Halliday, Resnick & Walker Chapter 13. Gravitation. Physics 1A PHYS1121 Professor Michael Burton

Size: px
Start display at page:

Download "Halliday, Resnick & Walker Chapter 13. Gravitation. Physics 1A PHYS1121 Professor Michael Burton"

Transcription

1 Halliday, Resnick & Walker Chapter 13 Gravitation Physics 1A PHYS1121 Professor Michael Burton

2 II_A2: Planetary Orbits in the Solar System + Galaxy Interactions (You Tube) 21 seconds 13-1 Newton's Law of Gravitation! The gravitational force o o o o o o o Holds us to the Earth Holds Earth in orbit around the Sun Holds the Sun together with the stars in our Galaxy Holds together the Local Group of galaxies Holds together the Local Supercluster of galaxies Attempts to slow the expansion of the Universe Is responsible for black holes! Gravity is far-reaching and very important!

3 13-1 Newton's Law of Gravitation! Gravitational attraction depends on mass of an object! Earth has a large mass and produces a large attraction! The force is always attractive, never repulsive! Bodies attract each other through gravitational attraction! Newton realized this attraction was responsible for maintaining the orbits of celestial bodies! Newton's Law of Gravitation defines the strength of this attractive force between particles! Between an apple & the Earth: ~0.8 N! Between 2 people: < 1 µn 13-1 Newton's Law of Gravitation r F F m 1 m 2! The magnitude of the force is given by: Eq. (13-1)! Where G is the gravitational constant: Eq. (13-2)! The force always points from one particle to the other, so this equation can be written in vector form: Eq. (13-3)

4 13-1 Newton's Law of Gravitation M M M! The shell theorem describes gravitational attraction for objects! Earth is a nesting of shells, so we feel Earth's mass as if it were all located at its centre! Gravitational force forms third-law force pairs (i.e. N3L)! e.g. Earth-apple and apple-earth forces are both 0.8 N 13-1 Newton's Law of Gravitation! Earth-apple and apple-earth forces are both ~0.8 N! The difference in mass causes the difference in the apple:earth accelerations: ~10 m/s 2 vs. ~ m/s 2

5 Consider the objects of various masses indicated below. The objects are each separated from another object by the distance indicated. In which of these situations is the gravitational force exerted on the two objects the largest? a) #1 b) #2 c) #3 d) #2 and #3 e) #1, #2, and # Gravitation and the Principle of Superposition! The principle of superposition applies.! i.e. Add the individual forces as vectors: Eq. (13-5)! For a real (extended) object, this becomes an integral: Eq. (13-6)! If the object is a uniform sphere or shell we can treat its mass as being at its centre instead M M M

6 13-2 Gravitation and the Principle of Superposition Example Summing two forces: Figure 13-4 Consider a system of particles, each of mass m. In which one of the following configurations is the net gravitational force on Particle A the largest? The horizontal or vertical spacing between particles is the same in each case. a) 1 b) 2 c) 4 d) 1 and 2 equally large e) 2 and 4 are equally large

7 13-3 Gravitation Near the Earth's Surface! Combine F = GMm/r 2 and F = ma g : Eq. (13-11)! Gives magnitude of gravitational acceleration at a given distance from the centre of the Earth! Table 13-1 shows the value for a g for various altitudes above the Earth s surface 13-3 Gravitation Near the Earth's Surface! The calculated a g will differ slightly from the measured g at any location on the Earth s surface! Three reasons. The Earth. 1. mass is not uniformly distributed 2. is not a perfect sphere 3. rotates

8 13-3 Gravitation Near Earth's Surface Example Difference in gravitational force and weight due to rotation at the equator: N2L : F N " ma g = "m V 2, the centripetal acceleration. R Here V = #R with # the angular velocity, and F N = mg. Thus g = a g "# 2 R.! Exercise for the student. Show this is about m/s 2. Use R=6,400km and!=2" radians/day. Question: do you weigh more or less at the equator than the Poles? Figure Gravitational Potential Energy! Gravitational potential energy for a two-particle system is written: Eq. (13-21)! Note this value is negative and approaches 0 for r! "! The gravitational potential energy of a system is the sum of potential energies for all pairs of particles Proof comes from integrating the force to obtain the work done. i.e. U = "W = " # F! d r! and using F = GMm. r 2!

9 13-5 Gravitational Potential Energy! The gravitational force is conservative.! The work done by this force does not depend on the path followed by the particles, only the difference in the initial and final positions of the particles.! Since the work done is independent of path, so is the gravitational potential energy change Eq. (13-26) Figure Gravitational Potential Energy! For a projectile to escape the gravitational pull of a body, it must come to rest only at infinity (if at all).! At rest at infinity: K = 0 and U = 0 (because r! ")! So K + U must be # 0 at surface of the body to escape:! This is the escape speed. The minimum value to escape.! Rockets launch eastward to take advantage of Earth's rotational speed, to reach v escape more easily

10 13-5 Gravitational Potential Energy You move a ball of mass m away from a sphere of mass M. 1. Does the gravitational potential energy of the system of the ball and sphere a) Increase, or b) Decrease. 2. Is the Work done by the gravitational force between the ball and the sphere a) Positive work, or b) Negative work r m M

