1. Circumference and Shape of the Earth 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 Known by at least 400 BC

2. Circumference of the Earth Eratosthenes (276-196 BC) measured the circumference of the Earth in Egypt. Syene(Aswan) Alexandria Suns rays A D C 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%) Web

3. The Pendulum and Gravity T =  1 g Period (T) is the time for one swing of the pendulum (ABA). A B Web Period (T) of a pendulum is inversely proportional to acceleration of gravity (g) g increases then T decreases = faster swing g decreases then T increases = slower swing

4. The Pendulum and Earth Shape F = M 1 *M 2 S2S2 G 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

5. The Pendulum and Earth Shape F = M 1 *M 2 S2S2 G T =  1 g Paris equator 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

6. Velocity of the Earth Circumference = Pi(  ) * Diameter Earth’s Diameter = 7,900 miles Latitude lines (east-west) Longitude lines (north-south) N S Earth circumference = 3.14 * 7,900 miles = 24,806 miles 24,000 miles 24 hours = 1,000 mph at the equator