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Brad,
Longitude of a body refers to ecliptic coordinates.
The navigators describe the position of the body
by declination and hour angle (or right ascension).
This is called equatorial coordinate system.

In astronomy, it is useful to take ecliptic (instead of the equator)
as the principal circle, then we have the pole of the ecliptic
and two spherical coordinates with respect to this pole and this circle.
See, for example, Wikipedia on "Ecliptic coordinates".

Alex.

> Hello Herbert
>
> Thank you for renaming this thread!  The original title was a friendly
> gesture towards Lu and completely irrelevant to the topic.
>
> In support of your statement, I found an interesting page by the
> University
> of Cambridge, on ephemerides of the period in general and Regiomontanus in
> specific.  http://www.hps.cam.ac.uk/starry/tables.html
>
> You (and the article) mention longitude of a body.  That seems to have
> only
> one of the two coordinates needed for definition of spherical position.
> What do they mean and how does this work?
>
> Best Regards
> Brad
> On Oct 21, 2012 3:40 AM, <666---org> wrote:
>
>> Dear Apache Runner,
>>
>>  I am curious to know what tables you have looked at. The ephemerides of
>> Regiomontanus, like any other that I have seen from that period, do not
>> contain RA or Dec of anything. The longitude of the sun, moon and
>> planets is all you get, plus the longitude of the ascending node of the
>> moon. To obtain the declination of the sun, further computation and/or
>> auxiliary tables are required. Even Origanus, 100 years later, provides
>> only the latitude of the moon in addition to the above. Not exactly
>> seaman-friendly!
>>
>> Herbert Prinz
>>
>>
>> -------- Original Message --------
>> Subject: [NavList] Re: I couldn't resist!
>> From: Apache Runner 
>> Date: Fri, October 19, 2012 10:37 am
>> To: NavList@fer3.com
>>
>> I'm quite sure the ephemerides of that period were quite accurate at
>> that
>> level.   I have a colleague who has a collection of ephemerides from
>> Regiomontanus, Copernicus, and Kepler.   They're fascinating to look at.
>>
>> There are two pages, side by side.   One contains information like
>> declination and RA, and the other page has astrological information.
>> Evidently this was quite common.
>>
>> The construction of solar declination was probably accurate to about 20
>> arc-minutes or better.   I can get this from my colleague, but I tried
>> constructing a table using Ptolemy's method, and somewhat crudely and
>> got
>> to this level, so I'm quite sure that Dias had an ephemeris that was
>> accurate to about this level.
>>
>> I suspect more one of two plausible problems for Dias.   The Portuguese
>> in
>> that period had a modified astrolabe.   Rather than being filled up with
>> a
>> star finder and a projection of altitutde/azimuth coordinates, it had
>> four
>> cut-outs on it to limit wind buffeting.   Still, they got buffeted by
>> the
>> wind.
>>
>> I don't know offhand whether Dias went ashore to take the sighting, but
>> it's possible in my thinking that he might have taken it on ship-board,
>> and
>> the instrument got pushed around in the course of taking the shot, and
>> he
>> didn't notice this.   It was at a time when the techniques were still in
>> their infancy.
>>
>> On Fri, Oct 19, 2012 at 1:24 PM, Lu Abel  wrote:
>>
>>>  It would be interesting to know why Dias's measurement was off by such
>>> a large amount.
>>>
>>> As I understand it, one of the achievements of the Portuguese
>>> navigators
>>> (who were the best in the world in the 15th century) was development of
>>> a
>>> declination table for the sun allowing sun shots to be used for
>>> calculating
>>> latitude (especially important south of the Equator where there's no
>>> Polaris to shoot).
>>>
>>> So to what do we attribute Dias's error?   Was the declination table
>>> off?  Was his "noon" shot off?  Were his measurements mis-recorded?
>>> Or
>>> what?   I doubt that it was the crudeness of his instrument (astrolabe?
>>> staff?) because even the crudest instrument wouldn't be off by 10
>>> degrees.   Heck, I could measure up from the horizon by fist-widths and
>>> be
>>> off by less than 10 degrees!
>>>
>>>
>>>
>>>
>>>   ------------------------------
>>> *From:* Apache Runner 
>>> *To:* NavList@fer3.com
>>> *Sent:* Friday, October 19, 2012 9:26 AM
>>> *Subject:* [NavList] Re: I couldn't resist!
>>>
>>> All Polaris or eclipse, according to Morison.    I'm attaching a few
