The Selenelion, and the Photograph at p. 169

The Moon list at p. 166 reads: “A partial lunar eclipse and the Sun can be seen in the sky at the same time. This is called the selenelion eclipse and is conveniently explained away with, you guessed it, REFRACTION.” The emphasis is ours, and it is worth keeping, because “partial” is exactly what Santa Fe got: the deep partial, with totality arriving after the Moon had set. It is worked on the facing page: p. 169 is a photograph captioned “taken at sunrise in the Santa Fe area, looking toward Los Alamos,” with the verdict: “The heliocentric model dictates that the ball’s shadow would be on the bottom of the Moon. Here we see the opposite.”

Everything on this page is about Earth’s shadow falling on the Moon. The same entry at p. 166 carries a second Moon complaint — that “the moon-tilt illusion explanation is not satisfactory” — and the spread at p. 168 works that one. It is a different mechanism entirely: the lit side of an ordinary Moon and which way it appears to point, the Moon’s own shadow on itself rather than ours on it. Running the two together is what makes the spread hard to answer, so they are answered separately. That one is at The Moon-Tilt Illusion, which is still in draft and has not been through the review pass this page has — so read it as work in progress rather than as an answer.

One thing at the outset, because it shapes everything below: that eclipse did have a selenelion, but neither the p. 169 frame nor the video it comes from caught it. The eclipse ran three and a half hours; the selenelion at Santa Fe was under two minutes at the very end of that, and the camera was elsewhere for all of it. What the book prints is an eclipsed Moon in a twilight sky — which is what an umbral eclipse looks like from almost everywhere, and is not the thing the word names.

Before any of the arithmetic, here is what the video actually shows.

And here is the whole descent that frame came from. Every moon in this strip is our own capture from the same segment — not a photograph of anyone else’s — and every one of them is an ordinary lunar eclipse in a twilight sky.

A selenelion is not a kind of eclipse

With that in mind, it is worth being plain about something the word hides, because the p. 166 entry treats a selenelion as an exotic event the model has to explain away, and it is nothing of the sort.

There is no special kind of eclipse behind the word. A lunar eclipse is the Moon passing through Earth’s shadow, 380,000 km away, and it runs identically for everyone who can see the Moon at all. Nothing about 10 December 2011 was unusual. What was mildly unusual was where one edge of its audience fell.

Start with who sees a lunar eclipse, because the answer is simpler than intuition expects. In a solar eclipse the Moon’s shadow falls on the Earth, in a strip barely a hundred kilometres wide, and you have to be standing in it. In a lunar eclipse the shadow falls on the Moon, and you need nothing but line of sight — and since a full Moon stands opposite the Sun, “line of sight to the Moon” means “standing in the night.” A lunar eclipse visibility map is a map of night.

Now the word itself, which is simpler than it sounds. To be in Earth’s shadow at all, the Moon has to be very nearly opposite the Sun — that is what an eclipse is. So if the Sun is coming up on your eastern horizon, the eclipsed Moon is going down on your western one, at the same moment. If “opposite” were exact, and if the two were points, and if there were no air, you would miss it by a hair: the Moon would set at the very instant the Sun rose, so you would see one or the other with no overlap at all — never both at once.

Three things give you slack, and none of them has anything to do with the eclipse. The Moon is not exactly opposite — it runs a degree or so off. Both discs have width, half a degree each. And near the horizon the air lifts every image by about another half-degree, so both are still showing after the bare geometry has parted them. Add those together and there is a thin strip of the planet, a degree or two wide, running along the day/night line, where the two just overlap. What that buys you in practice is a couple of per cent of wiggle room at the very fringe of an otherwise ordinary eclipse — a few minutes out of three and a half hours, in which you just might catch the Sun and the Moon on opposite horizons at once. Standing in that strip is a selenelion. It is not a property of the eclipse; it is a property of where you stood.

Counted properly, on that day:

The Moon’s cap is the smaller of the two because of parallax: standing on the surface rather than at the centre of the Earth costs the Moon 0.92° of altitude, more than its semidiameter and refraction together give back. The Sun, four hundred times further off, loses nothing worth counting.

Two things follow, and between them they are the whole content of the word.

Every umbral eclipse has one. The overlap in that table never goes to zero. It is narrowest at greatest eclipse, when the Moon is closest to the anti-solar point, and on 10 December 2011 even there it was 1.1°. The floor is lower for a more central eclipse than this one — a perfectly central pass, with the Moon dead on the anti-solar point, leaves the two cap radii less 180°, about three quarters of a degree at this lunar distance and two thirds at perigee. Lower, but never zero, which is the part that matters. There is nothing to arrange and nothing rare about it: the band is simply the seam where the night side ends.

And the Earth turns underneath it. At any single minute the band is a hairline. Over the three and a half hours between first and last umbral contact the planet rotates 53°, and the hairline sweeps.

