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    Re: Longitude by star clock
    From: Duane Smith
    Date: 2021 Aug 28, 12:52 -0700

    [NOTE from FER: I am passing this message from D. Smith through primarily for its entertainment value. It's been a quiet August, and it may provide some levity. Please do not reply, or if you do, please reply judiciously. Please do not quote back the entire lengthy message. If you're replying by email be sure to turn off the autoquote on any reply you may make. Believe it or not, the original message was longer still. I removed a few sections at the end, as marked]

    Yes as was pointed out I have posted on this forum before. It was some time ago, honestly I forgot which forum I had posted on. And thank you to Frank Reeds for making the previous conversations easily available. Recommended that you have a look at them to get some idea of the very basic concept and then come back here. See Frank Reeds post for Aug 19th. Those were admittedly somewhat poor descriptions of something I was just beginning to fully understand and work out the math on. I had just begun to explore this method and was thinking and working only in terms of time. The method has now been developed to include measuring by degrees. Knowing how sidereal time works makes the math very straightforward and easy. If you catch a star exactly on your meridian, upper branch, then exactly 24 sidereal hours later that star will again be exactly on your meridian. Now let's look at the meridian. If a plumb bob, piece of string with a weight attached to one end, is held up against Polaris, is that not a longitude line projected onto the sky? The weight on the string hangs towards the center of the earth, does it not? Polaris is rather close to the celestial pole is it not? If I am lined up with the string and the north celestial pole and the center of the earth, then must also be lined up with the Earth's north and south poles, looks like a longitude line to me.
    After posting the first description of this method, by the few responses I saw, it was clear those who read the description did not read with the intent to understand, but only to respond. So I was not sure if I ever wanted to try sharing this method with the world again. Before making bold claims in front of the world, I need to be sure I have all of the facts straight and math in order. My hopes were that Real navigators would easily understand the basic concept of the star clock. So far I am sadly disappointed. If you don't agree with my description of the longitude line, consider leaving now, this method is not for you. If you are Afraid to walk boldly into the unknown and maybe learn something you never knew before, you know where the door is, right? This will likely be a long post and most likely be the last post I will ever make on this forum. Does the fact that I'm selling my sextant and sight reduction tables mean nothing to a celestial navigator? With the star clock method, I don't need them. Is your thinking so stuck in traditional cel nav that you cannot get out of the confines of your sextant box? Is that the ONLY way to do accurate position finding with celestial? Or is it the only way you know and you don't want to consider anything else? If so you should not still be reading this.
    If you think maybe my math may be faulty and would like to prove it wrong? Fine, bring it on. IF, you do manage to prove the math I'm using to be wrong, it will also prove the math that is being used by by planetarium and navigation apps in many devices around the world to be wrong. And also the math that is used by the U S naval observatory, math used by navigators past and present, sight reduction tables and even the nautical almanac to be WRONG!...*.*.*.*.. Oh!..*.*.*.* .. Good job! Now crawl back into your sextant box and close the lid and don't you come out again, until you are ready to see the stars at Night. Yeah, All Night.
    There are planetarium apps that will draw a nice straight meridian line right through the North Celestial Pole to the north horizon. It looks a lot like the plumb bob example mentioned earlier. This is mentioned again for a very good reason. If you are still having trouble with this concept, the rest of this will likely be meaningless to you.
    If the impression is coming across that I find narrow minded thinking counterproductive, aggravating, and limiting, you're right.
    It's time to get serious about this, perhaps this will help to understand why most navigators will immediately have doubts, suspicions, criticisms, and will so quickly and casually dismiss this method as meaningless. GOOD!
    I have no desire to answer 673,489,723.7131589 emails on this subject.
    Now, the legal stuff, limitations, exclusions, disclaimers etc. You probably won't find this in books about cel nav, or on the internet, or being taught in any naval academy or online courses. I have looked through my paper back copy of Bowditch and found no mention of this method. The cel nav books that got me started in the 1980s made no mention of this. This is for Northern hemisphere only. Has Not been tested and approved by the celestial navigation community at large, maritime or international law. At higher northern latitudes this method will be increasingly difficult. Don't try to hold me accountable or responsible for any of this in any way. A sextant in it's current form will not work for this. Calm down, take it easy, we will get through this. This method is NOT a replacement for traditional, altitude intercept. It stands on it's own, can be used in addition to other methods. Or tossed aside as a silly trinket.
    Were you not warned this method is going places that, Real, wannabe, hope to be, think you are, oh so experienced professional navigators have likely Never been?
    With so much already against the method, how could it possibly work.
    If anyone is still reading this, RUN! Quick! It only gets worse from here. Much worse.
    Maybe it takes a landlubber that has never used celestial navigation to go from one place to another, to push aside the burdens of tradition and go direct to the source.