11 In a distant solar system where several planets are orbiting a single star of mass M, a large asteroid collides with a planet of mass m orbiting the star at a distance r. As a result, the planet is ejected from its solar system. What is minimum amount of energy that the planet must receive in the collision to be removed from the solar system? a) b) r c) m M d) e) 2_A3: Retrograde Motion of the Planets

12 13-6 Planets and Satellites: Kepler's Laws! The motion of planets in the solar system was a puzzle for astronomers, especially curious motions such as retrograde motion.! Johannes Kepler ( ) derived laws of motion using Tycho Brahe's ( ) measurements Figure Figure Planets and Satellites: Kepler's Laws! The orbit is defined by its semi-major axis a and its eccentricity e! An eccentricity of zero corresponds to a circle! Eccentricity of Earth's orbit is

13 Kepler2L: Kepler s 2 nd Law Equal Areas in Equal Times 13-6 Planets and Satellites: Kepler's Laws! Equivalent to Conservation of Angular Momentum! See later in this course.

14 13-6 Planets and Satellites: Kepler's Laws! The law of periods can be written mathematically as:! Holds for elliptical orbits if we replace r with a, the semi-major axis Planets and Satellites: Kepler's Laws

15 A spacecraft is in low orbit of the Earth with a period of approximately 90 minutes. By which of the following methods could the spacecraft stay in the same orbit and reduce the period of the orbit? a) Before launch, increase the mass of the spacecraft to increase the centripetal force on it. b) Remove any unnecessary equipment, cargo, and supplies to reduce the mass and decrease its angular momentum. c) Fire rockets to increase the tangential velocity of the ship. d) None of the above methods will achieve the desired effect Satellites: Orbits and Energy! Relating the centripetal acceleration of a satellite to the gravitational force, we can rewrite as energies:! Meaning that: Eq. (13-38)! Therefore the total mechanical energy is: Eq. (13-39) Eq. (13-40)

16 13-7 Satellites: Orbits and Energy! Total energy E is the negative of the kinetic energy! For an ellipse, we substitute a for r! Therefore the energy of an orbit depends only on its semi-major axis, not its eccentricity! All orbits in Figure have the same energy Figure Satellites: Circular Orbit! Graph of variation in Energy for a circular orbit, radius r! Note that:! E(r) and U(r) are negative! E(r) = -K(r)! E(r), U(r), K(r) all! 0 as r!!

17 13-7 Satellites: Orbits and Energy a) Which orbit (1, 2 or 3?) will the shuttle take when it fires a forward-pointing thruster so as to reduce its kinetic energy? b) Is the orbital period T then (i) greater than, (ii) less than or (iii) the same as, that of the circular orbit? 13 Summary The Law of Gravitation Superposition Eq. (13-1) Eq. (13-2) Gravitational Behavior of Uniform Spherical Shells! The net force on an external object: calculate as if all the mass were concentrated at the centre of the shell Gravitational Acceleration Eq. (13-5) Eq. (13-11)

18 13 Summary Free-Fall Acceleration and Weight! Earth's mass is not uniformly distributed, the planet is not spherical, and it rotates: the calculated and measured values of acceleration differ Gravitational Potential Energy Gravitation within a Spherical Shell! A uniform shell exerts no net force on a particle inside! Inside a solid sphere: Potential Energy of a System Eq. (13-19) Eq. (13-21) Eq. (13-22) 13 Summary Escape Speed Eq. (13-28) Kepler's Laws! The law of orbits: ellipses! The law of areas: equal areas in equal times! The law of periods: Energy in Planetary Motion Eq. (13-42) Kepler's Laws Eq. (13-34)! Gravitation and acceleration are equivalent

Halliday, Resnick & Walker Chapter 13. Gravitation. Physics 1A PHYS1121 Professor Michael Burton

Halliday, Resnick & Walker Chapter 13. Gravitation. Physics 1A PHYS1121 Professor Michael Burton Halliday, Resnick & Walker Chapter 13 Gravitation Physics 1A PHYS1121 Professor Michael Burton II_A2: Planetary Orbits in the Solar System + Galaxy Interactions (You Tube) 21 seconds 13-1 Newton's Law

More information

Chapter 13 - Gravity. David J. Starling Penn State Hazleton Fall Chapter 13 - Gravity. Objectives (Ch 13) Newton s Law of Gravitation

Chapter 13 - Gravity. David J. Starling Penn State Hazleton Fall Chapter 13 - Gravity. Objectives (Ch 13) Newton s Law of Gravitation The moon is essentially gray, no color. It looks like plaster of Paris, like dirty beach sand with lots of footprints in it. -James A. Lovell (from the Apollo 13 mission) David J. Starling Penn State Hazleton

More information

Chapter 13. Gravitation

Chapter 13. Gravitation Chapter 13 Gravitation 13.2 Newton s Law of Gravitation In vector notation: 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

More information

Notes: Most of the material in this chapter is taken from Young and Freedman, Chap. 13.

