[Physics] Galilean Satellites

[Thomas Goodey]

On 28 Jul 2017 at 12:00, Carl Johnson wrote:

> 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.

But let's look at the simple numbers. To make it easier, 
let's only consider Io and Europa, events where Europa 
comes in front of Io, either from the point of view of the 
Sun (type A) or from the point of view of the observer on 
Earth (type B).

>From Wikipedia, roughly, the diameters of Io and Europa are 
3700 km and 3100 km respectively, and the speed of Io in 
its orbit is 17 km/sec, while the speed of Europa in its 
orbit is 13.7 km/sec.

So Europa can't quite cover Io, but almost can. For 
simplicity, let's suppose that it can (ignore the bit 
sticking out).

As seen from the Sun or the Earth, so far away, the 
parallax is quite small, so it's a simple matter of one 
disk about 3000 km in diameter coming to overlap one 
another as they both move. And the relative speed between 
the disks cannot be more than about 4 km/sec. So, 
obviously, the total duration of the mutual event will be 
around 6000 km at 4 km/sec = 1500 seconds.

However the beginning and ending portions probably won't 
have much visual impact. We could say that the central part 
of the event, the main event, might take 500 seconds or so.

> 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. 

I don't see what's horrific about the above ball-park 
calculation.

> 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 don't understand that.

> 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.

This is all erroneous nonsense. The events can be seen from 
anywhere on the Earth that is in darkness and facing toward 
Jupiter at the time, granted that the sky is clear of 
course.

I don't see what's so subtle about it. 


> 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.

No, it wouldn't. Give chapter and verse to those archives, 
please.

> 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.

I can do the above ball-park calculation in my head. In 
fact I just did. Of course the actual details require 
knowledge of the positions and speeds of the moons, and 
much calculation.

>  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 am convinced that all the above is illusory. That's not 
how you do celestial mechanics. 

> 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.  

No doubt. I don't see what them being relatively near to 
one another has to do with it. At that distance, the Sun is 
effectively a point source.

> 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.

With regard to Type A (one GM eclipsing the Sun, from the 
point of view of another GM), you had better consult

https://academic.oup.com/astrogeo/article/50/2/2.17/183834/M
utual-eclipses-in-the-solar-system

which totally demolishes everything you have been saying. 
For example, I quote:

"During the current eclipse season 78 total, 3 annular and 
59 partial mutual eclipses take place among the Galilean 
moons."

The subject appears to be very well researched.

> 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. 

Well, I doubt that. Io, Europa, and Ganymede are in a 1:2:4 
resonance, but Callisto isn't.

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'