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How could you find the distance to the moon, knowing only its diameter, and having only a meter stick and pen?

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How could you find the distance to the moon, knowing only its diameter, and having only a meter stick and pen?

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  1. Yes.  If you hold the ruler at arm's length, there are two similar isosceles triangles--from your eye to the ruler, and from your eye to the diameter of the moon.  If we call:

    r = distance from hand to eye

    R = distance from moon to eye

    d = diameter of moon seen on ruler

    D = real diameter of moon.

    You can imagine then the two triangles with the same angle at your eye with legs r and base d, and with legs R and base D.  That means:

    R / r = D / d since the two triangles are similar

    Therefore:

    R = r * D / d

    Since the moon is about 2200 miles in diameter, and it is typically a finger's-width at arm's length, or 0.5 inch at 3 feet, this means

    R = 36in * 2200 miles / 0.5 in = 158,400 miles

    which is not really anywhere near the real value of 230,000 miles, but I'm only guessing at these numbers because it's daytime :)


  2. it is not possible with just a meter stick and a pen, but is possible if you have a theodelite or a protractor.

    measure the angular span of the moon using a theodelite. Let that value be x degrees. let the diameter of the moon be 'a' km, and its distance 'b' km.

    now,

    tan x = a/b

    so,

    b = a/tan x

    (tan is a trigonometric value, which can be calculated using a calculator.)

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