Notes: Most of the material in this chapter is taken from Young and Freedman, Chap. 13. Chapter 5. Gravitation Notes: Most of the material in this chapter is taken from Young and Freedman, Chap. 13. 5.1 Newton s Law of Gravitation We have already studied the effects of gravity through the

More information

Chapter 13 Newton s Theory of Gravity

Chapter 13 Newton s Theory of Gravity Chapter 13 Newton s Theory of Gravity Chapter Goal: To use Newton s theory of gravity to understand the motion of satellites and planets. Slide 13-2 Chapter 13 Preview Slide 13-3 Chapter 13 Preview Slide

More information

Orbital Mechanics. Angular Momentum

Orbital Mechanics. Angular Momentum Orbital Mechanics The objects that orbit earth have only a few forces acting on them, the largest being the gravitational pull from the earth. The trajectories that satellites or rockets follow are largely

More information

Physics 2101 Section 3 March 19th : Ch. : Ch. 13 Announcements: Quiz today. Class Website:

Physics 2101 Section 3 March 19th : Ch. : Ch. 13 Announcements: Quiz today. Class Website: Physics 2101 Section 3 March 19 th : Ch. 13 Announcements: Quiz today. Class Website: http://www.phys.lsu.edu/classes/spring2010/phys2101-3/ http://www.phys.lsu.edu/~jzhang/teaching.html Chapt. 13: Gravitation

More information

QUESTION BANK UNIT-6 CHAPTER-8 GRAVITATION

QUESTION BANK UNIT-6 CHAPTER-8 GRAVITATION QUESTION BANK UNIT-6 CHAPTER-8 GRAVITATION I. One mark Questions: 1. State Kepler s law of orbits. 2. State Kepler s law of areas. 3. State Kepler s law of periods. 4. Which physical quantity is conserved

More information

Newton s Law of Gravity

Newton s Law of Gravity Gravitational Potential Energy On Earth, depends on: object s mass (m) strength of gravity (g) distance object could potentially fall Gravitational Potential Energy In space, an object or gas cloud has

More information

Newton s Law of Universal Gravitation

Newton s Law of Universal Gravitation Newton s Law of Universal Gravitation The greatest moments in science are when two phenomena that were considered completely separate suddenly are seen as just two different versions of the same thing.

More information

Gravitation. Physics 1425 Lecture 11. Michael Fowler, UVa

Gravitation. Physics 1425 Lecture 11. Michael Fowler, UVa Gravitation Physics 1425 Lecture 11 Michael Fowler, UVa The Inverse Square Law Newton s idea: the centripetal force keeping the Moon circling the Earth is the same gravitational force that pulls us to

More information

Penn State University Physics 211 ORBITAL MECHANICS 1

Penn State University Physics 211 ORBITAL MECHANICS 1 ORBITAL MECHANICS 1 PURPOSE The purpose of this laboratory project is to calculate, verify and then simulate various satellite orbit scenarios for an artificial satellite orbiting the earth. First, there

More information

A. 81 2 = 6561 times greater. B. 81 times greater. C. equally strong. D. 1/81 as great. E. (1/81) 2 = 1/6561 as great.

A. 81 2 = 6561 times greater. B. 81 times greater. C. equally strong. D. 1/81 as great. E. (1/81) 2 = 1/6561 as great. Q12.1 The mass of the Moon is 1/81 of the mass of the Earth. Compared to the gravitational force that the Earth exerts on the Moon, the gravitational force that the Moon exerts on the Earth is A. 81 2

More information

Chapter 13 Newton s Theory of Gravity

Chapter 13 Newton s Theory of Gravity Chapter 13 Newton s Theory of Gravity The textbook gives a good brief account of the period leading up to Newton s Theory of Gravity. I am not going to spend much time reviewing the history but will show

More information

PHY121 #8 Midterm I 3.06.2013

PHY121 #8 Midterm I 3.06.2013 PHY11 #8 Midterm I 3.06.013 AP Physics- Newton s Laws AP Exam Multiple Choice Questions #1 #4 1. When the frictionless system shown above is accelerated by an applied force of magnitude F, the tension

More information

University Physics 226N/231N Old Dominion University. Chapter 13: Gravity (and then some)

University Physics 226N/231N Old Dominion University. Chapter 13: Gravity (and then some) University Physics 226N/231N Old Dominion University Chapter 13: Gravity (and then some) Dr. Todd Satogata (ODU/Jefferson Lab) satogata@jlab.org http://www.toddsatogata.net/2016-odu Monday, November 28,

More information

Black holes 101(beyond science fiction)

Black holes 101(beyond science fiction) Chapter 13: Gravitation Newton s Law of Gravitation Why is gravity important? Revisit the following: gravitational force, weight, and gravitational energy Stellar motions: the orbits of satellites and

More information

12/3/10. Copyright 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

12/3/10. Copyright 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. 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 s theory of gravity to understand the

More information

Name: Earth 110 Exploration of the Solar System Assignment 1: Celestial Motions and Forces Due in class Tuesday, Jan. 20, 2015

Name: Earth 110 Exploration of the Solar System Assignment 1: Celestial Motions and Forces Due in class Tuesday, Jan. 20, 2015 Name: Earth 110 Exploration of the Solar System Assignment 1: Celestial Motions and Forces Due in class Tuesday, Jan. 20, 2015 Why are celestial motions and forces important? They explain the world around

More information

Satellites and Space Stations

Satellites and Space Stations Satellites and Space Stations A satellite is an object or a body that revolves around another object, which is usually much larger in mass. Natural satellites include the planets, which revolve around

More information

Practice Test (Chapter 10)

Practice Test (Chapter 10) Practice Test (Chapter 10) 1) According to Kepler's laws, the paths of planets about the sun are A) parabolas. B) circles. C) straight lines. D) ellipses. Answer: D 2) Which of the following is not a vector

