Earth’s circumference

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.

Hypothesis

• I think that my results will differ from real results.

Materials

• Stick• Sun• Ruler • Calculator• Friends abroad

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

Formulas

z1

z2

y

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

Our Angle

a

b

a = 54.81°a = 54.87°a = 54.08°a = 50.92 ° a(average) = z1 = 53.67°

b= 36.33°

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

Distance between Madrid and Taurage

H = 7.95 cm

L= 200*7.95= 1590 km

Calculating…

L = 1590kmz1 = 36.33°z2 = 22.04°

Radius

R

Rreal= 6378,137km

Why don’t we use just a map?55.15°

40.24°

y = 55.15° - 40.24° = 14.91°

Calculating…

Radius

R

Rreal= 6378,137km

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.

Thank you for your attention