Document 4

The Other Three Galilean Moons
and the Test the Propagation Interpretation Cannot Pass

Introduction

Documents One through Three of this series established the condition of the observational record, the geometric account of the platform change and the hard measurement boundary that no instrument in history has crossed. This document returns to the specific 1676 record and examines the one piece of evidence that the propagation interpretation itself requires to be valid and that Rømer’s own superior, working from the same observatory with the same instruments, documented to be absent.

Giovanni Domenico Cassini

Giovanni Domenico Cassini was not a peripheral figure in the 1676 announcement. He was the director of the Paris Observatory, the institution where both he and Rømer worked and where the observations were made. He was one of the most accomplished observational astronomers of the seventeenth century. He had published his own ephemerides, precise tables of predicted eclipse times, for all four Galilean moons of Jupiter in 1668, eight years before Rømer’s announcement. He had been timing Io’s eclipses himself since before Rømer arrived in Paris.

It was Cassini, not Rømer, who first noticed that the eclipse timings of Io showed systematic variations correlated with Earth’s position relative to Jupiter. Historians of science including Laurence Bobis and James Lequeux of the Paris Observatory have argued that Cassini may have been the first to propose the finite velocity of light as a possible explanation for those variations and that at minimum the hypothesis was a joint development rather than Rømer’s alone. The conventional historical account credits Rømer because he pursued the interpretation further and made the formal announcement. Cassini’s role in the initial observation is not in dispute in the historical literature.

What is documented is that Cassini considered the propagation interpretation and then rejected it. He did not reject it out of ignorance or conservatism. He rejected it on the basis of a specific empirical observation: the other three Galilean moons did not show the same pattern.

The Four Galilean Moon

Their Orbital Parameters

Jupiter has four large moons discovered by Galileo in 1610. All four were known to Cassini and Rømer. All four had been timed extensively by Cassini before 1676. Their orbital parameters are documented.

Moon	Orbital Period	Distance from Jupiter	Eclipse Frequency	Observability from Earth
Io	1.769 days	421,700 km	Every ~1.77 days	High – most frequently observed
Europa	3.551 days	671,100 km	Every ~3.55 days	Good – regular observations
Ganymede	7.155 days	1,070,400 km	Every ~7.15 days	Good – longer orbital period
Callisto	16.689 days	1,882,700 km	Every ~16.69 days	Intermittent – long period, sometimes misses shadow

All four moons orbit Jupiter in nearly the same plane. All four pass through or near Jupiter’s shadow cone during their orbits. All four were observable from the Paris Observatory with the instruments available in the 1670s. All four had been timed by Cassini. If the timing variations that Rømer observed in Io’s eclipses were caused by light taking longer to travel as Earth moved away from Jupiter, then all four moons should show the same type of timing variation, scaled proportionally to their orbital periods.

What the Propagation
Interpretation Requires

The propagation interpretation makes a specific, testable and unavoidable prediction about the other three moons. If light travels at a finite speed, then any event in the Jupiter system that produces a detectable signal at Earth will be subject to the same transit delay. The delay depends on the distance between Earth and the Jupiter system, not on which moon is being observed. As Earth moves away from Jupiter, the transit time of light from the Jupiter system to Earth increases. Every observable event in the Jupiter system should appear progressively delayed as Earth moves away from Jupiter and progressively early as Earth moves toward Jupiter.

The magnitude of the delay for any specific moon’s eclipse event should scale with the change in Earth-Jupiter distance during the observation period. It should not depend on which moon is being observed or on that moon’s orbital period. The light from Io’s emergence, the light from Europa’s emergence, the light from Ganymede’s emergence, and the light from Callisto’s emergence all travel the same distance from the Jupiter system to Earth. They should all show the same accumulated timing shift as Earth moves in its orbit. The pattern should be consistent across all four moons.

This is not a subtle prediction. It is the direct, unavoidable consequence of the propagation interpretation. If light takes longer to travel a greater distance, then every observable event from every observable source at that greater distance takes longer to reach the observer. The four Galilean moons are all at the same distance, the Jupiter system distance from Earth. They should all show the same timing shift pattern as Earth’s distance from the Jupiter system changes.

If the timing variation Rømer observed in Io’s eclipses was caused by light taking longer to travel as Earth moved away from Jupiter, then Europa, Ganymede and Callisto must show the same pattern. They are at the same distance. Their light travels the same distance to Earth. The prediction is unavoidable and specific.

What Cassini Observed

Cassini had timing data for all four moons. He had been collecting it for years before Rømer’s announcement. When he examined the timing records of Europa, Ganymede and Callisto for the same type of systematic variation correlated with Earth’s orbital position that Rømer found in Io, he did not find it consistently. The other three moons did not show the same clear, systematic pattern that Rømer was pointing to in Io. This was documented and reported. It was the specific basis of Cassini’s rejection of the propagation interpretation.

Cassini’s objection was stated precisely in the historical record. He could not accept a hypothesis that was valid for one of the four moons but did not work for the other three. This was not a philosophical objection. It was an empirical one. He had the data. The propagation interpretation predicted a consistent pattern across all four moons. The data did not show that consistent pattern. Cassini rejected the interpretation on those grounds.

