Jupiter's Shadows Point at One Sun

The offset is one angle, applied to four orbits

You see a moon along the Earth line; the Sun casts its shadow along the Sun line. The two differ by one angle: α, the Sun–Jupiter–Earth phase angle.

For Jupiter, α never exceeds about 12°, because Earth’s whole orbit subtends only that much from Jupiter: arcsin(1 / 5.204) = 11.1 degrees — 11.08° at mean distances, nearer 11.9° when a perihelic Jupiter meets an aphelic Earth, about 10.4° in aphelion years. JPL Horizons gives 2026’s actual extremes as 10.994 degrees on 6 April and 10.704 degrees on 17 November — the two quadratures, Jupiter 90° from the Sun in our sky — falling to 0.049–0.064 degrees around the 10 January opposition, when Sun, Earth and Jupiter line up.

Because the Sun is effectively at infinity for a system 1.9 million km across, the sky-plane displacement is simply (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:

Jupiter’s own disk that week is 38.21 arcseconds wide (an arcminute is 1/60 of a degree; an arcsecond is 1/60 of that). 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.

In time, the observable an amateur records: between shadow contact and moon contact the moon must travel through α in its own orbit, so Δt = (α / 360) × P, where P is the moon’s sidereal period, one orbit measured against the stars. At α = 10.994 degrees the law gives Io 77.8 minutes, Europa 156.2, Ganymede 314.6, Callisto 733.9. Our integration of JPL Horizons state vectors (positions and velocities) 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 second or nearby source would need one contrived arrangement per moon.

The same angle, on the book’s own two figures

The worked instance is at pp. 160–161: two figures, both frames from other people’s videos, both captioned “image stacked and edited”, each with a QR code to its source.

The book’s argument, 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 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.” That is a real argument: Jupiter always looks fully lit, so the Sun is behind us, so a shadow should fall directly behind its moon. Every step follows except the last, and the reason is a lever arm.

No visible terminator, and a shadow three radii out

The book is right that we never see half the planet dark, by a wide margin: even at the extreme phase angle the unlit fraction of the disc is about one per cent — 0.93 per cent at 11.08°, 1.07 at 11.9 — far below the seeing in any amateur stack. There is no visible terminator on Jupiter, ever; the Galilean moons show no visible phases for the identical reason. But no visible terminator does not mean the phase angle is zero. It means it is small, and the same small angle acts on a far longer lever at the moons, five to twenty-six planetary radii out: multiply α by each orbital radius and the whole family follows, Io at 1.15 R_J to Callisto at 5.12. The offset is not evidence against the shadow; it is the shadow’s signature.

Figure 52, measured off the book’s own page

Figure 52 is labelled, so it can be measured, and Jupiter supplies the scale bar. On a 400 dpi render of folio 161, Ganymede and its shadow are separated, almost exactly horizontally, by 2.88 R_J: 2.9 ± 0.1 allowing for centroid and radius error (pixel counts in the method notes). The ceiling for Ganymede is about 2.9 R_J: the full Horizons computation gives 2.91 at the April 2026 quadrature, the simple a tan α law 2.93 at the mean-distance bound. The measurement sits at that ceiling and not past it, and the ceiling is what could have failed: nothing in a local arrangement caps Io at 1.15 and Callisto at 5.12, orders the four by orbital radius, and shrinks the whole set to nearly zero every thirteen months.

What the two figures show between them

The book prints figures 51 and 52 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 radii away — and the calendar sets the difference.

Two frames, taken nearly four years apart by strangers to each other at opposite points of Jupiter’s apparition, show 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 consistent with the quantity they are offered to refute. Consistent, not confirmed: upload dates bound captures from above but do not fix them. Astraveo’s frames could be older; Tampa Train Guy’s could be the November 2021 quadrature rather than late May 2022, which fits equally well. The moon in Astraveo’s clip is never named, so figure 51 gets no number, only a comparison; and figure 52’s measurement assumes the stacking moved nothing, which the near-exact horizontal alignment supports but does not prove.

The Astraveo video contains its own control. 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.” Sound for Venus, whose phase angle runs almost to 180°; wrong for Jupiter, where the maximum is about 11°. Narrating the sequence figure 51 is cropped from, he calls it “the movement of a solar eclipse on Jupiter cast by one of its moons”. Figure 52 is a 36-second silent clip — a Meade ETX-125, stacked frames, 25 minutes compressed to four seconds — offered without a thesis, which is why it can be measured. Between them the two videos hold the answer: the same phenomenon at two phase angles, the separation changing by the predicted factor.

“Can it be proven?” — watch a moon go out in empty sky

Q6’s second sentence asks: “are we assuming them to be shadows or can it be proven?” The book’s debate list at p. 232 asks whether extraordinary evidence exists that “the black circles on Jupiter are 100% proven to be shadows.” Behind both sits the flat-plane reply to everything above: Jupiter is a light, not a planet, so calling the dot a “shadow” assumes the answer. There is a direct test, and it needs no photograph of a disc.

