Το πείραμα του Ερατοσθένη

Who Was Eratosthenes?

Background and Contributions

• Eratosthenes was an ancient Greek mathematician, geographer, astronomer, and poet born in Cyrene (modern-day Libya) and later lived in Alexandria, Egypt's capital.

• At 40 years old, he became the chief librarian of the Library of Alexandria, where he conducted significant experiments that contributed to his legacy.

The Experiment: Calculating Earth's Circumference

Observations Leading to Calculation

• On June 21st (Spring Equinox), it was noted that sunlight fully reflected at the bottom of a well in Syene (Aswan), indicating the Sun was directly overhead.

• This phenomenon did not occur in Alexandria, leading Eratosthenes to conclude that the Sun could not be over both cities simultaneously due to Earth's curvature.

Understanding Earth's Shape

• The concept of a spherical Earth was already recognized by ancient Greeks through observations like ships disappearing hull-first and round shadows during lunar eclipses.

• Eratosthenes utilized these observations to devise a method for calculating Earth's circumference based on angles formed by sunlight at different locations.

Methodology: Measuring Angles and Distances

Angle Measurement

• He measured the angle between a vertical stick and sunlight in Alexandria as 7.2 degrees (1/50th of a circle). This angle represented the difference between two locations on Earth’s surface.

Distance Between Cities

• To find Earth's circumference, he needed the distance between Alexandria and Syene; initially measured at 5000 Stadia but later corrected to 5040 Stadia. Thus, he calculated Earth's circumference as approximately 252,000 Stadia.

Challenges and Mysteries

Measurement Techniques

• There are uncertainties regarding how Eratosthenes measured angles or distances; some suggest using camel caravan travel times while others propose counting steps with bematists (distance measurers).

Variability in Units

• The length of a Stadium varied across regions; estimates range from 157 meters to 185 meters per Stadion affecting accuracy in his final calculations for Earth’s circumference.

Accuracy of Eratosthenes' Calculation

Final Estimates

• His calculation resulted in an estimated circumference between 39,564 km and 46,620 km; modern measurements accept around 40,008 km for meridian circumference today.

Limitations Acknowledged

• Factors such as geographical inaccuracies (Alexandria not being directly north of Syene) and non-parallel sun rays contributed to potential errors in his calculations but still yielded impressively close results given his tools were primitive by today's standards.

Legacy of Eratosthenes' Work

Scientific Approach

• Eratosthenes exemplified scientific inquiry through observation combined with existing knowledge about Earth’s shape leading him to conduct meaningful experiments that changed our understanding of geography and astronomy.

Historical Context

• Fun fact: Christopher Columbus miscalculated distances based on erroneous assumptions about Earth’s size derived from earlier estimations which would have led him astray had he used Eratosthenes’ more accurate figures!