Two places are marked on the map below, because the rest of this page turns on them: Santa Fe, where the frame at p. 169 was shot, and Cahokia in Illinois, where the same video’s second observer set up his camera 1,443 km east. The band’s eastern edge runs between them.

And it is worth seeing what kind of object that band is, because it is not an exotic one. Measure longitude from the Sun instead of from Greenwich — hold the Sun still and let the Earth turn underneath — and the band takes its place in a family the reader already knows.

So a selenelion is the Moon sitting a degree or so off the shadow’s dead centre, plus the half-degree of lift the air gives every image at every horizon — the same half-degree that makes every sunrise arrive a couple of minutes early. There is no “dramatic bending” anywhere in it — only that half-degree, which anyone with a horizon and a clock measures daily. The rest is not merely possible. It is required: a spinning globe with an atmosphere has to lay this band down at every umbral eclipse, and the model would be in trouble if it did not. All that is uncommon is where the band happens to fall.

Where the photograph comes from

It is not a photograph. It is a frame from a video — and the footage is not Miller’s, though the upload the book links is.

Put the book’s crop beside a frame from the upload its p. 167 QR code reaches and it is plainly the same footage: the same snow-streaked peak with the same shoulder, the same secondary summit to its right, the same pattern of snow on the left flank, the same strung-out town lights below. The book uses a tighter, brighter crop, which is also why the image is soft. The upload’s own title card credits Steve Matthews; Sources has the channel, the date and the rest of the paperwork.

What matters here is not the paperwork but where that upload sits: on Shape Debate, the book’s own channel. Its description is where the p. 169 claim is written out:

“Forgot to include the biggest debunk of all, the impossible ‘selenelion’ eclipse. Sun is rising in the east, looking at moon towards the west, the ‘shadow’ is on the top instead of the bottom! How?????”

So the credit needs running in both directions. The observation is Matthews’, and so is the conclusion he draws from it in the narration — at 19:34 he says the footage “definitely proves this is not caused by the so-called ball.” But that description is not something the book inherited. It was written on the book’s own channel, over footage collected there, and its escalation — the biggest debunk of all, impossible, How????? — is this side of the argument in its own voice. p. 169 then prints the same claim with a premise attached: that the heliocentric model requires the shadow on the bottom.

None of which takes anything away from what the observation gets right, and we would rather say that plainly than leave it implied. The shadow really was on the top. The eastern sky really was brightening. The p. 169 caption locates the scene correctly, and this page will confirm each of those in turn. Nothing here is a case of anybody seeing badly. The error is in the sentence about what the model requires — and that sentence is the book’s own.

On our side it changes one thing: credit for the observation belongs to Steve Matthews, and we would rather say so than let a frame of his work sit here unattributed.

What a lunar eclipse looks like from the ground, and from anywhere else

Before measuring anything, it is worth being clear about what the photograph is a picture of, because the honest difficulty in this claim is not arithmetic.

From the ground you cannot see that the Moon is entering a shadow. You see a dark edge creeping across a disc. The cone is invisible, the alignment is invisible, and the diagrams meant to help are drawn from a viewpoint nobody has ever occupied. That is a real complaint and it deserves better than a wave. So here are both at once, from the same numbers.

Run it once and watch the first panel. The Moon slides into the cone, and nothing in that view tells you which side goes dark — which is the challenge with a good many of the common diagrams, all of them flattening a three-dimensional arrangement onto a page. Then look across to the third. The geometry has not changed by a hair. Only the direction you are looking from and which way is up — and now the answer is in front of you, and it matches the sky panel underneath.

The one-line rule that settles which side

Earth’s shadow points directly away from the Sun. So the centre of that shadow, projected on the sky, is the point exactly opposite the Sun. If the Sun is a degree below your horizon, the centre of Earth’s shadow is a degree above it, in the opposite direction. There is no more to the calculation than that. Strictly that rule is written from Earth’s centre, and the page has just docked the Moon 0.92° for standing on the surface rather than at the centre — so from your spot the shadow’s centre is about that much lower than the rule says. It does not matter here, because the shadow’s centre sits at the Moon’s distance and is displaced by the same 0.92° as the Moon itself. The two move together, the offset between them is untouched, and the table below computes both in one consistent frame rather than applying the rule by hand.

The whole eclipse, as it stood over Santa Fe

The umbral phase began at 05:46 MST. The Sun’s upper limb cleared the horizon at 07:02:23, and the Moon’s upper limb dropped below it at 07:04:22 — one minute fifty-nine seconds with both bodies in the sky at once, on a level horizon with standard refraction. That overlap is the selenelion. The Moon was 98% swallowed when the Sun came up and all but entirely inside the umbra as it went down; totality itself began at 07:06, after the Moon had set, and then ran its course below the horizon — so northern New Mexico saw the deep partial and missed the red phase.