More information

Kepler, Newton, and laws of motion

Kepler, Newton, and laws of motion Kepler, Newton, and laws of motion !! " The only history in this course:!!!geocentric vs. heliocentric model (sec. 2.2-2.4)" The important historical progression is the following:!! Ptolemy (~140 AD) Copernicus

More information

Gravitation and Newton s Synthesis

Gravitation and Newton s Synthesis Gravitation and Newton s Synthesis Vocabulary law of unviversal Kepler s laws of planetary perturbations casual laws gravitation motion casuality field graviational field inertial mass gravitational mass

More information

Physics 130 Astronomy Exam #1 July 19, 2004

Physics 130 Astronomy Exam #1 July 19, 2004 Physics 130 Astronomy Exam #1 July 19, 2004 Name Multiple Choice: 1. A scientist observes a new phenomenon that disagrees with his explanation or hypothesis. Following the scientific methods, he should

More information

Section 4: The Basics of Satellite Orbits

Section 4: The Basics of Satellite Orbits Section 4: The Basics of Satellite Orbits MOTION IN SPACE VS. MOTION IN THE ATMOSPHERE The motion of objects in the atmosphere differs in three important ways from the motion of objects in space. First,

More information

Clicker Question: Clicker Question: Gravitational Force. Newton's Law of Gravity. Inverse Square law Demo

Clicker Question: Clicker Question: Gravitational Force. Newton's Law of Gravity. Inverse Square law Demo Test results Last day to drop without a grade is Oct. 3 Grades posted in cabinet and online F D C B A A bullet is fired from a gun. Complete the following sentance to form a true statement. The speed of

More information

Problem Set 9 Angular Momentum Solution

Problem Set 9 Angular Momentum Solution MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics Physics 801 Fall 01 Problem 1 Sedna Problem Set 9 Angular Momentum Solution 90377 Sedna is a large trans-neptunian object, which as of 01 was

More information

Lecture 13. Gravity in the Solar System

Lecture 13. Gravity in the Solar System Lecture 13 Gravity in the Solar System Guiding Questions 1. How was the heliocentric model established? What are monumental steps in the history of the heliocentric model? 2. How do Kepler s three laws

More information

Chapter 5: Circular Motion, the Planets, and Gravity

Chapter 5: Circular Motion, the Planets, and Gravity Chapter 5: Circular Motion, the Planets, and Gravity 1. Earth s gravity attracts a person with a force of 120 lbs. The force with which the Earth is attracted towards the person is A. Zero. B. Small but

More information

First Semester Learning Targets

First Semester Learning Targets First Semester Learning Targets 1.1.Can define major components of the scientific method 1.2.Can accurately carry out conversions using dimensional analysis 1.3.Can utilize and convert metric prefixes

More information

Exemplar Problems Physics

Exemplar Problems Physics Chapter Eight GRAVITATION MCQ I 8.1 The earth is an approximate sphere. If the interior contained matter which is not of the same density everywhere, then on the surface of the earth, the acceleration

More information

1 Kepler s Laws of Planetary Motion

1 Kepler s Laws of Planetary Motion 1 Kepler s Laws of Planetary Motion 1.1 Introduction Johannes Kepler published three laws of planetary motion, the first two in 1609 and the third in 1619. The laws were made possible by planetary data

More information

Understanding the motion of the Universe. Motion, Force, and Gravity

Understanding the motion of the Universe. Motion, Force, and Gravity Understanding the motion of the Universe Motion, Force, and Gravity Laws of Motion Stationary objects do not begin moving on their own. In the same way, moving objects don t change their movement spontaneously.

More information

Chapter 3: Force and Motion

Chapter 3: Force and Motion Force and Motion Cause and Effect Chapter 3 Chapter 3: Force and Motion Homework: All questions on the Multiple- Choice and the odd-numbered questions on Exercises sections at the end of the chapter. In

More information

USING MS EXCEL FOR DATA ANALYSIS AND SIMULATION

USING MS EXCEL FOR DATA ANALYSIS AND SIMULATION USING MS EXCEL FOR DATA ANALYSIS AND SIMULATION Ian Cooper School of Physics The University of Sydney i.cooper@physics.usyd.edu.au Introduction The numerical calculations performed by scientists and engineers

More information

Concept Review. Physics 1

Concept Review. Physics 1 Concept Review Physics 1 Speed and Velocity Speed is a measure of how much distance is covered divided by the time it takes. Sometimes it is referred to as the rate of motion. Common units for speed or

More information

G U I D E T O A P P L I E D O R B I T A L M E C H A N I C S F O R K E R B A L S P A C E P R O G R A M

G U I D E T O A P P L I E D O R B I T A L M E C H A N I C S F O R K E R B A L S P A C E P R O G R A M G U I D E T O A P P L I E D O R B I T A L M E C H A N I C S F O R K E R B A L S P A C E P R O G R A M CONTENTS Foreword... 2 Forces... 3 Circular Orbits... 8 Energy... 10 Angular Momentum... 13 FOREWORD

More information

Lesson 5 Rotational and Projectile Motion

Lesson 5 Rotational and Projectile Motion Lesson 5 Rotational and Projectile Motion Introduction: Connecting Your Learning The previous lesson discussed momentum and energy. This lesson explores rotational and circular motion as well as the particular

More information

Chapter 13. Newton s Theory of Gravity

Chapter 13. Newton s Theory of Gravity 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 information

