Class_2 - What's so special about 360 Why not use 435 Is...

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Unformatted text preview: What's so special about 360? Why not use 435? Is there a natural choice? Ratio of arc length to radius: Angle = A1/R1 = A2/R2 A circle makes an angle of 2 at the center radians = 180 1 = /180 radians Trigonometry is much easier (next slide...) ' !"# !"# $ $ * * + # # $ ) ' ' % ( # ) ') % & ")" # & %& ' ' At any quarter, the sun, earth and moon form a right-angled triangle 3 hypotenuse is 19 times perpendicular (3 = 0.052 radians = 1/19.1) Sun-Earth = 19 x Sun-Moon Modern figure is 390 (89.85 ) (0.15 = 1/390 rad) DS:Dm = RS:Rm (similar triangles) Hence RS = 19 Rm (acc. to Aristarchus) What should be the modern value? RS = 400 Rm , . & 12 / 0 12 12 12 - 1 2 2 12 2 )" & 3 ") & !+! & " ))! & )'#4# & Nearer stars move w.r.t. farther stars sin(p) = 1 A.U. / d sin(p) $ p (small p) / * - 4 / 6' ") ' ") %+% 0 & & 8 9 " ) 6) #') "& + !"% " % +& ) 5-/ # % & 7 # % & 6) " + / 6- / 6) 6- ...
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Class_2 - What's so special about 360 Why not use 435 Is...

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