How Big is the Moon and How Far is the Sky?

Abstract

It is a matter of common observation that the Sun, the Moon and constellations appear much bigger when near the horizon than when they are high up in the sky1 . The Sun and the Moon when high up appear (to most people) a little less than a foot in diameter, and near the horizon they look from 2 to 3 times bigger – the effect is greater in twilight and when the sky is clouded. It is needless to add that the entire phenomenon is psychological for there is no physical reason why we should associate a linear size of one foot with an angle of about half a degree – the angle subtended by the Sun’s diameter is 31' 59" and the mean angle2 for the Moon’s diameter is 31' 5', and why the size should appear to vary with altitude though the angle subtended at the eye and hence the size of the retinal image remains constant. The apparent variation of size with altitude exists also in the after-image of the Sun (and also the Moon) which is obtained by viewing the Sun for an instant and then blanking. The after-image of the Sun at the horizon as background appears to be of the same size as the Sun, but is reduced to about half its size when projected on the sky near the zenith. If instead of projecting on the sky the after-image of the Sun when at horizon, we project it on a wall, then it appears smaller than the Sun if the distance of the wall is less than about 200 feet, but on a wall at about 200 feet or beyond the size appears to be the same as that of the Sun. This shows that the distance of the horizon-sky appears to be about 200 feet, and of the sky at zenith about half of this3 . There seems to be a possible connection between the apparent variation of the size of heavenly bodies with the altitude and the apparent flattening of the vault of heaven.