Circumference and Shape of the Earth Known by

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 A Syene(Aswan) D B Web Eratosthenes (276 -196 BC) measured the circumference of the Earth in Egypt. -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 M 1*M 2 S 2 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 M 1*M 2 S 2 Paris equator T= The clock in Paris ran faster than the one at the equator Interpreting the results: 1. Using the gravity equation, 2. 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