Copyright ©2003 by Paul Niquette. All rights reserved.
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Copyright ©2003 by Paul Niquette. All rights reserved.
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...but it's farther away. -- Paul Niquette, "Measuring the Moon"
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 hus
do we begin our analysis of the puzzle with
an idle non sequitur. As you know, the earth is about 25,000 miles
in circumference, 8,000 miles in diameter. Taking the word "size"
to mean surface area, we estimate that the moon must be about 2,000 miles
in diameter. Space-age measurements, in fact, have confirmed that
the moon is actually 2,162 miles in diameter and it is indeed 238,900 miles
"farther away."
A circle with a radius of 238,900 miles would have a diameter
of 477,800 miles and a circumference of 1,501,053 miles ( Meanwhile, a penny measures 3/4th of an inch in diameter. A circle made of $6.94 worth of pennies would measure 520 inches in circumference. Viewed from the center, each penny subtends an angle of 0.52 degress, just like the moon as viewed from the surface of the earth. A circle of 520 inches has a radius of 6 feet 11 inches. So the solution for the puzzle is...
he
phrase, "[n]ear the horizon," in the statement of the puzzle suggests that
the solution might be different at, say, midnight, when the moon is seen
high up in the night sky. Such would be the expectation based on
one of the most universal human experiences. Throughout history,
people have judged the moon to be much larger when it is rising or setting
than when it is seen at high elevations. A difference of 20% in diameter
is not untypical, and some people are willing to swear that they see as
much as a 2-to-1 ratio in size.
Sophisticated solvers know that
this is a mere illusion -- that, if anything, the moon ought to appear
slightly larger overhead, since it is nearly 4,000 miles closer.
In fact, an objective measurement of the angle subtended by the moon at
midnight will confirm that it is nearly 3% larger than it is at
moon-rise (0.5273o degrees vs 0.5185o).
The pictures above depict what has been long known as the The Moon Illusion. |
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times the diameter). That's the distance the moon travels in one
29-day orbit around the earth -- 694 times its own diameter for 360o.
The diameter of the moon itself, therefore, corresponds to 360/694 degrees.
That's 0.52o as viewed from the
surface of the earth.
