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--- Anabasis  wrote:

> Your methodology is very strange to me for the sunset numbers, and 
> gives you the wrong answers. 

Aha... I found the problem late last night, but didn't have time to
post it until this morning. This one's a little bizarre, and maybe only
peripherally related to the fact that we're working with E longitudes
here.

Going back to my original post, my calculations for SS/CT/NT are still
valid:

  SS: 18:18 Z
  CT: 18:41 Z
  NT: 19:08 Z

The error came when I applied the arc-to-time conversion (9h 41m,
rounding down and discarding the seconds) to change from Z/UT time to
local time:

  SS: 18:18 - 9:41 = 8:37
  CT: 18:41 - 9:41 = 9:00
  NT: 19:08 - 9:41 = 9:27

In my haste of working through this problem yesterday (and I got
interrupted a couple of times while in the middle of it), I took those
times as PM vs. AM - probably because they look "reasonable" for when
SS/CT/NT occurs at my location lately (and that would also explain the
2-hour difference between your calculations and mine - the wrong turn
with the conversion to 24 hours inadvertently added 2 hours to my
calculations).

But in 20/20 hindsight, if I had used 2 digits for the hours (like
we're taught to do, and like I would normally do for things like
sextant readings, time, etc.) the problem wouldn't have happened (d'oh,
haste makes waste and all that):

  SS: 18:18 Z - 09:41 = 08:37 Z
  CT: 18:41 Z - 09:41 = 09:00 Z
  NT: 19:08 Z - 09:41 = 09:27 Z

Now converting UT/Z times to local (i.e. using ZD "in reverse):

  SS: 08:37 Z + 10:00 = 18:37 (Local)
  CT: 09:00 Z + 10:00 = 19:00 (Local)
  NT: 09:27 Z + 10:00 = 19:27 (Local)

which agrees with your calculations within a minute (probably because I
rounded up from the 32 seconds).

Now using the correct time for CT (still nicely on a whole hour of
time, so we can just read the GHA value off the NT daily page), I get
0deg 34.7' and from that point on our calculations agree.

So, the last remaining mystery would be why Navigator agreed with my
calculations. Easy... since I used the UT for CT that I had derived
earlier (off by 2 hours from reality, as is now evident), of course the
computer would agree with my manual calculations for that time (garbage
in, garbage out, and all that...  ;-)). 

And if I'd bothered to calculate the SS/CT/NT times with Navigator that
would have raised a red flag because it wouldn't have agreed with mine
(and I think I'll check that and all of the other underlying data next
time I use the computer to check my manual work).

BTW, for me it's a lot easier/faster/straightforward to work problems
like this one involving time conversions from UT to local (SS/CT/NT,
LAN, etc.) by just doing the arc-to-time conversion on UT, then
converting to local time with the ZD. That way I don't have to worry
about where the nearest time zone meridian and "which way" I am from it
(i.e. do I add or subtract the correction?). 

But it also helps if the underlying calculations for the event are
valid first - bet I don't make that mistake again...  ;-)

