Universal Law of Gravitation Honors Physics
|
|
- Madlyn McBride
- 7 years ago
- Views:
Transcription
1 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 two different versions of the same thing. Newton s explanation that the motion of the moon around the Earth (and the planets around the sun) and of an apple falling to the ground are two expressions of the same phenomenon, gravity, represents a wonderful instance of this sort of synthesis. Newton conjectured that objects near the surface of the Earth fall towards the center of the Earth as a result of a universal attraction of all matter towards all other matter. He then considered that the circular motion of the moon around the Earth could then be explained if that same force of gravity were supplying the force towards the center of the moon s circular orbit, the Earth. That force of gravity would provide the unbalanced force necessary for circular motion. Universal Gravity Newton postulated that all matter in the universe is attracted to all other matter. He named this force of attraction gravity and he formulated the following expression to describe how the force of gravity depends on the mass of each object and the distance between their centers. In this equation, G is a constant that would need to be discovered by experiment, m1 and m2 are the masses of the two objects and r is the distance between their centers. It doesn t matter which mass you call m1 and which one you call m2 : That s a result of Newton s third law which states that the force on one object will be equal in size to the force on the other. Newton had to invent calculus in order to show that the distance between two spherical objects, the r in his equation, should be measured between the centers of the objects. He was able to show that spherical objects act, from the perspective of gravitational force, as if all of their mass were located at a point at their center. As a result, the distance from a spherical mass, such as the Earth or the sun, must always be measured from its center. It took more than a hundred years before Henry Cavendish was able to directly measure the value of G. The modern accepted value of G is: G = 6.67 x N m 2 /kg 2 1 Page
2 Example 1 What is the force between a 5.0kg spherical object and a 10 kg spherical object whose centers are located 2.5m apart? FG=Gm1m2/r 2 FG = (6.67 x N m 2 /kg 2 )(5.0kg)(10kg)/(2.5m) 2 FG = (6.67 x N m 2 /kg 2 )(5.0kg)(10kg)/(2.5m) 2 FG = 5.3 x N Example 2 What is the average gravitational force between the Earth and the sun? The mass of the Earth is 6.0 x kg, the mass of the sun is 2.0 x kg and the average distance between their centers is 1.5 x m. FG=Gm1m2/r 2 FG = (6.67 x N m 2 /kg 2 )( 2.0 x )( 6.0 x kg)(1.5 x m) 2 FG = (6.67 x N m 2 /kg 2 )( 2.0 x )( 6.0 x kg)/( 1.5 x m) 2 FG = 3.6 x N Example 3 What is the distance between two objects whose masses are 28,000 kg and 50,000 kg if the gravitational force between them is 50N? FG=Gm1m2/r 2 To solve for r, first multiply both side by r2 (FG)(r 2 )= Gm1m2 Then divide both sides by FG r 2 = Gm1m2/ FG And take the square root of both sides r= (Gm1m2/FG) 1/2 r= ((6.67 x N m 2 /kg 2 )(2.8 x 10 4 kg)(5.0 x 10 4 kg)/(50n)) 1/2 r = (1.86 x 10-3 ) r = 18.6 x 10-4 r = 4.3 x 10-2 m r = 4.3 cm 2 Page
3 Universal Gravitation:, G = 6.67 x10-11 Nm 2 /kg 2 Examples 1. Two spherical objects have masses of 200 kg and 500 kg. Their centers are separated by a distance of 25 m. Find the gravitational attraction between them. (1.067x10-8 N) 2. Two spherical objects have masses of 1.5 x 10 5 kg and 8.5 x 10 2 kg. Their centers are separated by a distance of 2500 m. Find the gravitational attraction between them. (1.361x10-9 N) 3. Two spherical objects have masses of 3.1 x 10 5 kg and 6.5 x 10 3 kg. The gravitational attraction between them is 65 N. How far apart are their centers? (0.045 m) 4. A 1 kg object is located at a distance of 6.4 x10 6 m from the center of a larger object whose mass is 6.0 x kg. a. What is the size of the force acting on the smaller object? 9.77 N b. What is the size of the force acting on the larger object? 9.77 N c. What is the acceleration of the smaller object when it is released? 9.77 m/s 2 d. What is the acceleration of the larger object when it is released? 1.63 x10-24 m/s 2 Class Work 5. Two spherical objects have masses of 8000 kg and 1500 kg. Their centers are separated by a distance of 1.5 m. Find the gravitational attraction between them N or 3.56 x10-4 N 6. Two spherical objects have masses of 7.5 x 10 5 kg and 9.2 x 10 7 kg. Their centers are separated by a distance of 2.5 x 10 3 m. Find the gravitational attraction between them x10-4 N 7. Two spherical objects have masses of 8.1 x 10 2 kg and 4.5 x 10 8 kg. The gravitational attraction between them is 1.9 x 10-3 N. How far apart are their centers? m 8. Two spherical objects have equal masses and experience a gravitational force of 85 N towards one another. Their centers are 36mm apart. Determine each of their masses kg 9. A 1 kg object is located at a distance of 7.0 x10 8 m from the center of a larger object whose mass is 2.0 x kg. a. What is the size of the force acting on the smaller object? 272 N b. What is the size of the force acting on the larger object? 272 N 3 Page
