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    Re: Navigation without Leap Seconds
    From: Fred Hebard
    Date: 2008 Apr 15, 19:59 -0400

    by knowing where those are with relation to the earth
    On Apr 15, 2008, at 7:50 PM, Gary J. LaPook wrote:
    > 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 90�  
    > 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  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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