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

Save this PDF as:

Size: px
Start display at page:

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

## Transcription

1 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 Fall 2013

2 Objectives for Chapter 13 (a) Use the concept of gravitational field to analyze the motion of objects near the surface of the Earth and in planetary motion. (b) Analyze the orbital motions (including escape velocity) using the gravitational potential energy of the system.

3 A cannon fires a ball vertically upward from the Earth s surface. Which one of the following statements concerning the net force acting on the ball at the top of its trajectory is correct? (a) The net force on the ball is instantaneously equal to 0 newtons at the top of the flight path. (b) The direction of the net force on the ball changes from upward to downward. (c) The net force on the ball is less than the weight, but greater than zero newtons. (d) The net force on the ball is greater than the weight of the ball. (e) The net force on the ball is equal to the weight of the ball.

4 The gravitational force is a mutual force between two separated objects (distance r) of masses m 1 and m 2 given by F = G m 1m 2 r 2 G = m 3 /kg-s 2.

5 If an object at the surface of the Earth has a weight W, what would be the weight of the object if it was transported to the surface of a planet that is one-sixth the mass of Earth and has a radius one third that of Earth? (a) 3W (b) 4W/3 (c) W (d) 3W/2 (e) W/3

6 From Newton s third law, we know that this force must have an equal but opposite pair; i.e., object 1 pulls on object 2, but object 2 also pulls on object 1.

7 Shell Theorem: a uniform sphere of matter attracts a particle that is outside as if all the sphere s mass were concentrated at its center. Uniform spherical objects just become points.

8 Principle of Superposition: If N objects interact with particle 1 gravitationally, the total force is just the vector sum. F 1,net = F 12 + F F 1N F 1,net = N i=2 F 1i

9 Example 1: Three particles of masses m 1 = 6.0 kg and m 2 = m 3 = 4.0 kg interact gravitationally as shown below. If a = 2.0 cm, what is the net gravitational force on particle 1 from 2 and 3?

10 We can apply to an object (m) near the surface of the Earth (M): F = G Mm r 2 a g = GM r 2 = ma g

11 The force due to gravity on the surface of the earth is not consistently 9.83 m/s 2. Earth is not a perfect sphere; the mass within the Earth is not uniformly distributed; Earth rotates.

12 Example 2: Find the percent difference in weight (F N ) for a crate at the equator relative to a crate at the north pole.

13 Example 3: An astronaut of height 1.70 m floats feet down a distance r = m away from the center of (a) Earth, (b) a black hole of mass kg. Find the difference in the gravitational force between her head and her toes.

14 Gravity is a conservative force, so lets find its potential energy using U = W. U = W U( ) U(R) = R F(r) d r 1 = GMm R r 2 dr [ ] GMm = r R U(R) = 0 + GMm R U(R) = GMm R

15 The change gravitational potential energy U is path independent. U = W

16 The force from this potential energy is just the derivative (since we used an integral to derive it). F(r) = du dr = d ( GMm ) dr r = GMm r 2 The minus sign indicates the force points radially inward.

17 Example 4: You stand on the surface of a planet of radius R and mass M. Derive the speed at which a projectile would need to be launched to escape the pull of the planet s gravity. This is known as the escape speed.

18

19 A large asteroid collides with a planet of mass m orbiting a star of mass M at a distance r. As a result of the collision, the planet is knocked out of its orbit, such that it leaves the solar system. Which of the following expressions gives the minimum amount of energy that the planet must receive in the collision to be removed from the solar system? (a) GMm/r (b) GMm/r 2 (c) GMm/ r (d) Gm/r (e) Gm/r 2

20 Example 5: An asteroid is headed toward Earth. Its speed is measured to be 12 km/s when it is 10 earth radii from the center of the planet. What is its impact speed, ignoring drag from the atmosphere?

21 Johannes Kepler was a 17th century mathematician who developed three laws of planetary motion. 1. The Law of Orbits: all planets move in elliptical orbits with the Sun at one focus.

22 2. The Law of Areas: a line that connects a planet to the Sun sweeps out equals areas in equal time intervals (i.e., da/dt = constant). A = 1 2 r2 ( θ) da = 1 2 r2 dθ da = 1 dθ r2 dt 2 dt = 1 2 r2 ω L = rp = rmv = rmrω da = L dt 2m

23 3. The Law of Periods: the square of the period of any planet is proportional to the cube of the semimajor axis of its orbit. F = ma GMm r 2 = m(rω 2 ) = mr 2 ( 4π 2 T 2 = GM ) r 3 ( ) 2π 2 T

24

25 Example 6: Halley s comet orbits the sun with a period of 76 years and, in 1986, had a distance of closest approach to the Sun at m. (a) What is its farthest distance from the Sun? (b) What is the eccentricity e of the orbit?