2. Orbits. FER-Zagreb, Satellite communication systems 2011/12

2. Orbits. FER-Zagreb, Satellite communication systems 2011/12 2. Orbits Topics Orbit types Kepler and Newton laws Coverage area Influence of Earth 1 Orbit types According to inclination angle Equatorial Polar Inclinational orbit According to shape Circular orbit

More information

Physics 2A, Sec B00: Mechanics -- Winter 2011 Instructor: B. Grinstein Final Exam

Physics 2A, Sec B00: Mechanics -- Winter 2011 Instructor: B. Grinstein Final Exam Physics 2A, Sec B00: Mechanics -- Winter 2011 Instructor: B. Grinstein Final Exam INSTRUCTIONS: Use a pencil #2 to fill your scantron. Write your code number and bubble it in under "EXAM NUMBER;" an entry

More information

Astro 110-01 Lecture 10 Newton s laws

Astro 110-01 Lecture 10 Newton s laws Astro 110-01 Lecture 10 Newton s laws Twin Sungrazing comets 9/02/09 Habbal Astro110-01 Lecture 10 1 http://umbra.nascom.nasa.gov/comets/movies/soho_lasco_c2.mpg What have we learned? How do we describe

More information

7.2 Calculate force of gravity at a given distance given the force of gravity at another distance (making use of the inverse square relationship).

7.2 Calculate force of gravity at a given distance given the force of gravity at another distance (making use of the inverse square relationship). Chapter 7 Circular Motion and Gravitation 7.1 Calculate force of gravity using Newton s Law of Universal Gravitation. 5. What is the gravitational force between the Earth and the Sun? (Mass of Earth: 5.98

More information

UCM-Gravity. 2. The diagram shows two bowling balls, A and B, each having a mass of 7 kilograms, placed 2 meters apart.

UCM-Gravity. 2. The diagram shows two bowling balls, A and B, each having a mass of 7 kilograms, placed 2 meters apart. 1. A space probe is launched into space from Earth s surface. Which graph represents the relationship between the magnitude of the gravitational force exerted on Earth by the space probe and the distance

More information

Website: Reading: Homework: Discussion:

Website: Reading: Homework: Discussion: Reminders! Website: http://starsarestellar.blogspot.com/ Lectures 1-5 are available for download as study aids. Reading: You should have Chapters 1-4 read, Chapter 5 by the end of today, and Chapters 6

More information

PHY131H1F - Class 13. Today: Gravitational Potential Energy. Newton s Law of Universal Gravitation. The Gravitational Field.

PHY131H1F - Class 13. Today: Gravitational Potential Energy. Newton s Law of Universal Gravitation. The Gravitational Field. PHY131H1F - Class 13 Today: Gravitational Potential Energy Newton s Law of Universal Gravitation The Gravitational Field Orbital Motion Two balls are launched along a pair of tracks with equal velocities,

More information

M OTION. Chapter2 OUTLINE GOALS

M OTION. Chapter2 OUTLINE GOALS Chapter2 M OTION OUTLINE Describing Motion 2.1 Speed 2.2 Vectors 2.3 Acceleration 2.4 Distance, Time, and Acceleration Acceleration of Gravity 2.5 Free Fall 2.6 Air Resistence Force and Motion 2.7 First

More information

PHY1 Review for Exam 5

PHY1 Review for Exam 5 Topics 1. Uniform circular Motion a. Centripetal acceleration b. Centripetal force c. Horizontal motion d. ertical motion e. Circular motion with an angle 2. Universal gravitation a. Gravitational force

More information

Physics Principles of Physics

Physics Principles of Physics Physics 1408-00 Principles of Physics Lecture 9 Chapter 6 February 5, 008 Sung-Won Lee Sungwon.Lee@ttu.edu Announcement I Lecture note is on the web Handout (4(or 6) slides/page) http://highenergy.phys.ttu.edu/~slee/1408/

More information

Universal Law of Gravitation Honors Physics

Universal Law of Gravitation Honors Physics Universal Law of Gravitation Honors Physics Newton s Law of Universal Gravitation The greatest moments in science are when two phenomena that were considered completely separate suddenly are seen as just

More information

Planetary Orbit Simulator Student Guide

Planetary Orbit Simulator Student Guide Name: Planetary Orbit Simulator Student Guide Background Material Answer the following questions after reviewing the Kepler's Laws and Planetary Motion and Newton and Planetary Motion background pages.

More information

Today. Laws of Motion Conservation Laws Gravity tides. What is the phase of the moon?

Today. Laws of Motion Conservation Laws Gravity tides. What is the phase of the moon? Today Laws of Motion Conservation Laws Gravity tides What is the phase of the moon? How is mass different from weight? Mass the amount of matter in an object Weight the force that acts upon an object You

More information

Gravitation. Gravitation

Gravitation. Gravitation 1 Gravitation Newton s observations A constant center seeking force is required to keep an object moving along a circular path. You know that the moon orbits the earth and hence there should be a force

More information

Introduction Newton s law of gravitation. Copyright Kinetic Books Co. Chapter 13

Introduction Newton s law of gravitation. Copyright Kinetic Books Co. Chapter 13 13.0 - Introduction The topic of gravity has had a starring role in some of the most famous tales in the history of physics. Galileo Galilei was studying the acceleration due to the Earth s gravity when

More information

PROBLEMS. sec Newton's Law of Gravitation. sec Gravitation and the Principle of Superposition