Run the geometry backwards. If Jupiter casts a shadow, it is a cone extending away from the Sun, and a moon entering it should disappear while still well clear of the limb, in apparently empty sky, on the side and at the distance α sets, and reappear on the other side later. Before opposition it goes out on one side; after, the other. A moon merely passing behind the planet would vanish at the limb, every time, with no sign change; a light that casts no shadow does not swallow things at a distance from its edge. That is watchable in a backyard telescope on dozens of nights a year, in minutes, and appeals to no one’s authority.

It is also the oldest quantitative result in the subject. In 1676 Ole Rømer, timing exactly these disappearances 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. The Mallama photometry below is the same measurement with a CCD, three centuries later. We have not pulled Rømer’s 1676 note or the 1677 Philosophical Transactions version; the account is from the standard secondary literature.

The test you can run on one photograph

The cheapest decisive measurement on this page requires nothing from us. On any night with two or more Galilean moons in simultaneous transit with their shadows on the disk, take one image, calibrate the plate scale (arcseconds per pixel) from Jupiter’s equatorial width, 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 shadow in the same direction, so the vectors must be parallel to within a few degrees. A nearby source fans them out radially from the sub-source point, not subtly when the moons are millions of kilometres apart.

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

α cancels out of those ratios, so they do not depend on the date, the distance to Jupiter, or anything we computed. They are exact only 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. Our April 2026 offsets in Jupiter radii, 1.15, 1.82, 2.91 and 5.12, have ratios 1 : 1.58 : 2.53 : 4.45. A source at finite distance breaks the linear scaling; a second source gives two shadows, or one no single α reproduces.

The shadows are also the right size

This is the appearance that most plausibly generated the claim. From Jupiter, at 5.2043 au, the Sun is a disk 6.14 arcminutes across: 2 × arctan(695,700 / (5.2043 × 1.495978707×10⁸)) = 0.1024 degrees. A moon’s umbra (the fully shaded core of its shadow) therefore narrows along its path to the cloud tops by (path length) × tan(3.07 arcminutes), and its penumbra (the partly shaded fringe) 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.

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 observation 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 corroboration comes from people who were not arguing about anything. NASA’s Hubble release for the 24 January 2015 triple transit records that shadow softness depends on each moon’s distance from Jupiter, farther moons casting softer, more dispersed shadows; Sky & Telescope writes that Callisto’s shadow has a large penumbra, fuzzier than the inner moons’. Our arithmetic reproduces the ranking and the magnitudes. We cite the NASA caption for that observation only: it offers no explanation of the offset, and its one causal remark, about orbital velocities, concerns how fast the moons cross rather than where their shadows fall. 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 an observer inside that oval would see a total solar eclipse. The umbra is a computable cone, and a spacecraft flew through where it lands.

It vanishes at opposition — and the November 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 at opposition and flip direction across it. The observers’ rule, as BBC Sky at Night states it: a moon trails its shadow before opposition and precedes it after. 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, Callisto covering most of its own shadow. We recomputed the event from JPL Horizons state vectors without consulting their prediction 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. That agreement tests our ray-tracer rather than the geometry, since a Sky & Telescope forecast descends from the same ephemeris family; it is not independent confirmation.

Observations from that night exist. On Cloudy Nights, the imager posting as “Borodog” captured a complete Jovian rotation on 10 January and, describing the processing, mentions “a slight gamma bump (to differentiate Calisto from its shadow)” — a contrast stretch. He does not say the two were inseparable at native contrast; but reaching for extra gamma to tell a moon from its own shadow describes the near-coincidence the geometry predicts, and it could have gone the other way. Two visual reports in a separate thread are consistent: an observer in Texas with 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 — and about fifteen minutes in found Callisto “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×. Their limits are set out under “Where this page could be wrong”.

Callisto’s shadow sits 5.12 Jupiter radii from Callisto in April and 0.02–0.03 in January: one published angle tracks the whole range, computable years in advance.

What would have failed if the geometry were wrong

Three bodies of work, none about cosmology. 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; 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 cartography and taxation: 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. A wrong shadow geometry would have gone straight into the coastline.

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 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), reduced to a standard deviation of 24 mas (milliarcseconds; 75 km at Jupiter) and an rms observed-minus-computed residual of 50 mas (150 km) against the NOE-5-2010-GAL ephemeris. The 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 where it would have shown up first.

These anchors are photometric and instrumental, not visual: the BAA’s Jupiter Section says visual timings of satellite phenomena are not likely to have scientific significance, and we claim nothing more.

What would change our mind

With thresholds, in advance.