26 When one object orbits a much larger object, mechanical energy is conserved. For a circular orbit, F = ma GMm r 2 = m v2 r GMm = 1 2r 2 mv2 = K E = K + U = GMm GMm 2r r E = GMm 2r (for an elliptical orbit, E = GMm/2a)

27 The total energy of an orbiting body is negative. E = GMm 2r

28 Example 7: An astronaut releases a bowling ball of mass 7.20 kg into a circular orbit about Earth at an altitude of 350 km. (a) What is the mechanical energy of the ball in its orbit? (b) What is the mechanical energy of the ball on the surface of the Earth?

### 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

### 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

### 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

### 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

### 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

### 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

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

### 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

### 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

### 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

### 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,

### 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

### 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.

### 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

### 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

### 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

### 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

### 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,

### 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

### Introduction to Gravity and Orbits. Isaac Newton. Newton s Laws of Motion

Introduction to Gravity and Orbits Isaac Newton Born in England in 1642 Invented calculus in early twenties Finally published work in gravity in 1687 The Principia Newton s Laws of Motion 1: An object

### 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

### 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

### 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

### 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

### 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

### AST 101 Lecture 7. Newton s Laws and the Nature of Matter

AST 101 Lecture 7 Newton s Laws and the Nature of Matter The Nature of Matter Democritus (c. 470-380 BCE) posited that matter was composed of atoms Atoms: particles that can not be further subdivided 4

### 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

### 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.

### 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.

### 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

### 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

### 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

### 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

### The Gravitational Field

The Gravitational Field The use of multimedia in teaching physics Texts to multimedia presentation Jan Hrnčíř jan.hrncir@gfxs.cz Martin Klejch martin.klejch@gfxs.cz F. X. Šalda Grammar School, Liberec

### 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

### 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

### 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

### Building Planetary Orbits (the Feynman way)

Building Planetary Orbits (the Feynman way) Using a method of computing known as finite differences we can quickly calculate the geometry of any planetary orbit. All we need are a starting position and

### 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

### 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,

### THE NATURE OF FORCES Forces can be divided into two categories: contact forces and non-contact forces.

SESSION 2: NEWTON S LAWS Key Concepts In this session we Examine different types of forces Review and apply Newton's Laws of motion Use Newton's Law of Universal Gravitation to solve problems X-planation

### 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

### 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

### 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

### A satellite of mass 5.00x10² kg is in a circular orbit of radius 2r around Earth. Then it is moved to a circular orbit radius of 3r.

Supplemental Questions A satellite of mass 5.00x10² kg is in a circular orbit of radius 2r around Earth. Then it is moved to a circular orbit radius of 3r. (a) Determine the satellite s GPE in orbit. (b)

### 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

### b. Velocity tells you both speed and direction of an object s movement. Velocity is the change in position divided by the change in time.

I. What is Motion? a. Motion - is when an object changes place or position. To properly describe motion, you need to use the following: 1. Start and end position? 2. Movement relative to what? 3. How far

### 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.

### 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

### 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

### Name Class Period. F = G m 1 m 2 d 2. G =6.67 x 10-11 Nm 2 /kg 2

Gravitational Forces 13.1 Newton s Law of Universal Gravity Newton discovered that gravity is universal. Everything pulls on everything else in the universe in a way that involves only mass and distance.

### 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

### 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

### 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

### Chapter 5: Circular Motion

Page 1 Chapter 5: Circular Motion Rotating Objects: Wheels, moon, earth, CDs, DVDs etc. Rigid bodies. Description of circular motion. Angular Position, Angular Displacement θ r s Angle (in radians) θ =

### Newton s Laws of Motion

Newton s Laws of Motion FIZ101E Kazım Yavuz Ekşi My contact details: Name: Kazım Yavuz Ekşi Email: eksi@itu.edu.tr Notice: Only emails from your ITU account are responded. Office hour: Wednesday 10.00-12.00

### 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

### Newton s Laws. Newton s Imaginary Cannon. Michael Fowler Physics 142E Lec 6 Jan 22, 2009

Newton s Laws Michael Fowler Physics 142E Lec 6 Jan 22, 2009 Newton s Imaginary Cannon Newton was familiar with Galileo s analysis of projectile motion, and decided to take it one step further. He imagined