Each limb is refracted at its own altitude here, and positions are apparent — light-time and aberration included — because the question is where each body was seen. Refracting the disc’s centre and then adding the semidiameter, which treats the disc as rigid, puts each upper limb about 2.2′ too high near the horizon: refraction is weaker up there than at the centre. That is the same error that used to sit in the shadow-edge figure above, and correcting it shortens this window by about forty seconds. Dropping aberration would shorten it by a further two.

Altitudes are of the disc centres, and the two columns are on deliberately different conventions. The Moon’s are apparent — refraction included — because it was in the sky and the question is where it was seen; in the last row its centre is just under the horizon while its upper half is still showing. The Sun’s are geometric, because for most of the morning it was below the horizon, and a body below the horizon has no apparent altitude to quote: no ray from it reaches the eye, and the standard refraction formula is not defined down there. That is also why the Sun is still 0.85° below the horizon in the row where it rises — 34.5′ of refraction lifts the disc and its own 16′ radius does the rest, which is the budget the refraction section below works through in full. Position angles are measured in the observer’s own frame: straight up in the photograph is straight up in the table.

The umbra crosses the Moon from the top throughout. Its centre never departs from the vertical by more than 20° while the Moon is up, so at no point in the eclipse, from that place, could the shadow have been on the bottom.

The photograph at p. 169, reduced

The photograph is a lunar eclipse — the selenelion of 10 December 2011, which the book’s own list raises two lines above the moon-tilt entry. So the claim is testable in the strongest sense available: the geometry was fixed by the date, we can compute it, and then we can measure the picture and see whether the two agree.

Everything above was computed without reference to the picture: the umbra covered the Moon from the top all morning, leaving a thin bright rim along the bottom. Now the picture. We fitted circles to the two edges of that rim — twice, off two different renderings of the same photograph, so that the measurement carries its own error bar rather than a single figure with an implied precision it does not have.

Two measurements of the same photograph, by the same script, differing only in what was fed to it. The page render is what a reader looking at the printed book is looking at; the embedded image is the 799 × 470 raster the file actually contains, which the render upsamples about three-fold. Upsampling adds no information, so the gap between the two columns is not resolution — it is where each run puts the edge of a bloomed rim on a disc sixty-six pixels wide. That spread — about a fifth on the first two rows, two to four per cent on the coverage and the arc — is the honest error bar on this measurement, and it is wider than we would like. It is also nowhere near wide enough to matter: every reading in both columns is a large circle centred well outside the disc, and the thing being ruled out sits at 1.00 and 0 and 180°.

The Moon is about 213 px across in that render, upsampled from sixty-six in the file itself, and the image is soft, so the bright rim blooms outward. The circle fits themselves are tight — 0.50 px rms on the Moon’s outer edge and 0.68 px on the dark one, against a 107 px radius — but that tightness is a fit statistic, not an accuracy. Re-run on the embedded raster the two circle quantities move by about a fifth, which is the number to trust: a rim that blooms shifts where the edge is, and no amount of tight fitting to the wrong edge fixes that. The coverage and the arc span are far steadier, at two and four per cent.

Four quantities, computed before they were measured, agreeing to within a few per cent. The dark edge in the photograph is a circle two and a half times the size of the Moon, centred just under two Moon-widths away, almost exactly above it. That is Earth’s umbra, at the size and in the place the ephemeris puts it — the round shadow of the Earth falling across the Moon, which is not a shape any phase of the Moon produces.

And round is doing more work here than it looks, because a circular shadow is only automatic when the thing casting it is a ball. On 10 December 2011 the anti-solar point — the direction Earth’s shadow points — stood 67° from the celestial pole. A flat Earth turning about that pole was therefore being lit from well off to one side, and would have laid down an ellipse roughly two-fifths as tall as it is wide. The edge in this frame fits a circle to better than one per cent. That is a measurement of the Earth’s shape, taken from a photograph the book prints itself, on a date the book chose.

Nor can something else be standing in for the Earth. The alignment does not merely permit Earth’s shadow to be there — it requires it. At an umbral eclipse the line from the Sun to the Moon passes through the Earth: that morning it missed Earth’s centre by 0.39 of an Earth radius. Sunlight heading for the Moon therefore runs into the Earth, and the shadow lands whether anything else is present or not. A rival occulter would have to sit where the Earth already is and intercept that sunlight before it arrived — which is to say, stand between us and the Sun and cause a solar eclipse instead.

