Eratosthene's explanation of the sun's ray

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SUMMARY

The discussion centers on Eratosthenes' method for determining the Earth's radius, as explained in "Conceptual Physics" by Paul G. Hewitt. Participants clarify that when the sun is directly overhead at a location like Syene, its rays are perpendicular to the Earth's surface, effectively passing through the Earth's center. This phenomenon occurs not only at Syene but also in equatorial regions and up to 23 degrees north or south of the equator during summer. The conversation emphasizes the geometric principles behind this observation, particularly the relationship between perpendicular lines and diameters in a spherical context.

PREREQUISITES
  • Understanding of basic geometry, particularly concepts of perpendicular lines and diameters.
  • Familiarity with the Earth's rotation and its effect on sunlight exposure.
  • Knowledge of Eratosthenes' historical contributions to geography and mathematics.
  • Basic comprehension of the concept of latitude and its implications on solar positioning.
NEXT STEPS
  • Explore the geometric principles of spherical geometry, focusing on perpendicular lines and their implications.
  • Study the historical context of Eratosthenes' measurements and their significance in ancient science.
  • Learn about the effects of Earth's axial tilt on solar angles and seasonal changes.
  • Investigate modern methods of measuring the Earth's radius and how they compare to Eratosthenes' approach.
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Students of physics, history enthusiasts, educators in mathematics and science, and anyone interested in the historical methods of measuring the Earth.

prashant singh
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How can we say that when the sun is overhead then its ray will pass through the centre of the Earth , does it happens only at the one place on the earth. How they knew that synene is situated in the middle of north and south
 
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prashant singh said:
How can we say that when the sun is overhead then its ray will pass through the centre of the Earth , does it happens only at the one place on the earth. How they knew that synene is situated in the middle of north and south
What are you referring to?
What is 'synene ?
Light from the Sun reaches all parts of the Earth which are in daytime.
Daytime comes and goes because the Earth is rotating.
 
I am referring to the explanation given by eratosthenes ( BOOK :CONCEPTUAL PHYSICS BY PAUL G. HEWITS) in finding the radius of the earth. He said that there was a placed named syene near south of alexandria . Where we can see that a veritical stick or a line will not cast any shadow and he declared that at that place sun's ray would pass through the center of the earth. I want to know why or how he declared this statement
 
OK. I understand the question now.
Yes, the ancient greeks did make measurements of the Sun's shadow, and concluded that the Earth was probably a sphere.
 
But I want to know that how he concluded that when sun is overhead then its ray will pass through the centre, I think its only for that particular place (syene ) which must be situated in the middle of North and South ( if it so, then how they found that it is situated in the middle of North and South).
 
The sun is directly overhead in many places on Earth when that place on the Earth is directly facing the Sun.
It's common in equatorial regions and can happen as far as 23 degrees north or south of the equator, we call it 'Summer'.
At the poles it is never directly overhead, but it does get above the horizon.
 
Okkkkkk, but how can we say that its ray will pass through the center of the Earth when sun is overhead.
 
Doesn't it include a diagram? Can you draw yourself one? It should be obvious from a diagram.
 
prashant singh said:
Okkkkkk, but how can we say that its ray will pass through the center of the Earth when sun is overhead.
"Overhead" is taken to mean perpendicular to the surface of the Earth. Any line perpendicular to the surface of a sphere, and continuing thru the sphere, is a diameter. Try drawing it.
 
  • #10
Ohh thank u man it waa just a silly question , I forget that
 

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