Mathematics and Society - OS X Lion Server

(Astronomers are able to construct a scale model of the solar system without knowing asingle actual distance in the system. The construction is based upon accurate observationsof the positions of the Sun and planets. One of the first men to gather suchobservations was Tycho Brahe (TIE-koeBRAH). He lived from 1546 to 1601. Tycho'sassistant, Johannes Kepler (yoe-HAHN-es KEP-ler) used the information to make a solarsystem model.Why is a model of this type useful? If one actual distance is measured, the scaleof the model can be established and other distances can be determined. For example, bymeasuring the distance from Earth to Venus, and using the model, the distance from theEarth to the Sun can be learned.Kepler's method is described below so you can make a scale model of the solar system.You will need a protractor, compass and two partners.I. The orbits of the inner planets, Mercury and Venus, can be positioned in the scalemodel by finding what is called their maximum angular separation from the Sun. (Inpositioning the inner planets we assume that the Sun is the center of the Solarsystem; that Mercury, Venus and Earth revolve around the Sun in roughly circularorbits; and that Mercury and Venus are closer to the Sun than the Earth.)1.To help you visualize Venus' motionaround the Sun as seen from Earth,choose one partner to represent Venusand the other to represent the Sun.You represent Earth. Have "Venus"walk slowly around the "Sun" as shownin the sketch.You point with one hand at "Venus"and with the other at the "Sun."As "Venus" moves, notice how theangle formed by your arms changes.When is the angle very small? Whendoes it get very large? Does it everget as large as 90°?--- ---- "VElJU5'" ,\I,, I------------ -~~/, ,, ,, ,JE-+----c,\, ,~ \', ,,'(_____ -~"'~':::::::: .:~"~ I'd~lJU'!>From his observations, Tycho Brahe 1""O---~jL--.:-o-r-~~~'concluded thaft the mafximumhangsula,;separation 0 Venus rom t e un 1S ~,~ ~ (47°. 'OE:P8