math problem: you see an object in the sky, it looks as big as the moon, and it is above the clouds, what is the range of its potential size?

information given: the height of the clouds are at 2000M elevation, the object is an undetermined distance above it.

Based on the fact that the object in the sky lines up with the moon perfectly, and the clouds and moon are the only two refference points, what is the estimated minimum and maximum size of the object, assuming it is within the atmosphere.

Specifically, the area at the angle at which it is seen, assuming the object were spherical, any given cross sectional area could be used to determine volume, but only area is what matters, what surface area is being seen?

disregard any magnification effects at play that might make the moon look larger.

The purpose here is to gain a rough estimate of an unknown object an undetermined distance between the clouds of known distance, and the moon.

thanks in advance

1 Answer

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  • 4 weeks ago
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    The moon is half a degree across. Anything that looks as big as the moon is also half a degree across. If an object such as a balloon is at a height of six thousand feet and it is half a degree across then it's diameter is about fifty two feet.

    in feet, a good approximation is:

    2 * (6000 * tan((0.25/360) * 2 * pi) ) =52

    another way is to simply use proportions as follows:

    diameterObject=6000 * diameterMoon / distanceMoon

    6000 * (2 * 1737) / 400000  = 52

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