[Physics] Physics Digest, Vol 7, Issue 7

[cj at mb-soft.com]

I don't question your math ability, and if you were right about 900 seconds, then, yes, such events would be useless regarding the speed of light.

But when Meeus first mentioned that a half dozen mutual eclipses had been witnessed by astronomers since about 1880 or so, he definitely mentioned that the events were extremely brief, a few seconds.  When I did the math, I was therefore comfortable that the Io-Europa events generally lasted from 8 seconds up to a maximum of  16 seconds.  Since I personally never witnessed any of those events, I mostly have to rely on the archival comments of the astronomers who did (unexpectedly) witness such an event.

You earlier said that you have seen references to such mutual eclipses.  If so, such sources certainly would make clear that the events lasted 900 seconds or 16 seconds.  Since I endured six months of horrific math to get my results, I certainly was uneasy that I might have made a math mistake in six months of figuring.  However, the fact that the events which I had calculated (from about 1970 through 1996) all seemed to indicate total durations of just a few seconds, I truly have doubts in any 900 second figure.

I also endured all that math due to the amazing complexity of the math problems.  If I had known that to start with, I would never have even started to do the math.  But after some weeks, it seemed "necessary" to complete my journey.

In case you are interested, the math is so subtle that even the rotation of our Earth, and its equatorial bulge, and seasonal changes of mass movement of snow and ice, definitely affects each of those four (distant) moons, enough to affect the timingn and the precise location.

Regarding "where on Earth", all those precise light paths need to arrive in the early morning hours.  I do not know why, but I did not find that any would be predicted for evening hours.  And, yes, I was so involved in the math that my thinking was just as intense regarding occultations as the mutual eclipses.  So I admit that I might have been calculating precise locations on Earth and feeling frustration that so many potential (occultations) did not occur where they might be seen anywhere on Earth.

But in any case, all of the historical astronomer archives mentioned "blinking out" or a similar phrase, and if the entire process took 900 seconds, that would not have been realistic, where a "fading" might instead have been mentioned.

You are free to doubt my math, but until and unless you actually experience doing the math, you will not convince me of your speculations.  Certainly at the time (1992), I could not figure out how to use a computer to do that math.  I wish.  But there are so many thousand terms which must be sorted out from the massive VSOP87 database, and then fairly nasty calculus where the equation contains thousands of terms, I could not figure out how to get a computer to know which terms to use and how all those integral calculus terms could be solved.  I remember that some of the differential calculus calculations were a little "simpler", regarding solving for velocities and accelerations.  

I get the impression that you think that the four GMs have EXACTLY the same orbital planes, but they do not.  And because of that factor, both Ganymede and Callisto generally cast shadows which pass above or below Io and Europa.  The two littler inner moons pass relatively near each other every orbit, in other words, every few hours, and whenever they happen to both be near Nodes, they can share a shadow, if Jupiter also happens to be near a Node.

Those various orbital angles caused a surprise for me.  I had assumed that the mutual eclipses could only occur doe a few DAYS near Jupiter's Node passage, but the interval of possible eclipses and occultations is actually something like five months. 

You are free to speculate things like Ganymede and Callisto causing lots of mutual eclipses, but I did the math, and I found that they are fairly rare.

Again, you said that you have seen where people have done the math more recently, and I am beginning to be curious as to what claims have been made and whether anyone has experimentally confirmed any of them.

If you really are interested in this stuff, you might know or might be able to find out another peculiar gravitational effect of the GMs, which I could never find or derive.  I have seen the claim that it is "impossible" for all four of the GMs to ever be on the same side of Jupiter.  If that is so, I would love to see the math proof, and the logical reasoning about WHY.

Carl Johnson
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