4 c. What is the acceleration of the smaller object when it is released? 272 m/s 2 d. What is the acceleration of the larger object when it is released? 1.36 x10-28 m/s 2 Homework 1. Two spherical objects have masses of 8000 kg and 5.0 kg. Their centers are separated by a distance of 1.5 m. Find the gravitational attraction between them N 2. Two spherical objects have masses of 9.5 x 10 8 kg and 2.5 kg. Their centers are separated by a distance of 2.5 x 10 8 m. Find the gravitational attraction between them x10-18 N 3. Two spherical objects have masses of 6.3 x 10 3 kg and 3.5 x 10 4 kg. The gravitational attraction between them is 6.5 x 10-3 N. How far apart are their centers? 1.50 m 4. Two spherical objects have equal masses and experience a gravitational force of 25 N towards one another. Their centers are 36 cm apart. Determine each of their masses kg 5. A 1 kg object is located at a distance of 1.7 x10 6 m from the center of a larger object whose mass is 7.4 x kg. a. What is the size of the force acting on the smaller object? 1.71 N b. What is the size of the force acting on the larger object? 1.71 N c. What is the acceleration of the smaller object when it is released? 1.71 m/s 2 d. What is the acceleration of the larger object when it is released? 2.31 x10-23 m/s 2 4 Page
5 Orbital Motion Newton based much of his theory on the work of Johannes Kepler, which was based on the astronomical observations of Tycho Brahe. Newton concluded that in order for the planets to proceed in their orbits around the sun there must be a force attracting them towards the sun. Kepler writings could be summarized into three laws: Kepler s first law states that the orbits of the planets are elliptical, with the sun at one focus. Sun An ellipse has two focal points and no real defined center like a circle. (Actually if Kepler didn t study the data concerning Mars, he probably would never have discovered this fact! Mars has an extremely elliptical orbit, while the other planets are nearly circular!) 5 Page
6 Kepler s second law states that if you extend an imaginary line between the sun and a planet, that that line would sweep out equal areas in equal times. In other words, Kepler found that the planets move faster when they are closer to the Sun and slower when they are farther away from the Sun. This means that the earth is closer to the sun in winter! (strange but true!) The following diagram shows this: 6 Page
7 Kepler s third law states that there is a specific mathematical relationship between the orbital periods of planets (the time to go around the sun) and their mean (average) distance from the sun. Specifically, for all planets orbiting the sun the ratio of their orbital period squared divided by their orbital radius cubed, T 2 /r 3, yields the same number. Thus, if the periods of the planets are TA and TB and the average distances from the Sun are ra and rb, the third law can be expressed as follows: TA 2 = ra 3 TB rb The following data table can be useful for using this equation: Planetary Data planets not shown to scale >> Mercur y Mean Distance to the Sun (AU) Orbital Period (years) Venus Earth Mars Jupite r Satur n Uranu s Neptun e Pluto Period Squared Mean Distance Cubed T 2 /r Equatori al Radius (km) AU=Astronomical Unit 1AU=distance from earth to sun=146,600 km This data can be used for any of Kepler s 3 rd law problems that compare orbits and periods of planets. 7 Page
8 This concept can also be used for orbits and periods of satellites (moons) of planets! The orbits of moons around planets are also ellipses. Example: Galileo discovered four moons of Jupiter. Io, which he measured to be 4.2 units form the center of Jupiter, has a period of 1.8 days. He measured the radius of Ganymede s orbit as 10.7 units. Use Kepler s third law to find the period of Ganymede. Given: For Io Period TB = 1.8 days Radius rb = 4.2 units Unknown: Ganymede s period, TA For Ganymede Radius ra = 10.7 units Basic Equation: TA 2 = ra 3 TB rb Solution: TA 2 = TB 2 ra rb 3 TA 2 = (1.8 days) units units TA 2 = 52.8 days 2 TA = 7.3 days 8 Page
