Mathematics and Society - OS X Lion Server

2. To construct a scale model of the orbits of Earth and Venus:a.b.Draw a circle, radius 5 cm torepresent the orbit of the Earth.Mark the Sun by placing a dot atthe center of the circle. At anypoint on the circle place a dotto represent the Earth. Since wedo not know the distance in kilometresfrom the Sun to the Earth,call the distance one astronomicalunit (1 a.u.) as Kepler did.Draw a line segment from the Earthto the Sun. Use your protractorto draw in the Earth-Venus line (EVfor the largest angle of separationTo draw the orbit of Venus, placethe compass point at the Sun and,by trial and error, adjust thecompass opening so that the circlejust touches the EV line. Make asmall dot at the point of contactand label it Venus. (Geometrically,the location of Venus is on theperpendicular from the Sun to theEV line.)Eline)(4r)..sl:ARTH Ic--l-----'--SUI\Jc. Measure the distance from the Sun to Venus in centimetres.How many astronomical units is Venus from the Sun?11\1 YOUR DRAWIt.lG5 CJYn REPRESEI\JTS. 1 A"',RONOM ICALUt.lIT. f-""-_''E v UI\JE3. The greatest angular separation of Mercury from the Sun is about 23°. Draw theorbit of Mercury in your scale model. Measure the distance from the Sun toMercury in centimetres.How many astronomical units is Mercuryfrom the Sun?II.As seen from Earth the positions of the outer planets (Mars, Jupiter, Saturn, Uranus,Neptune and Pluto) in relation to the Sun are much different than those of Mercuryand Venus. To observe this repeat the activity in I(a). Choose one partner to beMars and the other to be the Sun. Again you represent Earth. Arrange yourselves asshown in the figure. As Mars orbits the Sun, observe how the angle between your armsincreases up to 180° and then starts decreasing.1. Since the outer planets can appear anywherein relation to the Sun, Kepler hadto devise a new method to place Mars andthe other outer planets in the scalemodel./ '-'--11--- 'f," SUfV ;-'.......... _------"'.-a. Draw a circle, radius 5 cm as before,place a dot at the center to representthe Sun, and a dot on the circleto represent the Earth.e,UI.l. JEARTHIDEA FROM:Charting the Universe, Book 1, The University of Illinois Astronomy Program95