The historical record also documents something that the conventional account does not emphasize: Cassini incorporated corrections for the observed timing variations into his revised 1693 tables of Jupiter’s satellite eclipses, adjusting predicted times by up to 14 minutes to account for Earth’s position relative to Jupiter, but he did so without accepting Rømer’s propagation explanation. He treated the timing correction as an empirical correction to his tables, not as a confirmed measurement of light travel time. He separated the observational fact of the timing variation from the propagation interpretation of its cause.

Cassini could not admit that a hypothesis that was valid for one of the four moons did not work for the other three.
– Suzanne Débarbat, historian of science, Paris Observatory

Why the Geometric Account Predicts
Exactly What Cassini Observed

Document Two of this series established that Rømer’s platform changed as Earth moved in its orbit, and that his changing angle to the fixed shadow cone of Jupiter accounts for the timing variation he observed in Io’s eclipses. The geometric account makes a specific prediction about the other three moons that is different from the propagation interpretation’s prediction and that matches what Cassini observed.

The geometric prediction is this: the timing variation produced by the observer’s changing platform geometry will differ for each moon depending on the specific geometry of that moon’s shadow cone relative to the observer’s changing position. Io orbits Jupiter at 421,700 kilometers from Jupiter’s center. Its shadow cone has specific geometric dimensions. Europa orbits at 671,100 kilometers. Its shadow cone has different dimensions. Ganymede orbits at 1,070,400 kilometers. Callisto at 1,882,700 kilometers. Each moon traces a different shadow cone. The observer’s changing position relative to each of those differently-sized shadow cones produces different timing variations for each moon.

Furthermore, each moon has a different orbital period. Io completes an orbit in 1.769 days. Callisto takes 16.689 days. The rate at which the observer’s platform changes its angle to each moon’s shadow boundary, expressed as a fraction of each moon’s orbital period, is different for each moon. The accumulated timing shift over any given observational interval will therefore be different for each moon under the geometric account. Not proportionally identical as the propagation account requires. Different, because each moon’s shadow geometry and orbital period interact differently with the observer’s changing platform position.

Cassini had enough data on all four moons to observe that the pattern was not consistent across them in the way the propagation interpretation required. The geometric account predicts that the pattern would not be consistent in that way. The geometric account predicts exactly what Cassini found: a clear pattern in Io, the moon with the shortest orbital period, the closest orbit, and the most regularly observed shadow boundary and a less consistent or absent pattern in the moons with longer periods, wider orbits and differently-sized shadow cones. Cassini’s objection is not a problem for the geometric account. It is a confirmation of it.

What Happened to Cassini’s Objection

Cassini’s objection was not answered. It was set aside. The scientific community accepted Rømer’s propagation interpretation in the years following the 1676 announcement, a process that was not immediate. James Bradley’s 1729 discovery of stellar aberration, the apparent shift in star positions caused by Earth’s orbital motion, was taken as independent confirmation of the finite speed of light and with that confirmation the propagation interpretation became the accepted account. Cassini’s specific objection about the other three moons was not resolved. It was superseded by the apparent confirmation from an independent source.

However, Bradley’s stellar aberration observation is itself subject to the same geometric platform analysis that Documents One and Two applied to Rømer’s Io observations. Earth’s orbital motion changes the observational angle to distant stars continuously. The apparent shift in star positions, stellar aberration, is the accumulated expression of that changing angle. It is consistent with the geometric account of a moving observational platform as well as with the propagation interpretation. Bradley’s observation did not uniquely resolve Cassini’s objection. It added another observation that both interpretations can account for.

Cassini’s specific empirical objection, that the other three Galilean moons did not show the same pattern that the propagation interpretation requires them to show, has never been resolved in the published literature. It was set aside when broader acceptance of the propagation interpretation made it seem less pressing. The geometric prediction, that the pattern would differ across the four moons in exactly the way Cassini observed, has never been formally developed and compared against the historical data. That comparison is the work this series calls for.

What This Document Establishes

Giovanni Domenico Cassini was the director of the Paris Observatory, the most accomplished observational astronomer working on the Jupiter system in the 1670s, and a co-originator of the observation that Rømer interpreted as evidence of finite light speed. Cassini rejected the propagation interpretation on a specific empirical basis: the other three Galilean moons did not show the consistent timing variation pattern that the propagation interpretation requires all four moons to show. His objection was documented, specific, and based on timing data from all four moons collected over years of observation.

The geometric account of the platform change predicts exactly what Cassini observed: a clear pattern in Io and a different or absent pattern in the other three moons, because each moon’s shadow geometry and orbital period interact differently with the observer’s changing platform position. Cassini’s objection is a confirmation of the geometric account. It was never resolved by the propagation interpretation. It was set aside. The data that would resolve it — a full geometric analysis of the timing variation prediction for all four moons under both interpretations — has not been produced in the published literature.

Document Five of this series examines the arithmetic that Huygens performed on Rømer’s data — the calculation that produced the first numerical value for the speed of light — and what that arithmetic actually contains.

Produced by The Lilborn Equation Team:

Michael Lilborn-Williams

Daniel Thomas Rouse

Thomas Jackson Barnard

Audrey Williams