Thursday, June 16, 2011

Lunar eclipse

If clouds or anything else have prevented from seeing the lunar eclipse, here is a video:

Note that people could have used this event to figure out that the Earth was round. You may see the ratio radius(Earth)/radius(Moon) either from the curvature of the boundary of shadow, or from the timing of the longest lunar eclipses divided by the speed of the moving shadow.

The radius of the Moon may be converted to kilometer if you measure its angular size and its distance. The latter may be measured by comparing the position of the Moon on the skies as seen from two different places on Earth. Note that if you move by 3,000 km, the angular direction of the Moon changes by 0.01 rad = 0.57°.

You may calculate (from the period, a month or so, and the distance) that the speed of Moon is about 1.0 km/s in average so if the Moon is able to hide for 100 minutes, the object that is creating the shadow - the Earth - must have the diameter comparable to O(10,000 km).

Well, this lunar eclipse wasn't the longest one possible but at least I got the right answer up to a factor of two which would be good enough to exclude Flat Earth theories. ;-)

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