### 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/

### 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

### 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.

### 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

### Physics Midterm Review Packet January 2010

Physics Midterm Review Packet January 2010 This Packet is a Study Guide, not a replacement for studying from your notes, tests, quizzes, and textbook. Midterm Date: Thursday, January 28 th 8:15-10:15 Room:

### Astronomy 114 Summary of Important Concepts #1 1

Astronomy 114 Summary of Important Concepts #1 1 1 Kepler s Third Law Kepler discovered that the size of a planet s orbit (the semi-major axis of the ellipse) is simply related to sidereal period of the

### 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

### So if ω 0 increases 3-fold, the stopping angle increases 3 2 = 9-fold.

Name: MULTIPLE CHOICE: Questions 1-11 are 5 points each. 1. A safety device brings the blade of a power mower from an angular speed of ω 1 to rest in 1.00 revolution. At the same constant angular acceleration,

### 1 Newton s Laws of Motion

Exam 1 Ast 4 - Chapter 2 - Newton s Laws Exam 1 is scheduled for the week of Feb 19th Bring Pencil Scantron 882-E (available in the Bookstore) A scientific calculator (you will not be allowed to use you

### 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)

### 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

### 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

### Center of Mass/Momentum

Center of Mass/Momentum 1. 2. An L-shaped piece, represented by the shaded area on the figure, is cut from a metal plate of uniform thickness. The point that corresponds to the center of mass of the L-shaped

### Chapter 9 Circular Motion Dynamics

Chapter 9 Circular Motion Dynamics 9. Introduction Newton s Second Law and Circular Motion... 9. Universal Law of Gravitation and the Circular Orbit of the Moon... 9.. Universal Law of Gravitation... 3

### 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

### 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

### 2.1 Force and Motion Kinematics looks at velocity and acceleration without reference to the cause of the acceleration.

2.1 Force and Motion Kinematics looks at velocity and acceleration without reference to the cause of the acceleration. Dynamics looks at the cause of acceleration: an unbalanced force. Isaac Newton was

### Rotational Mechanics - 1

Rotational Mechanics - 1 The Radian The radian is a unit of angular measure. The radian can be defined as the arc length s along a circle divided by the radius r. s r Comparing degrees and radians 360

### 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

### 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

### 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

### Kepler s Laws of Planetary Motion and Newton s Law of Universal Gravitation

Kepler s Laws of lanetary Motion and Newton s Law of Universal Gravitation Abstract These notes were written with those students in mind having taken (or are taking) A Calculus and A hysics Newton s law

### Kepler s Laws and our Solar System

Kepler s Laws and our Solar System The Astronomical Unit, AU Kepler s Empirical Laws of Planetary mo=on The mass of the Sun, M O. A very brief tour of the solar system Major planets Dwarf planets (defini=on)

### 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

### 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

### PSI AP Physics I Rotational Motion

PSI AP Physics I Rotational Motion Multiple-Choice questions 1. Which of the following is the unit for angular displacement? A. meters B. seconds C. radians D. radians per second 2. An object moves from

### Summary Notes. to avoid confusion it is better to write this formula in words. time

National 4/5 Physics Dynamics and Space Summary Notes The coloured boxes contain National 5 material. Section 1 Mechanics Average Speed Average speed is the distance travelled per unit time. distance (m)

### 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

### Newton s Universal Law of Gravitation The Apple and the Moon Video

Name Date Pd Newton s Universal Law of Gravitation The Apple and the Moon Video Objectives Recognize that a gravitational force exists between any two objects and that the force is directly proportional

Section Review Answers Chapter 12 Section 1 1. Answers may vary. Students should say in their own words that an object at rest remains at rest and an object in motion maintains its velocity unless it experiences

### 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

### 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

### 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

### 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

### Physics 11 Fall 2012 Practice Problems 4 - Solutions

Physics 11 Fall 01 Practice Problems 4 - s 1. Under what conditions can all the initial kinetic energy of an isolated system consisting of two colliding objects be lost in a collision? Explain how this

### 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

### Is velocity constant? A = πr 2

Physics R Date: Circular Motion & Gravity Uniform Circular Motion What does uniform mean? Equations: (on reference table) Uniform circular motion means circular motion with C = 2πr = Is velocity constant?

### 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

### Chapter 5. Determining Masses of Astronomical Objects

Chapter 5. Determining Masses of Astronomical Objects One of the most fundamental and important properties of an object is its mass. On Earth we can easily weigh objects, essentially measuring how much

### Tennessee State University

Tennessee State University Dept. of Physics & Mathematics PHYS 2010 CF SU 2009 Name 30% Time is 2 hours. Cheating will give you an F-grade. Other instructions will be given in the Hall. MULTIPLE CHOICE.