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    Re: Navigation without Leap Seconds
    From: Lu Abel
    Date: 2008 Apr 15, 09:54 -0700

    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.
    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, frankreed@HistoricalAtlas.net wrote:
    >>>> The fascinating article which Fred Hebard linked:
    >>>>  http://www.physicstoday.org/vol-59/iss-3/p10.html
    >>>> includes 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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