[Physics] Eclipses of Galilean Moons

[Thomas Goodey]

Carl Johnson wrote:

> As to the results of my calculations, Io and Europa were
> generally involved

It seems to me that any one of the four Galilean moons 
could cast its shadow on any other. Of course if the former 
is the smaller, then the shadow could not completely cover 
the latter; and even if the latter is the smaller, the 
shadow will not usually cover it completely.

> ... and I was surprised at what a tiny area
> on Earth could witness such events.  Considering 25 years
> and my memory, I think that two of the events would only
> have been visible from somewhere in the ocean, one in
> African jungle, and one mostly in the Pacific but with a
> small possible area in southern California. 

I still don't understand what you are talking about. The 
location on the side of the Earth facing Jupiter at the 
time in question is of no importance, for viewing an 
eclipse. 

Or, are you talking about one of the moons occulting 
another, from the point of view of an Earth observer? That 
is not an eclipse; the Sun is not involved. But there would 
be no surprising visual effect. The two dots would just 
merge; there would be no sudden extinction as during an 
eclipse.

> It does not surprise me that technollogy has advanced where
> such "mutual occultations" are now probably regularly
> predicted.  Your point is well taken that the location  of
> the Sun and Jupiter's orbit are what is important, and the
> events can only occur twice every twelve years, when Jupiter
> passes its nodes.  At the time, I was focused on the exact
> position of the Earth as many such events occurred during
> the daytime and over our 75% oceans and such.  It was
> frustrating to have spent months in doing endless
> calculations only to discover that no one on Earth could
> have witnessed them.

The above paragraph is eloquent testimony to the above 
confusion.

> ... it had dawned on me
> that we have really accurate data regarding the precise
> locations and positions of the Galilean moons, and timing. 
> Obviously, if someone witnessed the event on Earth, we could
> also know that timing to microseconds or better.  And we
> would know the distance between that location on Earth and
> each of the two moons involved to a meter or so.  

That meter-accuracy might be a bit of an exaggeration.

> Even back then, I wondered if that available math might
> enable a really precise measurement of the speed of light,
> maybe to even fifteen-digit precision (that would be a
> million times more precise than the official speed of light,
> which is defined to nine-digit precision.)

The above is all very well taken. That would indeed be a 
way to measure the one-way speed of light. But there are 
some complex matters of definition to consider.

Unfortunately it only works one way. You can't use that 
method to measure the speed of light the other way!

> An additional observation.  Io and Europa are each about
> 2000 miles in diameter. 

That is not very accurate.

> Say that one passed the other 2000
> miles in the Z-axis.  Then no actual mutual eclipse even
> happens.  However, the Earth is bigger, and from certain
> locations on Earth, an observer could see a partial or total
> occultation of one by the other, even when no actual (solar)
> mutual eclipse had occurred.  Such detaills were part of why
> the math was so overwhelmingly complex.  And why an exact
> location on Earth was critical. 

Here you are not talking about solar eclipses at all. I 
understand.

> So my interest (and apparently also that of Meeus) was
> exclusively for total eclipses.  They only lasted a few
> seconds, (up to about 16 seconds max, as I recall), but they
> were apparently brain-jarring, as a reliable object rather
> suddenly disappeared, and then reappeared.

But that's my point. Nothing would disappear. It would be 
clear to the observer on Earth that the two little dots 
just merged together and then separated again. Nothing 
brain-jarring about that.

I accept that, to take the other interpretation of what you 
have been discussing, if for example Europa cast its shadow 
(solar shadow) on Io, then it would indeed appear to the 
observer that Io suddenly [almost] disappeared, and then 
reappeared. But that's quite a different event. And it 
would look the same from anywhere on Earth.

Thomas Goodey

*****************************
Anne's search for security 
holes in the localizer network 
software was close to 
impossible. Every year her 
zipheads pushed back their 
deadline for certainty another 
year or two. But the quagmire 
of Qeng Ho fleet software 
was almost eight thousand 
years deep.
--------- Vernor Vinge
----------'A Deepness in the Sky'