>>> pages I put together summarizing his measurements. Again, this is all
>>> from
>>> Morison's biography, I just pulled it all together.
>>>
>>> What's strange about Polaris is that he has to do a 4 degree correction
>>> to get latitude depending on where it was in the sky (e.g. relative
>>> position to Cassiopeia and the Big Dipper).
>>>
>>> As far as I can tell he only used the Regiomontanus information for
>>> eclipses and did the other sightings on Polaris because he memorized
>>> this 4
>>> degree trick with Polaris.
>>>
>>> Bartholomew Dias, on the other hand, didn't have the luxury of this
>>> Polaris trick, and I think he used a sun-shot for the latitude of the
>>> Cape
>>> of Good Hope (and was off by nearly 10 degrees, too).
>>>
>>>
>>>
>>> On Fri, Oct 19, 2012 at 11:53 AM, Brad Morris >> > wrote:
>>>
>>> No noon sunshots?  Okay, there's the end of my wild a**ed guess (wag).
>>> I had assumed he did, based upon my memory of the following items.  (1)
>>> The ephemeris compiled by Regiomontanus included tables of solar
>>> declination (2) That the ephemeris was of the period (3) That Columbus
>>> had
>>> instruments capable of the measurement of the sun's altitude at
>>> meridian
>>> crossing.
>>> Odd to think that he did not put these items together to sail a
>>> latitude
>>> line.
>>> Regards
>>> Brad
>>>  On Oct 19, 2012 10:33 AM, "Apache Runner" 
>>> wrote:
>>>
>>> I don't have all of Samuel Eliot Morison's bio of Columbus memorized,
>>> but
>>> I can try to summarize from memory.
>>>
>>> Western celestial nav was still in it's birthing stages when Columbus
>>> made his voyages.  I forget the precise year, but Don Joao II sent an
>>> astrologer on a Portuguese vessel down the coast of Africa in 1480.  He
>>> took a sighting of the sun and was off in latitude by about 7 degrees
>>> or so.
>>>
>>> Bartholomew Dias took a shot at the Cape of Good Hope and sighted 42
>>> degrees when it should've been 33 or so.
>>>
>>> Columbus knew some of these shots, and took an ephemeris with him,
>>> quadrant and astrolabe.   On his first voyage, he took a shot of
>>> Polaris,
>>> which required a 4 degree correction back then.   In Cuba he got a
>>> latitude
>>> of 42 degrees (i.e. Boston's latitude).   Morison speculates that he
>>> misidentified Polaris.   Later in Haiti, he got a better shot, but was
>>> still pretty far off.   On his return, he tried a shot on approaching
>>> the
>>> Azores, but the wind affected his instruments too much.
>>>
>>> On later voyages he did somewhat better.   On his 4th, he got a pretty
>>> good value of latitude for Saint Anne's Bay in Jamaica.   He also did a
>>> longitude measurement by using Regiomontanus' tables for an eclipse,
>>> but
>>> was off by a huge amount.
>>>
>>> On his 3rd voyage, he took three shots of Polaris while in the
>>> doldrums,
>>> but one of them was way off on one of them and concluded that there was
>>> a
>>> large bump in the ocean.
>>>
>>> So, very much experimental - he wasn't really using the stars to
>>> navigate, but he was playing around with it.
>>>
>>> Most of the navigation was dead reckoning using magnetic compass and
>>> log
>>> line.   Only later in the 1500's, however, did people seriously try to
>>> be
>>> more systematic in correcting for magnetic variation.
>>>
>>> On Thu, Oct 18, 2012 at 8:24 PM, Brad Morris
>>> wrote:
>>>
>>> (Okay,no list comments on the fact that Columbus didn't practice
>>> celestial,I only learned that later)
>>> Didn't he cross the ocean on a latitude line?  Most likely by using the
>>> noon altitude of the sun?  That's celestial!
>>> On Oct 18, 2012 7:20 PM, "Lu Abel"  wrote:
>>>
>>>    Brad:
>>>
>>> I totally agree on taking a run of sights.  I know of no text (either
>>> standard ones such as Dutton's or celestial navigation specific texts)
>>> that
>>> doesn't suggest this.  Some books even suggest plotting them on graph
>>> paper; where a consistent rise or fall in the curve and "outliers" are
>>> easily spotted.  In fact one can push beyond that and do a
>>> least-squares
>>> fit of a line to the data (impracticable in real life, but gives the
>>> mathematicians joy).
>>>
>>> I also agree with "the more, the merrier" implied in your quote from
>>> Dutton's.  I think that a "starburst" of LOPs will quickly show any
>>> LOPs
>>> that are outliers and should be eliminated.
>>>
>>> But nowhere in Duttons can I find a suggestion that one not trust two
>>> LOPs or that one's position must be in the center of the cocked-hat
>>> formed
>>> by the intersection of three LOPs.     And there was heated discussion