PROBLEMS. sec Newton's Law of Gravitation. sec Gravitation and the Principle of Superposition PROBLEMS sec. 13-2 Newton's Law of Gravitation 1 A mass M is split into two parts, m and M m, which are then separated by a certain distance. What ratio m/m maximizes the magnitude of the gravitational

More information

Unit 8 Lesson 2 Gravity and the Solar System

Unit 8 Lesson 2 Gravity and the Solar System Unit 8 Lesson 2 Gravity and the Solar System Gravity What is gravity? Gravity is a force of attraction between objects that is due to their masses and the distances between them. Every object in the universe

More information

From Aristotle to Newton

From Aristotle to Newton From Aristotle to Newton The history of the Solar System (and the universe to some extent) from ancient Greek times through to the beginnings of modern physics. The Geocentric Model Ancient Greek astronomers

More information

circular motion & gravitation physics 111N

circular motion & gravitation physics 111N circular motion & gravitation physics 111N uniform circular motion an object moving around a circle at a constant rate must have an acceleration always perpendicular to the velocity (else the speed would

More information

NEWTON S LAWS OF MOTION

NEWTON S LAWS OF MOTION NEWTON S LAWS OF MOTION Background: Aristotle believed that the natural state of motion for objects on the earth was one of rest. In other words, objects needed a force to be kept in motion. Galileo studied

More information

Niraj Sir GRAVITATION CONCEPTS. Kepler's law of planetry motion

Niraj Sir GRAVITATION CONCEPTS. Kepler's law of planetry motion GRAVITATION CONCEPTS 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 information

Motion and Gravity in Space

Motion and Gravity in Space Motion and Gravity in Space Each planet spins on its axis. The spinning of a body, such a planet, on its axis is called rotation. The orbit is the path that a body follows as it travels around another

More information

Understanding the motion of the Universe. Motion, Force, and Gravity

Understanding the motion of the Universe. Motion, Force, and Gravity Understanding the motion of the Universe Motion, Force, and Gravity Laws of Motion Stationary objects do not begin moving on their own. In the same way, moving objects don t change their movement spontaneously.

More information

Chapter 3.8 & 6 Solutions

Chapter 3.8 & 6 Solutions Chapter 3.8 & 6 Solutions P3.37. Prepare: We are asked to find period, speed and acceleration. Period and frequency are inverses according to Equation 3.26. To find speed we need to know the distance traveled

More information

CHAPTER 11. The total energy of the body in its orbit is a constant and is given by the sum of the kinetic and potential energies

CHAPTER 11. The total energy of the body in its orbit is a constant and is given by the sum of the kinetic and potential energies CHAPTER 11 SATELLITE ORBITS 11.1 Orbital Mechanics Newton's laws of motion provide the basis for the orbital mechanics. Newton's three laws are briefly (a) the law of inertia which states that a body at

More information

Math 1302, Week 3 Polar coordinates and orbital motion

Math 1302, Week 3 Polar coordinates and orbital motion Math 130, Week 3 Polar coordinates and orbital motion 1 Motion under a central force We start by considering the motion of the earth E around the (fixed) sun (figure 1). The key point here is that the

More information

Version PREVIEW Practice 8 carroll (11108) 1

Version PREVIEW Practice 8 carroll (11108) 1 Version PREVIEW Practice 8 carroll 11108 1 This print-out should have 12 questions. Multiple-choice questions may continue on the net column or page find all choices before answering. Inertia of Solids

More information

Today. Laws of Motion. Conservation Laws. Gravity

Today. Laws of Motion. Conservation Laws. Gravity Today Laws of Motion Conservation Laws Gravity Laws of Motion Motion notions: slow fast Speed: Rate at which object moves fast change in direction slow example: speed of 10 m/s Velocity: Speed and direction

More information

Use the following information to deduce that the gravitational field strength at the surface of the Earth is approximately 10 N kg 1.

Use the following information to deduce that the gravitational field strength at the surface of the Earth is approximately 10 N kg 1. IB PHYSICS: Gravitational Forces Review 1. This question is about gravitation and ocean tides. (b) State Newton s law of universal gravitation. Use the following information to deduce that the gravitational

More information

Chapter 4 Making Sense of the Universe: Understanding Motion, Energy, and Gravity

Chapter 4 Making Sense of the Universe: Understanding Motion, Energy, and Gravity 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 sp e e d = d ista

More information

Name Class Date. true

Name Class Date. true Exercises 131 The Falling Apple (page 233) 1 Describe the legend of Newton s discovery that gravity extends throughout the universe According to legend, Newton saw an apple fall from a tree and realized

More information

Physics 9e/Cutnell. correlated to the. College Board AP Physics 1 Course Objectives

Physics 9e/Cutnell. correlated to the. College Board AP Physics 1 Course Objectives Physics 9e/Cutnell correlated to the College Board AP Physics 1 Course Objectives Big Idea 1: Objects and systems have properties such as mass and charge. Systems may have internal structure. Enduring

More information

Solar System. 1. The diagram below represents a simple geocentric model. Which object is represented by the letter X?

