October 18, 2002

Could the illusion of the moon appearing larger when near the horizon be explained by how we see clouds? ("Lunar puzzle that has clues but no answers", Books, THES , October 4).

Suppose we have a large cumulus cloud overhead at 10,000ft. There is a rule of thumb that gives the distance to the horizon for an observer on a high vantage point overlooking flat ground: take the observer's altitude in feet above their surroundings, find the square root and add a third. The answer is the distance to the horizon in miles.

This same rule can be used in reverse to calculate how far away a high point can be seen from low ground. Our cumulus cloud could in theory be seen 133 miles away; in practice it would be too small to be seen and hidden by other clouds. But it could probably be seen near the horizon at 100 miles distant. Compared with overhead it would appear 50 times smaller and be moving 50 times as slowly.

We cannot judge by the naked eye the absolute size of clouds but we often see a procession of similar-sized clouds. Their direction of motion and appearance is important to commuters deciding if they need an umbrella.

We are used to the idea that objects near the horizon appear smaller but are really as big as those overhead. But the moon, does not shrink appreciably in diameter near the horizon, so our minds read it as bigger. Perhaps a psychologist could test this by projecting different-sized clouds at different elevations and asking people to judge their apparent size.

Hillary Shaw
School of Geography
University of Leeds