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Easy Java Simulations (2001- ) => Collaborative Community of EJS => Topic started by: lookang on June 21, 2012, 05:05:25 pm

Title: Ejs Open Source Eratosthenes Measures Earth Java Applet
Post by: lookang on June 21, 2012, 05:05:25 pm
Ejs Open Source Eratosthenes Measures Earth Java Applet by Todd Timberlake. Todd K. Timberlake (ttimberlake@berry.edu)
remixed by lookang
trying to make it suited for determination of circumference of earth and radius of earth!


General Description by Todd changes by lookang
This simulation shows the shadows cast by two gnomons at different locations on Earth. For one gnomon the sun is directly overhead (as would be the case if the gnomon was on the Tropic of Cancer at the summer solstice). The other gnomon is due north of the first gnomon. The sizes of the gnomons are greatly exaggerated for visibility. This simulation can be used to help illustrate how Eratosthenes was able to measure the radius and circumference of Earth using the shadows cast by two gnomons, one situated due north of the other, on a day when the southerly gnomon cast no shadow at all. The distance between the two gnomons (along Earth's surface) can be adjusted. The length of the shadow is given, and this length can be used to determine the angle between the gnomon lines and from that the radius and circumference  of Earth. The Earth can be hidden to give a better view of the relevant geometry which the alternate angles in Mathematics education in used.
Eratosthenes Measures Earth
Display Options Menu
Show Earth: show a disk (updated with graphics by lookang) representing Earth. Deselect this option to get a better view of the geometry.
Show Length of Shadow: display a panel at the bottom of the window that gives the length of the moveable gnomon's shadow.
Show Angle Between Gnomons: display a panel at the bottom of the window that gives the angle between the two gnomon lines. This can be used to help students who are unfamiliar with trigonometry (specifically the inverse tangent function that is needed to compute this angle from the length of the shadow).
Show Sunbeams: show lines representing rays of sunlight that graze the tops of the gnomons.
Show Center of Earth: show a dot at the center of Earth.
Visual Elements
Blue disk: Earth.  (updated with graphics by lookang)
Red lines: the two gnomons. If you hide Earth the gnomon lines extend down to Earth's center.
Yellow arrows: light rays from Sun. These lines are effectively parallel to each other (although strictly speaking they are not exactly parallel) because Sun is on the order of 10,000 Earth diameters from Earth.
Magenta line: shadow cast by the moveable gnomon (the fixed gnomon does not cast a shadow since Sun is assumed to be directly overhead for that gnomon).
Green dot: the center of Earth.
Controls, etc.
Distance: the distance (in km) along Earth's surface between the two gnomons.
The length of the moveable gnomon's shadow is given (in units of the gnomon's length).
The angle between the two gnomon lines is given (in degrees).
Input Fields and Feedback (lookang) for learning assessment

Title: Re: Ejs Open Source Eratosthenes Measures Earth Java Applet
Post by: lookang on June 21, 2012, 05:08:37 pm

tilted by 23.5 degree to simulate topic of cancer
color code the checkbox
add distance = arc length drawing
add text as hints
add top Gnomon checkbox
add shadow checkbox

22June 2012
add angle visualization
add Google earth picture
add assessment for learning input fields with feedback for Radius of Earth and Circumference of Earth

25 june 2012
add // which is taken from http://www.shadedrelief.com/natural3/pages/textures.html // who release it to the public domain // Tom Patterson, www.shadedrelief.com. //resize to 2000x1000 by lookang using GIMP and quality reduce to 80% for 200+kb filesize to use materials that are in public domain
disabled the html as the pop box from NTNU seems to be too many, testing

credits to Todd Timberlake!
i didn't make this, just remixing to customize it to suit the Wikipedia entry http://en.wikipedia.org/wiki/Eratosthenes

Eratosthenes' measurement of the Earth's circumference
illustration showing a portion of the globe showing a part of the African continent. The sun is shown and arrows indicate rays of the sun hitting earth. Rays or arrows point to Alexandria (labeled "A") and Syrene (labeled "S"). Blue lines are drawn from A and S towards the equator. There is a line representing the Tropic of Cancer running to S. Two small curved arrows indicating a measurement are drawn from the Greek symbol phi. One ends midway between the blue lines from A and S and the other ends between the ray of light hitting A and an extension of the blue line passing through A into space.
Measurements taken at Alexandria (A) and Syene (S)

Eratosthenes calculated the circumference of the Earth without leaving Egypt. Eratosthenes knew that on the summer solstice at local noon in the Ancient Egyptian city of Swenet (known in Greek as Syene, and in the modern day as Aswan) on the Tropic of Cancer, the sun would appear at the zenith, directly overhead (he had been told that the shadow of someone looking down a deep well would block the reflection of the Sun at noon). He also knew, from measurement, that in his hometown of Alexandria, the angle of elevation of the sun was 1/50th of a circle (7°12') south of the zenith on the solstice noon. Assuming that the Earth was spherical (360°), and that Alexandria was due north of Syene, he concluded that the meridian arc distance from Alexandria to Syene must therefore be 1/50 = 7°12'/360°, and was therefore 1/50 of the total circumference of the Earth. His knowledge of the size of Egypt after many generations of surveying trips for the Pharaonic bookkeepers gave a distance between the cities of 5000 stadia (about 500 geographical miles or 800 km). This distance was corroborated by inquiring about the time that it takes to travel from Syene to Alexandria by camel. He rounded the result to a final value of 700 stadia per degree, which implies a circumference of 252,000 stadia. The exact size of the stadion he used is frequently argued. The common Attic stadion was about 185 m,[9] which would imply a circumference of 46,620 km, i.e. 16.3% too large. However, if we assume that Eratosthenes used the "Egyptian stadion"[10] of about 157.5 m, his measurement turns out to be 39,690 km, an error of less than 2%.[11]

Title: Re: Ejs Open Source Eratosthenes Measures Earth Java Applet
Post by: lookang on September 13, 2012, 08:27:02 am

made the globe drawing more perfectly spherical by changing the resolution to "360,360,360,360"
http://en.wikipedia.org/wiki/Eratosthenes (http://upload.wikimedia.org/wikipedia/commons/thumb/9/98/Eratosthenes.png/220px-Eratosthenes.png)
Illustration showing a portion of the globe showing a part of the African continent. The sun beams shown as 2 rays hitting earth at Syene and Alexandria. Angle of sun beam and the gnomons (vertical sticks) is shown at Alexandria which allowed Eratosthenes' estimates of radius and circumference of Earth.