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    Re: About Lunars, part 4
    From: George Huxtable
    Date: 2002 Mar 21, 00:29 +0000

    I have received a message directly, off-list, from Chuck Griffiths, and
    presume that he would wish it to be posted up. Here it is, with a response
    from me.
    
    ==========================Envelope-to: george---.u-net.com
    From: 
    MIME-Version: 1.0
    Date: Wed, 20 Mar 2002 08:08:18 -0500
    Subject: Fwd:Re[2]: About Lunars, part 4
    To: george---.u-net.com
    
    George,
    
    I posted this to the list last night but it looks like the server is having a
    little trouble keeping up again. I'm most interested to hear your thoughts on
    correcting for Venus' parallax as you had me convinced that Letcher ignores the
    parallax of the other body because it's negligible.
    
    Chuck
    
    ____________________Forward Header_____________________
    Subject:    Re[2]: About Lunars, part 4
    Author: Chuck Griffiths
    Date:       3/19/02 8:46 PM
    
    I guess I should have thought to include more information. Here we go:
    
    Height of eye was about 10 feet, I used -3.1 for dip.
    
    Almanac information:
    
    00:00:00 on 19 March
    Moon GHA 125-58.0, Dec N 15-55.3
    Venus GHA 163-28.7, Dec N 4-26.2
    
    01:00:00
    Moon GHA 140-30.3, Dec N 16-5.3
    Venus GHA 178-28.4, Dec N 4-27.5
    
    HP 55.1
    I didn't correct for Venus parallax, I thought that there wasn't a good way to
    work planet parallax into the Letcher method. For SD I used George's recommended
    method of calculating augmented SD from HP.
    
    Chuck
    
    =======================
    
    Copied below once again is Chuck's earlier mailing of 19 March, which
    contains the rest of the necessary information.
    
    =======================
    
    First, I have a set of observations from last night that I'm hoping you might
    have a look at George, and see if it looks like I'm still headed in the right
    direction. From approximately 27-42.0 N, 82-44.2 W I took a set of observation
    as follows:
    
    (All times GMT 19 March followed by altitudes Degree-Minutes)
    
    Venus 00:11:41 7-50.6
    Moon 00:12:48 44-52.6
    Venus 00:14:02 7-25
    Moon 00:14:02 45-25.6
    
    Lunar Distances
    00:14:59 37-43.4
    00:15:27 37-43.2
    00:16:01 37-43.0
    
    Venus 00:16:36 6-43
    Moon 00:17:31 43-51.6
    Venus 00:18:09 6-24
    Moon 00:19:09 43-30
    
    I roughly averaged the sights and used the following for my calculations:
    
    Venus 7-5.6
    Moon 44-12.5
    Distance between 37-43.2
    
    >From which I calculated:
    
    B .69733
    P 38.43635
    R 6.65151
    d 37.97333
    D 38.72479
    
    SD 15.1995
    HP 55.1
    
    D1 (00:00:00) 38.58036
    D2 (01:00:00) 39.03829
    
    T 00:18:55 v. real time of observation of 00:15:29
    
    So, based on the fact that the Moon was rather high and, by my observations, was
    moving at an apparent speed of about 24 arc minutes an hour can I assume that
    some of my error is due to "parallactic retardation"? Or, did I make some more
    basic mistake?
    
    ================================
    
    From George-
    
    If the apparent Moon was moving at 24 arc-minutes per hour and Chuck has
    measured GMT to within 3 minutes 26 sec of time, then he has measured the
    lunar distance within 1.4 minutes of arc, if all the calculations are
    correct (I haven't checked). An error of 3 minutes 26 sec in GMT would
    correspond to an error in longitude (at 15 deg per hour) of 51 arc-minutes.
    These are not bad values at all, especially for a first try at lunars, and
    singlehanded.
    
    One factor to check (I haven't done so) is to ensure that the average time
    of measurement of the Moon and Venus altitudes corresponds well with the
    average time for the Lunar distances.
    
    Parallactic retardation doesn't in itself cause errors, in that these
    effects are corrected for in the parallax calculations. But it does degrade
    the accuracy of the whole process (by up to a factor of 2 when the Moon is
    very high), which is not quite the same thing.
    
    I hope the information provided above is useful grist to Arthur Pearson,
    and to anyone else who might wish to have a go with Chuck Griffiths'
    observations.
    
    Above, Chuck said-
    
    "I'm most interested to hear your thoughts on correcting for Venus'
    parallax as you had me convinced that Letcher ignores the parallax of the
    other body because it's negligible."
    
