Copyright ©2010 by Paul Niquette. All rights reserved.
Let us begin with a statement of the obvious: At any given instant in time, every object in the sky appears exactly overhead at some point on the surface of the earth. It's called the subpoint for that object. That applies to all celestial bodies -- stars and planets, sun and moon. Of course, the earth is busy rotating on its axis and orbiting the sun driving distant stars across the firmament. The planets ("wandering stars" Greek 1640) meander all over the night sky, while the moon makes its monthly orbit of the earth. Thus every subpoint traces an earthly pathway, unique and predictable.
The familiar word altitude in the aviation lexicon represents the instantaneous elevation of the aircraft itself above sea level, measured in feet. In nautical parlance, where the vessel itself is confined to one altitude -- sea level -- the word altitude indicates the elevation of a celestial body as it appears above the horizon, measured in degrees, minutes, and seconds.Here is another statement of the obvious: At a given instant in time, from any location on the surface of the earth, every object in the sky will appear at some angle above the horizon. That's its altitude for that time and location. At the subpoint for a given object, of course, its altitude is 90 degrees. Elsewhere, the object would be seen at -- well, a different altitude.
Here is the key to celestial navigation: At a given instant in time, every object in the sky appears at the same altitude for a set of locations that form a circle on the surface of the earth. The circle is called line of position (LOP), which is named for the celestial object and that time. Inasmuch as the earth is quite a big place, when a segment of a LOP is plotted on a local navigation chart, it looks like a straight line.
Here is an exceptionally convenient statement: The coordinates -- latitude and longitude -- of each sub-point can be predicted for any given instant in time. That makes it possible for a skilled navigator to ascertain the sub-points of 57 navigational stars and planets plus the sun and moon, all based on tabulatons published in an almanac. Since olden times, the celestial navigator at sea would take a sighting by sextant of a selected object in the sky to determine its altitude and note the precise instant in time read from the ship's chronometer. These readings taken together provided what the navigator needed for looking up the appropriate entries in the almanac, thence to perform the requisite computations for plotting the LOP on the navigator's chart.
To "shoot" one star or planet was not enough to determine a fix for the vessel's location. The navigator needed to obtain at least two LOPs, preferably intersecting at a near right angle -- and taken hurriedly to be as close to the same instant in time as possible. Alas, celestial navigation has always been fraught with errors. Moreover, way-finding from one fix to another required dead reckoning, itself error-prone. Common principles of navigation -- imperfections included -- apply to avigation. Inevitably, errors suffered in the sky are much larger than those experienced on the surface of the sea, as aircraft are so much faster than ocean-going vessels.Gary LaPook has served as an invaluable consultant for many aspects of this series of puzzles. He is arguably the world's leading authority on celestial navigation in general and on Amelia Earhart's round-the-world flight in particular. LaPook's website entitled "Fred Noonan and Amelia Earhart plus General Flight Navigation" contains an immense body of reference materials, including contemporaneous manuals, plus expert commentaries on many aviation topics, with an emphasis on celestial navigation -- its methods, its limitations, and its instruments.
The photograph on the right was provided by Gary LaPook. It shows a Mark 3 Octant, like the one used by Fred Noonan, navigator for the 1937 flight of Amelia Earhart.
The flight departed Lae, New Guinea on July 2, 1937 for Howland Island. Most of the 2,556-mile segment was flown at night, which enabled Noonan to take sightings of stars and planets for live reckoning. The flight plan assured arrival in daylight at Howland for landing on its unlighted strip. There would be no stars in the sky -- except one. One LOP for the sun is assumed by some historians to have been plotted by Fred Noonan prior to take off. That particular LOP received prominence in the last radio transmission by Amelia Earhart (see Simplexity Aloft). As an advanced LOP, it would not be used to determine the geographical location of the flight but to synthesize a "landfall line" for guiding the final stages of the approach to Howland (see Landfall Navigating). That sun LOP is shown in the diagram below as a cut across the course line at Howland Island and marked with its reciprocal headings 157-337 degrees.
Here is yet another statement of the obvious: No object in the sky appears exactly overhead of a fixed location (subpoint) at every instant in time. Well, almost obvious. Polaris is an exception. So too are geostationary communications satellites, come to think of it. In general, though, no LOP is statonary. Noonan's 157-337 sun LOP would be present at that location only at a certain instant in time -- the planned arrival time (1800 GCT). At that instant, the sun's altitude would be 6 degrees all along the 157-337 LOP passing over Howland Island.
Meanwhile, the sun LOP itself would be racing toward the West at 1,036 mph (see Here Comes the Sun). As a consequence of reported headwinds, Noonan would most likely have adjusted the ETA, by, say, one hour to 1900 GCT. The altitude of the morning sun, which increases relentlessly at 15 degrees per hour, would then be 21 degrees, as the delayed flight approached Howland Island Referring to tabulations in the almanac for 1937, Noonan would need to plot a new LOP passing over Howland Island, which would have its reciprocal headings slightly rotated toward 156-336. Using his octant and chronometer, Noonan would then be able to confirm the arrival of the flight intercepting the updated LOP. Thus by celestial navigation, using daylight's one and only celestial body in the sky, Noonan was able to keep track of the flight's progress along the course line toward -- well toward an intersecting line not a geographical point. So then, what about the course line itself?
In the figure above, solvers will see that the sun was not "the one and only celestial body in the sky" that morning. The previous sentence deserves exclamatory punctuation and so does the next one. The moon, which was in its last quarter, was also available to Fred Noonan for celestial navigation. Not only that, but the moon's LOP for 1902 GCT offered reciprocal headings of 067-247 degreas -- closely aligned with the course line (072) for the flight.Sophisticated solvers ought to be justified in concluding that by taking sightings of the moon, world renowned celestial navigator Fred Noonan would have been able to correct for lateral errors in navigating (see Live Reckoning and Wages of Flight) and thereby assure success for the flight. Amelia Earhart, with or without radio direction finding (see Simplexity Aloft), would thus fly the Lockheed Electra directly to Howland Island and land with plenty of fuel in reserve. Accordingly, we have a mystery to solve...
|Gary LaPook learned to fly in 1970 and has been an airline transport pilot since 1978. In the 1970s he ferried new airplanes from the factory to aircraft dealers, including crossing the Atlantic using celestial navigation to find the Azores. He started sailing in the 1960s and always brings his sextant along. He occasionally takes his sextants flying and shoots sights just to stay in practice.|