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    Re: Navigation without Leap Seconds
    From: Gary LaPook
    Date: 2008 Apr 15, 16:50 -0700
    Gary LaPook writes:

    OK, so you end up with a position defined by the lat-long of the spot on the surface of the earth directly between the spacecraft and the center of the earth (the spot that the spacecraft is directly above and where a person on the surface would measure 90º with his sextant to the spacecraft) and the radar distance. But is this useful for space navigation? how do you relate this to an inertial frame or sidereal frame or to determine if you are on course to the moon or mars?

    gl

    Fred Hebard wrote:
    Yes, it does.  One gathers elevation information with radar ranging;
    it's the same problem, you're just at a different elevation, so
    there's a larger (!) dip correction.  It was the method proposed by
    Weems, et al, in the delightful book, "Space Navigation Handbook,"
    Navpers92988,  US Govt Printing Office: 1962 0-628762.
    
    
    On Apr 15, 2008, at 7:27 PM, glapook@pacbell.net wrote:
      
    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.
    
    gl
    
    On Apr 15, 2:12 pm, Fred Hebard <F...@acf.org> 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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