Assignment 1: Ancient Astronomy - Size of the Earth

Eratosthenes

Eratosthenes 276 BC - 194BC

     Eratosthenes was not only a Greek scientist but also had many other occupations (Abreu, 2012). He was a mathematician, geographer, poet, astronomer, music theorist, and the chief librarian (Abreu, 2012). He invented many tools and technology that we still use today. If it hadn't been for Erathosthenes` intelligence, many of today's concepts about a wide range of subjects may not have progressed as well as they have. However from everything he has accomplished, Erathosthenes was best known for calculating the circumference of the Earth (Abreu, 2012).

One of his many accomplishments was that he was the founder of chronology (Ast, 2014). This is the science of arranging events in a timely order. This contributed to the discipline of earth history, and the study of the geologic time scale (Ast, 2014). Time keeping is an important concept because it allows for radiocarbon dating as well as dendrochronolgy (Ast, 2014). This allows for the estimation of living things relative to the proportion of carbon isotopes and estimation of the age of trees, respectively (Ast, 2014). These are two major methods of scientific research for it allows us to order events of all kind in chronological order.

Geography & Mathematics

     Eratothenes was also known as the father of Geography. Due to his interest in the geography of the Earth along with his exceptional knowledge of the Earth, he made a book called Geographika (Freedman et al, 2010). This book consisted of three volumes, and outlines different climate zones across the Earth - two freezing zones, two temperate zones, and a final zone. He also listed hundreds of cities in this book, as well as their locations and distances from one another (Freedman et al, 2010). It is here where he had come up with longitude and latitude system.
     One of his major accomplishments in mathematics is Sieve of Eratosthenes, which is a straightforward algorithm that helps recognize prime numbers (Freedman et al, 2010). It is here where he came up with both prime numbers and composite numbers. Prime numbers are those that cannot be divisible by any number except 1 and itself. Composite numbers are those that are multiples of prime numbers. This set foot many mathematical properties that we learn today. 

Measurement of the Earth`s Circumference 

Distance between Alexandira & Syene

     It was not until Eratosthenes` time that the public knew it was possible to measure the Earth`s circumference (Freedman et al, 2010). He was the first person to do this and received incredible recognition, as he is still remembered today. Using his knowledge in mathematics, he calculated the circumference of he Earth by measuring the angles between two shadow castes in two different cities, Alexandria and Syene, while also measuring the distance between those two cities (Freedman et al, 2010). He recorded his findings in the last volume of his book Geographika (Freedman et al, 2010).

     In order to precisely determine the circumference, after careful observation Eratosthenes noted that in his home city (Alexandria) in Egypt, the sun was never directly overhead while in a city further south (Syene), there was a certain day where the shadow never castes at the bottom of the well. During the summer solstice, at noon Eratosthenes realized that the Sun's rays reflected straight above the town of Syene (Freedman et al, 2010). This is because there was no shadow when the Sun's rays hit the zenith vertically - a zenith is the spot that is directly above a specific location (abstract) (Abreu, 2012). On the other hand, in Alexandria, a shadow can be seen (Abreu, 2012). According to his calculations, this shadow was 1/50 of the entire circle and was below the zenith.

     Using mathematical reasoning, the intelligent scholar realized that the shadow`s angle would be the same as the angle between the 2 different cities (Freedman et al, 2010). Since he had exceptional geographical knowledge, he used his knowledge of knowing that Alexandria was located North of Syene (Freedman et al, 2010). He assumed that the Earth was 360 degrees and so the distance between the two locations are 7.2 degrees apart (Freedman et al, 2010). Therefore, he stated that if he could find the distance between the two cities, he would have to multiply that distance by 50 in order to get the Earth`s circumference (Freedman et al, 2010). It is here where he also noted that the Earth was in fact curved and not Earth, and was able to estimate that it was 360 degrees due to its spherical structure. This is because if the Earth were to be flat, the Sun's rays would directly shine overhead both cities (Alexandria and Syene). If this were to occur, there would be no shadows at both locations (Freedman et al, 2010). However according to Eratosthenes there was a shadow at Alexandria indicating that the Earth was in fact curved and flat (Ast, 2014).

     After finding this remarkable discovery, Eratosthenes used this to contribute to science in many other aspects. For example, he created a system for the Earth`s latitude and longitude as well as a device that was able to view the motions of the stars by astronomers, while creating a 12 month calendar that included a leap year.


References

Abreu, A. (2012, June 3). Retrived from http://www.astro.cornell.edu/academics/courses/astro201/eratosthenes.htm

Ast, C., Eratosthenes 276-195 B.C.E. Retrieved from http://www.math.witchita.edu/history/men/ertosthenes. html

Freedman, R., Geller, R., & Kaufmann, W.J. (2010) Universe (8th ed). New York, NY: W.H. Freeman.



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