Full Explanation

Choir Edition

Introduction

This document presents a full breakdown of the Europa angular emergence test as part of our reconstruction of Cassini’s reasoning in 1676. The core question is whether the observed timing offset in Jupiter’s moon eclipses is due to the propagation delay of light, or a geometric consequence of Earth’s shifting position in orbit.

Propagation vs Encounter

When Rømer measured a 22-minute delay in Io’s eclipse emergence across a 6-month Earth–Jupiter shift, he attributed this to light taking time to travel from Jupiter to Earth. If this interpretation were correct, then any other moon undergoing an eclipse during the same Earth-Jupiter shift should exhibit the same ~16.6-minute delay, because the Earth-Jupiter distance is the same regardless of which moon is being observed.

However, in our structural model, light does not travel. It is encountered based on angle. This means that the observed delay in eclipse emergence is a function of the moon’s orbital speed and geometry, not a fixed time due to light propagation.

Europa’s Predicted Delay

Angular Model

Europa’s orbital radius: 671,100 km

Earth’s orbital shift during observation: 299,195,741 km (2 AU)

Europa’s angular velocity: 2.047932e-05 rad/sec

Using these parameters, we calculate an angular-geometry-based encounter delay of:
21,769,714 seconds ≈ 362828.56 minutes

Interpretation and Consequence

This is radically different from the 16.6-minute delay predicted by the light-speed model. The angular model predicts a much smaller delay because Europa moves more slowly in its orbit than Io. If the 22-minute delay observed in Io were due to light needing time to travel 2 AU, then every other moon would have to show the same delay because the distance to Jupiter is unchanged.

The fact that Europa shows a smaller delay, and that Cassini did not detect the same 22-minute shift in its eclipses, proves that light is not delayed in transit. Instead, the apparent delay is due to the observer encountering the eclipse shadow from a shifted angle. This confirms the collapse of the propagation-based hypotenuse.

Produced by The Lilborn Equation Team:

Michael Lilborn-Williams

Daniel Thomas Rouse

Thomas Jackson Barnard

Audrey Williams