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Tahanea problem
From: Mal Misuraca
Date: 1997 Dec 17, 8:03 AM
From: Mal Misuraca
Date: 1997 Dec 17, 8:03 AM
The solution: Looking in the back of the Nautical Almanac, you see a list of 273 stars with their sidereal hour angles and declinations month by month for 1997. It occurs to you that one of those stars may pass directly overhead or very close to Tahanea. If it is a prominent star, and one that passes overhead the island during your nighttime, there will be a specific moment in GMT when the star will be directly overhead the island and therefore will serve as a beacon directing you to the island. Figure out which star, and when it is over the island, and point the boat at the star at that instant, and you are on course for the island. Congratulations to Richard Stofer and Paul Hirose, who figured this out and named the brightest star in the winter sky, Sirius, as the likely candidate. Sirius passes just about seven miles north of Tahanea every night in winter time. Sirius cannot very easily be missed, both because of its intrinsic brightness (-1.6 mag) and because it lies very close to the winter constellation Orion, known to us all. Both Richard and Paul got the steps right. First, pick the star that seems to do the job---by looking for a star whose N or S declination matches or nearly matches the landfall you're looking for. Next, determine the time of sunrise and sunset at your DR (daily pages adjusted for arc to time). Next, determine when the star will be overhead the landfall (GHAA + SHA = GHA star = geographical position). In this case, Sirius is overhead Tahanea, actually a few miles north, at 12:10:06 GMT on November 24 and about 3 min 56.4 sec earlier each night thereafter. Point the boat at Tahanea at 12:10:06 on November 24, and you have a bearing to the island. Make a rough estimate how many degrees Sirius lies from your own zenith (zenith distance) at that moment, and at 60 nm per degree, estimate your distance from the island. You now have a heading from your compass and a rough distance to the island. Repeat each night at the appropriate time. Paul makes the good point that as the island draws near to your zenith, taking a bearing on it proves more and more challenging, as anyone who has tried to take very high altitude sights of the sun will attest. Thus, a bearing from about 600 nm out, when the island is 80 deg above the horizon, is the final bearing for heading. As it happens, Sirius lines up with Procyon to set a course to Tahanea. Procyon is another very bright star in the same area of the sky as Orion and Sirius. Thus, in this case you could put Procyon directly at your back, Sirius dead ahead, and your heading to Tahanea would be confirmed. Neither Richard nor Paul mentioned the extra hazards of the approach to the Pallisers and Tahanea, and you would certainly want to take those into account. This is a series of very low-lying reefed islets, hardly to be seen from a long way off. Contrast this problem, for example, with emergency navigating to, say, Oahu. The star Kornephoros, or Beta Hercules, passes directly overhead Kaneohe Bay on the windward side of that island in the summertime. Oahu, like the rest of the Hawaiian Islands, is a tall island and should give fair warning as we close on it, very much unlike Tahanea. There are islands close to Tahanea, adding to the hazard. We would therefore keep the closest watch for the island and attempt to make landfall during daylight hours, perhaps even heaving to in order to assure ourselves of not running up on a reef. We might even decide to go on to Tahiti, if we don't need our friend's water casks that much. What star might we use for that purpose? Is there any other method we might use during daylight hours to help us find Tahanea in November? More about this in about a week. Mal Misuraca Passage East Sausalito =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=--=-= =-= TO UNSUBSCRIBE, send this message to majordomo@ronin.com: =-= =-= navigation =-= =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=--=-=