And the cosmology this project has endorsed does not offer a rival occulter anyway. The book itself declines to advance a positive model — but its launch video carries a geocentric introduction by another presenter, which the author endorses as representing his own thinking, and that one commits to a self-luminous Moon. Under a Moon that makes its own light, an eclipse is not a shadow at all. It is the Moon dimming. That has to be said out loud, because it is a much harder thing to defend than an occulter. The dimming would have to be circular; sized to Earth’s cross-section at the Moon’s distance and not some other size; entered from the edge that faces away from the Sun and left by the other; timed to the exact instants of syzygy; and — this is the part the survey table below supplies — landing on the top of the disc in December 2011 and the bottom in June 2012, from the same back garden in New Mexico, for no reason available to a lamp. Every one of those is a free parameter under a self-luminous Moon and a consequence under a shadow. The table is the same table that answers p. 169; it happens to answer this too. We are quoting no wording from that introduction here, because this site’s rule is to cite it by timestamp only once each quotation has been checked against the audio rather than an automatic transcript. What is described above is its position, not its phrasing.

The model does not merely accommodate this photograph. It predicted its geometry — including the part the caption calls impossible.

The same video contains a second observer location, and the model predicts that too

Later in the video a second observer’s footage is shown from the same morning, and it provides an extremely useful correlation — a second, independent test of what the globe model predicts.

He is standing on top of Monks Mound at Cahokia, just east of St Louis — 1,443 km east of Santa Fe — and he narrates the clock as he films. His segment runs from 20:03 in the video, where the presenter introduces him, to 21:56. Everything he says is checkable, and it checks:

Two of those are quantities rather than impressions — not yet touched at 6:30, a bite at 6:55 — and both land. The third does not: at 7:04 he calls the Moon two-thirds covered when the umbra had taken a quarter of it. That miss is worth keeping rather than smoothing away, because it points the same way as everything else here. Overshooting by that much is what happens when you are trying to read a disc that has become a bright smudge in a brightening sky — which is what he says he is doing, in the very next breath.

Set against that, he is a careful reporter, working in the dark with a hand-held camera and calling what he sees, and it is worth saying so before anything is said about the conclusion he draws from it.

And here is the part worth keeping. The shadow is on the top for him too — he says so, and reports the same surprise. But it is tilted the other way. At any moment when both men could see the Moon, the umbra’s centre sits to the left of Cahokia’s vertical and to the right of Santa Fe’s: same Moon, same shadow, same minute, and about eight degrees of difference in how it is tilted, purely because the two men stand in different places and their verticals point in different directions. On a flat plane that difference would be zero — not small, but exactly zero, because on a plane every vertical is parallel to every other and a distant object shows the same tilt from everywhere on it. Each man’s own footage differs by more than that — nearer thirty degrees — but the two clips are three quarters of an hour apart, so most of that gap is the eclipse advancing rather than the distance between them. Eight degrees is the part that is purely about where you stand, and it is the part that matters here.

That is the whole of the moon-tilt idea, arriving unbidden inside the exhibit meant to refute it: how a thing in the sky is tilted depends on where you are standing.

Be careful about what has and has not been measured here. The qualitative prediction is tested at two stations at once and passes at both: the shadow is on top for each man, and each says so. The eight degrees is a different kind of statement — it is what the geometry predicts, not something read off the footage. Cahokia’s camera is hand-held and pans between the presenter and the sky, and a hand-held frame cannot fix which way is up; that is why discs 5 and 6 in the strip below are drawn from the ephemeris rather than captured. A tripod at Cahokia would have let us check it. What the pairing is still worth: the two men filmed independently and had no knowledge of each other, and putting their clips side by side was the video’s own editorial choice, made to argue something else. A model that merely accommodated the first clip would have nothing to say about why the second should be rotated at all. This one says eight degrees, before you look.

Moving a hundred kilometres either way changes the tilt by under two degrees, so nothing here is sensitive to the exact spot. Monks Mound is the largest earthwork north of Mexico and about thirty metres high, which is what “standing on top of” refers to.

Neither camera, and neither observer, caught the Sun and the Moon above opposite horizons at once

Which brings back the band from the top of this page, and the edge of it that runs between these two men. It settles something the video never thinks to ask.

The window at Santa Fe opened at 07:02:23. The frame the book prints at p. 169 is fixed at 06:47 by its own eclipse phase — a quarter of an hour earlier, with the Sun still 3.6° below the horizon. At Cahokia the Sun’s upper limb cleared the horizon at 07:06:58 and the Moon’s dropped below it at 07:07:04: an overlap of under six seconds, which is to say none at all. He was standing on the seam and fell on the wrong side of it.

At Santa Fe the window was behind a mountain. The frame is a long-lens shot of the skyline toward Los Alamos, and the Moon in it is its own ruler: its angular diameter that morning is known to four decimals, so a circle fitted to the lit outer arc calibrates the picture in degrees per pixel with nothing else assumed — no focal length, no sensor size, no claim about exactly where the tripod stood. The fitted disc is 183 pixels across; the skyline directly beneath it is 323 pixels lower. That is a different image at a different scale from the p. 169 measurement above, where the Moon came out about 213 px across on the 300 dpi book render — which is why the two sections quote different pixel counts for the same Moon. That is 0.885°, and the Moon has to fall all of it plus its own radius before the disc is gone. There are about seven minutes of Moon left in the shot. Dating the frame at 06:47 from its eclipse phase, it was behind the ridge by 06:54 — and the Sun did not clear even a flat horizon until 07:02:23. He stood inside the band and could not have seen it from where he stood.

