THE PURPOSE OF THIS PAPER is to compare the empirical methods of medieval Arab navigators on the Indian Ocean for determining latitudes with modern stellar methods using spherical trigonometry, the navigational triangle and data from nautical publications.
The heart of modern celestial navigation is the navigational triangle with solutions.
This can easily be shown using the navigational triangle. Only when the distance of the two stars from the meridian of the observer decreases to zero and both stars have "coalesced" on the meridian does the method work exactly--which, of course, reduces to the single-star method discussed above.
For such stars, Ibn Majid has left a few quantitative data, and these may be compared with modern calculations using the American Nautical Almanac for data on specific stars with which to enter the navigational triangle tables of Navy Pub.
Ibn Majid's data can then be compared with calculations made using the navigational triangle and the nautical tables cited earlier.(11) A few remarks about circles of equal altitude will provide background for "fettering." The altitude of the lettered star to the observer at the Geographical Position is 90 |degrees~, and extension of the line from the star to the Geographical Position passes through the center of the earth.
In order to compare abdal and "fettering" methods, table 3 shows one star pair of nearly equal declinations and another pair whose declinations differ considerably, and one star of each pair fettered--both pairs calculated using the modern nautical and navigational triangle tables.
Table 4 contains information obtained from navigational triangle calculations and nautical tables, and represents typical kinds of observations that a navigator might have made while checking out a pair of stars for use in determining latitude by the "fettering" method--in this case, Arcturus-Canopus.
SHA is used to calculate Meridian Angle of navigational triangle as in abdal calculations above.
Navy H.O.214 for navigational triangle solutions is entered with observer latitude, Meridian Angle and declination.
The main purpose of this section is to describe for those who want to go into considerable detail the navigational triangle and its use in calculating star altitudes according to U.S.