Mathematics and Society - OS X Lion Server

How fast is each planet traveling in its orbit? Doesa distant planet move more quickly or more slowly alongits orbit than a planet closer to the Sun?You already know that a planet travels slower when itis at aphelion than when it is at perihelion. As shownir the diagram it moves along its orbit so that an imag~inary line joining the planet and the Sun sweeps out2qua1 areas in equal times. The diagram is exaggeratedsince the orbits of the planets are nearly circular.Pretend that each planet does move on acircular orbit that is centered on the Sun.Because of the law of equal areas, theplanet would move at a constant speed.By assuming that the orbits of theplanets are circular, we can use Kepler'sthird law to find the average speed ofeach planet in orbit.OJ-l£MDJ-lTHEQUAL TIME::'>,EQUAL AREASo = o 0SIr-JCE. THE. QISTAN.CE. I~G£EATER I-\t:.RE.- FOR 010E.MOmH, THE. SPCED OFTHE PLANET I" GREATE-I2.III A CIRCLE THE EQUALARE-AS MAKE THI;:. ARC.'::>(DISTAl.\CE) EQUAL, SO THESPEE.D IS CONSTANt.(Remember:SPEED =DISTANCE TRAVELEDTIME TAKEklI. Find the average orbital speed of the Earth.(a.b.The average distance of the Earth fromthe Sun is 1 a.u. or 149,600,000 km.If we assume that the Earth's orbit isa circle, 149,600,000 km is the radiusof the circle. What is the circumferenceof the orbit? His about 940,000,000 km.c 0Ro°0C~ 2.1TR.CIRCUMFEREI.lCE ;RADIUS TIMES 2. 1T1T ~ 3,14-II.112c. The orbital period of the Earth is 1 year.Sospeed = 940,000,000 km1 yeard.IDEA FROM:1 yearspeed =365 days = 8760 hours = 525,600 minutes=,9"-;4:-;0~'.o:.O~00~,~0",O.o:.O-,k""m,,,;-= =,9"-;4:'.;0~'.o:.O",-00"--"k,,,,m,-;- =31,536,000 seconds 31,536 secondsC= 2.-rr >