Modeling the Jovian Satellite Events

It is important to have some kind of model of the effect we wish to observe. Four phenomena interest us in the Jovian system: EClipses, OCcultations, SHadow transits and body TRansits. Two discrete events are associated with each phenomenon: the Init and the Exit. Our notation for these events is 
    EC-I, EC-E
    OC-I, OC-E
    SH-I, SH-E
    TR-I, TR-E

As the Earth orbits the Sun, and Jupiter orbits the Sun, and Io orbits Jupiter, how do we expect the timing of these events to behave?

Eclipses and Occultations

Depending on the position of the Earth wrt Jupiter and the Sun, eclipses and occultations occur in pairs: {EC-I, OC-E} or {OC-I, EC-E}. For half the synodic year, from conjunction to opposition, one will see the pair {EC-I, OC-E}, then from opposition to the next conjunction one will see the other pair {OC-I, EC-E}. This is an experimental fact and confirms that the Jovian satellites orbits are prograde (counterclockwise when viewed from the North), as are the orbits of Jupiter and the Earth. It is clear the OC events will show much greater variation with the position of the Earth because they are "leveraged" by the Jupiter Io distance. This distance is actually 6 Jupiter radii from Jupiter's center, much more than this diagram indicates.

Shadow Transits and Body Transits

The point here is that the TR events, like the OC events in the previous diagram, will show much greater variation with the position of the Earth than the SH events.

Conclusion

We can already conclude that the EC events events are the ones we will want to study. They are expected to occur with metronomic regularity. By this I mean that we do not expect the position of the Earth to influence the timing of their occurences.

If timing shifts are observed they have a good chance of indicating a speed of light effect.

For half an Earth-Jupiter cycle, from Earth-Jupiter opposition to Earth-Jupiter conjunction, we should see the EC-I event occur regularly with an ever (so slightly) decreasing time between events. Then for the next half of the cycle, from conjunction back to opposition, the time between EC-E events should be ever (so slightly) increasing.

We already expect timing shifts for the other events, OC, TR and even SH, due to the varying position of the Earth. Because of that, these events are not very good candidates for a speed of light measure. We would first have to quantify the dominant effect and then look for deviations. This is harder than just simply looking for the presence of the effect.