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Research from Term Paper:
Astronomy
Calculating the Diameter of the The planet
Eratosthenes’ Approach
Eratosthenes produced a calculation of the Globe’s diameter, depending on one supposition and two measurements. The assumption was that the Earth was obviously a sphere. This kind of assumption is required since the approach relies on accepting that the Globe’s diameter is actually a total of 360o. The two measurements made are the amount of the Earth’s shadow in noon by two points plus the distance between those details.
Eratosthanes utilized the city of Syene in Egypt because the initially point. This point was picked because it was known that on noonday noontide, meridian on the first day of summer sunlight was straight overhead. It was known individuals observed that at this time, the buildings players no shadows (York University). Therefore , the level of the shadow at Syene was 0o.
Eratosthanes then simply needed to understand the degree of the shadow at another point either directly north or immediately south, as well of day. Eratosthanes chosen Alexandria because the second metropolis. The degree of the sun’s shadow was measured and found to be 7. 2o (HEASARC).
Eratosthanes then knew that the amount of difference among Syene and Alexandria was 7. 2o. The final item Eratosthanes necessary to know was your distance between the two metropolitan areas. This was done by sending a jogger to rate out the range (York University). Eratosthanes identified that the range between the two cities was 5000 stadia. A arena was an ancient measurement, thought to equal about 0. 12-15 kilometers (HEASARC).
From these kinds of measurements, it really is known that 7. 2o is comparable to a length of 5000 stadia. Because the circumference from the Earth can be 360o, the length will be comparable to:
360/7. a couple of x 5000 = two hundred and fifty, 000 stadia.
Since a stadia can be thought to be 0. 15 kilometers, the area of the The planet is comparable to:
250, 1000 stadia times 0. 12-15 km = 37, 500 kilometers.
The radius from the Earth can then be calculated by using the formula for the area of a ring, C = 2? r:
37, 500 km = 2 times 3. 18 x r
Since the diameter of a group, is 2 times the radius, the size will be corresponding to:
5971 kilometres x a couple of = 11942 km.
Therefore , Eratosthanes worked out the size of the Globe to be 11942 kilometers.
A single important point in the research is that among the locations does not need to have a shadow of 0o pertaining to the research to be successful. The calculation needs that the big difference in the perspective of the shadow at two locations be known. Eratosthanes simply manufactured the experiment a little less difficult by having the first area as a 0o shadow. This kind of meant that only one measurement of shadow needed to be made.
How you can Measure the Size of the Earth
This test can be repeated by calculating the degree of the shadows cast at two locations both directly north or southern of