Solar System. 1. The diagram below represents a simple geocentric model. Which object is represented by the letter X? Solar System 1. The diagram below represents a simple geocentric model. Which object is represented by the letter X? A) Earth B) Sun C) Moon D) Polaris 2. Which object orbits Earth in both the Earth-centered

More information

5. Universal Laws of Motion

5. 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 (1642 1727) Physicist 5.1 Describing Motion: Examples from Daily

More information

The Motions of Celestial Bodies, and Newton s Laws of Motion

The Motions of Celestial Bodies, and Newton s Laws of Motion The Motions of Celestial Bodies, and Newton s Laws of Motion Announcements The results of Quiz 1 are posted in OWL Looking ahead: Homework 1 is on-going, and is due on Thu, Sept. 29 th ; Homework 2 will

More information

Announcements. Eclipses 2/1/12. HW1 is due Thursday. You have to be registered at MasteringAstronomy to do the homework!

Announcements. Eclipses 2/1/12. HW1 is due Thursday. You have to be registered at MasteringAstronomy to do the homework! Announcements HW1 is due Thursday. You have to be registered at MasteringAstronomy to do the homework! TA Qufei Gu will be in RH111 4:00-5:00PM Wednesday to help with homework. Email: zyx88@unm.edu Feb

More information

13 Universal Gravitation. Everything pulls on everything else.

13 Universal Gravitation. Everything pulls on everything else. Everything pulls on everything else. Gravity was not discovered by Isaac Newton. What Newton discovered, prompted by a falling apple, was that gravity is a universal force that it is not unique to Earth,

More information

Described by Isaac Newton

Described by Isaac Newton Described by Isaac Newton States observed relationships between motion and forces 3 statements cover aspects of motion for single objects and for objects interacting with another object An object at rest

More information

Making Sense of the Universe: Understanding Motion, Energy, and Gravity

Making Sense of the Universe: Understanding Motion, Energy, and Gravity Making Sense of the Universe: Understanding Motion, Energy, and Gravity 1. Newton s Laws 2. Conservation Laws Energy Angular momentum 3. Gravity Review from last time Ancient Greeks: Ptolemy; the geocentric

More information

Homework 4. problems: 5.61, 5.67, 6.63, 13.21

Homework 4. problems: 5.61, 5.67, 6.63, 13.21 Homework 4 problems: 5.6, 5.67, 6.6,. Problem 5.6 An object of mass M is held in place by an applied force F. and a pulley system as shown in the figure. he pulleys are massless and frictionless. Find

More information

Lecture 5: Newton s Laws. Astronomy 111

Lecture 5: Newton s Laws. Astronomy 111 Lecture 5: Newton s Laws Astronomy 111 Isaac Newton (1643-1727): English Discovered: three laws of motion, one law of universal gravitation. Newton s great book: Newton s laws are universal in scope,

More information

DIRECT ORBITAL DYNAMICS: USING INDEPENDENT ORBITAL TERMS TO TREAT BODIES AS ORBITING EACH OTHER DIRECTLY WHILE IN MOTION

DIRECT ORBITAL DYNAMICS: USING INDEPENDENT ORBITAL TERMS TO TREAT BODIES AS ORBITING EACH OTHER DIRECTLY WHILE IN MOTION 1 DIRECT ORBITAL DYNAMICS: USING INDEPENDENT ORBITAL TERMS TO TREAT BODIES AS ORBITING EACH OTHER DIRECTLY WHILE IN MOTION Daniel S. Orton email: dsorton1@gmail.com Abstract: There are many longstanding

More information

Lecture 6: Newton & Kepler. Tycho Brahe ( ) Johannes Kepler

Lecture 6: Newton & Kepler. Tycho Brahe ( ) Johannes Kepler Lecture 6: Newton & Kepler Johannes Kepler (1600) was employed by Tycho to develop a mathematical theory to explain the observations made by Tycho Kepler was a pure theorist; Tycho a pure observer Issac

More information

4.1 Describing Motion. How do we describe motion? Chapter 4 Making Sense of the Universe: Understanding Motion, Energy, and Gravity

4.1 Describing Motion. How do we describe motion? Chapter 4 Making Sense of the Universe: Understanding Motion, Energy, and Gravity Chapter 4 Making Sense of the Universe: Understanding Motion, Energy, and Gravity 4.1 Describing Motion Our goals for learning:! How do we describe motion?! How is mass different from weight? How do we

More information

Lecture 07: Work and Kinetic Energy. Physics 2210 Fall Semester 2014

Lecture 07: Work and Kinetic Energy. Physics 2210 Fall Semester 2014 Lecture 07: Work and Kinetic Energy Physics 2210 Fall Semester 2014 Announcements Schedule next few weeks: 9/08 Unit 3 9/10 Unit 4 9/15 Unit 5 (guest lecturer) 9/17 Unit 6 (guest lecturer) 9/22 Unit 7,

More information

The Main Point. The Scientific Method. Laws of Planetary Motion. Lecture #3: Orbits and Gravity. Laws of Planetary Motion:

The Main Point. The Scientific Method. Laws of Planetary Motion. Lecture #3: Orbits and Gravity. Laws of Planetary Motion: Lecture #3: Orbits and Gravity Laws of Planetary Motion: Kepler's Laws. Newton's Laws. Gravity. Planetary Orbits. Spacecraft Orbits. The Main Point Motions of planets, moons, and asteroids can be very

More information

physics of biomolecular chemistry and structures under stress e.g. protein conformations protein-protein bonds cell membranes

physics of biomolecular chemistry and structures under stress e.g. protein conformations protein-protein bonds cell membranes Figure 12.4 physics of biomolecular chemistry and structures under stress e.g. protein conformations protein-protein bonds cell membranes unfolding/refolding single bond kinetics pore formation strength

More information

Kepler, Newton and Gravitation

Kepler, Newton and Gravitation Kepler, Newton and Gravitation Kepler, Newton and Gravity 1 Using the unit of distance 1 AU = Earth-Sun distance PLANETS COPERNICUS MODERN Mercury 0.38 0.387 Venus 0.72 0.723 Earth 1.00 1.00 Mars 1.52

More information

Question on Class IX» Science» Gravitation» The Universal Law Of Gravitation.

