Transcript Circumference and Shape of the Earth

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
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Eratosthenes (276-196 BC)
measured the circumference
of the Earth in Egypt.
A
Syene(Aswan)
D
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%)
The Pendulum and Gravity
Period (T) is the time
for one swing of the
pendulum (ABA).
T=
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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
M1*M2
S2
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
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The Pendulum and Earth Shape
F= G
M1*M2
S2
Paris
equator
T=
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
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