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    Re: Jupiter and the Moon
    From: Alexandre Eremenko
    Date: 2013 Jan 21, 10:38 -0500

    Paul,
    There are two reasons why such Lunars may be inconvenient for time
    and longitude.
    
    1. One reason is that the planet and the Moon move in the sky in
    the same direction as it is the case now. When a planet performs,
    retrograde motion, this helps the accuracy of the Lunar slightly.
    
    2. More importantly is that the Moon and planet do not move on the same
    circle. This is because both orbits are inclined to ecliptic.
    In the region of the sky where they come closest, imagine them moving
    on the straight lines which do not intersect. Then, near the time when
    they come closest to each other, the distance between them almost
    does not change. And this is bad for the Lunar.
    The worst case scenario is when the lines are parallel
    and on the significant
    distance from each other.
    
    So the answer to your question depends very much on the planet, and the time
    when it comes close to the Moon.
    
    But generally I feel that 30-40 degrees distance would be sufficient,
    and at all larger distances the accuracy will be ruughly the same.
    
    
    Alex.
    
    
    >
    >
    >
    > I’m curious: when does “close” become too close? Last night &
    > tonight’s Lunar shots gave pretty inaccurate results for GMT, (--- Is
    > there a rule of thumb about what the minimum distance should be for
    > halfway decent results?
    >
    >
    >
    > -Paul
    >
    > From: navlist-bounce---org [mailto:navlist-bounce---org] On Behalf Of
    > Frank Reed
    > Sent: Sunday, January 20, 2013 8:52 PM
    > To: NavList---org
    > Subject: [NavList] Re: Jupiter and the Moon
    >
    >
    >
    > Alex, you wrote:
    > "Near limb will be the dark one."
    >
    > Only for the first half of the night. Near closest approach, Jupiter will
    > be more or less in line with the terminator, and the choice of near or far
    > limb may be tough to make. Not that it matters. If there's any doubt, wait
    > it out. Then for a good while after, Jupiter will still be very close to
    > the Moon but the illuminated limb will be the near limb.
    >
    > You asked:
    > "Why is this a more "excellent test" than any other Lunar?"
    >
    > I didn't say it was "more excellent". I said it was "STILL excellent"
    > despite the fact that it does not represent a historical case. That is,
    > even though they would have avoided such sights for the method of
    > longitude by lunars, we can still shoot them today to test the instrument
    > and observer and also to understand the basic mechanics and manipulations
    > of shooting lunars. And it's a nice next step after measuring the Sun's
    > diameter (which I described recently as good "training" for lunars). Most
    > beginners find it much easier to start with a short distance lunar because
    > there's less flailing about with the sextant.
    >
    > Parenthetically, you wrote:
    > "I understand this could be a test for my conjecture about something wrong
    > happening with my sextant first two teeth."
    >
    > Actually, the suggestion from Bill Morris was a terrific idea. If you have
    > really concluded that there is some flaw in the arc near zero, then take
    > that portion of the arc out of the puzzle. Just adjust your sextant until
    > you have an index error of, say, 5 deg 0.0' exactly or, more likely, 5 deg
    > 0.5' (some small extra bit). There's no harm in that. For every sight, you
    > take, you just knock off 5 degrees before you even write it down. Treat
    > the 5 degree mark as your new zero. Incidentally, I asked if you're more
    > "optimistic" because the sights which you recently posted DO NOT display
    > that 0.3' offset which you say you always find. The average of the set
    > shows an error of less than a tenth of a minute of arc, and the standard
    > deviation is right around a quarter of a minute of arc, right in line with
    > the numbers that I have described for many, many years in NavList posts.
    >
    > You asked:
    > "Do you mean by the horizontal parallax? How else can the latitude affect
    > a lunar distance?"
    >
    > Yes, exactly. It's that "position fix by lunars when GMT is known" that I
    > have described in many earlier posts. You can fix your latitude and
    > longitude by measuring a pair of lunar distances at known GMT. Again, this
    > was never done in the early history of lunars (meaning 1770-1850 when they
    > were in active use at sea). But the Apollo spacecraft was equipped for
    > shooting lunars and "earthers" (ugly name which no one used --but you get
    > the idea: sights like lunars using the Earth's limb instead of the
    > Moon's), and on Apollo 8 in 1968, just to make sure it would work as a
    > backup, Jim Lovell shot many lunars for fixing the spacecraft's position.
    > So there's still a historical case involved here... not historical in the
    > sense of 200 years, but 55 years is starting to be quite a long leap back
    > into the history of navigation.
    >
    > I began the above paragraph with "yes, exactly". I suppose I should
    > qualify that slightly by saying that this depends on measuring the Moon's
    > "parallax in position" generally rather than saying "horizontal parallax"
    > specifically, but that's mostly a question of semantics. It's the Moon's
    > parallax that makes this possible.
    >
    > I mentioned that there were other issues (again, historically) with small
    > angle lunars, and you asked: "What are they?"
    >
    > There's the big one involving non-linear interpolation in the lunar
    > distance tables. If you watch the distance reaching a minimum tomorrow
    > night, you could easily see that the standard tables giving the distance
    > once every three hours would have been difficult to apply (quadratic and
    > possibly higher order interpolation would be required). Secondarily, many
    > methods for clearing lunars assumed that short distances would never be
    > used and by design those methods were allowed to be inaccurate for short
    > distances. If a navigator shot a short lunar, that might entail learning a
    > whole new procedure for clearing the sight.
    >
    > You also wrote:
    > "I understand that the distance changes very slowly because they have
    > different declination. But what else is bad about close lunars? Suppose
    > the declination happens to be the same."
    >
    > I think I answered your question above, but I just wanted to add that I
    > think you chose the wrong word here. The distance changes very slowly
    > because the two objects are passing each other at different "apparent
    > ecliptic latitudes" (not declinations), and hence the Moon is not
    > travelling across the sky directly towards/away from Jupiter. I don't mean
    > to quibble over a minor distinction. I'm saying this only because there's
    > a small chance someone following along might get the wrong idea.
    >
    > -FER
    >
    >
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    > View and reply to this message: http://fer3.com/arc/m2.aspx?i=122022
    >
    >
    >
    
    
    
    
    

       
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