# The process of calculating the earths circumference by eratosthenes

To calculate the circumference of the earth, eratosthenes measured the angle of the shadow to the earth brahe -he made the most precise observations that had yet been made by devising the best instruments available before the invention of the telescope. Now that eratosthenes knew the subtended angle and the actual distance between the two cities of syrene and alexandria, he could calculate the total circumference of the earth the concept he used was very simple. With the circumnavigation of the globe and subsequent scientific calculations, the accepted value of the circumference of the earth returned from ptolemy's calculation back to that of eratosthenes after countless millennia, scientists, explorers, clergy, and laymen finally knew the true shape and true size of the earth.

With this information he measured the circumference of the earth without leaving egypt by assuming that earth was a sphere and that the sun rays are parallel when they arrive to earth eratosthenes assumed that earth is a sphere and that the solar rays are parallel when they reach earth. Calculating the earths circumference in this fashion is assuming that the earth is a perfect sphere just as eratosthenes did, which it is not nonetheless, this value is quite accurate depending on the length of the stadia that eratosthenes used, the value could have been anywhere between 39,250 km - 52,250 km. Convinced that the earth is round, our genius eratosthenes set about tracing his famous amazingly simple geometrical figure (fig 3), which he used to calculate with ease the length of the earth's meridian. How did eratosthenes manage to determine the circumference of the earth without going anywhere how did eratosthenes calculate the circumference of the earth math centre the earth's.

Measure earth's circumference with a shadow then you can look up the distance between your city and the equator and use the same equation eratosthenes used to calculate earth's. Calculating the size of the earth is then just some simple geometry in the diagram above, syene and alexandria are on the circumference of the earth the 72 is also the angular separation between the cities, and the arclength between them is 5000 stadia. Eratosthenes therefore calculated the total circumference of the earth to be 40,000 kilometres (250,000 stadia) eratosthenes' calculation is about 15% too high, but the accuracy of his figure for the circumference of the earth would not be equalled until modern times. Calculation eratosthenes used the angular difference in latitude of two points on the same meridian and the corresponding linear distance between the points to determine the distance on the surface of the earth per degree of latitude. Originally answered: how was eratosthenes of cyrene able to calculate the circumference of the earth eratosthenes calculated the circumference of the earth without leaving egypt he knew that at local noon on the summer solstice in syene (modern aswan , egypt), the sun was directly overhead.

Accuracy of eratosthenes' circumference estimate is surprising the process is a bit information for finding circumference of the earth eratosthenes assumed . So from eratosthenes' calculation we know that 72 degrees spans the arc of the earth's circumference that runs from aswan to alexandria so the percentage of a circle between the two cities is: so the percentage of a circle between the two cities is. An in depth look at the method offered by eratosthenes shows that the original calculation for the earth's meridian circumference was made by the ancient egyptians thousands of years before eratosthenes' time. The circumference of the earth is 40,075 km, and the greek geographer erastosthenes was the first person to estimate the earth's circumference nearly accurately before erastosthenes, other scholars had attempted to estimate the figure, but their methods were not recorded, and their estimations were. Question about eratosthenes method for calculating the circumference of the earth.

Eratosthenes' measurement of the earth's circumference you don't care whether eratosthenes was the first to calculate the size of the earth or not logged. Not only did eratosthenes of cyrene calculate the circumference of the earth with impressive accuracy, but he did it without leaving egypt first, the greek astronomer figured out the sun's angle of elevation on the summer solstice in alexandria. Calculating the circumference of the earth science buddies you can use eratosthenes' method to calculate the circumference of the earth yourself you can even.

Eratosthenes measure of the earth's circumference solution commentary: solution of main problems: 1 because of eratosthenes's assumption that the sun's rays were parallel, we. Eratosthenes used geometry to estimate the circumference of the earth on that date, the sun is directly overhead at noontime at syene, in southern egypt (latitude = 235 degrees north) the zenith distance is the angle from the zenith to the point where the sun was at noon it is also 90 degrees minus the altitude. Eratosthenes lesson plans and worksheets from thousands of teacher-reviewed resources eratosthenes and the circumference of the earth our review process how.

Scientific process eratosthenes' calculation of earth's circumference of the size of the earth how did he do that eratosthenes used the lengths of shadows. However, approximations through a single plane of the e arth can be found by measuring angles and calculating from distances for example, eratosthenes estimated the circumference through. Eratosthenes divided 360° by 72° and got 50, which told him that the distance between alexandria and syene (500 miles) was 1/50 of the total distance around the earth so he multiplied 500 by 50 to arrive at his estimate of the earth's circumference: 25,000 miles. Read and/or distribute eratosthenes and background information review and/or distribute part a: estimate the circumference of the earth using eratosthenes' calculations.

Start studying eratosthenes' calculation of the earth's circumference learn vocabulary, terms, and more with flashcards, games, and other study tools. Materials: meter stick, pencil, paper, calculator with trigonometric functions, and student worksheet: eratosthenesdoc implementation: this rwlo can be used either in the classroom to demonstrate the learning objectives or provided as an activity / homework assignment enabling the students to discover the process themselves. The greek astronomer eratosthenes was the first person to compute an accurate measurement of the earth's circumference his process was based on the following elements he noted that while looking down a particular well in the city of syene, egypt, he could observe that the sun's reflection was directly in the middle of the water.

The process of calculating the earths circumference by eratosthenes
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