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The Moon illusion is an optical illusion which causes the Moon to appear larger near the horizon than it does higher up in the sky. It has been known since ancient times and recorded by various cultures.   The explanation of this illusion is still debated.   
Proof of illusion
A popular belief, stretching back at least to Aristotle in the 4th century B.C., holds that the Moon appears larger near the horizon due to a real magnification effect caused by the Earth's atmosphere. This is not true: although the atmosphere does change the perceived color of the Moon, it does not magnify or enlarge it. In fact, the visual image of the moon is about 1.5% smaller when it is near the horizon than when it is high in the sky, because it is farther away by nearly one Earth radius. Atmospheric refraction also makes the image of the Moon slightly smaller in the vertical direction.
The angle that the full Moon subtends at an observer's eye can be measured directly with a theodolite to show that it remains constant as the Moon rises or sinks in the sky (discounting the very small variations due to the physical effects mentioned). Photographs of the Moon at different elevations also show that its size remains the same.
A simple way of demonstrating that the effect is an illusion is to hold a small object (say, 1.4 inches or 36 millimetres wide) at arm's length (25 inches or 640 millimetres) with one eye closed, positioning it next to the seemingly large Moon. When the Moon is higher in the sky, positioning the same object near the Moon reveals that there is no change in size.
Note that between different full moons, the Moon's angular diameter can vary from 29.43 arc minutes at apogee to 33.5 arc minutes at perigee—an increase of around 14% in apparent diameter or 30% in apparent area. This is because of the ellipticity of the Moon's orbit.
The size of a viewed object can be measured objectively either as an angular size (the visual angle that it subtends at the eye, corresponding to the proportion of the visual field that it occupies), or as physical size (its real size measured in, say, meters). Perceived size is only loosely related to these concepts, however. For example, if two identical, familiar objects are placed at distances of five and ten meters, respectively, then the more distant object subtends approximately half the visual angle of the nearer object, but we normally perceive that as the same size (a phenomenon referred to as size constancy), not as half the size. Conversely, if the more distant object did subtend the same angle as the nearer object then we would normally perceive it to be twice as big.
One question concerning the Moon illusion, therefore, is whether the horizon moon appears larger because its perceived angular size seems greater, or because its perceived physical size seems greater, or some combination of both. There is currently no consensus on this point. Most recent research on the Moon illusion has been conducted by psychologists specializing in human perception. The 1989 book The Moon Illusion, edited by Hershenson, offers about 24 chapters written by various illusion researchers reaching different conclusions. After reviewing the many different explanations in their 2002 book The Mystery of the Moon Illusion, Ross and Plug conclude "No single theory has emerged victorious". They argue that the size of the illusion is variable, but is usually an apparent increase in diameter of about 50 percent. The most important factor is the sight of the terrain, but there is a small contribution from other factors such as the angle of regard, posture and oculomotor commands.
Refraction and distance
Ptolemy attempted to explain the Moon illusion through atmospheric refraction in the Almagest, and later (in the Optics) as an optical illusion due to apparent distance, or the difficulty of looking upwards, although interpretations of the account in the Optics are disputed. Similarly Cleomedes (about 200 A.D.), in his book on astronomy, ascribed the illusion both to refraction and to changes in apparent distance. In the Book of Optics (1011–1022 A.D.), Ibn al-Haytham (Alhazen) repeated refraction as an explanation, but also proposed a more detailed explanation based on intervening objects and apparent distance.
Through additional works (by Roger Bacon, John Pecham, Witelo, and others) based on Ibn al-Haytham's explanation, the Moon illusion came to be accepted as a psychological phenomenon in the 17th century.
Apparent distance hypothesis
An apparent distance theory evidently was first clearly described by Cleomedes around 200 A.D. The theory proposes that the horizon moon looks larger than the zenith moon because it looks farther away. Ibn al-Haytham was more specific. His argument was that judging the distance of an object depends on there being an uninterrupted sequence of intervening bodies between the object and the observer; however, since there are no intervening objects between the Earth and the Moon, the perceived distance is too short and the Moon appears smaller than on the horizon.
