Fun With Science  /  Globe Deconstruction  /  Q5 + Q6 · pages 48–49  /  Draft

Jupiter's Shadows Point at One Sun

Globe Deconstruction Review — Q6: whether the moon shadows on Jupiter line up the way a single distant Sun requires.

Q6's appearance: real and largeQ6's premise: fails to the minuteNASA's own HST caption: no cause givenLive signed prediction: November 2026
Where this lands

Q5, on why the whole sky sweeps at one rate, is answered on its own page.

Q6's appearance is real and large — at quadrature Callisto's shadow lands five Jupiter radii from Callisto — but the premise fails to the minute: the offsets are one angle applied to four orbits, they scale linearly with orbital radius, and they reverse sign across opposition. No reconstruction of the claim we were able to build survives contact with a plate scale and a clock — though we should say plainly what we have and have not seen: the book’s own worked figures at pp. 160–161 are reproduced and measured below, and p. 49 carries the question text without a figure. What no source gives us is a dated frame.

The sixty-second version. And a moon’s shadow falls along the Sun line while you look along the Earth line; those differ by one angle, so the shadow lands to one side of its moon by that angle times the moon’s orbital radius — small moons close in, large offsets far out, and nothing at all at opposition. That is Q6. Everything below is that paragraph with the numbers put in.

Q6: what would have failed if the geometry were wrong

A note on method, because this question is unlike the others on this site. The book is not short of material here. Q6 is posed at p. 49, and pp. 160–161 work two instances with labelled figures — a Jupiter frame with a black dot marked on the disc, and a second, explicitly captioned Ganymede and Ganymede’s shadow — each carrying a numbered QR code linking to the video it came from. What is missing is not diagrams or sources. It is dates. No frame is given with a time on it, so none can be set against an ephemeris and checked for that night.

What the figures do give us is a consistent configuration, repeated: a moon on one side, its shadow displaced across the disc, presented as an offset too large to be a shadow at all. That is a class of appearance rather than a timestamped event, and a class is something geometry can answer. So the work below does two things. It measures the offset the book itself prints, because a labelled figure with a planet of known size in it is a measurement whether or not it carries a clock. And it looks for cases where somebody staked something of their own on Jovian shadow geometry, and asks whether it came out right.

If a dated frame is produced we will retrieve it and publish what it shows — that remains the single most useful thing that could be added here.

Before any geometry, we want to put on the table three bodies of work that used Jovian shadow timings for purposes unconnected to cosmology, and which would have produced visibly wrong results had the shadows not come from a single distant source.

Nantes, 15 December 1679. Picard and La Hire timed Io's emergence from Jupiter's shadow at 4h 31m 25s and compared it against the simultaneous Paris timing. The difference was 15 minutes 30 seconds. That timing is the primary datum, and the conversion is ours: 930 seconds × 15 degrees per hour = 3.875 degrees = 3 degrees 52.5 arcminutes of longitude. The modern separation between Paris Observatory (2° 20' 14" E) and Nantes (1° 33' 13" W) is 3° 53' 27". The 1679 result agrees to 0.9 arcminutes — about 1.2 km on the ground.

The consequence was not astronomical. The campaign moved Brest and Nantes some 80 km east on the map of France, and Louis XIV is said to have complained that his astronomers had cost him more territory than his enemies. This was cartography and taxation. Had Jupiter's shadow geometry been wrong, the wrongness would have gone straight into the coastline of France, in a survey whose funder was actively unhappy about the answer.

