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Circumference and Shape of the Earth Known by at least 400 BC Measure angle to star from two locations. Calculate arc deg and circumference. Or Simply watch a ship disappear over the horizon - Earth must be round Circumference of the Earth Suns rays C Alexandria Web Eratosthenes (276-196 BC) measured the circumference of the Earth in Egypt. A Syene(Aswan) D B -AB, no shadow, sun directly overhead -CD, shadow -500 miles from Syene to Alexandria -angle DCB = angle CBA -circle = 360 degrees -angle DCB = 7.25 degrees -360/7.25 = 49.7 arc segments -49.7 * ~500 miles = 24,850 miles (good to < 2%) The Pendulum and Gravity Period (T) is the time for one swing of the pendulum (ABA). T= Web 1 g Period (T) of a pendulum is inversely proportional to acceleration of gravity (g) A B g increases then T decreases = faster swing g decreases then T increases = slower swing The Pendulum and Earth Shape F= G M1*M2 S2 T= 1 g Newton (1642-1727) set up pendulum clocks, one at Paris and one at the equator, to determine if the Earth is a flattened sphere. Paris equator Testing whether the radius is different Web The Pendulum and Earth Shape F= G M1*M2 S2 Paris equator T= The clock in Paris ran faster than the one at the equator Interpreting the results: 1. Using the gravity equation, gravity is greater at Paris (smaller radius). 2. Using pendulum equation, > g means smaller T, or faster swing 1 g Velocity of the Earth N Latitude lines (east-west) Longitude lines (north-south) Circumference = Pi() * Diameter Earth’s Diameter = 7,900 miles S 24,000 miles 24 hours Earth circumference = 3.14 * 7,900 miles = 24,806 miles = 1,000 mph at the equator