9 Free Response 1. As shown in the diagram below, a 5.0 kg space rock is located 2.5x10 7 m from the center of the earth. The mass of the earth is 6.0x10 24 kg. Earth Space Rock a. Determine the force of gravity acting on the space rock, due to the earth. Calculate the magnitude and state the direction. ( N) b. Compare your answer in a) to the force of gravity acting on the earth, due to the space rock. Indicate that force on the diagram above. ( N) c. On the diagram above, indicate the direction the space rock would accelerate if released. Label that vector a. ( )from rock towards earth d. Calculate the acceleration the rock would experience m/s 2 e. **If instead of falling, the object were in a stable orbit, indicate on the diagram above a possible direction of its velocity. Label that vector v. ( or ) up or down from rock f. **Calculate the velocity the rock needs to be in a stable orbit m/s g. **Calculate the period of the rock orbiting the earth s 9 Page
10 2. As shown in the diagram below, a 2000 kg spacecraft is located 9.2x10 6 m from the center of the earth. The mass of the earth is 6.0x10 24 kg. Earth Spacecraft a. Determine the force of gravity acting on the spacecraft, due to the earth. Calculate the magnitude and state the direction. ( N) b. Compare your answer in a) to the force of gravity acting on the earth, due to the spacecraft. Indicate that force on the diagram above. ( N) c. On the diagram above, indicate the direction the spacecraft would accelerate if released. Label that vector a. ( )from spacecraft towards earth d. Calculate the acceleration the spacecraft would experience m/s 2 e. **If instead of falling, the spacecraft were in a stable orbit, indicate on the diagram above a possible direction of its velocity. Label that vector v. ( or ) up or down from spacecraft f. **Calculate the velocity the spacecraft needs to be in a stable orbit m/s g. **Calculate the period of the spacecraft orbiting the earth s 10 Page
11 3. As shown in the diagram below, a 1000 kg asteroid is located 6.8x10 6 m from the center of the Mars. The mass of the Mars is 6.4x10 23 kg. Mars Asteroid a. Determine the force of gravity acting on the asteroid, due to the Mars. Calculate the magnitude and state the direction. 923 N left b. Compare your answer in a) to the force of gravity acting on the Mars, due to the asteroid. Indicate that force on the diagram above. 923 N right c. On the diagram above, indicate the direction the asteroid would accelerate if released. Label that vector a. ( )from asteroid towards mars d. Calculate the acceleration the asteroid would experience m/s 2 e. **If instead of falling, the asteroid were in a stable orbit, indicate on the diagram above a possible direction of its velocity. Label that vector v. ( or ) up or down from asteroid f. **Calculate the velocity the asteroid needs to be in a stable orbit m/s g. **Calculate the period of the asteroid orbiting the earth s 11 Page
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 informationGravitation 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 informationFrom 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 informationUse 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 informationLecture 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 informationGRAVITATIONAL FIELDS PHYSICS 20 GRAVITATIONAL FORCES. Gravitational Fields (or Acceleration Due to Gravity) Symbol: Definition: Units:
GRAVITATIONAL FIELDS Gravitational Fields (or Acceleration Due to Gravity) Symbol: Definition: Units: Formula Description This is the formula for force due to gravity or as we call it, weight. Relevant
More informationName: 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 informationName 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.
More informationHalliday, 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 informationNewton s Law of Universal Gravitation
12.1 Newton s Law of Universal Gravitation SECTION Explain Kepler s laws. Describe Newton s law of universal gravitation. Apply Newton s law of universal gravitation quantitatively. KEY TERMS OUTCOMES
More informationUnit 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 informationcircular 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 informationChapter 25.1: Models of our Solar System
Chapter 25.1: Models of our Solar System Objectives: Compare & Contrast geocentric and heliocentric models of the solar sytem. Describe the orbits of planets explain how gravity and inertia keep the planets
More informationVersion A Page 1. 1. The diagram shows two bowling balls, A and B, each having a mass of 7.00 kilograms, placed 2.00 meters apart.
