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Lesson Plan #5: Universal Gravitation i Lesson Plan #5: Universal Gravitation By Alan Zollner Teaching Science to Adolescents ED 5543.01, Fall 2008 Instructor: James Congelli Mount Saint Mary College Due: December 3, 2008 Lesson Plan #5: Universal Gravitation 1 Lesson Plan #3: Universal Gravitation Grade 11, 12 Regents Physics Topic: Newton’s Law of Universal Teaching Strategy: Direct Instruction Background: This lesson introduces the student to Newton’s Law of Universal gravitation, along with the inverse square law, particularly as these apply to the motion of planets. The student will experiment with these forces and motions in a PhET computer simulation called “My Solar System”. This lesson assumes the student has been introduced to circular motion including centripetal force in a prior lesson. I. Goals, Standards, and Objectives 1. Goals Given a reading from a Physics textbook, an introductory lecture, and a dynamic interactive computer simulation of up to four celestial bodies, the student will gain an understanding of the relationships given by Newton’s Law of Universal gravitation, and an understanding of how those relationships explain the orbits of satellites, planets, and other celestial bodies. The student will gain an intuitive feel for the inverse square law associated with force fields, and apply Newton’s Law of Universal Gravitation to solve problems mathematically. 2. Performance Objectives Objective 1: Given the Physics Reference Tables, the student will apply Newton’s Law of Universal Gravitation to correctly calculate any one of the unknown terms in that equation with 80% accuracy. Objective 2: Given the general motion of two celestial objects (orbital, colliding, or deflection) the student will explain the motion in terms of gravitational force, centripetal force, and inertia of the bodies involved. Lesson Plan #5 Universal Gravitation 2 Objective 3: Given a change in the distance between two massive objects, the student will apply their knowledge of the inverse square law of force fields to correctly calculate the resulting change in gravitational force between the objects. 3. Standards New York State Learning Standards: NYS MST STANDARD 1: Analysis, Inquiry, and Design – Mathematical Analysis Key Idea 1: Abstraction and symbolic representation are used to communicate mathematically. Key Idea 3: Critical thinking skills are used in the solution of mathematical relationships NYS MST STANDARD 1: Analysis, Inquiry, and Design – Scientific Inquiry Key Idea 1: The central purpose of scientific inquiry is to develop explanations of natural phenomena in a continuing, creative process. Key Idea 2: Beyond the use of reasoning and consensus, scientific inquiry involves the testing of proposed explanations involving the use of conventional techniques and procedures and usually requiring considerable ingenuity. NYS MST STANDARD 2: Information Systems: Key Idea 1: Information technology is used to retrieve, process, and communicate information as a tool to enhance learning. 1.5: Model solutions to a range of problems in mathematics, science, and technology, using computer simulation software. NYS MST STANDARD 4: Science - The Physical Setting Key Idea 5 : Energy and matter interact through forces that result in changes in motion. Performance Indicator 5.1 Major Understandings 5.1 e, f, l, n, q, s, t, u NYS MST STANDARD 5: Technology NYS MST STANDARD 6: Interconnectedness: Common Themes Key Idea 1 Systems Thinking: Through systems thinking, people can recognize the commonalities that exist among all systems and how parts of a system interrelate and combine to perform specific functions. Key Idea 2 Models: Models are simplified representations of objects, structures, or systems used in analysis, explanation, interpretation, or design. Lesson Plan #5 Universal Gravitation 3 Key Idea 4 Equilibrium and Stability: Equilibrium is a state of stability due either to a lack of change (static equilibrium) or a balance between opposing forces (dynamic equilibrium). NYS ELA STANDARD 3: Language for Critical Analysis and Evaluation. NYS Social Studies STANDARD 2: World History Crossdisciplinary National Science Education Standards: CONTENT STANDARD A: “…understandings about scientific inquiry….” CONTENT STANDARD B: “… motions and forces….” CONTENT STANDARD G: “ …Science as a human endeavor…Historical perspectives. II. Materials/Resources 4. Materials • • • Whiteboard and markers Tennis ball tied to 1 meter of string Copy of the NOAA tide-tables for the Hudson River (or other large body of water). 