His whole descent is above. Here is the second man’s, built the same way from the same video — and it ends even further from the event than the first.

Both men describe the eastern sky getting brighter, and both are right about that. But a brightening eastern sky is dawn, and dawn is available to anyone facing east on any clear morning; it is not the Sun. The second observer says so himself, at 21:40: “with the bright morning sun coming up, there’s not enough contrast to be able to see the moon there.” By the time his sky was bright enough to argue about, his Moon had gone.

This does not weaken the claim under examination. It sharpens it. The shadow really was on top in both clips, and that is the thing worth explaining, which is what the rest of this page does. But the selenelion is not what either camera recorded: the footage offered as proof of it stops a quarter of an hour short at one station — with a mountain range in the way of the rest — and six seconds short at the other.

Both figures are for a level, sea-level horizon, and at Cahokia the real one is not level — but it leans the other way from the way that would help. Monks Mound does not stand on a bluff: it stands on the American Bottom, the Mississippi floodplain, and the bluffs — the Collinsville escarpment — are four or five kilometres to the east, in the direction he needed the Sun to come from. On published elevations rather than a survey, they put the skyline in the sunrise direction something like a quarter of a degree above level, which delays his sunrise by a minute and a half. His western horizon really is flat bottomland, so the mound’s own thirty metres depress it by 0.16° and hold the Moon up about a minute longer. Run together: sunrise 07:08:27, moonset 07:08:15 — the six seconds do not widen, they close. Anything above a fifth of a degree of bluff does that, so the conclusion does not hang on the exact figure. And in any case, by then his Moon was four tenths of a degree up, a quarter covered, and on his own account invisible.

One more thing the word does badly. The photograph people most often reach for when “selenelion” comes up — Michael Zeiler’s multiple-exposure chain of ten moons dropping toward a ridge, published here — is of this same eclipse, from this same corner of New Mexico. We have not reproduced it, because the point does not need it. The caption printed directly under it says the Sun had not yet come up: “the moon was setting in Los Alamos, N.M., the sun was just about to rise.” So none of its exposures caught the selenelion either — the same answer as the two clips examined above, on the same morning, for the same reason. The photographer and the publication reported it accurately. What does not survive being shared is the caption.

What the caption gets right, and what it does not

“The ball’s shadow” means Earth’s shadow, which is the reading the book’s usage supports and the correct one here. “Taken at sunrise in the Santa Fe area, looking toward Los Alamos” is right too: Los Alamos bears 303.5° from Santa Fe, the Moon was at azimuth 296°, and at 06:47 the Sun stood 3.6° below the eastern horizon in bright civil twilight — which is the sky in the frame, blue with the snow on the Jemez lit. Nor is the location the book’s inference: the footage carries its own on-screen caption, “View is towards Los Alamos, New Mexico — Vantage point is just north of Santa Fe”, near enough word for word. And the frame can be checked without taking anyone’s word for it, because it carries its own longitude. How deeply the Moon is eclipsed depends only on the clock and is the same everywhere; how far the Sun has climbed depends on where you stand. At 83% covered the Sun is 3.6° down at Santa Fe and 12.3° down at Los Angeles — near darkness, not this. The west coast is excluded twice over: by the time Los Angeles had the Sun up, the Moon there was totally eclipsed, so there was no bright rim left to photograph. Everything in the caption checks out.

The single thing that does not is “the heliocentric model dictates that the ball’s shadow would be on the bottom of the Moon.” It dictates nothing of the kind. It computes which side from where the Moon crosses the shadow, and for 10 December 2011 it says the top — which is what the photograph shows, to within a few degrees. The observation is accurate, carefully described, and correctly located. It is the premise about what the model requires that does not hold, and that is a claim about the model rather than about the sky.

The model has no favourite side

It is worth answering the p. 169 claim on its own terms even though its photograph does not support it, because the underlying idea — that the model commits to one side and can be caught out — is testable and false. Which side goes dark is set by where the Moon crosses the shadow, and it changes from eclipse to eclipse. Here is every morning selenelion visible from Santa Fe between 1995 and 2030, and where the shadow sat on the disc in each.

