[Physics] Galilean Satellites

Sat Jul 29 19:46:24 CEST 2017

I have not done even a simple calculation but I would tend to believe that the Meeus calculation is correct.  The idea that one disk eclipses another in a static 2-dimensional geometry is too simple.  In fact all the objects are moving including Jupiter so Europa's shadow sweeps across the surface of Io.  The sweep rate is multiplied by the lever arms involved.  Even the simple case is a complex problem in geometry.  

However the major discrepancy can be resolved if you consider that it would be extremely rare for the eclipse to occur with jupiter, the sun, and both moons on the same alinement.  in that rare case the event could approach 1500 seconds.  However, more likely the eclipse would occur when the moons are far from that line, in which case the eclipses would be short because of the high angular sweep rates that occur at the orbital extremeness.  

I am curious, why does it matter where you are on the earth when the eclipse occurs?  Shouldn't you be able the see the eclipse from anywhere on earth?  

---Maurice Daniel---

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Maurice Daniel, Master Inventor
mdaniel at masterinventor.com

On Jul 29, 2017, at 3:59 AM, Thomas Goodey wrote:

> 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'
> 
> 
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