Mathematics and Society - OS X Lion Server

We can use a base line on the Earth to determine the distance to the Moon. However,the Earth is too small to provide a long enough base line to accurately find the distanceto the Sun. How then do we measure the distances to stars?To obtain an adequate base line, astronomersuse the motion of the Earth. The Earth travels inan orbit around the Sun that is almost circular.The diameter of the orbit provides a base line ofabout 300,000,000 km or 2 astronomical units.Astronomers sight the same star fromopposite sides of the Earth's orbit. Insteadof using the angles at both ends of the baseline, astronomers measure only the anglewhose vertex is at the star. From the anglesize and the length of the base line thestar's distance can be found. ,\ .......2. A.iJ, ,,,,I, ,I,ASTROtllOMERSMEASURE THISAI\JGLE.At first it may seem impossible to measure the angle whose vertex is at the star.Astronomers have devised a method called parallax to help them.I. Understanding parallax shift.A. Hold a pencil at arm's length. Lookat the pencil first with one eye andthen the other (close or cover theother eye). The pencil should appearto shift back and forth against thebackground. Hold the pencil close,then far away. The apparent shift isgreater when the pencil is close andsmaller when it is more distant.B. Use the range finder from"How Far Is the Sun." Onthe range finder, draw anarc of a circle with centerat the vertex pin andwith radius equal to thelength of the sightingline. Hold your headabout 30 cm from the vertexpin. Close yourright eye and sight withyour left across therange finder. Have aclassmate place a pin onthe arc so that it linesup with the vertex pin.SIG.H~LII\JE:FROM RIGHT -f------,/ SIGHT LH0EEYEFROI\I\ LEFT EY£:30 em /t:1;if::===='====~VERi!O.llPI\\\IDEA FROM:Charting the Universe, Book 1, The University of Illinois Astronomy Program89