# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

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Tahanea problem
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

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,

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

Mal Misuraca
Passage East
Sausalito

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