WHAT
IS A CIRCUMFERENTOR?
Attach an
upright piece of wood to a sturdy base. Tape a
protractor to the upright, at about your eye level, and use
a pin to fasten a fat drinking straw to the center of the
protractor. (That is not a straw for drinking fat. It is a drinking straw
that is not skinny. After all, you're going to be looking through the
straw.)
Sight through
the straw to the top of a distant object, then read the figure on the
protractor at the bottom edge of the straw. Then sight on the bottom edge
of the object and note the reading.
The difference
between the two readings is the angular
diameter of the object being observed. By sighting on
objects of various sizes from various distances, you will
discover that:
1) objects
with the same angular diameter are not always
the same size,
2) the angular
diameter becomes smaller as the distance
increases, and
3) angular
diameter depends both on the distance and on
the real size of the object.
The instrument
you have constructed is called a circumfer
entor. That word is not in any of my dictionaries, nor is
it in my encyclopedia. It might or might not be the correct word for that
instrument; however, that word was
used by the brilliant scientist who gave me his notes for
these projects.
To determine
the real size of the object, draw the angle to
scale. For example, if a basketball is 10 feet away when its angular diameter
is measured, draw a 10 inch line on a sheet of paper (1 in. = 1 ft.),
use the circumferentor to measure to the angular diameter of the basketball
(e.g., 10 degrees), and draw the angle from the 10 inch line. When the
angle is extended to the same length (10 inches), an imaginary triangle
is formed whose sides have the same ratio as those of the imaginary triangle
formed by the viewer and the basketball.
Since 1 inch
equals 1 foot in the scale, the distance between the ends of the two lines
represents the diameter of the object. If this distance is 1 1/2 inches,
then in this scale, the diameter of the basketball is 1 1/2 feet.
Astronomers
have used instruments such as the circumferentor to determine that the
angular diameter of the moon is 1/2 a degree. Use a protractor to draw
an angle of 1/2 degree on a long sheet of paper.
Extend the
sides of the angle to represent the distance to
the moon (about 240,000 miles). A scale of 1 inch for each
10,000 miles would produce an angle with sides 24 inches
long. When the imaginary triangle between the two sides is
completed, you will find the angular diameter of the moon to be about
1/5 inch long.
This scale
indicates that the diameter of the moon is about
2,000 miles (actually 2,160 miles).
The encyclopedia,
even when it doesn't seem to have what I
want, is a wondrous item! When looking for circumferentor, the list of
topics relative to "circumference" came up, and guess what was
on that list? Picard, Jean. Well, now all of us Trekkies know who Jean
(Luc) Picard is. Here is the brief biography it gave: "Picard, Jean,
16201682, French astronomer. His measurements led to a much improved
determination of the length of a degree of meridian and consequently of
the circumference of the earth. Sir Isaac Newton used Picard's figures
to verify the accuracy of his principle of gravitation." Isn't that
marvelous!!
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