When we see objects such as clouds, birds, and aeroplanes in the sky, those near the horizon are typically farther away from us than those overhead. This may result in the perception of the sky itself as a comparatively flat or only gently curving surface in which objects moving towards the horizon always recede away from us.
In 1813, Schopenhauer wrote about this, that the moon illusion is "purely intellectual or cerebral and not optical or sensuous." The brain takes the sense data that is given to it from the eye and it apprehends a large moon because "our intuitively perceiving understanding regards everything that is seen in a horizontal direction as being more distant and therefore as being larger than objects that are seen in a vertical direction." The brain is accustomed to seeing terrestrially–sized objects in a horizontal direction and also as they are affected by atmospheric perspective, according to Schopenhauer.
If we perceive the Moon to be in the general vicinity of the other things we see in the sky, we would expect it to also recede as it approaches the horizon, which should result in a smaller retinal image. But since its retinal image is approximately the same size whether it is near the horizon or not, our brains, attempting to compensate for perspective, assume that a low Moon must be physically larger.
Extensive experiments in 1962 by Kaufman and Rock showed that a crucial causative factor in the illusion is a change in the pattern of cues to distance, comparable to the Ponzo illusion. The horizon moon is perceived to be at the end of a stretch of terrain receding into the distance, accompanied by distant trees, buildings and so forth, all of which indicate that it must be a long way away, while these cues are absent from the zenith moon. Experiments by many other researchers have found the same result; namely, when pictorial cues to a great distance are subtracted from the vista of the large-looking horizon moon it looks smaller. When pictorial cues to an increased distance are added into the vista of the zenith moon, it appears larger.
A potential problem for the apparent distance theory has been that very few people (perhaps about 5%) perceive the horizon moon as being both larger and farther away. Indeed, most people (perhaps 90%) say the horizon moon looks both larger and closer than the zenith moon (Boring, 1962; Hershenson, 1982; McCready, 1965, 1986; Restle, 1970). Most of the rest say it looks larger and about the same distance away as the zenith moon, with a few people reporting no Moon illusion at all. However, the response that the horizon moon appears larger, but not closer than the zenith moon could be because the viewer's logic confounds his or her perception; because the viewer knows that the moon can't possibly be physically farther away, he or she is not consciously aware of the perception. This is reinforced by the idea that we do not consciously perceive distance and size, as spatial awareness is a subconscious, retino cortical cognition. Nevertheless, the apparent distance explanation is the one most often found in textbooks.
Those advocating the apparent distance hypothesis might counter that in the Ponzo illusion, people do not perceive one line to actually be farther away than another either, or that everything on the horizon is perceived as farther away, out of the habit that this is true for every object ever seen there (average-altitude clouds are about 100 times farther away at the horizon than when overhead).
Relative size hypothesis
Historically, the best-known alternative to the "apparent distance" theory has been a "relative size" theory. This states that the perceived size of an object depends not only on its retinal size, but also on the size of objects in its immediate visual environment. In the case of the Moon illusion, objects in the vicinity of the horizon moon (that is, objects on or near the horizon) exhibit a fine detail that makes the Moon appear larger, while the zenith moon is surrounded by large expanses of empty sky that make it appear smaller.
The effect is illustrated by the classic Ebbinghaus illusion, where a circle appears larger when surrounded by smaller circles, than it does when surrounded by larger circles.
Angle of regard hypothesis
According to the "angle of regard" hypothesis, the Moon illusion is produced by changes in the position of the eyes in the head accompanying changes in the angle of elevation of the Moon. Though once popular, this explanation no longer has much support. Looking through one's legs at the horizon moon does reduce the illusion noticeably, but this may be because the image on the retina is inverted. Raising the eyes or tilting the head when in an upright posture gives only a very small reduction in the illusion.
