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    Re: Jupiter and the Moon
    From: Alexandre Eremenko
    Date: 2013 Jan 21, 10:13 -0500

    Thanks for your detailed explanation.
    unfortunately the snow is falling here in the Midwest, and I do not
    except even the Moon to be visible on this night:-(
    > 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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