1Greek Astronomy / Motions of the sky• Erathosthenes’ measurement of the Earth• Hipparchus’ measurement of distance to the moon• Motions of the sky that we have seen with our naked eyes. A model to explain the motions.• Homework 1• Due Mon, Sept 14. (Delayed one class.) • Missouri Club on Fri, Sept 11. Show me …• You may work with your Ast207 buddies, but you must write your own homework. (No copies.)Erathosthenes ~200 BC• A correspondent in Syene reports that at noon on the summer solstice, the sun illuminates the bottom of a well. In Alexandria (where Erathostheneslived), a stick makes at 7° shadow.• It takes a camel 50 days to travel from Syene to Alexandria. A camel can travel 100 stadia/day.1. The distance between Alexandria & Syene is 500 km? 2. Draw a picture to show the relationship between the sun, the well, the stick, and the two locations. “A clear picture is 90% of clear thinking.”• Picture shows Alexandria & Syeneare 7° apart in latitude.• The circumference is 360° around Earth• 500km ×360°/7°=25,000km• Actual circumference is 40,000km.2Hipparchus measures the moon’s distance~200BC • At the Hellespont, the solar eclipse of 189BC was total. (Sparta defeated Athens there in 405 BC.)• In Alexandria, the moon covered ¾ of the sun. Alexandria is 1000km from the Hellespont.• The diameter of the sun is ½ degree. In Alexandria, the angle between the sun and moon is ¼*1/2=1/8 degree.• “A clear picture is 90% of clear thinking.” • Draw a picture to show the relationship between the sun, the moon, the two locations, and the angle between the sun and moon in Alexandria.http://mkatz.web.wesleyan.edu/medea_lecture/hellespont.gifView @ HellespontView in Alexandria. Moon is offset by 1/4 diameter of sunhttp://www.livius.orgWhat triangle did Hipparchus use?• Parts of triangle• Angle is due to parallax: moon in foreground shifts with respect to sun in the background.• One leg of triangle is the baseline.• Other leg is distance to moon.• Small-angle approximationAngle = Baseline/Distance• Angle must be in radians•180° in π rad•57°/rad• Find distanceDistance = Baseline/AngleMoonSunfrom HSunfrom ADistance MoonangangbaselineHellespontAlexandria3• Small-angle approximationAngle = Baseline/Distance• Angle must be in radians• 180° in π rad•57°/rad1. From Alexandria to the Hellespont, the angle between the sun and moon shifts by 1/8°. What is the shift in radians? Explain how to do this without remembering a formula.A. 1/8 radB. 57/8 = 6 radC. 1/8/57=1/440 radWhat triangle did Hipparchus use?• Parts of triangle• Angle is due to parallax: moon in foreground shifts with respect to sun in the background.• One leg of triangle is the baseline.• Other leg is distance to moon.• Small-angle approximationAngle = Baseline/Distance• Angle must be in radians•180° in π rad•57°/rad• Find distanceDistance = Baseline/Angleangle = 1/440 radD = 1000km 440 = 440,000kmMoonSunfrom HSunfrom ADistance MoonangangbaselineHellespontAlexandria4Changes in the Sky• Name two motions of objects in the sky or changes in the sky that you have observed.Changes in the Sky• The sun sets south of west in winter.• Winter days are short.• Stars move east to west over a night.• The constellations change over the months.• The sun (and moon and stars) rises & sets.• The sun is higher in the sky in summer than winter. • Planets move with respect to the stars.• Comets appear
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