An honesty flag on that source. The Patrimonia Nantes account states both the 15m 30s time difference and a longitude of 3° 32' 30", and those two cannot both be right — only the timing matches the modern separation. We could not establish which figure the original manuscript gives. We have quoted the timing, presented the conversion as our own arithmetic, and we are not quietly using whichever figure suits us. Separately: we could not establish any credible figure for the total land area the survey removed from the French map, and so we report only the 80 km eastward shift.
Mallama, Collins, Nelson, Park and Krobusek, Icarus, 2000. CCD photometry of nearly 200 Galilean eclipses between 1990 and 2000, compared against the E5 ephemeris. Root-mean-square differences: Io 3.6 seconds, which is 62 km along-track; Europa 19.5 s (267 km); Ganymede 13.0 s (142 km); Callisto 17.8 s (146 km). Jupiter's shadow is where a single distant Sun puts it, to a few seconds of time, at a range of six hundred million kilometres. The PHEMU15 campaign (Saquet et al., MNRAS 474, 4730, 2018). Seventy-five observing sites, 609 usable light curves out of 643 received, 236 distinct mutual events — one Galilean moon's shadow falling on another Galilean moon — reduced to a standard deviation of 24 mas (75 km at Jupiter) and an rms observed-minus-computed residual of 50 mas (150 km) against the NOE-5-2010-GAL ephemeris. That campaign runs to sharpen satellite ephemerides for the JUICE and Europa Clipper missions. If Jovian shadows did not come from one distant source, this is the dataset in which it would have shown up first, and it is run by people who would have been delighted to find a discrepancy.

We note honestly that these anchors are photometric and instrumental, not visual. The BAA's own Jupiter Section says that visual timings of satellite phenomena are not likely to have scientific significance. We are not claiming otherwise, and we are naming which observations carry the weight.

Q6: the offset is one angle, applied to four orbits

The geometry is short enough to state completely.

You see a moon along the Earth line. The Sun casts its shadow along the Sun line. Those two lines differ by one angle: α, the Sun-Jupiter-Earth phase angle. Everything else follows.

For Jupiter, α is bounded. Its maximum is arcsin(1 / 5.204) = 11.1 degrees, and JPL Horizons gives 2026's actual extremes as 10.994 degrees on 6 April and 10.704 degrees on 17 November, falling to 0.049–0.064 degrees around the 10 January opposition.

Because the Sun is effectively at infinity for a system 1.9 million km across, the sky-plane displacement is simply displacement = (moon's orbital radius) × tan α — linear in the moon's height above Jupiter, and in the same direction for every moon at the same instant.

At the April 2026 quadrature, α = 10.994 degrees:

MoonSimple law (km)Full Horizons computation (km)DifferenceJupiter radiiOn the sky at 5.159 au
Io81,94481,652−0.36%1.1521.9″
Europa130,376129,636−0.57%1.8234.8″
Ganymede207,948207,799−0.07%2.9155.6″
Callisto365,755no transit in windowunchecked5.1297.8″

Jupiter's own equatorial disk that week is 38.21 arcseconds wide. Callisto's shadow lands nearly a hundred arcseconds from Callisto. Anyone who looked at that and said the shadows do not line up was describing what they saw accurately.

The same angle expressed in time is the observable an amateur actually records. Between shadow contact and moon contact, the moon must travel through the angle α in its own orbit, so Δt = (α / 360) × P, where P is the moon's sidereal period. One angle, four periods, four wildly different times: at α = 10.994 degrees the law gives Io 77.8 minutes, Europa 156.2, Ganymede 314.6, Callisto 733.9. Our own integration of JPL Horizons state vectors over 5–7 April 2026 gives Io +77.2, Europa +155.5 and Ganymede +311.1 minutes — agreement of about one percent.

A single number — the Sun-Jupiter-Earth angle — drives offsets running from 77 minutes to over twelve hours, purely through each moon's own period. There is no free parameter anywhere in it.

A two-source or near-source hypothesis would need one contrived arrangement per moon to reproduce a set of times that one angle reproduces for free.

Q6: the same angle, on the book’s own two figures

The worked instance is at pp. 160–161, and it is two figures rather than one. Both are frames lifted from other people’s videos, both are captioned “image stacked and edited”, and each carries a numbered QR code linking to its source.

