Re:School kids measure distance to the Moon
by RiderOfGiraffes on Sunday September 06, 2009 @06:45AM
(#807676)
OK, I've done some more homework ...
The pendulum method gives the equation
l L^2 R^2 = P^2 D^3
l = pendulum length (assume 1m)
P = pendulum period (roughly 2s)
L = Lunar orbital time (27.32 * 86400)
R = Radius of the Earth
D = Distance to the Moon
Now we also know that in a total Lunar eclipse the Moon moves through the Earth's shadow. Assume it moves directly through the center. Measure the time for the Moon to move from touching the umbra to completely exiting the umbra. The distance it moves is then pretty much one Earth diameter, because the apparent sizes of the Sun and Moon are the same.
So R/D = (T/2)(2pi/L) where T is the transit time, and turns out from observations to be around 12500 seconds.
The pendulum method gives the equation
Now we also know that in a total Lunar eclipse the Moon moves through the Earth's shadow. Assume it moves directly through the center. Measure the time for the Moon to move from touching the umbra to completely exiting the umbra. The distance it moves is then pretty much one Earth diameter, because the apparent sizes of the Sun and Moon are the same.So R/D = (T/2)(2pi/L) where T is the transit time, and turns out from observations to be around 12500 seconds.
Combining these equations we get:
They turn out pretty well.