How did early man attempt to discover the circumference of the earth without ever traveling it?
This is how it was accomplished by a man without much apparatus. Eratosthenes simply needed the sun, a deep well and a wall. Eratosthenes was in Alexandria , Egypt the home of the best sailors and navigators of the age. He was getting lots of first hand geographical information from every other man on the street with a desire to explore the earth. Alexandria (at that time) had the best stocked library and museum in the world.
On 21st of June (250 BC), Eratosthenes noticed that the sun at Syene was so straight over head that it completely lighted up a deep well. If that well but continued to the center of the earth the shaft would be a sunlit radius without a shadow.
But Eratosthenes was sure that at this very moment in Alexandria north of here, the walls were all casting shadows. This is because the earth is spherical. Due to the curving of the earth if everything in Syene cast no shadows then in Alexandria everything had to meet the sun's rays at an angle. As depicted below:
He calculated (see aside for details) the angle (O) the wall (at Alexandria) made with the sun's rays and it was 7.2 degrees. After finding Angle(O) he also knew from the following geometric truth that Angle(C) at the center of the earth would equal to Angle (O):
Once he knew the length of the arc (500 miles distance between Syene and Alexandria), and the angle(O=A=7.2 degrees) it was easy to find the circumference of the circle :
Eratosthenes calculated the circumference of the earth to be 25,000 miles (using the above ratio). Modern computations put the circumference of the earth at 24,860 miles. After Erastosthenes geographers came up with a figure of 18,000 miles (which Columbus used) and Ptolemy advocated. It overrode Eratosthenes' figure perhaps because men really wanted to circumnavigate the earth (and preferred a shorter inaccurate estimate rather than a more accurate estimate perhaps?).
[Aside : How did Erastosthenes Find the Angle (O) or Angle(theta) as below]
Find the height of the wall : h.
Find the length of the shadow : s.
Calculate angle(theta) using tangent equation.
[End Aside: How did Erastosthenes Find the Angle O or theta]
[Begin Aside: How did Eratosthenes know at what time he ought to measure the angle At Alexandria]
Perhaps a way of coordinating times over large distances by means of flags placed on horizons. You could raise the flag from source. When viewers view it upon horizon they raise their flag to trigger the next flag holder on a horizon to raise his flag. It would need 50 flag bearers to communicate to a spot 500 miles away. Other communication devices could be mirrors (to shine light to the next horizon) , smoke signals etc. One person could see when the light reaches the bottom of the well. Then signal to the flag bearer on the horizon by waving his flag. The flag bearer on the horizon could signal the person on the next horizon and so on till the person by the wall sees the flag on the horizon and he could measure the angle at that point. Thus we would know precisely when to measure on both ends.
If anyone can provide a better answer or improve on this one that would be great.
[End Aside: How did Eratosthenes know at what time he ought to measure the angle At Alexandria]
Today men may use satellites and fly in spaceships to outer space and view earth and other planets far beyond earth. (well not all men, just the men who are blessed and have excellent space programs).
This is how it was accomplished by a man without much apparatus. Eratosthenes simply needed the sun, a deep well and a wall. Eratosthenes was in Alexandria , Egypt the home of the best sailors and navigators of the age. He was getting lots of first hand geographical information from every other man on the street with a desire to explore the earth. Alexandria (at that time) had the best stocked library and museum in the world.
On 21st of June (250 BC), Eratosthenes noticed that the sun at Syene was so straight over head that it completely lighted up a deep well. If that well but continued to the center of the earth the shaft would be a sunlit radius without a shadow.
But Eratosthenes was sure that at this very moment in Alexandria north of here, the walls were all casting shadows. This is because the earth is spherical. Due to the curving of the earth if everything in Syene cast no shadows then in Alexandria everything had to meet the sun's rays at an angle. As depicted below:
 | |
| Parallel lines when intersected have equal opposing angles. |
Eratosthenes calculated the circumference of the earth to be 25,000 miles (using the above ratio). Modern computations put the circumference of the earth at 24,860 miles. After Erastosthenes geographers came up with a figure of 18,000 miles (which Columbus used) and Ptolemy advocated. It overrode Eratosthenes' figure perhaps because men really wanted to circumnavigate the earth (and preferred a shorter inaccurate estimate rather than a more accurate estimate perhaps?).
[Aside : How did Erastosthenes Find the Angle (O) or Angle(theta) as below]
Find the height of the wall : h.
Find the length of the shadow : s.
Calculate angle(theta) using tangent equation.
[End Aside: How did Erastosthenes Find the Angle O or theta]
[Begin Aside: How did Eratosthenes know at what time he ought to measure the angle At Alexandria]
Perhaps a way of coordinating times over large distances by means of flags placed on horizons. You could raise the flag from source. When viewers view it upon horizon they raise their flag to trigger the next flag holder on a horizon to raise his flag. It would need 50 flag bearers to communicate to a spot 500 miles away. Other communication devices could be mirrors (to shine light to the next horizon) , smoke signals etc. One person could see when the light reaches the bottom of the well. Then signal to the flag bearer on the horizon by waving his flag. The flag bearer on the horizon could signal the person on the next horizon and so on till the person by the wall sees the flag on the horizon and he could measure the angle at that point. Thus we would know precisely when to measure on both ends.
If anyone can provide a better answer or improve on this one that would be great.
[End Aside: How did Eratosthenes know at what time he ought to measure the angle At Alexandria]
Today men may use satellites and fly in spaceships to outer space and view earth and other planets far beyond earth. (well not all men, just the men who are blessed and have excellent space programs).
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