A stacked amateur image of Jupiter, banded and slightly blurred, with a small dark round spot on the disc near the right-hand limb marked by a yellow arrow, and a tiny bright point just off the limb to the right marked by a white arrow.
Figure 51, folio 160. A yellow arrow marks the dark spot on the disc; a white arrow marks the moon just off the limb. The book’s caption reads “Once you use the laws of optics to conclude this black dot can’t be a moon shadow, heliocentrism quickly falls apart.” Reproduced at low resolution from Globe Deconstruction? for criticism and review; the underlying frame is from the Astraveo video the page’s QR code links to.
A wider frame on black. Jupiter as a small pale banded disc on the right with a dark round spot on it, and a tiny dot well off to the left. Yellow labels read Ganymede, moon of Jupiter, pointing at the distant dot, and Ganymede's shadow, pointing at the spot on the disc.
Figure 52, folio 161. The same claim with the parts named — and naming them is what makes it measurable. Reproduced at low resolution for criticism and review; the underlying frame is from the Tampa Train Guy video the page’s QR code links to.

The argument the book builds on them is stated at p. 160: “If Jupiter has no eclipse, this means we know which direction the sunlight is coming from. The black dot is not aligned with the sunlight. Therefore, it cannot be a shadow.” And at p. 161: “For the moon to achieve this kind of shadow, we would need to achieve a vantage point to see at least half the planet in darkness.”

Read plainly, that is a real argument and it deserves the compliment of being answered rather than dismissed. Jupiter always looks fully lit; a fully lit planet means the Sun is behind us; and if the Sun is behind us a moon’s shadow should fall directly behind the moon, where we would see the two on top of each other. Every step follows except the last, and the reason it fails is a lever arm.

No visible terminator, and a shadow three radii out

Jupiter’s phase angle — the Sun–Jupiter–Earth angle — never exceeds about 12°, because Earth’s whole orbit subtends no more than that from Jupiter’s distance. Arcsin(1/5.204) gives 11.08° at mean distances; the all-time bound is nearer 11.9° when a perihelic Jupiter meets an aphelic Earth, and in aphelion years the maximum falls to about 10.4°. The 2026 values used below — 10.994° in April, 10.704° in November — are the ones doing the work. The book is therefore right that we never see half the planet dark. It is right by a wide margin: even at the extreme the unlit fraction of the disc is about one per cent — 0.93 per cent at 11.08°, 1.07 at 11.9, a sliver thinner than the seeing in any amateur stack. There is no visible terminator on Jupiter, ever, and any argument that measures a shadow against one is measuring limb darkening and processing falloff.

But “no visible terminator” does not mean the phase angle is zero. It means it is small. And the same small angle does something completely different at the other end of the system, because the moons are not on the planet’s surface — they are five to twenty-six planetary radii away from it.

One angle, two lever arms Two panels. Left, a plan view from above: sunlight travels left to right, Ganymede sits on the Sun-Jupiter line about fifteen Jupiter radii out, and its shadow falls on Jupiter's sunward limb, so moon and shadow lie exactly in line along the direction the light travels. Earth views from the lower left, offset from that direction by the phase angle alpha, and projected onto the sky the moon and its shadow are pulled apart by roughly the orbital radius times the tangent of alpha. Right, the same situation as Earth sees it, drawn to scale: Ganymede lies about 2.9 Jupiter radii from its own shadow on the disc. Below, the same angle acting across the planet's own radius leaves 0.93 percent of the disc unlit, a sliver too thin to see, which is why Jupiter always looks fully illuminated. From above sunlight Jupiter Ganymede 15 RJ out to Earth α the sky as Earth sees it — moon and shadow pulled apart by a × sin α α drawn at 30° for legibility; its true maximum from Earth is about 11° at mean distances. Planet and orbit are not to the same scale in this panel. What Earth sees, to scale 2.9 RJ Ganymede its shadow, on the disc unlit sliver the same α across 1 RJ: 0.93% unlit, which is why no phase is ever visible

The section above has already done the rest: multiply that angle by each moon’s orbital radius and the whole family follows, from Io at 1.15 RJ to Callisto at 5.12. The offset is not evidence against the shadow — it is the shadow’s signature, and its size is fixed in advance by which moon it is and where Jupiter sits in its apparition.

