Circumference and Shape of the Earth

Measure angle to star from two locations. Calculate arc deg and circumference.

OrSimply watch a ship disappear over

the horizon - Earth must be roundKnown by at least400 BC

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

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

The Pendulum and Earth Shape

F = M1*M2

S2G 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

equatorTesting whether the radius is different

Web

The Pendulum and Earth Shape

F = M1*M2

S2G 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

Velocity of the Earth

Circumference = Pi() * DiameterEarth’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