--
GregR










 
> -JCA Oh boy Greg, this is going to take a bit of writing.  Your
> methodology is very strange to me for the sunset numbers, and gives
> you the wrong answers.  I will try to work my way through it and
> explain my methods.
> 
> Using the handy Arc to Time converter in the NA, 145deg 22' E yields
> a
> time correction of 09h 41m 28s.
> -----------------------
> -JCA  We agree thus far.
> -----------------------
> Interpolating the Sunset, Civil Twilight, and Nautical Twilight times
> for N 10deg and N 20deg latitude for the 3-day period including 7 May
> 2008 (at Greenwich):
>   SS: 18:18 Z
>   CT: 18:41 Z
>   NT: 19:08 Z
> ----------------------
> -JCA.  I got 1907 for NT, but I�m not going to quibble.  What is
> wrong
> is that this is the Time in LAT which must be converted to ZT before
> use.  These times are only good on the Zone reference meridians,
> including Greenwich (divisible evenly by 15).
> ----------------------
> Applying the Arc-to-Time correction to get local time:
>   SS: 20:37 (Local)
>   CT: 21:00 (Local)
>   NT: 21:27 (Local)
> ----------------------
> -JCA  Here is where we get really different.  The correction from LAT
> to ZT should be fairly small (<1 hr) if we are keeping the correct
> zone description.  Sunset should not jump 2 hours between LAT and ZT.
>   There are 2 methods to do this, apply the arc to time of the whole
> longitude to bring the time back to UTC and then apply the reverse
> zone description to find zone time; or 2), find the difference in
> Longitude (Dlo) between the DR Longitude and the reference Longitude.
> The trouble with the second is that you have to apply the correction
> in the correct direction which can be confusing, especially if you
> are
> in East Longitude and are from the Western Hemisphere.  I prefer
> using
> the whole arc to time of Longitude to get GMT (which will be used to
> get the GHA Aries later).
> 
> So we apply the -9h 41m 28s to each to get the following UTC times.
> We know that we are ahead of UTC in East Longitude, so we subtract
> this number:
> SS: 08h 36m 32s Z
> CT: 08h 59m 32s Z
> NT: 09h 25m 32s Z
> Add 10 hours for ZD and you get the following local ZT:
> SS: 18h 36m 32s L
> CT: 18h 59m 32s L
> NT: 19h 25m 32s L
>  ------------------
> And applying the ZD-10 correction to get Z time for this location:
>   SS: 10:37 Z
>   CT: 11:00 Z
>   NT: 11:27 Z
> Now we need to calculate LHA Aries for the time we're going to be
> doing
> the star sights. Since the time for Civil Twilight falls neatly on an
> exact hour, we can just look up GHA Aries from the NA daily page (and
> don't have to do the correction for minutes/seconds)
>   GHA Aries: 30deg 39.6'
> --------------------------
> -JCA The method is sound, the math is obviously incorrect.  I too
> chose 1900L (0900 UTC) as my star time, but I got a nice easy GHA of
> Aries of 000deg 34.7�.
> --------------------------
> Using an AP of 14deg N / 145deg 20.4' E, we add GHA Aries to our
> Assumed Longitude to get:
>   LHA Aries: 176deg
> -------------------------
> -JCA  I got 146 degrees since we add 22� longitude to 34.7� GHA
to
> get
> 56.7 which is close to 60, and we carry the one to 145 to equal 146.
> --------------------------------
> Now using Pub 249 Vol. 1 (Epoch 2005.0), for Latitude 14deg N and LHA
> Aries 176deg we get this list of stars to shoot (ALL CAPS = first
> magnitude stars, [x] =  stars suitable for a 3-star fix):
>   Star      Hc         Zn
>   ------------------------
>   Dubhe     41deg 44'  354   [x]
>   ARCTURUS  53deg 19'  077
>   SPICA     54deg 24'  134   [x]
>   ACRUX     12deg 25'  175
>   Suhail    22deg 25'  210
>   PROCYON   29deg 16'  268   [x]
>   POLLUX    33deg 10'  295
> --------------------------------------------
> 
> -JCA  I also use Pub 249 Vol 1 but Epoch 2010 (available online).
> Obviously since my LHA is different from yours, there will be
> slightly
> different results:
> 1)    Dubhe  40deg 10� @012 deg
> 2)    Arcturus 24 deg 59� @075 deg
> 3)    Spica 29deg 32� @112 deg
> 4)    Suhail 31deg 57� @ 188 deg
> 5)    Sirius 36deg 18� @ 237 deg
> 6)    Betelgeuse 33deg 39� @ 270 deg
> 7)    Capella 26deg 11� @ 315 deg
> ------------------------
> There's also a correction for precession and nutation of 03' / 110deg
> T
> to be applied to the LOPs and/or fix.
> -------------------------
> -JCA.  This is correct, but not necessary for precalculation as we
> only need an approximate Hs and Zn to find the body.  Also, I was
> taught to only apply this correction in off-epoch years to the actual
> fix instead of the LOP�s (unless there is just one LOP of course).
> The point of pre-calculating stars at sea is so that you can go out
> and just point the sextant in the correct Azimuth, then the star just
> pops into view.  A tiny adjustment on the micrometer drum and you
> take
> your sight.  I can shoot a round of stars in under 10 minutes, and am
> just usually waiting for the dimmer ones to appear.  For this round,
> I
> shot 5 bodies in just over 7 minutes.
> JCA
> 
> > 
> 


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