Figure 52, measured off the book’s own page

Figure 52 is labelled, so it can be measured, and Jupiter supplies its own scale bar. From a 400 dpi render of folio 161: the disc is 557 by 516 pixels, an axis ratio of 0.926 against Jupiter’s true 0.935, so the frame is not appreciably distorted. Ganymede and the shadow are separated by 802 pixels, almost exactly horizontally, against an equatorial radius of 278.5 pixels.

That is 2.88 RJ, or 2.9 ± 0.1 allowing for centroid and radius error. The ceiling for Ganymede is about 2.9 RJ: the full Horizons computation in the section above gives 2.91 at the April 2026 quadrature, and the simple a tan α law gives 2.93 at the mean-distance bound. Our measured 2.9 ± 0.1 sits at that ceiling and not past it. The figure the book prints to show the offset is impossible is a measurement of the largest offset the model allows.

The ceiling is the part that could have failed. Nothing in a local arrangement caps Io at 1.13 and Callisto at 5.06 and orders the four by orbital radius, and nothing in a local arrangement makes the whole set shrink to nearly zero every thirteen months.

What the two figures show between them

The book prints figure 51 and figure 52 together as a pair of impossibilities. They look nothing alike — in 51 the moon sits just off the limb beside its shadow, in 52 it is nearly three planetary radii away. That difference is the whole argument, and it is set by the calendar.

Figure 51Figure 52
SourceAstraveo, We CHALLENGE Flat Earthers [CASH PRIZE]Tampa Train Guy, Time-lapse of the shadow of Jupiter’s largest moon…
Uploaded18 January 202631 May 2022
Jupiter’s apparitionopposition falls in early January 2026 — days awayopposition 26 September 2022 — near quadrature
Phase anglea degree or twoclose to the maximum
Predicted separationa fraction of one radius2.8–2.9 RJ for Ganymede
What the figure showsmoon beside its shadow, well under one radiusmeasured 2.88 RJ

Two frames, taken nearly four years apart by strangers to each other, at opposite points of Jupiter’s apparition, showing separations that differ by roughly a factor of six — in the direction and by the amount their dates require. Printed side by side as twin anomalies, they are a two-point confirmation of the quantity they are offered to refute.

An honesty note on the dates. Upload dates bound captures from above but do not fix them. Astraveo’s frames could be older footage; Tampa Train Guy’s could be the November 2021 quadrature rather than late May 2022, which fits equally well and gives the same answer. The moon in Astraveo’s clip is never named — his “closest moon” remark is about a different sequence — so figure 51 gets no number here, only a comparison. And figure 52 is captioned stacked and edited, so its measurement assumes compositing did not move anything, which the near-exact horizontal alignment supports but does not prove.

The same reasoning on Venus, where it works

There is a useful control inside the Astraveo video itself. Speaking about Venus at 20:18, the presenter says the sunlight “is coming from the left, which gives it a shadow, just like the phases of the moon.” That inference is sound for Venus, an inner planet whose phase angle runs almost to 180°, which is why Venus shows crescents through binoculars. Carried across to Jupiter, where the maximum is about 11°, the identical sentence fails. The reasoning is not wrong in general; it is wrong for one planet, for a reason that is a number.

Where the two figures came from

Both sources are worth naming plainly, and neither point below is a refutation of anything — the geometry above does that work on its own.

Figure 51 comes from an Astraveo video whose whole subject is that these observations can be reproduced from a back garden with a small telescope and a planetary camera. Narrating the very sequence the figure is cropped from, the presenter says: “the movement of a solar eclipse on Jupiter cast by one of its moons. This is exactly what happens on Earth when there is a solar eclipse, because fundamentally, these systems are the same.” The eclipse framing on p. 160 is the source’s own, and so is the answer to it. Earlier in the same video the presenter points viewers at planetarium software so they can “step forward in time and see exactly when any eclipse will happen” — and a configuration that free software predicts in advance is not an arbitrary one.

Figure 52 comes from a 36-second silent clip by an amateur imager, no narration and no argument, whose description states the method — a Meade ETX-125, stacked frames, 25 minutes compressed to four seconds — and labels the parts. It is an observation, offered without a thesis, which is exactly why it is the one that can be measured.