5. Electronic Technology A computer for each student (or pair of student) with the following: - Internet access, - Java 1.5 software installed - Access to the PhET simulation, “My Solar System” at the following website: http://phet.colorado.edu/simulations/sims.php?sim=My_Solar_System III. Teaching and Learning Strategies 6. Introduction o Link to prior lesson demonstration Begin lesson swinging the tethered tennis ball in a circular orbit over the teacher’s head. While the ball is circling, refer to the previously discussed centripetal force (Fc) in the string pulling on the tennis ball and on the teacher’s hand. (refer to Newton’s 3rd Law). Lesson Plan #5 Universal Gravitation 4 o Newton’s hypothesis Like curious people all over the world before him, including the astronomers Nicolaus Copernicus, Johannes Kepler, and Tyco Brahe, Isaac Newton thought about the motion of the planets and moons in our solar system. Newton’s brilliant hypothesis was that the same force that causes an apple to fall to the ground – gravity, is what causes planets to orbit the sun, and is the centripetal force that keeps planets orbiting the sun. 7. Development – Direct Instruction o Describe Newton’s brilliant thought experiment “Here’s how we think Newton thought about it: Seeing an apple accelerating when falling from a tree, he recognized there must be a force involved. Further more, an apple falling from the top of a very tall tree also accelerates, so what if that force reached not only to the top of the tree, but all the way up to the moon! We saw the force of gravity is independent of the horizontal velocity of a projectile. “Horizontal velocity” in essence is a velocity tangential to the surface of the earth. So Newton thought, ‘what if we shot a cannon ball fast enough and from a high enough mountain?’ Newton imagined the following: Draw a diagram of progressively longer trajectories as shown below: Earth Source: Wikimedia Commons: Image: Newton Cannon.svg o Newton’s Law of Universal Gravitation: Note: The following explanations of Newton’s conclusion and the universal law of gravitation are provided by Astrowiki, a collaborative project of University of Tennessee organizing the free sharing of astronomy educational resources for the public. (Astrowiki, 2007) “Newton reasoned that if the cannon projected the cannon ball with exactly the right velocity, the projectile would travel completely around the Earth, always falling in the gravitational field but never reaching the Earth, which is curving away at the same rate that the projectile falls. That is, the cannon ball would have been put into orbit around the Earth. Newton concluded that the orbit of the Moon was of exactly the same nature: the Moon continuously "fell" in its path around the Earth because of the acceleration due to gravity, thus producing its orbit. Lesson Plan #5 Universal Gravitation 5 By such reasoning, Newton came to the conclusion that any two objects in the Universe exert gravitational attraction on each other, with the force having a universal form: The constant of proportionality G is known as the universal gravitational constant. It is termed a "universal constant" because it is thought to be the same at all places and all times, and thus universally characterizes the intrinsic strength of the gravitational force. An article in your textbook (Serway& Faughn, 2006) describes the fascinating experiment devised by Henry Cavendish in 1798, to experimentally determine the constant G. Your Physics Reference tables lists G = 6.673 x 10-11 N•m2/kg2 o Examining Newton’s Law of Universal Gravitation: First: Note that this law describes the force between two objects, but does not say how it works. That theory is yet to come. Second, From the equation Fg = G(m1 x m2)/r2 we see that the gravitational force is proportional to the product of the masses. Third, We see that the gravitational force is inversely proportional to the square of the distance between the centers of the objects. This is known as an “inverse square law” and will show up again in our study of fields. Fourth, Since the earth’s mass is constant, and it’s radius is nearly constant, on planet Earth, this equation reduces to a form we are familiar with in our study of one dimensional free fall: If the force of gravity on earth on an object of mass m is Lesson Plan #5 Universal Gravitation 6 Fg = G(mEarth x m)/r2, But G(mEarth)/ r2 becomes the constant g, and we get our good friend: Fg =gm Finally, Recall from our study of uniform circular motion that centripetal force can be expressed as: Fc = mv2t/r “centripetal force = mass x (tangential speed)2 / radius of circular path” So, if the centripetal force of an orbiting mass equals the gravitational force between two masses, you can bet that some kind of dynamic equilibrium is going to take place. o Invitation to look at planetary motion Let’s take a look at how three factors combine to affect the motion of the moon, planets, stars, and other objects in space: 1) Mass of objects (It turns out that gravitational mass and inertial mass are identical) 2) distance between objects 3) velocity vectors of objects 8. Guided Practice and Feedback o Examining celestial motion with using the “My Solar System” computer simulation Distribute the “Exploring Gravitation” worksheets, and guide students to initialize the computer simulation “My Solar System” on their computers at the following website: http://phet.colorado.edu/simulations/sims.php?sim=My_Solar_System and clicking Run Now! For this guided practice, I chose to use a worksheet posted on the PhET My Solar System site by David Simmons (2007), a high school teacher at St. John’s Jesuit High School in Toledo Ohio. The worksheet called “Exploring Gravitation” is given in the Appendix. During the Lesson Plan #5 Universal Gravitation 7 simulation, the teacher should facilitate by encouraging student inquiry and