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.

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).

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?