1. The single-image test. On a calibrated frame with two moons and their shadows on the disk, show the two moon-to-shadow vectors not parallel by more than a few degrees, or their offsets departing from the orbital-radius ratio by more than about five per cent.
2. 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.
3. 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.
4. 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.
5. The shadow sizes. Show a Galilean shadow whose dark umbral core is larger than its moon’s disk, or Callisto’s shadow as sharp-edged and narrow-penumbra as Io’s.
6. A better model. Produce any light-source configuration — two suns, a near source, whatever — that reproduces all four shadow positions on a single date better than one distant Sun does, without a free parameter per moon.

Where this page could be wrong

Our shadow-contact times are not ephemeris grade. They come from our own ray-tracing of JPL Horizons state vectors with a simplified Jupiter (method notes below). Our 10 January figures agreed with Sky & Telescope’s published time to about three minutes; take them as a check that reproduces a published prediction, not as ephemeris output. The Δt = (α/360) × P rule is likewise an approximation: about one percent for Io, Europa and Ganymede in our tests, worse for Callisto and near the edges of the transit window.

Callisto’s April quadrature offset is unchecked (simple law only), the Nantes source contradicts itself on the longitude, and the Galilean periods carry a 0.36 percent ambiguity — all in the method notes.

We answer Q6 as the book poses it, and its two figures. Q6 at p. 49 is a question with no figure, phrased as shapedebate.com phrases it (moon shadows failing to align heliocentrically); the worked instances at pp. 160–161 we have reproduced and measured. If the argument turns on a specific dated image, our reply has to survive that image too, and the geometry can be recomputed for any dated, timed frame.

Our January observational evidence is amateur and unmeasured. We confirmed the text of the Cloudy Nights posts and the existence of their attachments; we did not render the image files, so we cannot attest to what the pixels show — open the threads and look. No UT times, telescope, camera or location are given in the imaging thread; the two visual reports are eyeball estimates, consistent with the prediction at the several-minute level and not a measurement. A third post in that thread was a planetarium simulation and is excluded. AstroBin holds nothing dated 10 January 2026; the ALPO Jupiter Section could not be reached.

Sources & further reading

• JPL Solar System Dynamics, Planetary Satellite Mean Elements — Galilean and lunar orbital radii and periods. https://ssd.jpl.nasa.gov/sats/elem/
• JPL Solar System Dynamics, Planetary Satellite Physical Parameters — Galilean mean radii. https://ssd.jpl.nasa.gov/sats/phys_par/sep.html
• JPL Solar System Dynamics, Planetary Physical Parameters — planetary sidereal periods, Jupiter radii. https://ssd.jpl.nasa.gov/planets/phys_par.html
• JPL Horizons system — Sun-Jupiter-Earth phase angles for 2026 (target 599, centre 500@399, quantity 24) and state vectors for the January, April and November windows (targets 501, 399, 10; centre 500@599)
• Mallama, Collins, Nelson, Park & Krobusek, 'Precise Timings of Galilean Satellite Eclipses and Assessment of the E5 Ephemeris', Icarus (2000), DOI 10.1006/ICAR.2000.6455
• Saquet et al., 'PHEMU15 catalogue and astrometric results...', MNRAS 474, 4730 (2018). https://academic.oup.com/mnras/article/474/4/4730/4644838
• Sky & Telescope, 'An extremely rare Callisto event on January 10th' — advance prediction of the 10 January 2026 contact time and Callisto's penumbra
• BBC Sky at Night Magazine, 'See Jupiter and its Galilean moons' — the observers' rule on shadow lead and lag across opposition
• NASA / STScI, Hubble release for the 24 January 2015 Jovian triple transit — cited for its observational statement on shadow softness only; its causal remark is discussed in the text
• NASA/JPL, PIA25015, 'Juno Captures Moon Shadow on Jupiter'. https://www.jpl.nasa.gov/images/pia25015-juno-captures-moon-shadow-on-jupiter/
• Cloudy Nights, Major & Minor Planetary Imaging, 'Jupiter Opposition 2025-2026 with Calisto & Shadow Transit — Complete Rotation', posted 11 January 2026. https://www.cloudynights.com/forums/topic/990065-jupiter-opposition-2025-2026-with-calisto-shadow-transit-complete-rotation/
• Cloudy Nights, Solar System Observing, 'Are you ready for Jupiter opposition of the century?' — two visual reports from 10 January 2026. https://www.cloudynights.com/forums/topic/987523-are-you-ready-for-jupiter-opposition-of-the-century/
• Patrimonia Nantes, 'Decembre 1679 : observation de Picard et de la Hire'. https://patrimonia.nantes.fr/home/decouvrir/themes-et-quartiers/decembre-1679-observation-de-pic.html — internally inconsistent, as flagged in the text
• Astronomy.com, 'Do the outer planets have phases?' — the arcsin(1/r) bound on Jupiter’s phase angle
• British Astronomical Association, Jupiter Section — on the scientific weight of visual satellite-phenomenon timings