Both videos are, in their own terms, arguing for the standard picture rather than against it. That is context about how the exhibit was assembled and nothing more. Where the two videos do bear on the argument is that between them they contain the answer: the same phenomenon photographed at two phase angles, with the separation changing by the predicted factor.

Q6: “can it be proven?” — watch a moon go out in empty sky

Q6’s second sentence asks the sharper question: “are we assuming them to be shadows or can it be proven?” Everything above answers it indirectly — by the size law, the sign flip, the timing law. There is a direct answer too, and it needs no photograph of a disc at all.

Run the same geometry backwards. If Jupiter casts a shadow, that shadow is a cone extending away from the Sun, and a moon entering it should disappear while it is still well clear of the planet’s limb, out in apparently empty sky. It should vanish on the side the phase angle predicts, at a distance from the limb that the same α sets, and reappear on the other side later. Before opposition it goes out on one side; after opposition, the other. A moon that merely passed behind the planet would instead vanish at the limb, every time, with no sign change.

That is watchable in a backyard telescope on dozens of nights a year, it takes minutes rather than a season, and it disposes of the “how do you know the dot is a shadow” question without appealing to anyone’s authority: you are watching the shadow swallow something, at the place and on the side the model says it should.

It is also the oldest quantitative result in this whole subject. In 1676 Ole Rømer, timing exactly these disappearances and reappearances at the Paris Observatory, found the intervals ran early when Earth was near Jupiter and late when it was far, and read the difference as the time light takes to cross Earth’s orbit. That inference required the eclipses to be clockwork and the geometry to be real; a light-travel time fell out of it as a bonus. The Mallama photometry cited above is the same measurement with a CCD, three centuries later, agreeing with the ephemeris to a few seconds of time. We have not pulled Rømer’s 1676 note or the 1677 Philosophical Transactions version ourselves, and the account here is from the standard secondary literature; the primaries are accessible and should be cited directly when someone does.

One thing worth stating plainly, because it confuses readers who go looking: a moon transit and a shadow transit are separate events, and whether both are on the disc at once depends on α. Near opposition they nearly coincide. Near quadrature the shadow can be crossing the face while its moon is still off to one side, which is exactly what figure 52 shows — and, at the far end of a transit, the moon can be on the disc with its shadow already past it.

Q6: the test you can run on one photograph

We want to promote this out of the footnotes, because it is the cheapest decisive measurement on this page and it requires nothing from us.

On any night with two or more Galilean moons in simultaneous transit and their shadows on the disk, take one image. Calibrate the plate scale from Jupiter's equatorial width. Then, on that single frame, draw the vector from each moon to its own shadow and measure two things.

One: are the vectors parallel. A single source at effectively infinite distance projects every moon's shadow in the same direction, so the moon-to-shadow vectors must be parallel to within a few degrees. A nearby source fans them out radially from the sub-source point, and the fanning is not subtle when the moons are separated by millions of kilometres. Two: do the lengths scale linearly with orbital radius. The orbital radii are Io 421,800 km, Europa 671,100, Ganymede 1,070,400, Callisto 1,882,700. Divide through by Io's:

> Io : Europa : Ganymede : Callisto = 1 : 1.591 : 2.538 : 4.464

Those ratios are very nearly fixed: α cancels out of them, so they do not depend on the date, on the distance to Jupiter, or on anything we computed. They are exact only when each moon sits at maximum line-of-sight elongation. A moon transiting near the limb is foreshortened — about 1.4% at worst for Io, negligible for Callisto — and orbital eccentricity adds up to about a further one per cent. As a consistency check, our April 2026 offsets in Jupiter radii were 1.15, 1.82, 2.91 and 5.12, whose ratios are 1 : 1.58 : 2.53 : 4.45. The same numbers, arrived at from the other end.

A nearby light source breaks the linear scaling, because for a source at finite distance the displacement grows faster than linearly with the moon's height and depends on the moon's position relative to the source, not just its orbital radius. A second source produces two shadows, or one shadow displaced from the geometric prediction by an amount that no single α reproduces.