Immanuel Kant refers to the Moon illusion in his 1781 text Critique of Pure Reason, when he writes that "the astronomer cannot prevent himself from seeing the moon larger at its rising than some time afterwards, although he is not deceived by this illusion". Schopenhauer (1813) was cited above. Wade shortly summarizes historical references to the Moon illusion starting with Aristotle; he lists quotes by Aristotle (~330 BC), Ptolemy (~142, 150), Ibn al-Haytham (Alhazen) (1083), John Pecham (~1280), Leonardo da Vinci (~1500), René Descartes (1637), Benedetto Castelli (1639), Pierre Gassendi (1642), Thomas Hobbes (1655), J. Rohault (1671), Nicolas Malebranche (1674), William Molyneux (1687), J. Wallis (1687), G. Berkeley (1709), J.T. Desaguliers (1736), W. Porterfield (1737), R. Smith (1738), C.N. Le Cat (1744), D. Hartley (1749), Thomas Young (1807), and Carl Friedrich Gauss (1830).
- Wade, Nicholas J (1998). A natural history of vision. A Bradford Book. Cambridge MA, London, UK: The MIT Press. p. 377 ff. ISBN 0-262-23194-8.
- Ross, Helen E.; Plug, Cornelis (2002). The mystery of the moon illusion. Oxford, New York: Oxford University Press. ISBN 019 850862 X.
- Hershenson, Maurice (1989). The Moon illusion. ISBN 0-8058-0121-9.
- McCready, Don (November 10, 2004). "Finally! Why the Moon Looks Big at the Horizon and Smaller When Higher Up". Psychology Department, University of Wisconsin-Whitewater. Retrieved December 2, 2015.
- "See a huge moon illusion". USA Today. 17 June 2008.
- Lynch, D and Livingstone, W (2001). Color and Light in Nature. Cambridge University Press. par. 7.10
- Astronomy Picture of the Day — large and small full moons, NASA
- Helen Ross; Cornelis Plug (2002). The Mystery of The Moon Illusion. USA: Oxford University Press. p. 180.
- Good, Gregory (1998). Sciences of the Earth: An Encyclopedia of Events, People, and Phenomena. Psychology Press. pp. 50–. ISBN 9780815300625. Retrieved 15 July 2012.
- Robinson, J.O. (1998). The Psychology of Visual Illusion. Dover Publications. p. 55. ISBN 0486404498. Retrieved 15 July 2012.
- Ross, Helen E; Ross, George M (1976). "Did Ptolemy understand the moon illusion?". Perception. 5 (4): 377–85. doi:10.1068/p050377. PMID 794813.
- Plug, Cornelis; Ross, Helen E. (1989). "Historical Review". In Hershenson, Maurice. The Moon Illusion. Psychology Press. pp. 5–30. ISBN 978-0-8058-0121-7.
- On the Fourfold Root of the Principle of Sufficient Reason, § 21 [ist also rein intellektual, oder cerebral; nicht optisch oder sensual]
- On the Fourfold Root of the Principle of Sufficient Reason, § 21 [... daß unser anschauender Verstand, nach dem Horizont hin, alles für entfernter, mithin für größer hält, als in der senkrechten Richtung]
- Restle, Frank (February 1970). "Moon Illusion Explained on the Basis of Relative Size". Science.
- Kant, Immanuel (1900). Critique of Pure Reason. Translated by J. M. D. Meiklejohn. New York: Dover Publications. p. 189. (B 354)
- Kaufman, Lloyd; Kaufman, James H. (January 4, 2000). "Explaining the moon illusion". 97 (1): 500–505. doi:10.1073/pnas.97.1.500. Retrieved June 22, 2016.
|Wikimedia Commons has media related to Moon illusions.|
- A vision scientist reviews and critiques moon illusion theories (and argues for oculomotor micropsia).
- Another careful review of moon illusion research.
- A physicist offers opinions about current theories
- Summer Moon Illusion – NASA
- "Finally! Why the Moon Looks Big at the Horizon and Smaller When Higher Up" by Don McCready, Professor Emeritus, Psychology Department, University of Wisconsin-Whitewater, Revised November 10, 2004, retrieved October 31, 2015
- Why does the moon look so big now?
- Why does the Moon appear bigger near the horizon? (from The Straight Dope)
- Moon illusion illustrated
- Moon illusion discussed at Bad Astronomy website
- New Thoughts on Understanding the Moon Illusion Carl J. Wenning, Planetarian, December 1985
- Father-Son Scientists Confirm Why Horizon Moon Appears Larger
- NASA Astronomy Picture of the Day: Moonrise Over Turkey (16 June 2009)