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    Re: Perigee Full Moon 23 June
    From: Frank Reed
    Date: 2013 Jun 19, 11:41 -0700

    Rommel, you wrote:
    "Isn't it funny and optically deceptive what the atmosphere can do to disproportionately represent objects at near or far distance in space?"

    I would quibble with one word here (just a quibble! no big deal). It's not the "atmosphere" that creates the weird Moon illusion. It's something else. It's a perceptual illusion caused by some "visual clues" involving distant objects. It's perhaps an important distinction because many people who have learned just enough physics to get in trouble have suggested (incorrectly) that the atmosphere optically "magnifies" the Moon. If that were the case, this would be measurable with a sextant. In fact, the Moon is measurably SMALLER when it is low in the sky by a small fraction despite the extremely convincing illusion that it is HUGE. And though any re-tread of this story in popular science sources today will create the impression that this is some new mystery, perhaps only recently studied by experts in human perception and cognition, it has actually been discussed for centuries. For example, Andrew Mackay wrote a very good book on longitude, primarily on lunars, published back in 1809, "The Theory and Practice of Finding the Longityude at Sea or Land". In it, he included a few paragraphs on the Moon illusion as follows:

    "Of the Horizontal Moon:
    That the moon is imagined to appear much larger when in or near the horizon, than when at any considerable degree of elevation, is an observation familiar to every person: whereas, the semidiameter of the moon really subtends a less angle in the first case, than in the second, by the quantity of the augmentation.

    To account for this seeming paradox, has exercised the skill of many eminent astronomers and philosophers, who have given various solutions for that purpose. These, however, we may probably have occasion to mention in another work—and, therefore, we shall confine ourselves to that solution which is now generally received. For this purpose, it will be necessary to premise the following lemmata.
    The nearer that any object is to the eye of an observer, it will appear under a greater angle.
    Let there be two objects of the same magnitude, and placed at equal distances from an observer; but from some illusion, one of them is imagined to be more distant than the other; then, that object which is judged to be at the greatest distance, will be considered as the largest of the two.
    The expanse, or firmament, from whatever cause, whether from the appearance of clouds in the atmosphere, these towards the zenith being nigher than those near the horizon; from the appearance of a number of interposed objects between the observer and the most distant, parts of the horizon; the greater quantity of vapours near the horizon, which render objects fainter than when elevated, or otherwise; is imagined to be a small portion of a spherical surface,f the nearest point being the zenith, and the most distant the horizon. Now, since the heavenly bodies are, to imagination, disposed on the surface of this circular or vaulted arch; and since, therefore, an object is judged to be more distant when in or near the horizon, than it is when at any considerable degree of elevation; it hence follows, that of two objects of the same magnitude, and at equal distances from an observer, that which is apparently farthest distant will, to imagination, be the largest of the two. Now, let one of these objects be near the horizon, and the other near the zenith; then, in consequence of the vaulted appearance of the sky, the former will be imagined to be more distant than the latter. [...]"

    Although the language has changed, this is still fundamentally the explanation of the illusion today. It's the appearance of "interposed objects" that causes the Moon near the horizon to look so huge.

    Of the apparent size of the Moon, you wrote that it is "still rarely larger in circumference than a dime held at arm's length."

    Rarely? How about NEVER! A dime is much too large. I often recommend this as a friendly "bet" that you can share with people. What size coin just perfectly covers the Full Moon? Most will guess a penny or even a nickel, and when the Moon has just risen and they have just come inside from seeing it in the sky, many will eagerly bet ten dollars that a dime is too small to cover the Moon. But all US coins are much too big, even the dime. Lincoln's face on a penny held at arm's length is about the same angular size as the Moon or Sun in the sky. A child-dose aspirin tablet is about the right size. Half a degree is a SMALL angle!

    More on the Supermoon in another post...


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