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    Re: Friendly challenge : Jupiter Lunar Exercise 09 Feb 2011
    From: Harri Ojanen
    Date: 2011 Feb 22, 22:02 -0800

    Re: http://www.fer3.com/arc/m2.aspx?i=115625
    ”Friendly challenge: Jupiter Lunar Exercise 09 Feb 2011” from antoine.m.couette---fr

    Hello Antoine,

    Here's yet one more solution to your very interesting first problem:

    Since the extra information provided about the location was quite vague (intentionally), I started with a more "global" view. This also seemed like a fun place to take advantage of the parallactic angle of the nautical triangle (but this requires using some computing power for plotting the circles of equal altitude):

    Step 1:

    So start by taking the sets of three altitude sights, average the five repeated sights, and reduce to obtain observed altitudes. Then plot the corresponding circles of position, using the approximate watch error as given in the original description (the circles are computed by using the spherical triangle cosine rule as a function of the parallactic angle). This shows a fix somewhere near 46.6°N 1.5°E, which is inland France. Ok so far, since the exact time is not yet known.

    Step 2:

    Use this point 46.6°N 1.5°E as an AP in computing a watch correction with the Jupiter-Moon distance. I used the formulas for lunar distance based on spherical triangle cosine rule as described e.g. in John Karl's book.

    At least the latitude is probably reasonably close so that the lunar distance gives meaningful results. The calculation indicates a watch error of 917s to be added to the original estimate.

    Step 3:

    So increase the clock correction by 917s, and again compute the circles of position. Now the fix has moved, from the plot it's estimated (visually) at 46.7°N, 2.5°W

    Step 4:

    Use the found intermediate position 46.7°N 2.5°W as an AP (and the 917s as the additional watch correction) in a standard St Hilaire calculation. It gives a fix at 46°42.8'N 002°27.8'W. Repeating the lunar time calculation with the sama data gives 0s as the watch error, which suggests the 917s is sufficient.

    Thus arriving at fix 46°42.8'N 002°27.8'W
    Additional watch correction 917s = 15min 17s
    Total watch correction: 15h 45m 00s + 15m 17s = 16h 00m 17s

    I have created a pdf file that has some plots that should explain the above steps, but apparently I'm not allowed to attach it to the message (this is my first post to Navlist - maybe it will work out later...).

    Thanks for this challenge, it was most interesting and fun to work out!

    Harri Ojanen

    PS. I'm located in Finland at roughly 60N 25E. We have currently about -20 degrees Celsius and a lot of snow. The Baltic is frozen from coast to coast. Seems still like a long way to Spring.

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