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Eratosthenes earth radius formula

WebJul 29, 2024 · After hiring a man to pace the distance between Syene and Alexandria, he found out that the two cities were five thousand stadia apart, which is about eight hundred kilometers. He could then use simple proportions to find the Earth’s circumference—7.2 degrees is 1/50 of 360 degrees, so 800 times 50 equals 40,000 kilometers. WebJan 10, 2015 · The point is that the ancients had a valid mathematical and astronomical basis for calculating the radius of the earth (Eratosthenes) and for determining the distance to the moon in earth radii (Hipparchus). If you have a broadly correct figure for these two things you can express the distance to the moon in whatever units you like. – …

No. 1457: Eratosthene

WebApr 1, 2014 · An eclipse of the Moon occurs when the Moon passes through the shadow of the Earth, on the opposite side from the Sun (therefore, we must be seeing a full Moon). If r is the radius of the Earth, the shadow's width is close to 2r. Let t be the time it takes the mid-point of the Moon to cross the center of the shadow, about 3 hours (in eclipses ... WebSome formulas you’ll need (r = radius of circle / sphere) Circumference of a Circle: Volume of a Sphere: Question 1: What is the radius of the Earth? Use Eratosthenes’ estimate for the circumference of the Earth to find its … harry and the sports competition en español https://royalkeysllc.org

Eratosthenes’ Determination of Earth’s Circumference

http://www-personal.umich.edu/~copyrght/image/books/Spatial%20Synthesis/Eratosthenes/ http://homework.uoregon.edu/pub/emj/121/lectures/eratosthenes.html WebApr 14, 2024 · To Eratosthenes’ measurements, they point out that in principle the same effect can be achieved if the Sun is much smaller and closer (which is true). ... In the case of the Earth, the mean radius is 6371 km, so the surface area should be about 510 million km^2, which indeed is the answer Google will give you. ... In this case there’s no ... charities for school shooting

The History of Geodes: Global Positioning Tutorial - National Ocean Service

Category:Eratosthenes: Measuring the Impossible OpenMind

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Eratosthenes earth radius formula

Eratosthenes Biography, Discoveries, Sieve, & Facts

http://www.geo.hunter.cuny.edu/~jochen/gtech201/lectures/lec6concepts/Datums/Determining%20the%20earths%20size.htm Webr = radius of earth s = distance of arc θ = central angle Then to find the circumference of the earth use the below formula: c = 2 π r Given s = 500 miles θ = 7. 2 ° Step 2. Finding the radius of earth The central angle θ is: θ = 7. 2 ° Now convert it into radian by multiplying with π 180, we get θ = 7.2 ∘ × π 180 = 7.2 ∘ 180 r a d i a n s

Eratosthenes earth radius formula

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WebJune, ca. 240 B.C. Eratosthenes Measures the Earth. By around 500 B.C., most ancient Greeks believed that Earth was round, not flat. But they had no idea how big the planet is until about 240 B.C., when Eratosthenes … WebThe difference in the two measured angles (or, if the shadows point away from each other, the sum) equals the angle at the vertex at Earth’s center where extended vertical lines of …

WebFeb 3, 2024 · So using Eratosthenes own estimate for the circumference of the Earth, and the equation above rearranged with basic algebra to solve for radius ( r ), we get: Once again, depending on the length of the stade … WebDec 27, 2024 · Eratosthenes hired a man to pace the distance between the two cities and learned they were 5,000 stadia apart, which is about 800 …

WebSep 14, 2024 · Exactly how Eratosthenes calculated the radius of the Earth has been lost. What is presently taught as his method is a simplified version described by Cleomedes. It is unlikely that Eratosthenes assumed the Sun was infinitely distant, since he apparently also estimated the distance to the Sun himself.

WebEratosthenes used a simple formula that relates the proportionality of the relation of the distance between two places on the meridian (d) and their difference in latitude (α) to the …

WebDec 10, 2016 · So, if one would know the distance between Syene and Alexandria, s/he could calculate the circumference of the Earth. 360/7 is close to 1/50th of a circle, so Eratosthenes concluded that the Earth’s … charities for spinal cord injuriesWebMay 31, 2024 · In this way, with a simple rule of three he could calculate the length of the circumference of the Earth. If the angle of incidence gives rise to a length of an arc of circumference equal to the distance between Alexandria and Siena, then the total length will correspond to 360 degrees (the full circumference). harry and tonks fanfiction house potterWebEratosthenes of Cyrene (/ ɛr ə ˈ t ɒ s θ ə n iː z /; Greek: Ἐρατοσθένης [eratostʰénɛːs]; c. 276 BC – c. 195/194 BC) was a Greek polymath: a mathematician, geographer, poet, astronomer, and music theorist.He … harry and the sports competition pdfWebThe study of the size and shape of the earth is known as geodesy and has been practiced for centuries. Contrary to common misconceptions, many historical mathematicians and scientists were aware that Earth was … charities for service dogsWebAround 250 B.C., another Greek philosopher, Eratosthenes, measured the circumference of the Earth using the following equation: (360° ÷ θ) x (s) In this calculation, (s) is the distance between two points that lie north and south of … charities for special needs children ukWebThis video shows how Eratosthenes determined the approximate radius of the Earth. The data available were the angle of the shadow of the Sun in Alexandria, ... harry and tom hollandWebThe arc in the Eratosthenes case was of 7.2 degrees and the distance between the two locations is 787 kilometre. So, for him the following relationship between objects will apply: 7.2 / 360 = 787 / x. Here x is the circumference of the earth. On solving the circumference of the earth we get 39,350 kilometres. So the radius of the earth will be charities for the blind