    Well, if that's what I said, then it wasn't quite what I intended. Letcher
    ignores the parallax of the other body whether it's negligible or not. It
    is unable to take into account the horizontal parallax of the other-body,
    only that of the Moon. Or at least, I know of no way to get it to do so.
    It's a weakness of Letcher's method. But for bodies other than the Moon,
    the HP is usually small enough for the approximation to be acceptable.
    
    The Sun's HP is around 0.15 arc-minutes. I have checked the distance
    between the Earth and Venus at the date of Chuck's observation (19 March
    02) by pocket-calculator, and this is 1.6 AU (AU = Astronomical Unit: 1 AU
    being the mean distance between Earth and Sun).
    
    So the HP of Venus at that date is 0.15 / 1.6, or just less than 0.1
    arc-minute. This follows because Venus is away on the other side of the Sun
    from the Earth. This is fortunate because it implies that in those
    circumstances there will be no great error in using Letcher's method.
    
    However, when Venus is near perigee, its distance to the Earth can be as
    little as 0.25 AU, which would increase its HP to 0.15/0.25, or 0.6
    minutes, at which time Letcher's method could give serious errors. However,
    when Venus is closest to the Earth, it's also near the Sun in the sky, so
    Venus is quite invisible near perigee.
    
    Mars is another matter. Having a larger orbit than that of the Earth, when
    near perigee it is opposite to the Sun, so is highly visible. At perigee it
    can come within 0.4 AU of the Earth, so its HP can reach nearly 0.4
    arc-minutes.
    
    What this means is that users of Letcher's method, observing Mars or Venus
    at times anywhere near to perigee, should do so with their eyes open. The
    table on page 259 of the Nautical Almanac should be consulted, where the
    value of p will indicate the maximum error in lunar distance that can be
    caused by that Letcher approximation. The observer will at least be aware
    how big that error can be, although unable to allow for it using Letcher's
    method.
    
    For example, with Steven Wepster's Mars lunar, taken on 8 April 2001, the
    Earth-Mars distance happened to be .84 AU, so the HP of Mars would be 0.15
    / 0.84, or 0.18 arc-minutes. If Steven had used Letcher's method (which he
    didn't), he would have to take into account a possible error of up to .18
    arc-min (either way) because of the approximation. Most navigators would, I
    think, regard that as acceptable.
    
    For any other object in the sky, Jupiter, Saturn, or any star, parallax can
    be taken as zero.
    
    =======================
    
    A suggestion : any takers?
    
    For anyone that's really keen to squeeze out all the information that can
    be got from Chuck's observations, it can I think be taken a step further.
    Once the GMT is agreed, then dec and GHA for Moon and Venus at that time
    can be established (using interpolation, as we have two values from the
    Almanac, 1 hour apart, for each of these quantities). From this, the
    location of the observer can be deduced.
    
    For a first shot (as we have no idea yet where Chuck was observing from)
    the geographical positions of Moon and Venus at that time could be marked
    on a globe. Chuck's measured altitudes for these bodies should be corrected
    in the ordinary way (ie corrections as for altitudes, not corrections as
    for lunar distances), and then the corrected altitudes converted to zenith
    distance by taking the 90-degree complement. Now draw circles of that
    radius about the two GPs on the globe. These intersect in two places, so
    you have to guess which one is most likely. This paragraph could be
    bypassed if we had a rough idea of whereabouts Chuck lived, in advance.
    
    Having done that, choose an AP near or at one of those places, calculate
    altitudes and intercepts for Moon and Venus, and where they cross will be
    our best guess at where Chuck lives. If it has all gone right, you should
    get a position within 2 or 3 miles in latitude. In longitude, if you are
    within 30 minutes, that will be very good going.
    
    You will realise that the above procedure, in this section, really has
    nothing to do with lunars, except that it has used the GMT derived from a
    lunar, and has used the observations of altitude, as taken for a lunar, for
    a different purpose.
    
    If you used Letcher's method to calculate your lunars, than you will
    realise one disadvantage of that method. It bypassed the need to work out
    individual altitude corrections for the two bodies, so those will have to
    be calculated anew. With other methods, you will have done much of the work
    in finding the altitudes corrections already, in the process of correcting
    the lunar distance.
    
    I haven't tried working out these figures myself, but it seems to me that
    all the information should be there to establish where Chuck Griffiths
    lives, if not to the nearest block...
    
    George Huxtable.
    
    ------------------------------
    
    george---.u-net.com
    George Huxtable, 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    Tel. 01865 820222 or (int.) +44 1865 820222.
    ------------------------------
    
    
    

       
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