discussion, and providing scaffolding guidance as needed. The worksheet is a guideline. Students should also be encouraged to examine different initial velocities and distances between objects. The following table contains screenshots of images students might obtain for sections I – V of their worksheets: Table 1: Exploring Gravitation Sample Images Example of initial velocity vectors for a 3 body system: I. Simple sun-planet system: II. 3 bodies: Sun, planet, moon: III: 4 bodies, with inner planet: IV: 2 bodies: binary star: V: 3 bodies: twin planets: Lesson Plan #5 Universal Gravitation 8 9. Accommodations and Modifications for Learners with Special Needs Early Mastery: Encourage students to “benchmark” the simulation, but testing initial conditions at zero velocities, or at different starting distances. Ask them to verify whether the dynamic behavior they see is consistent with the Newton’s Universal Law of Gravitation. Encourage experimentation with other configurations. Students with difficulty with mathematics: Encourage a conceptual understanding of the inverse square law using the simulation. Provide a pair of magnets for students to get a physical feel for the inverse relationship between force and distance. Difficulty paying attention: Students who have difficulty paying attention love this simulation, because it places them in control and in the center of the learning experience. ESL: The “My Solar System” simulation is available in some foreign languages including Spanish. The mathematical and drawing responses should be relatively accessible to ESL students, depending on their level of English language proficiency. A foreign language version of the worksheet might be provided, as might an interpreter. Since the topic of this lesson is studied all over the world, it is likely that the student, interpreter, or the teacher can readily obtain foreign language versions of the theory if needed. IEP & 504 Plan: Any student with an IEP or 504Plan will be given the modifications or environmental assistance required. Note: This assignment referred to “2 Sp. Ed.” students. As such, several different accommodations have been listed. I have not assumed that “Sp. Ed” necessarily refers to students with cognitive disabilities. The IEP would provide guidance regarding accommodations or modifications specific to the individual and the disability identified. 10. Closure o Pose the following question to students to quickly review today’s lesson: Were you able to see that as the masses of the objects were increased, the gravitational force (or acceleration) between them increased? Ans: Yes. What happened to the objects when they were closer to each other? Ans: They accelerated faster What happened if the tangential velocity was too small? Ans: The objects collided. What happened if the tangential velocity was too fast, or the objects were too far apart? Ans: They pass each other but do not fall into an orbital system. Lesson Plan #5 Universal Gravitation 9 I hope everyone was able to see the role that distance, mass, and velocity can play in orbiting systems. 11. Independent practice o Inverse Square Relationship for Gravitational Force: The worksheet “Inverse Square Relationship for Gravitational Force” (Mader & Winn, 2008) will be assigned as homework or independent class work. Answer sheet is provided. o Homework problems: Student are to complete 5 assigned homework problems that include calculating m, Fg, and d using Newton’s Law of Universal Gravitation. II. Evaluation Methods of Evaluation Guided Practice with “My Solar System” Completion of simulation worksheet - 10 points Active participation in the simulation activity – 10 points Independent Practice: Inverse Square Relationship (1 point for each correct response) 20 Independent Practice: Homework Problems (1 point for each correct response) Quiz (See answer key for scoring rubric) 5 Total Possible Points 50 10 15 Lesson Plan #5 Universal Gravitation 10 Bibliography Brondel, B (2007). Image: Newton Cannon. In Wikimedia Commons [Web]. Retrieved December 3, 2008, from http://images.google.com/imgres?imgurl=http://upload.wikimedia.org/wikipedia/common s/thumb/7/73/Newton_Cannon.svg/240pxNewton_Cannon.svg.png&imgrefurl=http://blackjack000.blogspot.com/2008/06/explanati on-of-scientificmethod.html&usg=__G5YspsbUh8NgmgSSjsVGWHSvYI4=&h=240&w=240&sz=24&h l=en&start=2&um=1&tbnid=5xwZUZXaZ04N2M:&tbnh=110&tbnw=110&prev=/image s%3Fq%3Dnewton%2527s%2B%2Bgravitational%2Bthought%2Bexperiment%26um%3 D1%26hl%3Den%26client%3Dfirefox-a%26rls%3Dorg.mozilla:enUS:official%26sa%3DN Astrowiki, (2007). Sir Isaac Newton: The Universal Law of Gravitation. Retrieved December 3, 2008, from UT Astrophysics - Astrowiki Web site: http://csep10.phys.utk.edu/astr161/lect/history/newtongrav.html Mader, J. & Winn, M. (2008). Teaching Physics for the first time. College Park, MD: American Association of Physics Teachers. Simmons, D. (2007, September). Exploring gravitation. Retrieved December 2, 2008, from PhET My Solar System - Motion, Acceleration, Velocity, Circular Motion Web site: http://phet.colorado.edu/teacher_ideas/viewcontribution.php?contribution_id=108&referrer= Planning and preparation: Lesson plan rubric. (2005, January). Newburgh, NY: Mount Saint Mary College.