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    Re: Navigation without Leap Seconds
    From: Gary LaPook
    Date: 2008 Apr 15, 16:27 -0700

    Gary LaPook writes:
    But that doesn't solve the problem. The only reason that CN works on
    the earth is that the direction of "up" varies with your position on
    the earth. The altitudes measured on earth (and in aircraft) rely on
    the direction of "up" for the measurement. The sea horizon used with a
    marine sextant is where it is due to the local gravitational field
    which causes water to assume a shape at right angles to "up" and
    gravitational "down." A bubble sextant uses a bubble to sense "up."
    Because local "up" changes at a constant rate of one nautical mile per
    minute of altitude we can find our place on or above the surface of
    the earth. This relationship does not hold on the way to the moon.
    On Apr 15, 2:12 pm, Fred Hebard  wrote:
    > I believe they measured altitudes from a limb of the Earth, more-or-
    > less in the "normal" way.
    > On Apr 15, 2008, at 4:00 PM, Gary J. LaPook wrote:
    > > Gary LaPook wrote:
    > > If I remember correctly, the Apollo spacecraft had a sextant on
    > > board used to mesure angles of celestial bodies in order to compute
    > > their position in space on the way to the moon, (maybe only as a
    > > backup.)
    > > gl
    > > Fred Hebard wrote:
    > >> So it would have to be sun/moon/planet-star distances. I suppose
    > >> those are limited by the low degree of parallax of the planets and
    > >> sun, not to mention one has to know where one is on earth to
    > >> determine the "position" of other bodies in the solar system,
    > >> which I guess would be a circular argument. On Apr 15, 2008, at
    > >> 12:54 PM, Lu Abel wrote:
    > >>> Fred: You're right about traditional surveying. But your proposal
    > >>> is to use star-to-star distances to locate one (if I understand
    > >>> correctly) in 3-D space relative to some very distant stars.
    > >>> Imagine a couple of stars several hundreds of light-years away
    > >>> (that's on the order of 10^20 cm). Suppose I move a few cm closer
    > >>> to them. By how much would the angle between them change? Not by
    > >>> much at all. Lu Fred Hebard wrote:
    > >>>> Lu, Why billionths of an arcsecond? One arcsecond gets one to
    > >>>> 1/60th of 100 feet in traditional surveying, or about 50 cm. One-
    > >>>> thousandth of an arcsecond would drop one to 5 mm. I wonder if
    > >>>> refraction is a problem here.  Fred On Apr 15, 2008, at 12:33
    > >>>> PM, Lu Abel wrote:
    > >>>>> Fred: In theory, yes; in practice, no. To position oneself
    > >>>>> using star-star distances would require require measuring
    > >>>>> angles to billionths of an arc-second. Maybe something an
    > >>>>> astronomer could do, but not something you or I are going to do
    > >>>>> with our sextants! BTW, I remember a conversation with a radio-
    > >>>>> astronomer about 20   years ago where he said that his team had
    > >>>>> measured the distance between two radiotelescopes on opposite
    > >>>>> sides of the US to within a cm or so using a technique called
    > >>>>> long-baseline interferometry. But the whole experiment took
    > >>>>> them a year or so... Lu Abel Fred Hebard wrote:
    > >>>>>> Completely unrelated, but stemming from the same article. The
    > >>>>>> author states that height can only be known to some few cm or
    > >>>>>> whatever because of variations in gravity, if I remember
    > >>>>>> correctly. It would seem that this is due to our tradition of
    > >>>>>> assuming we are on the surface of a spheroid or ellipsoid when
    > >>>>>> doing navigation. Confining ourselves to a surface makes the
    > >>>>>> trig easier, but couldn't one position oneself with greater
    > >>>>>> accuracy (with feet firmly planted on earth, not on a boat)
    > >>>>>> using only stars or stars plus the sun, ignoring the earth's
    > >>>>>> horizon, by measuring star-star distances? Make it a true 3-D
    > >>>>>> problem. Or would uncertainties in the positions of stars
    > >>>>>> still hamper ones efforts, especially uncertainty in their
    > >>>>>> distance from us? Fred Hebard On Apr 14, 2008, at 9:50 PM,
    > >>>>>> frankr...@HistoricalAtlas.net wrote:
    > >>>>>>> The fascinating article which Fred Hebard linked: http://
    > >>>>>>>www.physicstoday.org/vol-59/iss-3/p10.htmlincludes a
    > >>>>>>> detailed discussion about the problems of gravitational time
    > >>>>>>> dilation and extremely accurate clocks. That's the main
    > >>>>>>> topic, and it's great stuff. The article also mentions leap
    > >>>>>>> seconds and navigation: "Celestial navigators --that
    > >>>>>>> vanishing breed-- also like leap seconds. The Global
    > >>>>>>> Positioning System, however, cannot tolerate time jumps and
    > >>>>>>> employs a time scale that avoids leap seconds." So here's my
    > >>>>>>> question: what's the best way of doing celestial navigation
    > >>>>>>> if leap seconds are dropped from official time-keeping? I
    > >>>>>>> don't think it should be all that difficult to work around,
    > >>>>>>> but I'm not sure what the best approach would be. Assume we
    > >>>>>>> get to a point where the cumulative time difference is, let's
    > >>>>>>> say, 60 seconds (that shouldn't happen for decades, so this
    > >>>>>>> is just for the sake of argument). Should we treat the
    > >>>>>>> difference as a 60 second clock correction before working the
    > >>>>>>> sights? Or should it be a 15 minute of arc longitude
    > >>>>>>> correction after working the sights? Or something else
    > >>>>>>> entirely?? -FER Celestial Navigation Weekend, June 6-8, 2008
    > >>>>>>> at Mystic Seaport Museum:www.fer3.com/Mystic2008
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