>>> on
>>> this list about the latter, starting with the simple fact that if one
>>> assumes there's a 50/50 chance of one's true LOP being on one side or
>>> the
>>> other of the plotted LOP then there's only a 1 in 8 chance of the fix
>>> being
>>> inside the cocked hat.
>>>
>>> Last but not least, Debra said she's a beginner in celestial
>>> navigation.
>>> I've taught a lot of beginners and in my experience it's a whole lot
>>> easier
>>> to help them see the magic of celestial when they can start with sights
>>> taken during daylight (ie, sun or moon).  I remember when I reduced my
>>> first sight 30 years ago (a sun shot) and I felt like Christopher
>>> Columbus
>>> when I reduced to an LOP only a mile or so from my KP!   (Okay, no list
>>> comments on the fact that Columbus didn't practice celestial, I only
>>> learned that later)
>>>
>>> Celestial has a steep learning curve -- handling the sextant properly,
>>> reading it properly (especially the vernier), measuring IE, bringing a
>>> body
>>> down correctly, rocking the sextant, etc, etc, not to mention
>>> timekeeping,
>>> and sight logging.  (In the last celestial class I taught we did Sun
>>> shots
>>> three hours apart and the second set of sights was for almost every
>>> student
>>> better than the first set for consistency and closeness to our KP).
>>> So
>>> why make it more difficult by insisting that even a beginner has to
>>> take
>>> shots at twilight?
>>>
>>> My 0.0153 Euro's worth.
>>>
>>> Lu
>>>
>>> PS - my Dutton's, which is the 1976 edition, seems to have lost a
>>> chapter
>>> -- your quotes are in my paragraph 2509.   Any reader have an idea what
>>> was
>>> dropped between 1972 and 1976?
>>>
>>>
>>>   ------------------------------
>>> *From:* Brad Morris 
>>> *To:* NavList@fer3.com
>>> *Sent:* Thursday, October 18, 2012 3:07 PM
>>> *Subject:* [NavList] Re: Line of Position Fix
>>>
>>>  Hi Lu
>>> Dutton's Navigation & Piloting
>>> Twelfth Edition
>>> Naval Institute Press
>>> Annapolis
>>> 1972
>>> PARAGRAPH 2609
>>> quote
>>> A fix is obtained when two or more lines of position are
>>> crossed,adjusted
>>> to a common time. ... At twilight, in clear weather, he will observe a
>>> minimum of five stars, well distributed in azimuth.  He will make 3
>>> observations of each body. ... This gives a check on the consistency of
>>> observations and therefor their probable reliability.
>>> End quote
>>> The purpose of taking 15 observations of 5 bodies is to provide a more
>>> reliable fix, consistent for each body (3 observations), and consistent
>>> among bodies (5 stars).
>>> If it was good enough for US Navigational Officers at the height of
>>> celestial navigation, then that's good enough for me.
>>> In deference to your considered opinion, you may follow the practice
>>> you
>>> see fit.
>>> Regards
>>> Brad Morris
>>> On Oct 18, 2012 5:42 PM, "Lu Abel"  wrote:
>>>
>>>  I agree that even on land LOPs are likely to be off by a mile or even
>>> more and so fixes have that uncertainty; it's just the nature of
>>> celestial
>>> navigation.
>>>
>>> But I have to question the claim that getting three LOPs will give a
>>> better fix.  As someone pointed out in a discussion on this list a few
>>> years ago, there's only a one in eight chance of a fix even being
>>> inside
>>> the cocked hat and there's no certitude at all that the fix will be in
>>> the
>>> center of the hat.
>>>
>>>
>>>   ------------------------------
>>> *From:* Brad Morris 
>>> *To:* NavList@fer3.com
>>> *Sent:* Thursday, October 18, 2012 12:45 PM
>>> *Subject:* [NavList] Re: Line of Position Fix
>>>
>>>  Hi Debra
>>> The best two times of the day are the civil twilights.  Those are just
>>> before dawn and just after sunset.  The best bodies to use are the 57
>>> navigational stars.
>>> Just as a note, you will want 3 bodies in your fix.  It is unlikely
>>> that
>>> 2 LOPs will cross at your position, in general, and 3 will produced a
>>> 'cocked hat'.
>>> Best Regards
>>> Brad Morris
>>> On Oct 18, 2012 3:23 PM, "Debra Hillman"  wrote:
>>>
>>>  Could somebody help me with my problem . I am learning on my own at
>>> present from books on celestial navigation.I need to get a fix with two
>>> lines of position but not sure which celestial body other than the sun
>>> and
>>> the best times of the day to achieve the fix.
>>>
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>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>
>
>
>
>
> : http://fer3.com/arc/m2.aspx?i=120899
>
>
>

   

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