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...

Parts of this document are hidden

View Full Document
svg-one

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

Astronomy the Terrestrial Planets Are Defined As
Words: 1690 Length: 5 Document Type: Essay

Astronomy The Terrestrial planets are defined as rocky planets or telluric planets, and they are Mercury, Venus, Earth and Mars. These planets have a lot of similarities that allow them to be grouped together, especially in contrast to the Jovian or gas planets. The telluric planet is one given type of planet, defined as one that is primarily composed of rocks and heavy metals. Thus, the composition of these planets is

Astronomy Explain How the Hertzsprung-Russell
Words: 2790 Length: 7 Document Type: Essay

Of those 1,235, 68 are estimated to be Earth-size; 288 are super Earth-size; 662 are Neptune-size; 165 are the size of Jupiter, and 19 are larger than Jupiter (Science Daily). Of the 54 planet candidates that have been found in the habitable zone, five are near Earth-size. The other 49 left in the habitable zone range from super-Earth-size (up to twice the size of the Earth) -- to larger than

Astronomy Please Answer All Questions
Words: 870 Length: 3 Document Type: Term Paper

The first telescope is a 10 m telescope that is planned to be located at the L2 Lagrangian point 1.5 million kilometers past the orbit of the Earth. The second telescope is a 2 m telescope that is planned to be placed on the far side of the moon (average distance to the moon is 380,000 km from the Earth). (a). Which telescope will have the greater light gathering power (10

Astronomy Carbon Dioxide Snow on Mars the
Words: 706 Length: 3 Document Type: Essay

Astronomy Carbon Dioxide Snow on Mars The research and mission reported by this article regards unique weather patterns occurring on Mars. According to data gathered by the Phoenix Mars lander and the Mars Reconnaissance Orbiter data, there are clouds of water vapor on Mars and there is the only known stance of carbon dioxide snow falling in this solar system. The research on this phenomenon was first published in the Journal of

Astronomy the Electromagnetic System Is
Words: 962 Length: 3 Document Type: Essay

They appear as dark circles on the sun's surface. Ex. 6: The lifecycle of a star is determined by its mass. A typical star will follow the main sequence, become a yellow star like the Sun, and die as a Red Giant and then settle as a White Dwarf. A black hole is an area that has had gravity pull in on itself due to a supermassive explosion. Black holes

Astronomy Explain How the Hertzsprung-Russell Diagram Is
Words: 1675 Length: 6 Document Type: Essay

Astronomy Explain how the Hertzsprung-Russell diagram is constructed of the four main groupings of stars. Identify characteristics of the four main groupings of stars on the diagram. How are the axes of graph labeled? The Hertzsprung-Russell diagram is much like a common graph used in mathematical subjects like algebra and other mathematical domains. Like any graph, there is an X axis and a Y axis with each axis representing different majors traits

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