Physics Unit Exam, Kinematics 1. The diagram shows two bowling balls, A and B, each having a mass of 7.00 kilograms, placed 2.00 meters apart. What is the magnitude of the gravitational force exerted by
More informationA. 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 informationHalliday, 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 informationastronomy 2008 1. A planet was viewed from Earth for several hours. The diagrams below represent the appearance of the planet at four different times.
1. A planet was viewed from Earth for several hours. The diagrams below represent the appearance of the planet at four different times. 5. If the distance between the Earth and the Sun were increased,
More informationNotes: 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 information2. 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 informationHow To Understand The Theory Of Gravity
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 informationSolar 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 informationAstronomy 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 informationPlanetary 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 informationLab 6: Kepler's Laws. Introduction. Section 1: First Law
Lab 6: Kepler's Laws Purpose: to learn that orbit shapes are ellipses, gravity and orbital velocity are related, and force of gravity and orbital period are related. Materials: 2 thumbtacks, 1 pencil,
More informationForces between masses
Forces between masses Gravity is arguably the first force that people really learn about. People don't really think of it as learning about gravity because it is such a big part of our everyday lives.
More informationThe University of Texas at Austin. Gravity and Orbits
UTeach Outreach The University of Texas at Austin Gravity and Orbits Time of Lesson: 60-75 minutes Content Standards Addressed in Lesson: TEKS6.11B understand that gravity is the force that governs the
More informationOrbital 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 informationExercise: Estimating the Mass of Jupiter Difficulty: Medium
Exercise: Estimating the Mass of Jupiter Difficulty: Medium OBJECTIVE The July / August observing notes for 010 state that Jupiter rises at dusk. The great planet is now starting its grand showing for
More informationUSING 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 informationName: Date: Period: Gravity Study Guide
Vocabulary: Define the following terms. Law of Universal Gravitation Gravity Study Guide Weight Weightlessness Gravitational Field Black hole Escape velocity Math: Be able to use the equation for the law
More informationEDMONDS COMMUNITY COLLEGE ASTRONOMY 100 Winter Quarter 2007 Sample Test # 1
Instructor: L. M. Khandro EDMONDS COMMUNITY COLLEGE ASTRONOMY 100 Winter Quarter 2007 Sample Test # 1 1. An arc second is a measure of a. time interval between oscillations of a standard clock b. time
More informationChapter 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 informationThe orbit of Halley s Comet
The orbit of Halley s Comet Given this information Orbital period = 76 yrs Aphelion distance = 35.3 AU Observed comet in 1682 and predicted return 1758 Questions: How close does HC approach the Sun? What
More informationBackground Information
Background Information The Second Law of Motion and The Law of Gravitation Student Activities 1. Round and Round They Go! 2. onic Sections - Movement in Newton s Gravitational orce Notes to Teachers Teacher
More informationVocabulary - Understanding Revolution in. our Solar System
Vocabulary - Understanding Revolution in Universe Galaxy Solar system Planet Moon Comet Asteroid Meteor(ite) Heliocentric Geocentric Satellite Terrestrial planets Jovian (gas) planets Gravity our Solar
More informationNewton 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 informationAngular Velocity vs. Linear Velocity
MATH 7 Angular Velocity vs. Linear Velocity Dr. Neal, WKU Given an object with a fixed speed that is moving in a circle with a fixed ius, we can define the angular velocity of the object. That is, we can
More informationNewton s Law of Gravitation
Newton s Law of Gravitation Duration: 1-2 class periods Essential Questions: How do the acceleration and force due to gravity depend on the radius and mass of a planet? How does the mass of a falling body
More informationChapter 3 The Science of Astronomy
Chapter 3 The Science of Astronomy Days of the week were named for Sun, Moon, and visible planets. What did ancient civilizations achieve in astronomy? Daily timekeeping Tracking the seasons and calendar
More informationGRAVITY CONCEPTS. Gravity is the universal force of attraction between all matter
