Moon illusion

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.

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, metres). 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.

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