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Classical Mechanics, Volume 4 The universal law of gravitation Classical Mechanics, Volume 4 The universal law of gravitation Gregory A DiLisi John Carroll University, University Heights, Ohio, USA Morgan & Claypool Publishers Copyrightª2019Morgan&ClaypoolPublishers Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem ortransmittedinanyformorbyanymeans,electronic,mechanical,photocopying,recording orotherwise,withoutthepriorpermissionofthepublisher,orasexpresslypermittedbylawor undertermsagreedwiththeappropriaterightsorganization.Multiplecopyingispermittedin accordancewiththetermsoflicencesissuedbytheCopyrightLicensingAgency,theCopyright ClearanceCentreandotherreproductionrightsorganizations. 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ISBN 978-1-64327-302-0(ebook) ISBN 978-1-64327-299-3(print) ISBN 978-1-64327-300-6(mobi) DOI 10.1088/2053-2571/ab1895 Version:20190801 IOPConcisePhysics ISSN2053-2571(online) ISSN2054-7307(print) AMorgan&ClaypoolpublicationaspartofIOPConcisePhysics PublishedbyMorgan&ClaypoolPublishers,1210FifthAvenue,Suite250,SanRafael,CA, 94901,USA IOPPublishing,TempleCircus,TempleWay,BristolBS16HG,UK This book is dedicated to my family: to my grandparents, Tommaso and Carmela Frate, to my parents, Richard and Mary DiLisi, to my siblings, Rick DiLisi, Carla Solomon, and Jennifer Newton, to my wife, Linda, to my daughter, Carmela, and to the wonderful creatures who inhabit our home. Contents Preface viii Author biography xiii 1 Motivation 1-1 2 Getting ready 2-1 2.1 Anticipatory set 2-1 2.2 Objective 2-5 2.3 Purpose 2-6 3 Giving information 3-1 3.1 Instructional input 3-1 3.1.1 History of modern astronomy 3-1 3.1.2 The universal law of gravitation 3-15 3.1.3 Determining the universal gravitation constant, G 3-19 3.2 Modeling 3-24 3.3 Instructional input 3-30 3.3.1 Weight 3-30 3.4 Modeling 3-30 3.5 Instructional input 3-35 3.5.1 The ‘field’ 3-35 3.5.2 Calculating the gravitational field 3-41 3.6 Modeling 3-41 3.7 Checking for understanding 3-47 4 Keeping information 4-1 4.1 Closure 4-1 4.2 Independent practice 4-4 4.3 Peer teaching 4-5 4.3.1 Universal Law of Gravitation and Weight 4-5 4.3.2 The Gravitational Field 4-6 vii Preface We derive the word ‘physics’ from the Greek word ‘physika,’ which translates into ‘pertainingtonaturalthings.’Therefore,aswebeginourstudyof‘physics,’wequite literally begin our study of ‘natural things.’ When I was in high school, my physics teacher, Mr Lamovsky, once asked me: ‘Who is the greatest physicist? Newton? Einstein?Galileo?’Ithoughtforamomentandgavehimananswerthatabsolutely flooredhim.‘Batman,’Isaid,‘becausehisentirelifeisdedicatedtofiguring-outhow and why things move … grapplings, cables, levers, cars, projectiles, etc.’ In short, that’s what this book is about—figuring out how and why things move. Instead of viewing physics as the study of ‘natural things’ (from its literal Greek translation), a good way to view physics is to simply think of it as the study of motion. In fact, Albert Einstein once said: ‘Nothing happens until something moves.’ Think about it … you cannot generate a thought without some electrical signalmovinginyourbrain.Evenyouremotionsinvolvethecomplexmovementof chemical and electrical signals throughout your body. I think we can all agree with Einstein that indeed nothing happens until something moves! Pay careful attention and you will notice that every problem you will encounter in this book involves somethingmoving.Therefore,thegoalofanygoodphysicsbookisquitesimple:to develop problem-solving techniques that handle different types of motion. The situations we encounter in everyday life vary considerably and so our problem- solvingtechniques mustvaryaccordingly.Wewill discoverthatthe techniquesthat defeat the Joker may not work well on the Riddler or Penguin. Therefore, we will developanentirearsenalofproblem-solvingtactics—allofwhicharemeanttohelp us understand the behavior or movement of objects in motion! Before developing these problem-solving techniques, I will describe how I designed thisseriesofbooksandhowtheycametobecreated.First,Iwilldescribe the structure and topics covered in a typical introductory physics sequence of courses. This overarching structure will provide the context for which these texts were designed. Next, I will describe the format of how each topic is presented. The formatwilldemonstratehoweachsectioniswrittenandhoweachtopicinthetextis arranged.Finally,Iwillmorethoroughlydescribetheoverallpurposeoftheseriesof books. 1. Structure of the typical introductory physics sequence of classes: The introductory physics sequence of classes is typically divided into three distinct courses. This series of books focuses on only the first course, ‘Classical Mechanics.’ However, the distinctions among these three courses are useful to see because they frame the context under which ‘Classical Mechanics’ is housed. The distinctions among these three courses are briefly described below: 1. ‘Classical Mechanics’—The term ‘Classical Mechanics’ describes the motion or behavior of objects whose dimensions and/or speeds are familiar to all of us. The objects we examine must have mass. Your intuition from everyday experiences will be generally correct because, viii ClassicalMechanics,Volume4 likeitornot,youhavemass(maybemorethanyouwouldlike)andare used to interacting with the Earth through the force of ‘gravity.’ 2. ‘Classical Electricity and Magnetism’—The term ‘Classical Electricity and Magnetism’ describes the motion or behavior of objects whose dimensionsand/orspeedsarealsofamiliartoallofus.However,unlike the objects examined in ‘Classical Mechanics,’ the objects we now examine must have charge. Your intuition from everyday experiences will be somewhat challenged because you typically do not carry huge amountsofstaticormovingchargewithyou,soarethereforenotused to interacting with other objects through the forces of ‘electricity’ or ‘magnetism.’ 3. ‘Modern Physics’ or ‘Quantum Mechanics’—Finally, the terms ‘Modern Physics’ or ‘Quantum Mechanics’ describe the motion or behavior of objects whose dimensions and/or speeds are very unfami- liar (i.e. extremely small or large) to all of us. Your intuition from everyday experiences will tell you nothing about a particular problem because you are neither extremely small nor extremely fast. The distinction of these courses is summarized in the following diagram: PHYSICS PARTICLES PARTICLES PARTICLES WITH WITH WITH MASS CHARGE SPEEDS NEAR THAT OF LIGHT MECHANICS ELECTRICITY QUANTUM & OR MODERN MAGNETISM PHYSICS The distinct topics covered in each of the three typical introductory physics courses. 2. Formatofthisseries:Thisseriesofbookswasgeneratedfromthesetofnotes that I have used to teach my introductory physics courses on Classical Mechanics. After decades of teaching these courses, I finally decided to convertthese notesinto aseriesoftexts. Thisconversion fromnotestotexts wassimplyanaturalprogressionasanext-stepalongthedevelopmentofmy Classical Mechanics courses. I only assume that the reader understands mathematics at the level of high school Algebra. The reader need not be familiar with high school physics, nor Calculus. What makes this series of books unique (indeed distinctive from typical Algebra-based introductory physics books) is that it combines my experience as a physicist with my ix