions for Problem set # 6. Textbook problem 5.27: The acceleration vector a of the particle has two components, the tangential acceleration a t d v dt v lim t 0 t (1) parallel to the velocity
More informationChapter 5 Part 2. Newton s Law of Universal Gravitation, Satellites, and Weightlessness
Chapter 5 Part 2 Newton s Law of Universal Gravitation, Satellites, and Weightlessness Newton s ideas about gravity Newton knew that a force exerted on an object causes an acceleration. Most forces occurred
More informationCircular Motion and Gravitation Notes 1 Centripetal Acceleration and Force
Circular Motion and Gravitation Notes 1 Centripetal Acceleration and Force This unit we will investigate the special case of kinematics and dynamics of objects in uniform circular motion. First let s consider
More informationBasics of Kepler and Newton. Orbits of the planets, moons,
Basics of Kepler and Newton Orbits of the planets, moons, Kepler s Laws, as derived by Newton. Kepler s Laws Universal Law of Gravity Three Laws of Motion Deriving Kepler s Laws Recall: The Copernican
More informationIn this chapter, you will consider the force of gravity:
Gravity Chapter 5 Guidepost In this chapter, you will consider the force of gravity: What were Galileo s insights about motion and gravity? What were Newton s insights about motion and gravity? How does
More informationChapter 3 - Gravity and Motion. Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Chapter 3 - Gravity and Motion Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. In 1687 Isaac Newton published the Principia in which he set out his concept
More information