IT S UNIVERSAL GRAVITY CONCEPTS Gravity is the universal force of attraction between all matter Weight is a measure of the gravitational force pulling objects toward Earth Objects seem weightless when
More informationNewton s derivation of Kepler s laws (outline)
Newton s derivation of Kepler s laws (outline) 1. Brief history. The first known proposal for a heliocentric solar system is due to Aristarchus of Samos (ancient Greece, c. 270 BC). Following a long period
More informationAstronomy 110 Homework #04 Assigned: 02/06/2007 Due: 02/13/2007. Name:
Astronomy 110 Homework #04 Assigned: 02/06/2007 Due: 02/13/2007 Name: Directions: Listed below are twenty (20) multiple-choice questions based on the material covered by the lectures this past week. Choose
More informationEarth in the Solar System
Copyright 2011 Study Island - All rights reserved. Directions: Challenge yourself! Print out the quiz or get a pen/pencil and paper and record your answers to the questions below. Check your answers with
More informationThe 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
More informationThe Hidden Lives of Galaxies. Jim Lochner, USRA & NASA/GSFC
The Hidden Lives of Galaxies Jim Lochner, USRA & NASA/GSFC What is a Galaxy? Solar System Distance from Earth to Sun = 93,000,000 miles = 8 light-minutes Size of Solar System = 5.5 light-hours What is
More informationThe Solar System. Unit 4 covers the following framework standards: ES 10 and PS 11. Content was adapted the following:
Unit 4 The Solar System Chapter 7 ~ The History of the Solar System o Section 1 ~ The Formation of the Solar System o Section 2 ~ Observing the Solar System Chapter 8 ~ The Parts the Solar System o Section
More informationDIRECT 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 informationNewton 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
More informationGRADE 8 SCIENCE INSTRUCTIONAL TASKS. Gravity
GRADE 8 SCIENCE INSTRUCTIONAL TASKS Gravity Grade-Level Expectations The exercises in these instructional tasks address content related to the following science grade-level expectation(s): ESS-M-C3 Relate
More informationName 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 informationWhat Do You Think? For You To Do GOALS
Activity 2 Newton s Law of Universal Gravitation GOALS In this activity you will: Explore the relationship between distance of a light source and intensity of light. Graph and analyze the relationship
More informationELEMENTS OF PHYSICS MOTION, FORCE, AND GRAVITY
1 Pre-Test Directions: This will help you discover what you know about the subject of motion before you begin this lesson. Answer the following true or false. 1. Aristotle believed that all objects fell
More informationForces. When an object is pushed or pulled, we say that a force is exerted on it.
Forces When an object is pushed or pulled, we say that a force is exerted on it. Forces can Cause an object to start moving Change the speed of a moving object Cause a moving object to stop moving Change
More informationThis paper is also taken for the relevant Examination for the Associateship. For Second Year Physics Students Wednesday, 4th June 2008: 14:00 to 16:00
Imperial College London BSc/MSci EXAMINATION June 2008 This paper is also taken for the relevant Examination for the Associateship SUN, STARS, PLANETS For Second Year Physics Students Wednesday, 4th June
More informationPhysics 53. Gravity. Nature and Nature's law lay hid in night: God said, "Let Newton be!" and all was light. Alexander Pope
Physics 53 Gravity Nature and Nature's law lay hid in night: God said, "Let Newton be!" and all was light. Alexander Pope Kepler s laws Explanations of the motion of the celestial bodies sun, moon, planets
More information4 Gravity: A Force of Attraction
CHAPTER 1 SECTION Matter in Motion 4 Gravity: A Force of Attraction BEFORE YOU READ After you read this section, you should be able to answer these questions: What is gravity? How are weight and mass different?
More informationSection 1 Gravity: A Force of Attraction
Section 1 Gravity: A Force of Attraction Key Concept Gravity is a force of attraction between objects that is due to their masses. What You Will Learn Gravity affects all matter, including the parts of
More informationAP Environmental Science Graph Prep
AP Environmental Science Graph Prep Practice Interpreting Data: The following questions are to help you practice reading information shown on a graph. Answer each question on the separate answer sheet.
More informationStudy Guide: Solar System
Study Guide: Solar System 1. How many planets are there in the solar system? 2. What is the correct order of all the planets in the solar system? 3. Where can a comet be located in the solar system? 4.
More information1.1 A Modern View of the Universe" Our goals for learning: What is our place in the universe?"
