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Re: In the Wake of Magellan
From: Brad Morris
Date: 2019 Oct 12, 19:14 -0400

Hello Doug

Re: your first question, sun's declination table.

The Tables of Toledo were developed in 1080 AD, using the work of al-Zarqali. al-Zarqali is also reputed to have developed an astrolabe to determine the positions of the planets based upon the work of Claudius Ptolemy, Almagest, 150 AD.

The Alphonsine Tables (So named for King Alphonse of Spain) were developed for the Kings birthday, in 1252, and updated the Tables of Toledo.

Magellan sailed in 1519, over 250 years after the Alphonsine Tables and 1350 years after the Almagest. Does anyone know what tables Magellan used?

Of course, the Almagest was based on the works of Hipparchus, a Greek astronomer from the second century bc.

Further, neolithic peoples appear to be aware of solar declination, in the construction of monuments which only permit illumination on certain days of the year [dolmens] or specific alignments with stones [Stonehenge]. These, of course, did not represent tabular data. Yet they seem to have been aware of the changing of the sun's positions over the course of a year and that these positions repeated, the very basis of knowledge necessary to create a table.

This topic is a rich vein of research, and as Robert indicated, rife with scholarly articles. I have attempted only the crudest of summaries, likely containing inaccuracy. There is no clear lineage of solar declination tables, unless you closely restrict what you wish to discover. There is really no "first" without caveats.

Brad

On Thu, Oct 10, 2019, 2:34 PM Doug MacPherson <NoReply_MacPherson@fer3.com> wrote:

Recently sailing in my armchair I was pondering the navigational challenges Magellan and other European sailors of his time must have experienced. (Early 16th century).
I assume that the sun was the primary source of information for determinig latitude and that they had some table showing them the declination of the sun over the course of the year.
Three questions came to mind:
1. Where did the sun's declination table come from? Did the Spanish, Portuguese or other governments supply it? How did they get it?
2. What tool were they using to determine the altitude of the sun at noon? A cross staff? kamal? backstaff? John Davis Did not invent his "Davis" quadrant (a backstaff) till 1594.
3. If, in an unfortunate accident, the declination table blew overboard, and our intrepid captain remembered that the sun's declination was about 23.45° South and North on December 21 and June 21 respectively, and 0° on March 21 and September 21, would a linear approximation of the sun's declination from that rememebered data be accurate enough to navigate with? What would be the max error from the sun's actual declination and when would that occur?
Finally, would the max error matter given the tools they were using?
Cheers,
Doug
38° 34.3' N
121° 28.5' W

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