The list is swept, not assembled by hand: scripts/selenelion_survey.py walks every full Moon in the window, keeps the ones where Earth’s umbra actually touches the disc, and asks of each whether Santa Fe ever had the Sun’s upper limb and the eclipsed Moon’s above opposite horizons at the same instant. Nothing is filtered by judgement, so nothing can be quietly left out. It finds twelve events; the four not shown here are evening ones, with the Moon rising as the Sun set, which is the same seam with the roles swapped. The tilt is measured at the middle of each window — the sequence table above gives 19.0° for 10 December 2011 because it is quoting the very last instant, at moonset, by which time the shadow has rotated a further degree. One near-miss is worth naming, because it shows how fine the edge is. On 15 April 1995 the Sun’s upper limb cleared Santa Fe’s eastern horizon and the eclipsed Moon’s dropped below the western one in the same second — a computed overlap of about a tenth of a second the wrong way — which is the script’s raw output and far inside any real uncertainty, since the limb convention and the morning’s refraction are each worth thousands of times that — with a tenth of the Moon in shadow. On a standard atmosphere it is out by a hair; on a slightly kinder morning it would have been in. Which is the whole point about the band: it is a fact about where you stood and what the air was doing, not about the eclipse.

Look down the time column first. Twenty-two years of eclipses, and this spot’s entire lifetime allowance of simultaneous Sun and eclipsed Moon comes to about thirty-nine minutes — the longest a single event ever managed was nine, and one of them lasted eighteen seconds. That is the width of the band, felt as a clock rather than as a number of degrees.

Three of the eight put the shadow squarely on the bottom, which is the appearance p. 169 says the model requires. The model produces that too — on other dates, from the same spot, with the same arithmetic. It also produces the top, the sides and both diagonals. There is no preferred side to be caught contradicting; there is only a date, and an answer.

Yes, it is refraction — and this much of it

That leaves the other half of the p. 166 entry: that the selenelion is “conveniently explained away” with refraction. It is right that refraction is doing real work, and it deserves a straight answer. At Santa Fe, without refraction there would have been no simultaneous view. At the moment their true altitudes crossed, the Sun and Moon were both 0.675° below the horizontal. Neither was up. So how much bending does the explanation need?

That is a fact about that spot, not about the eclipse. Both discs are about half a degree wide, and their width alone opens a band without any refraction at all — up to 1.18° of it, over roughly seven eighths of the morning. It closes only for about three quarters of an hour either side of greatest eclipse, when the Moon sits closest to the shadow’s centre. So refraction widens the seam, roughly doubling it; it does not create it. What refraction did at Santa Fe was decide whether that particular hillside fell inside the band or just outside it.

Quantity	Value	As a share of the ordinary horizon lift
What the air actually gives a body at the horizon, standard atmosphere	34.5′ — a little over half a degree, 0.58°	100% — the everyday amount, and the yardstick for every row below
Lift the two disc centres would have needed	40.5′ each — 0.68°	117% — more than the air gives, so at this site the two centres never both cleared
Lift the two upper limbs needed — which is what an eye actually sees	25.5′ Moon, 24.3′ Sun — 0.42° and 0.41°	74% and 70% — about three-quarters of it
So the margin, on the limbs that matter	about 9′ to spare — 0.15°	26% left over

That second row is about Santa Fe, not about the eclipse, and it is worth being careful here. Centre-to-centre was perfectly possible that morning — just not there. Because the discs bring their own half-degree to the sum, a centre-to-centre band existed at every moment of the eclipse somewhere on Earth: 0.6° to 1.8° wide, narrower than the limb band above it but never closed. So the reason to work in upper limbs is not that centres are impossible. It is that a limb is what an eye sees — the Sun “rises” when its top edge clears the horizon, not when its middle does, and the same goes for the Moon still setting behind you.

The shadow is lifted too, and by nearly the same amount. The Moon is raised by refraction as it falls — and so is Earth’s shadow, because the shadow’s place in the sky is fixed by the Sun, so the shadow’s lift is the solar half of the same story. The two run together all the way down: 5′ and 5′ at ten degrees up, 12′ and 13′ at four degrees, 30′ and 32′ near the horizon. Near the horizon the shadow’s edge is lifted slightly more than the Moon — by 2.3′ — because that edge hangs below it and sits in thicker air. That difference is the entire effect of refraction on the eclipse itself: two arcminutes on a 30′ disc, or under 8% of its width, at the very end. It is why the bite looks the same whether you plot the true positions or the seen ones, and why refraction cannot move a shadow from one side of the Moon to the other. Computed by scripts/refraction_tracks.py.

Refraction turns up twice in this event, and it is worth naming the second one because it is the same physics doing a much smaller job. Earth’s shadow is not a clean geometric cone: the air around the planet bends and absorbs light at the edge, so the umbra arrives at the Moon about 2% wider than pure geometry gives — Danjon’s rule, in every eclipse prediction since the 1950s, and drawn as the outer of the two rings in the animation above. It changes how much of the disc is covered by a couple of per cent. It changes which side by nothing at all.

