Circumference and Shape of the Earth

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

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

4. Web The Pendulum and Earth Shape M1*M2 1 G F = T =  S2 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 Testing whether the radius is different equator

5. The Pendulum and Earth Shape M1*M2 1 G F = T =  S2 g Paris The clock in Paris ran faster than the one at the equator equator • Interpreting the results: • Using the gravity equation, • gravity is greater at Paris (smaller radius). • 2. Using pendulum equation, • > g means smaller T, or faster swing

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