<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<HTML><HEAD>
<META content="text/html; charset=iso-8859-1" http-equiv=Content-Type>
<META name=GENERATOR content="MSHTML 8.00.6001.23588">
<STYLE></STYLE>
</HEAD>
<BODY bgColor=#ffffff>
<DIV><FONT size=2 face=Arial>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.</FONT></DIV>
<DIV><FONT size=2 face=Arial></FONT> </DIV>
<DIV><FONT size=2 face=Arial>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.</FONT></DIV>
<DIV><FONT size=2 face=Arial></FONT> </DIV>
<DIV><FONT size=2 face=Arial>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.</FONT></DIV>
<DIV><FONT size=2 face=Arial></FONT> </DIV>
<DIV><FONT size=2 face=Arial>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.</FONT></DIV>
<DIV><FONT size=2 face=Arial></FONT> </DIV>
<DIV><FONT size=2 face=Arial>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.</FONT></DIV>
<DIV><FONT size=2 face=Arial></FONT> </DIV>
<DIV><FONT size=2 face=Arial>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.</FONT></DIV>
<DIV> </DIV>
<DIV><FONT size=2 face=Arial>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.</FONT></DIV>
<DIV> </DIV>
<DIV><FONT size=2 face=Arial>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. </FONT></DIV>
<DIV> </DIV>
<DIV><FONT size=2 face=Arial>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.</FONT></DIV>
<DIV> </DIV>
<DIV><FONT size=2 face=Arial>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.</FONT> </DIV>
<DIV><FONT size=2 face=Arial></FONT> </DIV>
<DIV><FONT size=2 face=Arial>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.</FONT></DIV>
<DIV><FONT size=2 face=Arial></FONT> </DIV>
<DIV><FONT size=2 face=Arial>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.</FONT></DIV>
<DIV><FONT size=2 face=Arial></FONT> </DIV>
<DIV><FONT size=2 face=Arial>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.</FONT></DIV>
<DIV><FONT size=2 face=Arial></FONT> </DIV>
<DIV><FONT size=2 face=Arial>Carl Johnson</FONT></DIV>
<DIV> </DIV></BODY></HTML>