Apparent dimensions of the moon

How big does a full moon appear to you in the sky? From different people it is necessary to hear very different answers to this question. The most unexpected answer can be heard the following: I don't know. I'm not from here. Therefore, the question of the apparent dimensions of the moon is very interesting.

Therefore, the question of the apparent dimensions of the moon is very interesting

Although we are all here in the sublunar world, however, what most people report about the apparent size of the Moon is not much better than this naive answer. The moon is "the size of a plate", "the size of an apple", "the size of a human face", etc. - all these are extremely vague, indefinite estimates, indicating only that the respondents are not aware of the essence of the issue.

The correct answer to such a seemingly ordinary question can only be given by someone who clearly understands what, in fact, should be understood by the "apparent" or "apparent" magnitude of an object. Few people suspect that we are talking here about the magnitude of a certain angle, namely the angle that is formed by two straight lines drawn to our eye from the extreme points of the object under consideration; this angle is called the "angle of view", or "the angular magnitude of the object". And when the apparent dimensions of the Moon in the sky are estimated by comparing it with the size of a plate, an apple, etc., then such answers are either completely meaningless, or they must mean that the Moon is visible in the sky from the same angle of view as a plate or an apple. But such an indication in itself is not enough: after all, we see a plate or an apple from very different angles, depending on their distance: near - at large angles, far - at smaller ones. To introduce certainty, it is also necessary to indicate from what distance this plate or apple is considered.

This distance turns out to be much greater than is usually thought. Holding an apple in your outstretched hand, you obscure not only the moon, but also a vast part of the sky. Hang an apple on a thread and move away from it gradually farther and farther until it covers just the full moon disk: in this position, the apple and the moon will have the same apparent size for you. By measuring the distance from your eye to the apple, you will see that it is approximately 10 meters. That's how far you need to push the apple away from you so that it really seems the same size as the moon in the sky! And the plate would have to be removed by 30 meters, that is, by fifty steps.

What has been said seems incredible to anyone who hears about it for the first time - meanwhile, this is indisputable and follows from the fact that the apparent dimensions of the Moon are seen by us from an angle of view of only half a degree. We almost never have to evaluate angles in everyday life, and therefore most people have a very vague idea of the magnitude of an angle of 10, 20, 50, etc. a small number of degrees, not to mention surveyors, draftsmen and others professionals who are used to measuring angles in practice. Only large angles we estimate more or less plausibly, especially if we guess to compare them with the angles between the hands of the clock familiar to us; everyone, of course, knows the angles of 900, 600, 300, 1200, 1600, which we are so accustomed to seeing on the dial (at 3 o'clock, at 2 o'clock, at 1 o'clock, at 4 o'clock., at 5 o'clock), that even without distinguishing the numbers, we guess the time by their value. But we usually see small and distant objects at a much smaller angle, and therefore we are completely unable to even approximately estimate the angles of vision.