This test needs a planetary camera, a plate scale, and a ruler. No ephemeris. No trust in JPL, in us, or in anyone's tables. The prediction is a set of four fixed ratios, and the measurement either lands on them or it does not. If a calibrated double-shadow image shows the two moon-to-shadow vectors non-parallel by more than a few degrees, or their offset ratio departing from the orbital-radius ratio by more than about five per cent, the single-distant-source model is in serious trouble and we will say so on this page. Note the test is pairwise by necessity: at the phase angles that make offsets large, Ganymede and Callisto have their shadows off the disk entirely while the moons transit, and a Callisto transit season comes round only about every six years. Io against Europa at moderate phase, or Io against Ganymede at low phase, is the version anyone can actually shoot; the four-way ratio is the prediction those pairs sample.

We would rather Miller ran this than trusted our arithmetic. It is his kind of measurement — direct, visual, and unmediated by an ephemeris.

Q6: the shadows are also the right size

This is the appearance that we think most plausibly generated the claim, and it deserves its own arithmetic.

From Jupiter, at 5.2043 au from the Sun, the Sun is not a point. It is a disk 6.14 arcminutes across — our own computation, 2 × arctan(695,700 / (5.2043 × 1.495978707×10⁸)), returning 0.1024 degrees. A moon's umbra therefore narrows along its path to the cloud tops by (path length) × tan(3.07 arcminutes), and its penumbra widens by the same amount. Path length is the moon's orbital radius minus Jupiter's equatorial radius, so the outer moons lose far more.

MoonUmbra at cloud topsMoon's diameterUmbra as %Penumbra
Io3,017 km3,643 km83%4,269 km
Europa2,050 km3,122 km66%4,193 km
Ganymede3,477 km5,262 km66%7,048 km
Callisto1,584 km4,821 km33%8,058 km
Callisto's shadow genuinely does not match Callisto. Its dark core is a third of its width, wrapped in a penumbra almost twice as wide as the moon. Io's is a sharp black dot at 83 percent. That is the observation, and it is correct. It is not two suns. It is one sun of finite angular size, and the size it implies is 6.14 arcminutes at 5.2 au — which is the Sun.

The independent corroboration comes from people who were not arguing about anything. NASA's Hubble release for the 24 January 2015 triple transit records that the varying shadow softness depends on each moon's distance from Jupiter, with farther moons casting softer, more dispersed shadows. Sky & Telescope writes that Callisto's shadow has a large penumbra, appearing fuzzier than the shadows of the inner moons. Our arithmetic reproduces both the ranking and the magnitudes.

We are citing that NASA caption for its observational statement only. It offers no explanation of the moon-shadow offset; the one causal remark it makes, about orbital velocities, is about how fast the moons cross rather than where their shadows fall, as we set out at the top. Quoting an authority selectively and then leaning on its authority is exactly the failure mode this review exists to avoid, so we are saying which half we are using and why.

One view from inside the system: JunoCam imaged Ganymede's shadow on 21 April 2022 from about 71,000 km above the cloud tops, at 55 degrees south latitude. JPL's caption notes that an observer standing inside that oval would see a total solar eclipse. The umbra is not a diagram. It is a finite, computable cone, and a spacecraft flew through the region where it lands.

Q6: it vanishes at opposition — and our live prediction

This is the decisive move, because it has a sign and a date.

If α causes the offset, the offset must go to zero when Earth, Sun and Jupiter line up, and it must flip direction on the two sides of opposition. The observers' rule, as BBC Sky at Night states it, is that a moon trails its shadow before opposition and precedes it after. That is a falsifiable claim about direction, and direction is not something a fudge factor can supply.