Chapter 1 Our Place in the Universe 1.1 A Modern View of the Universe What is our place in the universe? What is our place in the universe? How did we come to be? How can we know what the universe was
More informationAE554 Applied Orbital Mechanics. Hafta 1 Egemen Đmre
AE554 Applied Orbital Mechanics Hafta 1 Egemen Đmre A bit of history the beginning Astronomy: Science of heavens. (Ancient Greeks). Astronomy existed several thousand years BC Perfect universe (like circles
More informationPhysics 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:
More informationLesson 29: Newton's Law of Universal Gravitation
Lesson 29: Newton's Law of Universal Gravitation Let's say we start with the classic apple on the head version of Newton's work. Newton started with the idea that since the Earth is pulling on the apple,
More informationLab 7: Gravity and Jupiter's Moons
Lab 7: Gravity and Jupiter's Moons Image of Galileo Spacecraft Gravity is the force that binds all astronomical structures. Clusters of galaxies are gravitationally bound into the largest structures in
More informationUC Irvine FOCUS! 5 E Lesson Plan
UC Irvine FOCUS! 5 E Lesson Plan Title: Astronomical Units and The Solar System Grade Level and Course: 8th grade Physical Science Materials: Visual introduction for solar system (slides, video, posters,
More informationSection 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 informationRelated Standards and Background Information
Related Standards and Background Information Earth Patterns, Cycles and Changes This strand focuses on student understanding of patterns in nature, natural cycles, and changes that occur both quickly and
More informationChapter 1 Our Place in the Universe
Chapter 1 Our Place in the Universe Syllabus 4 tests: June 18, June 30, July 10, July 21 Comprehensive Final - check schedule Website link on blackboard 1.1 Our Modern View of the Universe Our goals for
More informationCorrect Modeling of the Indirect Term for Third-Body Perturbations
AAS 07-47 Correct Modeling of the Indirect Term for Third-Body Perturbations Matthew M. Berry * Vincent T. Coppola The indirect term in the formula for third body perturbations models the acceleration
More informationNewton s Law of Universal Gravitation describes the attractive gravitational force that exists between any two bodies with the following equation:
Newton s Laws & Gravitation Newton s Law of Universal Gravitation describes the attractive gravitational force that exists between any two bodies with the following equation: F G = GMm 2 r G is the gravitational
More informationLecture 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 informationQ3.2.a The gravitational force exerted by a planet on one of its moons is 3e23 newtons when the moon is at a particular location.
Q3.2.a The gravitational force exerted by a planet on one of its moons is 3e23 newtons when the moon is at a particular location. If the mass of the moon were three times as large, what would the force
More informationOrbital Dynamics with Maple (sll --- v1.0, February 2012)
Orbital Dynamics with Maple (sll --- v1.0, February 2012) Kepler s Laws of Orbital Motion Orbital theory is one of the great triumphs mathematical astronomy. The first understanding of orbits was published
More informationPractice TEST 2. Explain your reasoning
Practice TEST 2 1. Imagine taking an elevator ride from the1 st floor to the 10 th floor of a building. While moving between the 1 st and 2 nd floors the elevator speeds up, but then moves at a constant
More informationPlanets and Dwarf Planets by Shauna Hutton
Name: Wow! Technology has improved so well in the last several years that we keep finding more and more objects in our solar system! Because of this, scientists have had to come up with new categories
More informationRETURN TO THE MOON. Lesson Plan
RETURN TO THE MOON Lesson Plan INSTRUCTIONS FOR TEACHERS Grade Level: 9-12 Curriculum Links: Earth and Space (SNC 1D: D2.1, D2.2, D2.3, D2.4) Group Size: Groups of 2-4 students Preparation time: 1 hour
More informationGrade 6 Standard 3 Unit Test A Astronomy. 1. The four inner planets are rocky and small. Which description best fits the next four outer planets?
Grade 6 Standard 3 Unit Test A Astronomy Multiple Choice 1. The four inner planets are rocky and small. Which description best fits the next four outer planets? A. They are also rocky and small. B. They
More informationStudy Guide due Friday, 1/29
NAME: Astronomy Study Guide asteroid chromosphere comet corona ellipse Galilean moons VOCABULARY WORDS TO KNOW geocentric system meteor gravity meteorite greenhouse effect meteoroid heliocentric system
More informationNiraj 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 information1. Mass, Force and Gravity
STE Physics Intro Name 1. Mass, Force and Gravity Before attempting to understand force, we need to look at mass and acceleration. a) What does mass measure? The quantity of matter(atoms) b) What is the
More informationPlease be sure to save a copy of this activity to your computer!
