Leonids and the lingering Moon

Here is a diagram I made for Astronomical Calendar 2016 but did not find space for, because the Leonids of tomorrow night (Nov. 17/18) may not be among this year’s best meteor showers.

Leonid meteor shower diagram

Earth, seen from the north, travels along the direction of the arrow that skewers it, and rotates in the direction of the smaller arrow pasted onto it.  It passes through the Leonid meteor stream, which is vastly wider; the dots represent only those particles of comet dust that arrive from overhead.  The time is midnight in eastern North America, which is coming into view of these almost head-on super-swift  meteors.

Maybe, in one of the best hours, 15 or so “shooting stars” that appear to radiate from Leo will cross various parts of the sky.  But even if your sky is cloudless, the fainter ones will suffer competition from the light of the Moon, which was Full on November 14.  The Moon now rises around 8 PM and will be up throughout the after-midnight hours, which are the best hours for these morning-side meteors.

I hope you had a clear sky to see Monday’s so-called Supermoon.

Because it was nearer to Earth than in several decades, it appeared larger.  And, if you saw it when it was rising, or within an hour or two after, it will have seemed larger still, because of the amazing Moon Illusion.   This morning before dawn I saw it in the west, nearly two days past its perigee and two hours to the left of the anti-Sun position, and looking noticeably less swollen.

A natural reaction to the sight of the near-horizon Moon is to deny that its increased size is an illusion.  I have had people answer back to me that “No, no, I don’t believe you!  I believe my eyes!  It’s obviously, definitely huge!”  We’ve had such reactions this time.  “Despite all the debate, I still believe the moon is actually larger over a horizon than high above, it’s seen through more atmosphere so I figure some refraction makes it look larger. Same as stars looking further apart when they’re closer to the horizon.”

First, we have to separate the Nearest Moon from the Moon Illusion.  The illusion applies not just to the Moon when it is near perigee but to any Moon seen at or near the horizon, most strongly to the Full Moon but, perhaps in lesser degree, to other fairly broadly-sunlit states of the Moon, such as First or Third Quarter.

Then, about the Illusion, we have to separate two aspects: the geometrical reality, and the eye-brain impression, which happens to be an illusion.

About the geometry, there is no debate.  The Moon is farther away from you when near the horizon than when nearer to being overhead; therefore appears slightly smaller – subtends not a larger but a smaller angle.

This is true for any given moment in the Moon’s orbit.  Let’s take that moment of perigee, when the Moon’s center was 55.9 Earth-radii, or 356,509 kilometers, from the center of the Earth.  So if it was for you high in the sky – let’s say, for simplicity, vertically overhead – its distance for you was that minus the 6378-kilometer radius of the Earth: 350,131 kilometers.

If, however, it was for you at that moment down on the horizon, then to that distance was added the “distance to the horizon.”

There isn’t really such a thing as the distance to the horizon.  And “the distance to the position of someone for whom the Moon was overhead” wouldn’t be quite right.  Here’s a diagram (not to scale).

Moon Illusion diagram

E is the center of the Earth, M is the overhead Moon, N is the horizon Moon, Y is you, O is the other observer.

YM, your distance to the overhead Moon, is equal to ON, the other observer’s.  YN is larger.

(To find how much larger, we could do some trigonometry with the isosceles triangle NOA.)

QED, quod erat demonstrandum.

The debate is about why, to the contrary, we perceive the horizon Moon as larger, which we so persuadly do.  Whole books have been written about it, and the lines of thought that arise from it.  Water in the eye?  Comparison with distant terrestrial objects?  Subconsciously imagining the celestial sphere as a jelly which has slightly collapsed, so that we think of the near-horizon part as farther away?  Refraction through a greater length of atmosphere?

This last is another geometrical fact and is not the answer, indeed reduces the Moon’s angular size and thus adds to the mystery of its perceived greater size.  Yes, refraction, besides removing blue light, bends light.  But what that does is to raise lower points more than higher points.  So the effect on the Moon is that its lower edge is raised more than its upper: it stays the same width horizontally, but becomes narrower vertically.  It isn’t swollen by refraction, but squashed.

The effect on the constellations is the same.  Down near the horizon, the stars appear slightly raised, stay the same distance apart horizontally, but appear slightly closer together vertically.  The near-horizon constellations are slightly flattened,  But to our minds the Moon Illusion makes them seem enlarged, and that’s why projections that have to show them enlarged are forgivable.

Among optical illusions, the Moon Illusion is perhaps the oldest; and it’s perhaps the strongest.  I don’t know whether this aspect of it has been studied: since it is psychological, are there people for whom it is less strong, or non-existent?

Why did it evolve?  Some survival-advantage to noticing moonlight seconds earlier?


5 thoughts on “Leonids and the lingering Moon”

  1. I woke around 3:AM and looked out my north-east-facing window (Moon then rather West of South) and can say that I immediately noticed the enhanced illumination of the environment. Stepping out the door I could see more color than usual – I believe that I can say, to the degree that I believe I would have noticed it without special knowledge of the perigee/FM event. I was standing in the shadow of the house. Looking more directly at the Moon; well, it was less certainly more bright then. It was the immediate environ that really hit me. (I remember the 1999 great solar eclipse also by the very special lighting of my surroundings immediately approaching and during totality; unforgettable.)
    I cannot say that I perceived the Moon to be any larger to my eye – even though I was looking for it to be. This did not surprise me. There is an interesting limit to comparison-memory in judging sameness/difference in various sensations. Usually the limit is only within several seconds between observations! (is this the same shade of color? which tone is louder? which ball is heavier? etc.)
    I do recall a Frenchman(?) producing an animated .gif of serial Full Moons. Both librations and proximity make one feel almost drunk watching it!
    Also, it is quite often the case that I fail to see the “Moon Illusion” when I’m looking for it. It only comes unexpectedly to me. In any case, I think of the illusion in the opposite way to what is customary. I say that the large Moon is nearer the true perception, and that the small one is more the illusory one.

    1. One of the cool little illusory tests of lunar apparant size is to hold your “pinky” finger vertically in front of you at arm’s length as a measure of the lunar diameter. Your pinky subtends an angle of arc of about one degree; the moon subtends an angle of about half that, or 0.5 degrees of arc, so that the moon is about half the width of your finger. No matter how big it looks, it’s the same 0.5 degrees on the horizon as it is at the highest point above the horizon.

  2. What I want to know is something about the “illusion”, if indeed it is entirely an illusion, of the celestial sphere. The sky definitely looks to me like a dome with stars, planets, moon, sun, comets pasted on it. Is it that our brains as hunter-gatherers had no need to evolve an interpretation of “infinite” distance, only of near or far finite distances (up to, say, distant mountains), so the former is interpreted as the latter; or is there “something” out there 50, 100, whatever miles up that we really are seeing?

  3. No matter what your explanations be, some almost too technical for me to follow, it’s still a wondrous sight to see the moon rise or set near a horizon. As for the Leonids,,, well, even the brightest leave trails worth watchin. The storm in 2001 left one trail lingering for over 10 minutes as the upper atmosphere whisked it into what looked like a cloud. No matter how gibbous the moon will be, I’ll still be looking

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