Kepler's laws of planetary motion | Definition, Diagrams, & Facts

Kepler's laws of planetary motion, in astronomy and classical physics, laws describing the motions of the planets in the solar system. Kepler’slawsofplanetarymotion TableofContents Introduction&TopQuestions FastFacts Facts&RelatedContent Media Videos Images More MoreArticlesOnThisTopic Contributors ArticleHistory Home Science Astronomy Kepler’slawsofplanetarymotion astronomy Print Cite verifiedCite Whileeveryefforthasbeenmadetofollowcitationstylerules,theremaybesomediscrepancies. Pleaserefertotheappropriatestylemanualorothersourcesifyouhaveanyquestions. SelectCitationStyle MLA APA ChicagoManualofStyle CopyCitation Share Share Sharetosocialmedia Facebook Twitter URL https://www.britannica.com/science/Keplers-laws-of-planetary-motion More GiveFeedback ExternalWebsites Feedback Corrections?Updates?Omissions?Letusknowifyouhavesuggestionstoimprovethisarticle(requireslogin). 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ExternalWebsites UniversityofNebraska,Lincoln-AstronomyEducation:Kepler'sLawsofPlanetaryMotion WesternWashingtonUniversity-Kepler'sThreeLawsofPlanetaryMotion KansasStateUniversity-MathematicsDepartment-Kepler'sLawsofPlanetaryMotionandNewton'sLawofUniversalGravitation UniversityofRochester-DepartmentofPhysicsandAstronomy-JohannesKepler:TheLawsofPlanetaryMotion By TheEditorsofEncyclopaediaBritannica • EditHistory Kepler'sfirstlaw Seeallmedia KeyPeople: JohannesKepler ...(Showmore) RelatedTopics: celestialmechanics Kepler’sfirstlawofplanetarymotion Kepler’sthirdlawofplanetarymotion Kepler’ssecondlawofplanetarymotion ...(Showmore) Seeallrelatedcontent→ TopQuestionsWhatdoesKepler’sfirstlawmean?Kepler’sfirstlawmeansthatplanetsmovearoundtheSuninellipticalorbits.Anellipseisashapethatresemblesaflattenedcircle.Howmuchthecircleisflattenedisexpressedbyitseccentricity.Theeccentricityisanumberbetween0and1.Itiszeroforaperfectcircle.orbitReadmoreaboutplanetaryorbit.Whatiseccentricityandhowisitdetermined?Theeccentricityofanellipsemeasureshowflattenedacircleitis.Itisequaltothesquarerootof[1-b*b/(a*a)].Theletterastandsforthesemimajoraxis,½thedistanceacrossthelongaxisoftheellipse.Theletterbstandsforthesemiminoraxis,½thedistanceacrosstheshortaxisoftheellipse.Foraperfectcircle,aandbarethesamesuchthattheeccentricityiszero.Earth’sorbithasaneccentricityof0.0167,soitisverynearlyaperfectcircle.ellipseReadmoreaboutellipses.WhatisthemeaningofKepler’sthirdlaw?HowlongaplanettakestogoaroundtheSun(itsperiod,P)isrelatedtotheplanet’smeandistancefromtheSun(d).Thatis,thesquareoftheperiod,P*P,dividedbythecubeofthemeandistance,d*d*d,isequaltoaconstant.Foreveryplanet,nomatteritsperiodordistance,P*P/(d*d*d)isthesamenumber.celestialmechanics:TheapproximatenatureofKepler’slawsReadmoreabouttheapproximatenatureofKepler’sthirdlaw.Whyisaplanet’sorbitslowerthefartheritisfromtheSun?AplanetmovesslowerwhenitisfartherfromtheSunbecauseitsangularmomentumdoesnotchange.Foracircularorbit,theangularmomentumisequaltothemassoftheplanet(m)timesthedistanceoftheplanetfromtheSun(d)timesthevelocityoftheplanet(v).Sincem*v*ddoesnotchange,whenaplanetisclosetotheSun,dbecomessmallerasvbecomeslarger.WhenaplanetisfarfromtheSun,dbecomeslargerasvbecomessmaller.principlesofphysicalscience:ConservationlawsandextremalprinciplesReadmoreabouttheconservationofangularmomentum.WhereisEarthwhenitistravelingthefastest?ItfollowsfromKepler’ssecondlawthatEarthmovesthefastestwhenitisclosesttotheSun.ThishappensinearlyJanuary,whenEarthisabout147millionkm(91millionmiles)fromtheSun.WhenEarthisclosesttotheSun,itistravelingataspeedof30.3kilometers(18.8miles)persecond.LearnhowKepler'slawsanalyzeellipses,eccentricity,andangularmomentumaspartofthephysicsofthesolarsystemKepler'slawsofplanetarymotionexplainedinfivequestions.EncyclopediaBritannicaINC.SeeallvideosforthisarticleLearnhowJohannesKeplerchallengedtheCopernicansystemofplanetarymotionKepler'stheoryofthesolarsystem.EncyclopædiaBritannica,Inc.SeeallvideosforthisarticleKepler’slawsofplanetarymotion,inastronomyandclassicalphysics,lawsdescribingthemotionsoftheplanetsinthesolarsystem.TheywerederivedbytheGermanastronomerJohannesKepler,whoseanalysisoftheobservationsofthe16th-centuryDanishastronomerTychoBraheenabledhimtoannouncehisfirsttwolawsintheyear1609andathirdlawnearlyadecadelater,in1618.Keplerhimselfnevernumberedtheselawsorspeciallydistinguishedthemfromhisotherdiscoveries.Kepler’sthreelawsofplanetarymotioncanbestatedasfollows:(1)AllplanetsmoveabouttheSuninellipticalorbits,havingtheSunasoneofthefoci.(2)AradiusvectorjoininganyplanettotheSunsweepsoutequalareasinequallengthsoftime.(3)Thesquaresofthesiderealperiods(ofrevolution)oftheplanetsaredirectlyproportionaltothecubesoftheirmeandistancesfromtheSun.Knowledgeoftheselaws,especiallythesecond(thelawofareas),provedcrucialtoSirIsaacNewtonin1684–85,whenheformulatedhisfamouslawofgravitationbetweenEarthandtheMoonandbetweentheSunandtheplanets,postulatedbyhimtohavevalidityforallobjectsanywhereintheuniverse.NewtonshowedthatthemotionofbodiessubjecttocentralgravitationalforceneednotalwaysfollowtheellipticalorbitsspecifiedbythefirstlawofKeplerbutcantakepathsdefinedbyother,openconiccurves;themotioncanbeinparabolicorhyperbolicorbits,dependingonthetotalenergyofthebody.Thus,anobjectofsufficientenergy—e.g.,acomet—canenterthesolarsystemandleaveagainwithoutreturning.FromKepler’ssecondlaw,itmaybeobservedfurtherthattheangularmomentumofanyplanetaboutanaxisthroughtheSunandperpendiculartotheorbitalplaneisalsounchanging.Kepler'ssecondlawKepler'ssecondlawofplanetarymotion.AradiusvectorjoininganyplanettotheSunsweepsoutequalareasinequallengthsoftime.EncyclopædiaBritannica,Inc./PatrickO'NeillRileyKepler'sthirdlawKepler'sthirdlawofplanetarymotion.Thesquaresofthesiderealperiods(P)oftheplanetsaredirectlyproportionaltothecubesoftheirmeandistances(d)fromtheSun.EncyclopædiaBritannica,Inc./PatrickO'NeillRileyplanetaryorbits:Kepler,Newton,andgravityBrianGreenedemonstrateshowNewton'slawofgravitationdeterminesthetrajectoriesoftheplanetsandexplainsthepatternsintheirmotionfoundbyKepler.ThisvideoisanepisodeinhisDailyEquationseries.©WorldScienceFestival(ABritannicaPublishingPartner)SeeallvideosforthisarticleTheusefulnessofKepler’slawsextendstothemotionsofnaturalandartificialsatellites,aswellastostellarsystemsandextrasolarplanets.AsformulatedbyKepler,thelawsdonot,ofcourse,takeintoaccountthegravitationalinteractions(asperturbingeffects)ofthevariousplanetsoneachother.Thegeneralproblemofaccuratelypredictingthemotionsofmorethantwobodiesundertheirmutualattractionsisquitecomplicated;analyticalsolutionsofthethree-bodyproblemareunobtainableexceptforsomespecialcases.ItmaybenotedthatKepler’slawsapplynotonlytogravitationalbutalsotoallotherinverse-square-lawforcesand,ifdueallowanceismadeforrelativisticandquantumeffects,totheelectromagneticforceswithintheatom.TheEditorsofEncyclopaediaBritannicaThisarticlewasmostrecentlyrevisedandupdatedbyBarbaraA.Schreiber.