1. What is the true size of the Earth?
Mr. Clark
Bethpage HS

2. How can the Earth’s size be determined?
Method of Eratosthenes

3. Method of Eratosthenes
Eratosthenes believed the Earth to be a sphere and that the Sun was so far away that its rays were essentially parallel.

4. Method of Eratosthenes
Formula of Eratosthenes
Shadow angle/360o = s/C
(part / whole = part / whole)
Where s is the distance between the cities and C is the circumference of Earth.

5. Eratosthenes

7. Eratosthenes
Eratosthenes' calculations were based on two assumptions. The first was that Syene lay on the Tropic of Cancer (23.5oN).

8. Eratosthenes
The second assumption was that Alexandria lay due north of Syene on exactly the same line of longitude (the meridian line).

9. Eratosthenes
At noon during the summer solstice (June 21), the rays of the sun always shine directly perpendicular to the Earth's surface, only on the Tropic of Cancer.

10. Eratosthenes
If Alexandria was exactly due north of Syene, then Eratosthenes could argue that the key measurements he used –
The length of the column's shadow in Alexandria (used to determine the shadow angle) and
The distance between Alexandria and Syene -- were geographically sound.

11. Eratosthenes
Obviously, Eratosthenes could not go to the center of the Earth, so he got the angle measurement using the rays of the sun to determine the shadow angle.
At noon on the longest day of the year, the summer solstice, the sun shone directly into a deep well at Syene (which is now Aswan, Egypt), casting no shadow.

13. Eratosthenes
Eratosthenes reasoned that:
Shadow angle/360o = s/C

14. Eratosthenes
At the same time in Alexandria, Egypt, he found that the sun cast a shadow angle equivalent to about 1/50th of a circle or 7.12°.
Eratosthenes combined this measurement with the distance (s) between Syene and Alexandria, about 4,400 stades.

15. Eratosthenes Calculation
If we plug these numbers into the above equation, we get:
Shadow angle/360o= s/C
7.12o/360o = 4400 stades/C
C= 220,000 stades

16. Eratosthenes

17. Eratosthenes 220,000 stades is about 25,000 miles.(40,000 km)
The accepted value of the Earth's circumference today is about 24,855 miles.(40,007 km)