School kids measure distance to the Moon

Re:School kids measure distance to the Moon by gjm11 on Thursday September 03, 2009 @12:59PM (#802895)

Yes, I do mean other than apart from the original definition which, after all, is not the current definition. (You could say "but everyone knows ...", but then you could equally say that "everyone knows" g ~= 9.8m/s^2.) The Eratosthenes method is lovely but surely rather difficult in a classroom. (Am I missing a trick?) All I know about the al-Biruni method is a couple of sentences from Wikipedia, but it sounds as if it effectively needs some external (geographical) data that you can't measure in a classroom. Hmm.

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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.

Combining these equations we get:

    D = l*(pi*T/P)^2
    R = l*pi^3*T^3/(L*P^2)

They turn out pretty well.

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Re:School kids measure distance to the Moon by RiderOfGiraffes on Sunday September 06, 2009 @12:51PM (#807923)

Bother - forgot that asterisks have a special meaning. Sorry about the formatting.

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