So the ordinary, everyday, textbook number does it comfortably, with room left over. It does not need to be stretched, and no special atmosphere has to be invoked. That is the whole of the “dramatic bending of sunlight” the spread asks about: about half a degree, the same half a degree that makes every sunrise arrive a couple of minutes early and every sunset leave a couple of minutes late, and which has been in navigational tables since long before anyone had a camera.

The observing site is also 2,130 m up, which on a level horizon would depress it a further 1.35° and widen the window considerably. We have deliberately not counted that, because northern New Mexico’s horizons are mountains rather than sea, and the terrain correction could go either way. The numbers above stand without it.

A selenelion photograph measures the refraction it disputes

This is the part we would most like a reader to take away, because it turns the objection into an experiment rather than a stand-off.

Refraction is not uniform. It is strongest right at the horizon and falls off fast with altitude, so it lifts the bottom of a low disc more than the top. That squashes the disc — vertically only, never horizontally. The amount is not adjustable; it follows from the same standard-atmosphere curve used above.

Any selenelion photograph shows a Moon within a degree or two of the horizon, so its disc should be visibly oval, and by a stated amount. Measure it and you have measured the refraction the objection says is being invented to cover a gap. Anyone can run the same check on any sunset, in an afternoon. If the setting Sun is a circle, the standard refraction curve is wrong and so are we — and a good deal of surveying and navigation goes with us.

If you do run it on the Sun, use a proper solar filter, and do not look at the Sun through any lens without one. That is first a matter of your eyes, and second a matter of the measurement: an unfiltered image of the Sun is mostly bloom, and bloom is round. Glare spreads the disc symmetrically and will hide the very flattening you are trying to measure, or invent an edge where there is none — so an unfiltered phone shot is not a null result, it is no result. A certified solar film or eclipse-viewing filter over the lens turns the Sun into a clean measurable disc. The Moon needs no filter, and a low full Moon is flattened by the same air in the same way — 16% at half a degree up, per the table above. If you want to do this safely with no equipment at all, do it on the Moon.

What would change our mind

• The original of the p. 169 photograph. Ours is measured off a render of the book page. An original file, with a timestamp, would tighten every number in the comparison table and could move the agreement either way. We would rather have it than not, and we will publish whatever it says.
• An eclipse whose shadow lands on the wrong side. The rule is public and the arithmetic is short: compute the antisolar point, compare with the Moon, take the difference. One clear counter-example retires the method.
• A selenelion needing more lift than refraction supplies. A documented case with the Sun and Moon more than about 1.7° from opposite, both seen at once over a level horizon.
• A round Moon at the horizon. If a low Moon photographs circular rather than flattened by roughly an eighth, the refraction account is in trouble, because the same curve produces both numbers.

Where this page could be wrong

• The bloom is real, and it is the largest error on the page. The book prints a soft, low-resolution frame lifted from video — the raster it embeds is 799 × 470, with the Moon about sixty-six pixels across — so the bright rim spreads outward into the dark. That is why both measured arc spans, 105.5° and 101.2°, sit below the computed 117.6°, and why the two runs disagree with each other by about a fifth on the radius and the offset. A better original exists: the footage itself, where our own capture puts the disc at 183 pixels. We have not re-fitted the rim on it, because the printed page is what the printed claim is about — but anyone wanting the residuals settled rather than bounded should start there.
• The identification rests on the inner edge, not the outer one. A circle fitted to the outer edge of the bright sliver looks convincing and proves nothing, because that edge is the Moon’s own outer edge whether the dark part is night or shadow. Everything here turns on the inner edge and the horn span instead. If either of those measurements is wrong, so is the conclusion — and they are the two we would most like checked against an original.
• Horizon refraction genuinely varies. The 34.5′ figure is a standard atmosphere. Real values at the horizon swing by tens of arcminutes with the temperature profile — which is why we are careful about refraction elsewhere on this site, and it would be inconsistent to be casual about it here. Our claim is only that the standard value suffices, not that no morning ever falls short. What that concession costs is worth naming, because it is less than it looks. A morning with anomalously low refraction would simply have given Santa Fe no simultaneous view — the band would have fallen a little further west and missed that hillside. It would not have moved the eclipse, the shadow, or which side of the Moon went dark, which are the things p. 169 is about. That is the same point the refraction section makes above: whether a particular spot lands inside the seam is a fact about the spot, and the discs’ own width opens a seam somewhere regardless.
• Terrain is unmodelled. Santa Fe looks east at the Sangre de Cristos and west across the valley toward the Jemez. Both shift the visible window, and neither is in our numbers.
• The band map is convention-dependent at its pale edge, and only there. The 27% figure counts anywhere with more than ten seconds of overlap, on upper limbs with a sea-level horizon. Tighten the criterion to whole discs, or count only places with a full minute, and the outer fringe moves; the median of five minutes and the shape of the swath do not. The claim we are making is about the band always existing and always sweeping, and that survives every convention we tried.
• The second observer location is placed from what he says, not from a fix. “On top of Monks Mound… just east of St Louis” puts him within a kilometre or so, which is plenty for the thirty-degree tilt difference — that changes by under two degrees over a hundred kilometres. It is not plenty for his six-second window, which sits exactly on the footprint’s edge and is far more sensitive to his horizon than to his coordinates. We say he did not get a selenelion; the safer statement is that he did not get one worth the name, and that his own footage shows why.