    THE STAR CLOCK Created and set in place by almighty God. This clock has been keeping Very Good time since time began.
    I see God as the author, I am just the paperboy trying to deliver the news.

    May I be so bold as to point out a few things about the altitude intercept method that I learned way back in the 1980s that bothered me then and still do now? First, the position the navigator is trying to pin down accurately. I do understand DR position is a best guess based on various information gathered along the way. So when a sextant is used to measure the altitude of a star, is that measurement taken exactly at the DR position? Probably not. Once the sights are taken and the plotting begins an Assumed Position appears on the plotting sheet at a different location than the DR. Sometimes a couple of miles or so? Yes I understand the why and wherefore of that. But is that the exact position where the sights were taken? Again, most likely not. And sometimes an Estimated Position makes an appearance, is that where?.... No. So a navigator is faced with starting from a somewhat ambiguous position.
    Perhaps using the longitude of the observer to measure from may have some advantage. No previous or guesstimated position is needed. Yes, it sounds like oxymoronic idiocy, I'm going to use my longitude to find out what longitude I'm on. Makes no sense, can't possibly work. Big surprise, it works very well, I have been using my longitude to measure from for several months.
    ACCURACY? Measuring with straight edge and angle meter in degrees is probably the easiest. Measuring the angle to the nearest whole degree will give longitudes Less than about half a degree of longitude, from the True position or approximately 25 nautical miles. Measuring to the nearest Tenth of a degree, which is quite possible, will give a longitude Less than 10 nautical miles from the point the measurement is taken. And it's the, Less Than, that is sometimes quite interesting. How about less than 500 ft? Or less than 200 ft? Of course you will need to know your accurate position to know how far East or West the resulting longitude is. At 45 degrees latitude an error of one minute of time, will push the resulting longitude off from perfect by 6.36 nautical miles. At least according to my calculations. Also if there is a DR, GPS or some such it's easy to see how well the resulting longitude fits with what you have.
    On the other end is the altitude and intercept. What are you doing with that sextant? Reaching over the horizon trying to accurately pin down a fast moving target that you cannot even see. What wizardry is that? How fast is the Earth's surface carrying you along at your current latitude? One degree of longitude in four minutes. Is that the Coriolis effect thing?
    Which brings up the whole big point of why I'm going on about this subject in this way. It seems previous readers have totally missed the abstract concept of an imaginary, theoretical, hypothetical, fictitious, invisible, clock face or at least circle on the actual, real sky. We are measuring angles on a circle with Polaris at the center, close enough for me.
    With the star clock there is no need to reach over the horizon and chase imaginary butterflies. Does it make sense that measuring the altitude of a star is an attempt to pin down an imaginary, fictitious, invisible, theoretical, hypothetical, fast moving point? The GP of the celestial target.