The January event, now closed. Jupiter's 2026 opposition fell on 10 January, when α dropped to 0.054 degrees. Sky & Telescope published in advance that Callisto and its shadow would touch Jupiter's disk together at 6:55 Universal Time, with Callisto covering most of its own shadow — the outermost moon, the one whose shadow sits five Jupiter radii away at quadrature, sitting on top of it. We recomputed the event from JPL Horizons state vectors without consulting their prediction — which tests our ray-tracer rather than the geometry, since a Sky & Telescope forecast descends from the same ephemeris family, so this agreement is not independent confirmation and we do not offer it as such — and got transit ingress 06:52 UT, umbral shadow ingress 06:57 UT, penumbral first contact 06:49 UT, and a residual moon-to-shadow separation of roughly 1,600–1,850 km — 0.02 to 0.03 Jupiter radii, about 0.5 arcseconds — against Callisto's apparent diameter of 1.57 arcseconds.

We went looking for observations from that night, and they exist. On Cloudy Nights, the imager posting as "Borodog" captured a complete Jovian rotation on the night of 10 January and, in describing the processing, mentions applying "a slight gamma bump (to differentiate Calisto from its shadow)." That parenthesis is the load-bearing detail. He does not say the two were inseparable at native contrast, and we should not put the words in his mouth — but an imager reaching for extra gamma specifically to tell a moon from its own shadow is describing exactly the near-coincidence the geometry predicts, and it is an outcome that could plainly have gone the other way. Two visual reports from the same night, in a separate thread, are consistent. An observer in Texas using a 160mm refractor at 300× in 20–30 mph gusts reported the transit beginning around 1:00 a.m. CST — 07:00 UT, against the predicted 06:55 UT contact — and watched roughly the first forty minutes, noting that Callisto darkened as it moved onto the disk and that about fifteen minutes in it looked "more light black than grey." An observer in northern California recorded a frame afocally with an iPhone at a Questar Seven's 12mm eyepiece at about 260×.

How far we can push those observations, and no further. We confirmed the text of these posts and the existence and filenames of their attachments through two independent extractions of each thread. We did not render or visually inspect the image files. So we can say that amateur images from that night exist, are publicly posted, and carry their observers' own descriptions; we cannot personally attest to what the pixels show. Anyone citing this should open the threads and look. The visual time estimate — "around 1:00 a.m." — confirms the prediction at the several-minute level, not better. A third post in that thread contained a planetarium simulation rather than an observation, and we exclude it; simulations are not evidence here. We also searched AstroBin for material dated 10 January 2026 and found none, and could not reach the ALPO Jupiter Section at all.
Now the part that has not happened yet. The January event was published before the fact and observed after it, which makes it a closed prediction. What follows is an open one.
At the western quadrature of November 2026, α reaches 10.704 degrees, and the sign of the offset is the opposite of April's. Our computation from JPL Horizons state vectors puts Io's shadow ingress 74.9 to 76.0 minutes BEFORE Io's transit ingress over 15–17 November 2026. In April 2026, after the January opposition, the same computation puts it 76.7 to 78.3 minutes AFTER. The simple law agrees: (10.704 / 360) × 42.4593 hours = 75.7 minutes. Europa's offset should be about twice Io's and Ganymede's about four times, in the ratio of their periods.

That is roughly 87 days from the date on this page. It is published before the fact. It needs a telescope and a wristwatch — no photometry, no plate scale, no ephemeris beyond a transit prediction of the moon itself. The falsifiable content is the interval and its sign, and both come off a stopwatch: start it when the shadow touches the disc, stop it when the moon does. Two directly observed events, nothing computed in between. If, in mid-November 2026, Io's shadow arrives on Jupiter's disk after Io rather than before, or if the interval is not somewhere near 75 minutes, this account of Jovian shadows is wrong and we will say so here.

The magnitude of the swing is what makes this hard to fake. Callisto's shadow sits 5.12 Jupiter radii from Callisto in April and 0.02–0.03 Jupiter radii in January. One published angle tracks the whole range, and it was computable years in advance.

What would change our mind

Stated with thresholds, in advance, and capable of going against us.

