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    Re: Navigation without Leap Seconds
    From: Frank Reed
    Date: 2008 Apr 18, 02:20 -0400

    Fred, you wrote:
    "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."
    The assumption they mentioned is the "geoid" which is a complicated surface
    of contant gravitational potential. So we're well beyond the ellipsoid
    already when it comes to extremely precise measurements.
    "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?"
    Stars? No. Much too far away. We need much closer objects whose positions
    would shift noticeably relative to the distant starry background. So why
    don't we launch some fake stars into orbit close to the Earth? And since
    timings are easier to measure than angles, we'll put some transmitters on
    our fake stars. As I'm sure you've recognized, this is just the GPS system.
    But it wasn't designed for that next level of accuracy, a couple of orders
    of magnitude higher, required by the next generation of atomic clocks.
    That's the trouble. Necessity is the mother of invention, and I'm sure
    someone will invent a solution, especially if anyone can think of a
    practical application of these super-clocks. It may be the case, though,
    that the business of ever more accurate time measurement has hit a brick
    wall with no means of comparing clocks at different locations which may last
    for a few decades conceivably.
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