    When I pulled that fictitious, imaginary, invisible, theoretical, abstract altitude circle up off the earth and put it up in the stars, where it belongs, things suddenly got Very easy. Some increments and corrections fell off. No sextant, no index corrections. Not using horizon, atmospheric refraction ? Haven't noticed any effect. Height of eye (altitude?), I live at an altitude of a bit more than 6,000 feet ASL. Altitude is NOT a factor. We are dealing only with stars, so All times are Sidereal. Time corrections needed ? The altitude circle becomes the declination circle the star appears to make as the earth turns. The azimuth line is from Polaris to the selected star. This is the line you want to define with the straight edge and smartphone. Remember, _ the zero point must be directly vertical above the pivot point.
    So we can let gravity help define the vertical line. It's always there, works every time, don't have to pay a monthly fee to keep it turned on just for you, right? Another of God's creations.
    Perhaps pictures will help, I'll try to send some.
    I hope at least there is a twinkling of understanding by now.
    Very basically the method works like this; Read the clock, Measure the angle, Get longitude.
    If it seems like I'm making fun of the tried and true altitude method, Marcq St Hilaire, etc. Perhaps I am a little bit. The aim was to point out a couple of significant differences between the two methods. It's just that the star clock is so much faster and easier. The intercept method has a major advantage, has been tested and proven and used by many people all over the world. By comparison, in my estimate, the overall usefulness of the star clock may be less than half that of the altitude intercept method.
    This is an abstract concept that has been in the faces of many people for a very long time. Think of all the drawings, diagrams and illustrations we have looked at while learning cel nav. Think of a polar plot showing how various angles are measured: GHA Aries, LHA body, GHA observer, LHA observer, SHA of star, SHA of potato soup, bearing angle, GAST, Stacked Higher than toast etc. Curved arrows pointing in clockwise and counterclockwise directions. I wonder If or How such a concept could be used in a real world application? If anyone out there is still having difficulty grasping this. They should retreat to the safety of the sextant box, build walls of books that are filled with rows and columns of numbers. And at the gate, set the most terrifying guard of all..**.. spherical trigonometry!
    Since about 1950 precession has been pushing the NCP closer than one degree to Polaris. Now, Polaris is close enough to be used, with a fair amount of accuracy, as a reference for both longitude and pivot point. By using Polaris for observer's longitude reference to measure from, that part becomes a known point. Then using Polaris as the pivot point to measure the angle to a convenient star such as; Dubhe, Kochab, Alioth , Schedar, Alderamin, the observer directly Sees Both points that are being used.
    Does this make sense? ? Wait a minute, is this something like plotting sextant sights? Simply use the ready made plot on the sky, use two points to get an angle, do a bit of math and get a longitude that may well be useful?
    Measure the angle of the selected star, then combine this with the Right Ascension, RA, of the selected star to get LST\LHA Aries. Then combine LST\LHA Aries with GST\GHA Aries in the proper way to get longitude. That is basically how the math works. This method can be used to get a visual, naked eye guesstimate of a star's angular position that SOME times yields a longitude that's less than 5 nautical miles from the observing position.
    Does anyone still reading this think that, I, a landlubber would present this to the entire world, without knowing for sure that it will indeed stand up to all the scrutiny the world can throw at it?
    As for the sextant and sight reduction tables they are from the 1980s purchased from Celestaire. All in good, seldom used condition. The sextant is a metal Astra III, made in China. I see Celestaire has the modern equivalent priced close to a thousand dollars. Shall we start the bidding for mine at say [DELETED. No, not here. If you want to sell it, post it on ebay. You're welcome to post a link to the ebay auction after you list it.... As for the 229/249 tables, they are worth nothing] ...pretty sure that's less than I paid for it. Could at least make a nice backup or practice sextant. For the tables I have, volumes 2,3,4 of ho 229, and volumes 1,2,3 of ho 249, make an offer. I'm a landlubber and it's very unlikely I will ever need or use them.
    Example using degrees.
    With the Right Ascension -RA- of the star converted to degrees. And the angle measured COUNTER clockwise in degrees. ADD these together to get LHA Aries in degrees. If the result is more than 360 degrees, subtract 360, no more no less. If the angle is measured CLOCKwise, this is to be SUBTRACTED from RA.
    NOTE: WESTern hemisphere. If GHA Aries is less than LHA Aries, add 360 to GHA Aries, no more, no less. Now subtract LHA Aries from GHA Aries to get longitude.
    EASTern hemisphere. If LHA Aries is less than GHA Aries, add 360 to LHA Aries, no more no less. Now subtract GHA Aries from LHA Aries to get longitude.
    See below for a copy of what I posted about a year ago [DELETED. Your post from a year ago is in the archives, and I already provided a link to it in a message last week]. The math for time or degrees is pretty much the same as far as the steps to take.
    The photo of the basic time to arc conversion tool shows Dubhe just past 12 hours and 40 minutes and Altais at about 4 hours and 40 minutes. The photo of the circular protractor with the added index arm shows Mucida at 131 degrees Clockwise angle. In practice these tools are somewhat difficult to use, they work well enough but require calm conditions and steady platform. The string is a lubber line for vertical reference while holding tool perpendicular to the line of sight to Polaris. A small weight slides freely along the length of the string to act as plumb bob. The photo of various angle tools shows a cell phone on an "index arm". The index arm has an eye bolt attached perpendicular to the arm. Aiming the eye bolt at Polaris keeps the index arm perpendicular to the line of sight to Polaris. Very important for accurate measurement. Angle meters like the orange Klein are easily available on Amazon for less than 50 dollars. In practice angle meter and index arm I think would have a chance of being more useful in real world conditions. So with adding modern technology to rearrange the sextant, index error came back. Whatever digital meter you choose, learn the calibration procedure. Maybe one could aim the index arm directly at Polaris and get something of a latitude?

    As can be seen, this basic concept has been out there for a year. Yes perhaps poorly explained, but with pictures, does anyone SEE it now?

    I will gladly answer further questions of those who are genuinely interested. Photos and further information on the above are available.
    Hoping you all have good skies and smooth travel.
    Duane Smith, USA

       
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