Verified Document

Astronomy Measuring The Diameter Of The Earth Term Paper

Astronomy Measuring the Diameter of the Earth

Eratosthenes' Method

Eratosthenes made a calculation of the Earth's diameter, based on one assumption and two measurements. The assumption was that the Earth was a sphere. This assumption is required since the method relies on accepting that the Earth's diameter is a total of 360o. The two measurements made are the degree of the Earth's shadow at noon at two points and the distance between those points.

Eratosthanes used the city of Syene in Egypt as the first point. This point was selected because it was known that on noon on the first day of summer the sun was directly overhead. This was known because people observed that at this time, the buildings cast no shadows (York University). Therefore, the degree of the shadow at Syene was 0o.

Eratosthanes then needed to know the degree of the shadow at another point either directly north or directly south, at the same time of day. Eratosthanes selected Alexandria as the second city. The degree of the sun's shadow was measured and found to be 7.2o (HEASARC).

Eratosthanes then knew that the degree of difference between Syene and Alexandria was 7.2o. The final item Eratosthanes needed to know was the distance between the two cities. This was done by sending a runner to pace out the distance (York University). Eratosthanes found that the distance between the two cities was 5000 stadia. A stadium was an ancient measurement, thought to equal around...

Since the circumference of the Earth is 360o, the distance will be equal to:
360/7.2 x 5000 = 250,000 stadia.

Since a stadia is thought to be 0.15 kilometers, the circumference of the Earth is equal to:

250,000 stadia x 0.15 km = 37,500 kilometers.

The radius of the Earth can then be calculated by using the formula for the circumference of a circle, C = 2?r:

37,500 km = 2 x 3.14 x r

Since the diameter of a circle, is twice the radius, the diameter will be equal to:

5971 km x 2 = 11942 km.

Therefore, Eratosthanes calculated the diameter of the Earth to be 11942 kilometers.

One important point in the experiment is that one of the locations does not need to have a shadow of 0o for the experiment to be successful. The calculation requires that the difference in the angle of the shadow at two locations be known. Eratosthanes simply made the experiment a little simpler by having the first location as a 0o shadow. This meant that only one measurement of shadow had to be made.

How to Measure the Diameter of the Earth

This experiment can be repeated by measuring the degree of the shadows cast at two locations either directly north or south of each other at noon on the same day. Before beginning the experiment it is necessary to organize with…

Sources used in this document:
Works Cited

HEASARC: High Energy Astrophysics Science Archive Research Center. "The Earth." 2001. NASA. Retrieved March 30, 2003. URL:

http://heasarc.gsfc.nasa.gov/docs/cosmic/earth_info.html

York University. "An Historical Perspective." 2003. YesICan!Science. Retrieved March 30, 2003. URL: http://resources.yesican.yorku.ca/eratosthenes/history.html
Cite this Document:
Copy Bibliography Citation

Related Documents

Earth Science / Astronomy Ptolemy
Words: 1330 Length: 4 Document Type: Essay

The Moon is believed by many to have been part of the earth and that it was tore off as a result of an initial spin that was too great to hold the planet together. One of the prevailing theories was that involving an impact of large magnitude involving the newly formed Earth and a giant object of the size of Mars hitting Earth and blowing up material that

Price Beauty 'For Though Beauty Is Seen
Words: 6265 Length: 20 Document Type: Term Paper

Price Beauty? 'For though beauty is seen and confessed by all, yet, from the many fruitless attempts to account for the cause of its being so, enquiries on this head have almost been given up" William Hogarth, The Analysis of Beauty, (1753) Not very encouraging words, but if the great artist William Hogarth felt himself up to the task, we can attempt at least to follow his lead. That beauty is enigmatic

History of Construction Technology of
Words: 9139 Length: 24 Document Type: Essay

Staircase ramps which are comprised of steep and narrow steps that lead up one face of the pyramid were more in use at that time with evidence found at the Sinki, Meidum, Giza, Abu Ghurob, and Lisht pyramids respectively (Heizer). A third ramp variation was the spiral ramp, found in use during the nineteenth dynasty and was, as its name suggests, comprised of a ramp covering all faces of the

Sign Up for Unlimited Study Help

Our semester plans gives you unlimited, unrestricted access to our entire library of resources —writing tools, guides, example essays, tutorials, class notes, and more.

Get Started Now