Question on Class IX» Science» Gravitation» The Universal Law Of Gravitation. Question on Class IX» Science» Gravitation» The Universal Law Of Gravitation. Q.1. When we move from the poles to the equator. Hence, the value of g decreases. Why Ans: The shape of earth is an ellipse

More information

AP1 Gravity. at an altitude equal to twice the radius (R) of the planet. What is the satellite s speed assuming a perfectly circular orbit?

AP1 Gravity. at an altitude equal to twice the radius (R) of the planet. What is the satellite s speed assuming a perfectly circular orbit? 1. A satellite of mass m S orbits a planet of mass m P at an altitude equal to twice the radius (R) of the planet. What is the satellite s speed assuming a perfectly circular orbit? (A) v = Gm P R (C)

More information

Chapter 13: Universal Gravitation

Chapter 13: Universal Gravitation Chapter 13: Universal Gravitation I. The Falling Apple (13.1) A. Isaac Newton (1642-1727) 1. Formulated ideas based on earlier work by Galileo (concept of inertia) 2. Concept if object undergoes change

More information

Astronomy 1140 Quiz 1 Review

Astronomy 1140 Quiz 1 Review Astronomy 1140 Quiz 1 Review Prof. Pradhan September 15, 2015 What is Science? 1. Explain the difference between astronomy and astrology. (a) Astrology: nonscience using zodiac sign to predict the future/personality

More information

The Cosmic Perspective Seventh Edition. Making Sense of the Universe: Understanding Motion, Energy, and Gravity. Chapter 4 Lecture

The Cosmic Perspective Seventh Edition. Making Sense of the Universe: Understanding Motion, Energy, and Gravity. Chapter 4 Lecture Chapter 4 Lecture The Cosmic Perspective Seventh Edition Making Sense of the Universe: Understanding Motion, Energy, and Gravity Making Sense of the Universe: Understanding Motion, Energy, and Gravity

More information

VELOCITY, ACCELERATION, FORCE

VELOCITY, ACCELERATION, FORCE VELOCITY, ACCELERATION, FORCE velocity Velocity v is a vector, with units of meters per second ( m s ). Velocity indicates the rate of change of the object s position ( r ); i.e., velocity tells you how

More information

Newton s Law of Gravity and Kepler s Laws

Newton s Law of Gravity and Kepler s Laws Newton s Law of Gravity and Kepler s Laws Michael Fowler Phys 142E Lec 9 2/6/09. These notes are partly adapted from my Physics 152 lectures, where more mathematical details can be found. The Universal

More information

Chapter 6 Circular Motion, Orbits and Gravity

Chapter 6 Circular Motion, Orbits and Gravity Chapter 6 Circular Motion, Orbits and Gravity Topics: The kinematics of uniform circular motion The dynamics of uniform circular motion Circular orbits of satellites Newton s law of gravity Sample question:

More information

Lecture Outlines. Chapter 2. Astronomy Today 7th Edition Chaisson/McMillan Pearson Education, Inc.

Lecture Outlines. Chapter 2. Astronomy Today 7th Edition Chaisson/McMillan Pearson Education, Inc. Lecture Outlines Chapter 2 Astronomy Today 7th Edition Chaisson/McMillan Chapter 2 The Copernican Revolution Units of Chapter 2 2.1 Ancient Astronomy 2.2 The Geocentric Universe 2.3 The Heliocentric Model

More information

Rotation, Rolling, Torque, Angular Momentum

Rotation, Rolling, Torque, Angular Momentum Halliday, Resnick & Walker Chapter 10 & 11 Rotation, Rolling, Torque, Angular Momentum Physics 1A PHYS1121 Professor Michael Burton Rotation 10-1 Rotational Variables! The motion of rotation! The same

More information

3.6 Solving Problems Involving Projectile Motion

3.6 Solving Problems Involving Projectile Motion INTRODUCTION 1-2 Physics and its relation to other fields introduction of physics, its importance and scope 1-5 Units, standards, and the SI System description of the SI System description of base and

More information

Lecture L17 - Orbit Transfers and Interplanetary Trajectories

Lecture L17 - Orbit Transfers and Interplanetary Trajectories S. Widnall, J. Peraire 16.07 Dynamics Fall 008 Version.0 Lecture L17 - Orbit Transfers and Interplanetary Trajectories In this lecture, we will consider how to transfer from one orbit, to another or to

More information

Physics 271 FINAL EXAM-SOLUTIONS Friday Dec 23, 2005 Prof. Amitabh Lath

Physics 271 FINAL EXAM-SOLUTIONS Friday Dec 23, 2005 Prof. Amitabh Lath Physics 271 FINAL EXAM-SOLUTIONS Friday Dec 23, 2005 Prof. Amitabh Lath 1. The exam will last from 8:00 am to 11:00 am. Use a # 2 pencil to make entries on the answer sheet. Enter the following id information

More information