  1. The single-image test, part one. Photograph two Galilean moons in simultaneous transit with their shadows on the disk, calibrate the plate scale, and show the two moon-to-shadow vectors are not parallel by more than a few degrees.
  2. The single-image test, part two. Show a measured pair of offsets departing from their orbital-radius ratio by more than about five per cent on a calibrated frame.
  3. The November sign. Time one Io shadow transit in mid-November 2026. If the shadow does not lead the moon onto the disk by roughly 75 minutes, our account fails.
  4. The January event. If archived images from 10 January 2026 show Callisto and its shadow clearly separated on Jupiter's disk, the phase-angle account is dead. We have named the threads we found; we invite anyone holding better-resolved frames to post them.
  5. The ephemeris residuals. Show shadow-transit ingress times departing from published ephemerides by more than a few minutes on a routine basis, reproduced across observers. Mallama et al. found 3.6 seconds rms for Io.
  6. The shadow sizes. Show a Galilean shadow whose dark umbral core is larger than its moon's disk, or show Callisto's shadow to be as sharp-edged and narrow-penumbra as Io's.
  7. A better model. Produce any light-source configuration — two suns, a near source, whatever — that reproduces all four moons' shadow positions on a single date better than one distant Sun does, without a free parameter per moon. We will publish it here under Miller's name.

Where this page could be wrong

We would rather flag these ourselves than have them found.

Our shadow-contact times are not ephemeris grade. Our transit and shadow ingress times come from our own ray-tracing of JPL Horizons state vectors, modelling Jupiter as a sphere of equatorial radius 71,492 km. We ignore the 0.0649 flattening, ignore limb curvature at the contact point, and treat the intra-Jovian light time of about six seconds as negligible. Our 10 January figures agreed with Sky & Telescope's published time to about three minutes. Present them as an independent check that reproduces a published prediction, not as ephemeris output. Anyone recomputing with a proper oblate model will get slightly different numbers, and we are saying so first. The Δt = (α/360) × P rule is an approximation. It assumes the moon crosses near the disk centre, treats the phase angle as lying in the orbital plane, and ignores the difference between the umbra's radius and the moon's radius. It held to about one percent for Io, Europa and Ganymede in our tests. It degrades for Callisto and near the edges of the transit window. We give it as a rule of thumb with the full computation alongside. The Galilean periods are not unambiguous. The commonly published sidereal periods and JPL's own mean-elements table disagree by up to 0.36 percent for Io (1.769138 d against 1.762732 d), because the latter are Laplace-plane mean elements rather than inertial sidereal periods. Our own fit to Horizons vectors over 5–8 April 2026 favours the published sidereal values, reproducing them to 0.07–0.15 percent for the inner three. Our Callisto fit is unreliable: a three-day window covers only 18 percent of its orbit. Callisto's April quadrature offset is unchecked. Callisto did not transit in the window we sampled, so its 365,755 km figure is the simple law only, with no full computation behind it. The Nantes source contradicts itself, as noted above, and we could not establish the area figure for the French survey. We are answering the strongest version of Q6, and now also two specific images. Q6 is posed at p. 49 as question text with no figure, so that much was reconstructed from shapedebate.com's phrasing about Jupiter's moon shadows failing to align heliocentrically. The book's worked instances at pp. 160–161 we have seen, reproduced and measured. What none of them carries is a date or a time. If Miller's argument turns on a specific dated image, our reply has to survive that image too. We will recompute the geometry for any dated, timed image he supplies, publish the working here whichever way it comes out, and we mean that. Our January observational evidence is amateur and unmeasured. We read the posts; we did not inspect the pixels or verify equipment, sites, or times independently. No UT times, telescope, camera or location are given in the imaging thread at all. The two visual reports are eyeball estimates. They are consistent with the prediction at the several-minute level and they are not a measurement. And the sourcing gaps we did not paper over. We dropped figures for Bradley's aberration constant, Rømer's speed-of-light determination, and Barnard's Star's proper motion, because the sources we had for them were secondary compilations rather than the primary records, and this page's rule is that we cite what we actually pulled. Their absence costs the argument nothing; their presence with a shaky citation would have cost it more.

Sources & further reading

This list is shared with the companion page on the sky’s rate of turning; not every entry is used here.