Thank you for your purchase Please be sure to save a copy of this activity to your computer! This activity is copyrighted by AIMS Education Foundation. All rights reserved. No part of this work may be
More informationChapter 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
More informationThe Two-Body Problem
The Two-Body Problem Abstract In my short essay on Kepler s laws of planetary motion and Newton s law of universal gravitation, the trajectory of one massive object near another was shown to be a conic
More informationOrbital Dynamics. Orbital Dynamics 1/29/15
Orbital Dynamics Orbital Dynamics 1/29/15 Announcements Reading for next class Chapter 5: Sections 5.1-5.4 Homework #2 due next class (Tuesday, Feb. 3) Project #1 topic ideas due next Tuesday (Feb. 3)
More informationExam # 1 Thu 10/06/2010 Astronomy 100/190Y Exploring the Universe Fall 11 Instructor: Daniela Calzetti
Exam # 1 Thu 10/06/2010 Astronomy 100/190Y Exploring the Universe Fall 11 Instructor: Daniela Calzetti INSTRUCTIONS: Please, use the `bubble sheet and a pencil # 2 to answer the exam questions, by marking
More informationBarycenter of Solar System Earth-Moon barycenter? Moon orbits what?
Barycenter of Solar System Earth-Moon barycenter? Moon orbits what? Dr. Scott Schneider Friday Feb 24 th, 2006 Sponsored by the Society of Physics Students (SPS) Webpage : http://qbx6.ltu.edu/s_schneider/astro/astroweek_2006.shtml
More informationF N A) 330 N 0.31 B) 310 N 0.33 C) 250 N 0.27 D) 290 N 0.30 E) 370 N 0.26
Physics 23 Exam 2 Spring 2010 Dr. Alward Page 1 1. A 250-N force is directed horizontally as shown to push a 29-kg box up an inclined plane at a constant speed. Determine the magnitude of the normal force,
More informationSatellites 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 informationGravity. in the Solar System. Beyond the Book. FOCUS Book
FOCUS Book Design a test to find out whether Earth s gravity always pulls straight down. A pendulum is a weight that hangs from a string or rod that can swing back and forth. Use string and metal washers
More informationWhy don t planets crash into each other?
1 Just as we know that the sun will rise every morning, we expect the planets and the moon to stay in their orbits. And rightly so. For 400 years, people have understood that the movements of Earth, the
More information11 Gravity and the Solar System Name Worksheet AP Physics 1
11 Gravity and the Solar System Name Worksheet AP Physics 1 1. Use Newton s irst Law of Motion to describe how a planet would move if the inward force of ravity from the sun were to suddenly disappear.
More informationA.4 The Solar System Scale Model
CHAPTER A. LABORATORY EXPERIMENTS 25 Name: Section: Date: A.4 The Solar System Scale Model I. Introduction Our solar system is inhabited by a variety of objects, ranging from a small rocky asteroid only
More informationChapter 6. Work and Energy
Chapter 6 Work and Energy The concept of forces acting on a mass (one object) is intimately related to the concept of ENERGY production or storage. A mass accelerated to a non-zero speed carries energy
More information2007 Pearson Education Inc., publishing as Pearson Addison-Wesley. The Jovian Planets
The Jovian Planets The Jovian planets are gas giants - much larger than Earth Sizes of Jovian Planets Planets get larger as they get more massive up to a point... Planets more massive than Jupiter are
More informationLecture 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 informationPenn 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 informationSOLVING EQUATIONS WITH RADICALS AND EXPONENTS 9.5. section ( 3 5 3 2 )( 3 25 3 10 3 4 ). The Odd-Root Property
498 (9 3) Chapter 9 Radicals and Rational Exponents Replace the question mark by an expression that makes the equation correct. Equations involving variables are to be identities. 75. 6 76. 3?? 1 77. 1
More informationSolar System Fundamentals. What is a Planet? Planetary orbits Planetary temperatures Planetary Atmospheres Origin of the Solar System
Solar System Fundamentals What is a Planet? Planetary orbits Planetary temperatures Planetary Atmospheres Origin of the Solar System Properties of Planets What is a planet? Defined finally in August 2006!
More informationOur Planetary System. Earth, as viewed by the Voyager spacecraft. 2014 Pearson Education, Inc.
Our Planetary System Earth, as viewed by the Voyager spacecraft 7.1 Studying the Solar System Our goals for learning: What does the solar system look like? What can we learn by comparing the planets to
More informationSample Questions for the AP Physics 1 Exam
Sample Questions for the AP Physics 1 Exam Sample Questions for the AP Physics 1 Exam Multiple-choice Questions Note: To simplify calculations, you may use g 5 10 m/s 2 in all problems. Directions: Each
More information