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
Circumference of the Earth
Web
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 lt 2)
Syene(Aswan)
Alexandria
D
B
3
The Pendulum and Gravity
Web
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
The Pendulum and Earth Shape
Web
M1M2
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
M1M2
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,
• gt g means smaller T, or faster swing

6
Velocity of the Earth
Latitude lines (east-west) Longitude lines
(north-south)
N

• Circumference Pi(?) Diameter
• Earths Diameter 7,900 miles

Earth circumference 3.14 7,900 miles
24,806 miles
S