Mathematics and Society - OS X Lion Server

.Kep!eys seconcfJa11lTycho's data on the orbit of Mars allowed Keplerto figure Mars' speed, regardless of where Mars was inits orbit. Looking over the speeds of Marsat different parts of the orbit, Keplerfound something quite unexpected: TheSltJCE A PLANG TRAVelS FASTE12speed of Mars is not always the same!NEAR. P(R.II-\WOt0, IT TRAVRS AWhat's more, Kepler noted that the speedchanges in a regular pattern. When MarsGREATER DISTANCE IIJ O!JE MOI\lTHpasses perihelion, it is moving fasterTHAIJ IT DOE'S l\leAR AR-iELION Itothan at any other point in its orbit.O!JE MOf\)TH. 0Then the speed decreases until it isoslowest at the aphelion. Mars picksup speed until it returns to perihelionagain.Kepler found the same behavior tobe true of all the planets he studied.A planet's greatest speed occurs atperihelion and its least speed ataphelion.1MOrJTH•1 MOt\lTHKepler decided to draw an imaginaryline from Mars to the Sun. As the planetmoves, the line sweeps out an area ofspace. Kepler discovered that Marsmoves so that it always sweeps out thesame amount of area every day. Hefound that other planets also sweepout areas in a similar way: that is,each planet moves along its orbit sothat an imaginary line joining theplanet and the Sun sweeps out equalareas in equal times. This is Kepler'ssecond law.MO~T~;j!&t~w?,,·o".).r~J(:~{E:~.]~JEij[0Fto:MomHa . '1 0o 0o TI-\E. AREAS OF e,OTHSHADED REGIONS ARt;: TI-\1OSAMe.(Exercises:1.a. Use cardboard, thumbtacks and stringto draw several ellipses.b. Label one focus the Sun.c. Choose a portion of the ellipse torepresent the distance traveled bya planet in one unit of time. Drawline segments to join the endpointsof the chosen arc to the Sun. Shadein the area.C .SUIJ• ~-----(108IDEA FROM:The Universe in Motion, Book 2, The University of Illinois Astronomy Program