Eclipse: Lunar - Earth's Shadow
Eclipse: Lunar - Earth's Shadow
MoonIn a lunar eclipse, if the width of the shadow of the Earth is twice the width of the Moon, then the width of the Earth itself is (very nearly) three times that of the Moon--not twice, as one might perhaps think. Here is why.
The Sun is not a point of light but an extended source, with a disk covering a circlular patch in the sky, about 0.5° across. This makes the shadow of the Earth not a cylinder, stretching to infinity without narrowing down, but a cone, with an angle of 0.5° across its apex C (drawing). AB is here the diameter of the Earth, and the directions AC and BC represents rays from opposite edges of the Sun's disk, rays whose directions differ by 0.5°.
Image:Shadow.gif
"Drawing" (Source: David P. Stern)
If x is the diameter of the Moon and R its distance, then according to Aristarchus, the width ED of the shadow at distance R equals 2x (actually, 2.5x comes closer to the mark). We add to the drawing points H and K so that HA = KD = x.
The width of the Moon as seen from point H is KD = x, and since the Moon's size in the sky is about the same as the Sun's, the angle KHD (shaded) should also equal 0.5°. We now extend the line AD = R a further distance R to point F. Then the two shaded triangles HKD and KFD are congruent (= same in size and shape) and have the same 0.5° angle as the angle at C. Indeed, one can prove now that the triangles GFC and AHD are also congruent to the two shaded ones.
It follows then that AC = 3R, and from simple proportions (see drawing) AB = 3x.
Preview Image
- NASA - John F. Kennedy Space Center Media Gallery: In this lunar eclipse viewed from Merritt Island, Fla., the full moon takes on a dark red color because it is being lighted slightly by sunlight passing through the Earth's atmosphere. This light has the blue component preferentially scattered out (this is also why the sky appears blue from the surface of the Earth), leaving faint reddish light to illuminate the Moon. Eclipses occur when the Sun, Earth and Moon line up. They are rare because the Moon usually passes above or below the imaginary line connecting Earth and the Sun. The Earth casts a shadow that the Moon can pass through - when it does, it is called a lunar eclipse. (Eclipse Date: November 8, 2003.)
Disclaimer: This article is taken wholly from, or contains information that was originally published by, David P. Stern - "Educational Web Sites on Astronomy, Physics, Spaceflight and the Earth's Magnetism." Topic editors and authors for the Encyclopedia of the Cosmos may have edited its content or added new information. The use of information from David P. Stern should not be construed as support for, or endorsement by, that David P. Stern for any new information added by EoC personnel, or for any editing of the original content. The EoC has a specific working relationship with David P. Stern, and any changes to any of his content is to be done only with his approval or the approval of those appointed by him to represent his interests in this content.
Citation
Stern, David P. Ds.C. (Contributing Author); Bernard Haisch (Topic Editor). 2008. "Eclipse: Lunar." In: Encyclopedia of the Cosmos. Eds. Bernard Haisch and Joakim F. Lindblom (Redwood City, CA: Digital Universe Foundation). [First published March 5, 2008].
<http://www.cosmosportal.org/articles/view/135542/>
Contact Us
Send to a Friend
Comments
There are no comments.