earth’s circumference. eratosthenes he invented a system of latitude and longitude. he was the...
TRANSCRIPT
Eratosthenes
• He invented a system of latitude and longitude.
• He was the first to calculate the tilt of the Earth's axis
• He also created the first map of the world incorporating parallels and meridians
• He was the first person to calculate the circumference of the earth
Eratosthenes of Cyrene was a Greek mathematician, geographer , poet, athlete, astronomer, and music theorist.
History
Eratosthenes calculated the circumference of the Earth without leaving Egypt. Eratosthenes knew that on the summer solstice at local noon in the Ancient Egyptian city of Swenet on the Tropic of Cancer, the sun would appear at the zenith, directly overhead. He also knew, from measurement, that in his hometown of Alexandria, the angle of elevation of the sun was 1/50th of a circle (7°12') south of the zenith on the solstice noon. He find out that a circumference is about of 46,620 km, i.e. 16.3% too large.
Purpose
• Find the circumference of the Earth without using modern inventions
• Verify Eratosthenes's theory.
Process
• Our school and others schools (from project LULATS) measure shadows in daylight.
• We send each other results• We chose Spain’s results.
What we need?
• C - Earth’s circumference • L – distance between
Taurage and Madrid• Y – angle • z1 z2 – the angles of
elevation of the sun
Tauragė
Madrid
z2
y
z1
L
C
How find the angle of elevation of the sun?
• We need a stick• Stick’s shadow at noon • An angle between a stick and its shadows
Our results
Stick length• 139 cm• 140cm• 127 cm• 133 cm
Shadow lelngth
• 98 cm• 98,5 cm • 92 cm• 108 cm
Madrid Results
• Stick’s length – 100cm • Shadow’s length –
40.5 cm• Angle 22.04°
Madrid is in a different geographic longitude. So we need to add two hours and then we will get right result.
Spain time12:0013:0014:0014:13
Solar time10:0011:0012:0012:13
length70,5051,0040,5039,00
Results Name With shadows With a map Real results
Angle 14.29° 14.91°
Earth’s circumference
40055.98km 38390.38km
Radius 6378.34km 6113.1km 6378,137km
Findings
• Eratosthenes's theory has been reasserted.• We got almost the same result without leaving
Taurage• We can easily find Earth’s circumference,
when we know two different cities’ geographic latitudes.