How to check this yourself

The script that produced every eclipse number on this page, and the frame table the animation is driven from, is in the repository at scripts/selenelion_2011.py. It needs skyfield and downloads JPL’s DE421 ephemeris on first run. It prints the sequence table, the refraction budget, the disc-flattening predictions, the survey of morning selenelions, and four cross-checks against published eclipse elements it did not use:

The sign of gamma is a convention — negative means the Moon passed south of the shadow’s axis, which is what our computation also finds. The small residual in umbral magnitude is the umbra-enlargement rule, where different sources use slightly different conventions.

The picture measurements are checkable too, and both routes are two commands. scripts/measure_p169_moon.py fits the two edges of the rim in whatever image you hand it, so the only difference between the columns above is what you feed it:

# the page as printed, rasterised
pdftoppm -f 196 -l 196 -r 300 -png book.pdf page
python3 scripts/measure_p169_moon.py page-196.png

# the raster the file actually embeds, at its own resolution
pdfimages -f 196 -l 196 -png book.pdf p169
python3 scripts/measure_p169_moon.py p169-000.png

Mind the page number. Book folio 169 is page 196 to pdftoppm and pdfimages — an offset of 27, constant through this chapter and checked at four landmarks — in the copy these commands were run against: the 500-page Canva export of 3 August 2026, MD5 0182065c1fc8cddb431dcaa67d64c8f1. Two cautions. The prerelease circulates in renders whose leading pages differ, so anyone working from another copy should find folio 169 by eye rather than trust 196. And our own text dump of this same file numbers its pages one lower than poppler does, which is where the landing page’s offset of 26 comes from — same copy, two counting tools, one page apart. The folio is the citation; the index is a command-line argument. The second command writes a single 799 × 470 image, which is the whole of what the book has. We are not reproducing that file here — it is the book’s, and anyone with the prerelease can pull it in a second.

Sources & further reading

• The footage at p. 169 is by Steve Matthews, YouTube channel Teeth of the Lamb (youtube.com/teethofthelamb), as credited on the title card of the upload the book’s own QR link reaches; consulted 31 August 2026. That upload is on Shape Debate, the book’s own channel, posted unlisted on 25 June 2026 under the generic title moon observations, with Matthews’ title card intact; the narration quoted above is at 19:34. Frames from that upload are reproduced here, cropped, for criticism and review: one scene frame, nine Moons captured from the Santa Fe segment, and four from the Cahokia segment. Nothing inside a crop is altered. The p. 169 comparison measurements are a separate thing and were taken from the book page, not from the video, so that the measurement answers the printed claim rather than a frame of our own choosing. They were made twice over: once off a 300 dpi render of the page, and once off the raster the file embeds, extracted at its own resolution. The upload is unlisted and could be withdrawn at any time; anyone checking this later should expect to need an archived copy.
• Levi Miller, Globe Deconstruction? (prerelease) — p. 166 (the moon-tilt and selenelion entries in the Moon-observations list), p. 168 (“Moon-tilt = illusion?”, Examples 1 and 2, and shapedebate.com/moontilt), p. 169 (the Santa Fe photograph). The visual-geometry passages quoted above are pp. 129, 141, 143 and 145.
• Eclipse elements for 10 December 2011 — EclipseWise (Saros 135, greatest eclipse 14:33 TD, gamma −0.3882, umbral magnitude 1.1061).
• Local circumstances for northern New Mexico — timeanddate.com.
• Positions computed from JPL’s DE421 ephemeris via Skyfield. Refraction from Bennett’s 1982 formula, the standard-atmosphere approximation used in almanac work.
• Cross-references on this site: Self-Test Protocol (Test 3 sets up the lamp-and-ball version of the tilt), Chicago & Pontchartrain (where refraction is the hard case rather than the easy one), Where’s the Moon’s Silhouette? and Full-Moon Lighting (the other Claim #3 strands), Is the Moon a Ball? (the shape this argument assumes), and Mislabels, Not Arguments — the p. 167 QR codes ran one position out of step when we first resolved them, so the code headed SUN reached the lunar-eclipse upload this page works from. That has since been corrected, and the codes now resolve to their printed labels. Nothing here turned on it either way: the upload is identified above by its contents, its title card and its description, not by which code points at it.