NavList:

   

Reply

(I sent this last night but it never showed up.)

-----------------------------------------------------------------------

I posted this stuff before.


One thing you can use a calculator for is computing the GHA of Aries.
All you need to write down, or, memorize, is three numbers. First, the
rate that Aries advances each day which is 59.139 minutes each day.
Second, the rate of advance each hour which is 15.041 degrees per hour.
The third number you need is the GHA of Aries at 0000Z on the 31st of
December from the prior year which is, for right now, 99° 33.4'. Knowing
these three numbers makes it easy to calculate the GHA of Aries for any
time during the year.

The first step is to determine how many days have passed since December
31st and this is easy since it is merely the number of the day in the
present year. January 1st is one day later, etc. Just add up all the
days in the months preceding the current month and then add the date of
the current month. "Thirty days hath September, April......" If you
haven't noticed it before, there is a pattern to the calendar, long
months alternate with short months with the one exception that two long
months are adjacent, July and August.

So just add up all the days and multiply by 59.139 minutes per day. If
you add this to the starting GHA on December 31st you would have the GHA
for 0000Z on the current day but it is easier if we wait until the end
of the computation to add in the starting value.

The next step is to multiply the time since 0000Z today. If you are
using a calculator with Degree, Minute and Second input simply put in
Hours, Minutes and Seconds, convert to decimal format and multiply by
15.041 degrees per hour. Add this to the result of the first step and to
the December 31st GHA and you have the value for the current time.


You can also do this computation by hand but it is tedious and you have
to be very careful doing the long hand multiplication but it does work
without electrons.

The first step is the same as above, calculate the change for the days
as in the first step in the first example.

So the next step is to calculate the change for each whole hour at the
rate of 15.041° per hour which is the same as 15° 02.46' per hour. This
is also the same as 902.46 minutes per hour, so multiply the whole
number of hours by 902.46' per hour and write the result under the
result from the first step. (902.46 is 15 times 60 plus 2.46.) It's easy
to remember, 90 plus 2-4-6.

It is quite a bit easier, if doing the computation by hand, to
convert the minutes and seconds of time to decimal hours, add them to
the whole hours and then multiply by 902.46. You do this conversion in
two steps, divide the seconds by 60 to get decimal minutes which you add
to the whole minutes. Then divide the minutes and decimals by 60 again
to get decimal hours which are added to the whole hours and the result
multiplied by 902.46'.

It takes about 7 minutes doing the long hand multiplication. It's a lot
faster with a calculator.

If you also memorize the coordinates of about ten well chosen stars then
you can do celnav without an almanac, completely from memory.

I wanted stars well arrayed in SHA, bright, and mostly at low declinations so 
they could be used from both hemispheres.

I settled on

Fomalhaut;
Altair;
Vega;
Antares;
Spica;
Regulus;
Pollux;
Sirius;
Capella;
Schedar.

All are first magnitude except Schedar which is 2nd magnitude but was the best 
I could find to fill in the gap in SHAs. The furthest south is Fomalhaut at 
29 south so it is visible in most of the northern hemisphere. Only Capella 
and Schedar are difficult to see from far southern latitudes.


I checked my selection of stars by use of the 2102-D and in the northern 
hemisphere there are never fewer than three of these stars above the horizon 
and usually 5 to 7. In the southern hemisphere, south of 55 south, there are 
occasions when only 2 stars are above the horizon, but usually more, even 
that far south. North of 55 south there are at least 3 stars up and usually 
more,

You can
figure the dip correction in your head as simply the square root of the
height of eye in feet, and the refraction correction is also easy to
remember, 5 above 10° ;  4' above 12° ; 3' above 16° ; 2' above 21° ; 1'
above 33° and 0' above 63°. Now just add a Bygrave, a sextant and a
watch and you can navigate without any electrons or books.

gl

--------------------------------------------
On Thu, 6/12/14, Peter Monta  wrote:

Subject: [NavList] Re: Longhand Sight Reduction
To: garylapook@pacbell.net
Date: Thursday, June 12, 2014, 2:16 PM

Hi
Hanno,

The
multiplications show each partial product separately in the
array.  It's less compact than the usual method, but
somehow I find it more reliable to add up everything at the
end.  It's essentially the lattice method:
...

So no-table sight reduction seems
tractable.  The other part of this is the almanac, and here
we really have to memorize a few numbers.  The minimal set
might be something like (ra,dec){at}J2000 of half a dozen
bright stars plus the expression for sidereal time at
Greenwich (including an estimate of the current delta-T). 
The Sun seems a bit too complicated to memorize to any
usable accuracy, let alone the Moon and planets; but any of
these bodies could be used as "transfer standards"
by measuring them against the stars.





Here are my assumptions, which are of
course pretty absurd:

- available: sextant; chronometer showing
UTC; pencil and paper
- not
available: tables or any other computational aid; almanac




- known: micro-almanac of a few stars; sight reduction
algorithm

Hanno,
just read your reply:  yes, exactly, Napier's bones. 
The desert-island guy might well want to make a set.


Cheers,
Peter

   

Reply