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ASTR 200, reminder Center section = 'no laptop' zone Laptops OK 1 NO Laptops Blackboards Laptops OK ASTR 200 – Frontiers of Astrophysics 2 Instructor: Professor Gladman Office: Hennings 300B Lectures here (Henn 202) 12:00 on M,W,F Units for astronomy and astrophysics au 3 Units for astronomy and astrophysics au 4 Angular Measurements Full circle = 360º 1º = 60 (arcminutes) 1 = 60 (arcseconds) 6 angular diameter Diameter Angular diameter(o) Angular diameter ---------------------- = ---------------------- = ---------------2 Distance 360 o 2 radians 8 For those with integral calculus: Prove by integrating the surface element (sinθ dθ dφ) on a unit sphere that the area is 4π 9 Units for astronomy and astrophysics au 10 Units for astronomy and astrophysics au +c 11 Their values depend on the system of units one is using! 12 A light year Julian year is exactly 365.25 days so: 365.25 d * 24 h/d * 60 min/h * 60 s/min = 31,557,600 seconds = 3.15576 x 107 s unit c = 2.99792 x 108 m/s physical constant (what would it be in cm/s?) ly = 2.99792 x 108 m/s * 3.15576 x 107 s = 9.46072 x 1015 m This is a 'derived unit' based on a constant 13 Starting our steps out into the universe The first human steps were to understand the scale of : Our planet The Moon The Sun 14 Observations of the Moon Aristotle realizes the Earth is a sphere Erathostenes uses simple geometry to determine the size of the Earth Aristarchus realizes this gives the diameter of the Moon via eclipse observations Once one knows the diameter of the Moon, you can calculate its distance! Lunar Eclipse Sequence Lunar Phase Cycle Lunar Eclipse Sequence On the summer solstice, the sun shone straight down a well in Syene On the summer solstice, the sun shone straight down a well in Syene On the same day, an obelisk in Alexandria cast a 7.2 degree shadow... The Eratosthenes experiment Relies that Sun is far away. 7.2/360 must be distance from SyeneAlexandria divided by circumference (D) of the Earth 5000 stades The distance from Syene to Alexandria was known, which gives Earth's diameter! D see also text Fig on p. 33 The Eratosthenes experiment Relies that Sun is far away. 7.2/360 must be distance from SyeneAlexandria divided by circumference (D) of the Earth 7.2 5000 --- = -----360 πD 5000 stades The distance from Syene to Alexandria was known, which gives Earth's diameter! D 360*5000 see also text D = ----------= 80,000 Fig on p. 33 st 7.2*π *0.185 km/st D=14,800 km So, we knew the Earth's diameter How does that help get the MOON's diameter or distance? So, we knew the Earth's diameter How does that help get the MOON's diameter or distance? Does the relation : Diameter Angular diameter(o) Angular diameter ---------------------- = ---------------------- = ---------------2 Distance 360 o 2 radians help??? Lunar Eclipse Sequence Aristarchus Eclipse observations implied ; Diameter of Moon about 1/3 diameter of Earth Thus, diameter of Moon about 5000 km This gives distance to Moon! Board : use angular diameter of Moon is 0.5 deg. Conclude: D ~ 573,000 km. Actually 385,000 km... First step in the cosmic distance scale... Distance to Sun Trickier... Aristarchus had an argument about the quarter moon, but was off by a lot (see text) Wasn't done correctly until transits of Venus were done using telecope This didn't prevent (next week) accurately getting the RELATIVE scale of the planetary orbits What about distances to Stars? The ancients had a REALLY tough time with this question IF stars are physical objects like planets, they SHOULD exhibit parallax... Geocentric parallax (diurnal) Heliocentric parallax (annual, stellar)