|MadSci Network: Science History|
I have read that the Greeks used information from solar eclipses to calculate the distance to the moon. A philosopher by the name of Aristarchus noted that the moon was just barely able to cover the sun during a total solar eclipse, meaning that the two have the same angular size, or apparent size, even though they are at different distances from the Earth. This means that the actual sizes of the moon and the sun could be used to determine their distances by the use of proportions (see below). Of course, for this to work you need to know the actual sizes of the sun and moon, and the distance of the earth to the sun (all of these were known to the Greeks). distance to moon actual size of moon ---------------- = ------------------- distance to sun actual size of sun Another way the Greeks were able to determine the distance from the earth to the moon comes from a concept called parallax, which is a sort of triangulation. This means that a stationary object appears to move if an observer changes his position. You can test this idea by placing a pencil at arms length in front of your eyes and directly in front of your nose. Close your left eye and note the position of the pencil. Now, at the same time open your left eye and close your right eye. The pencil appears to have shifted position. We can pretend that the moon is the pencil, and that each eye represents an observer. If we can find the angle that the moon makes with one observer (one eye), we can use the that angle to find the distance of the moon using the following equation: distance to the moon = (1/2 distance between observers) * (tangent of the angle between the observer and the moon) This equation works if the moon makes the same angle with each observer as seen in the "illustration" below where "a" and "b" are observers and "m" is the moon. This means that the moon and the observers make a huge isosceles triangle. Of course, we can still do this if the observers see the moon at different angles. It all has to do with the distance from one observer to a perpendicular line dropped from the moon multiplied by the tangent of the angle that the moon mmakes with that observer. Below are some web sites with great illustrations on how to do this. m *|* * | * * | * * | * a----|----b The following site actually shows how the Greeks used parallax to calculate the distance to the moon and the sun. http://space boy.nasda.go.jp/Note/Shikumi/E/Shi08_e.html A fellow Mad Scientists posted an experiment one can do at home showing how to use the parallax concept. http: //www.madsci.org/posts/archives/mar97/858790120.Ph.r.html The following web site shows how to use parallax to find the distance to the stars, but the same principles can be used to find the distance to the moon. http://zebu.uo regon.edu/~soper/Stars/parallax_ly.html
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