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REAL SIZE vs. APPARENT SIZE

Measure the diameter of a fifty-cent piece (1 1/2 inches
across), then, using transparent tape, affix the coin to an
object at a distance of 20 feet or so. Although you know
that the size of the coin hasn't changed, you will realize
that the coin appears to be only a fraction of an inch
in diameter.

The measurement taken with the ruler was the object's real
size. The observation at a distance was of its apparent
size.

Whenever the size of a distant object is measured, astro-
nomers must remember that they never see the real size of an object, but only its apparent size.

Hold a coin (or your thumb) in front of you, close one eye,
and sight on a clock or a basketball at the front end of the room. Move the coin nearer or further until it exactly hides the object (the apparent sizes of the coin and the clock are now the same).

An analogy can be made to the apparent sizes of the sun (the clock) and the moon (the coin).

How is it that the sun and the moon often appear to be the
same size?

Next, note what happens when the coin is moved nearer or
further away from the eye. (The apparent size changes as it moves nearer and farther away -- an inch appears shorter as the distance increases, and appears larger as the distance decreases.)

Place a fifty-cent piece on a piece of paper so that its edge is near one edge of the paper. With a pencil, make a dot on the opposite edge of the paper, and use a ruler to draw straight lines from the dot to each side of the coin.

Now move the coin to the middle of the paper and do the same. Next, move the coin to within 2 inches of the dot, and draw the lines.

Use a protractor to measure the size of each angle. Each angle is the apparent size of the coin as seen from a different distance from the dot. Note that the angle decreases as the distance increases, and vice versa.

The angle determined by the apparent size of an object is
called the object's angular diameter.

The difference between real size and apparent size is well
illustrated by taking a photograph of two people. one is
kneeling about 10 feet in front of you, with his/her hand
reaching out as though to hold an object. The other person
is standing ten or so feet farther from you, in line with the person who is kneeling. When you line up the people carefully, and take the picture, you will see that it appears as though the kneeling person is holding the standing person in his/her outstretched hand! Isn't it called "perspective?"

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