to sailors --- James Lawrence
Ꙩ
OZ |
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OP ____________________________________|_________________ GH /SH
| GP
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CH
ON
We're back in Ptolemy's world for purposes of Celestial Navigation. And for our purposes we're at sea level, sailing, sailing over the bounding main. For purposes of the first diagram we are at the Observer's Position (OP). Looking straight up, the highest point in the sky we can see is the Observer's Zenith (OZ). Looking down between our feet and through our suddenly transparent boat down into the depths of the suddenly transparent Earth, the lowest point we can see is the Observer's Nadir (ON). So, for our purposes, we are inside a vast cube.
For our simplified purposes the bottom line of that cube is the Celestial Horizon (CH).
We aren't standing on the CH which is actually far below us at the center of our flat Earth . Instead we're standing on a boat on an ocean on the surface of the Earth. Look left, right, ahead and behind, and the visible edges of the Earth form the Geoidal Horizon (GH).
Looking straight ahead out of our eyes the limit of our vision forms the Sensible Horizon (SH) (for our purposes, the GH and the SH are essentially the same; were we flying or mountainclimbing or not at sea level they'd be different).
To use the stars or the Sun, Moon, or other planets to pinpoint our location on the Earth, first we have to select a Celestial Object (CO) in the sky. On our very simplified diagram we've chosen the Sun.
The spot over which the CO seems to be hovering at any given moment is called the Geographic Position (GP). When we imagine the GP we imagine it reaching down to the CH, just as we imagine the OP reaching down to the CH.
Celestial Navigation works by measuring the angular position of the CO / GP against the measuring points of the CH, and the OP / GH / SH. Find the sum of these angles and we know where we are on the ocean.
Modern GPS uses satellite signals to give us those numbers to a fare-thee-well, but let's pretend that the battery in our GPS is dead and that Billy "Bligh" Malloy forgot to pack the charger. Besides, we want to feel like real sailors, not Astroboy.
It seems self evident on our simplified diagram (its my own invention), but remember, the Earth is not really flat. So it isn't just a matter of drawing neat 45 degree angles from one point to the other. The Earth is a three dimensional sphere, and a big one, with a lot of potential OPs, each one of which forms a slightly different angle to the CO and its GP.
On our curved diagram the CH would remain the same, basically a straight line connecting the two ends of the arc, but the GH / SH line would be the arc. The GP and the OP would be two points along that arc. The CO and the OZ would hover above them respectively. The angles between these points would give us our position on the sea.
Since the Earth is not a perfect sphere and since
light rays bend when entering the atmosphere there are a number of
mathematical corrections that must be applied to the numbers derived
from the sextant measurement. It is also critical to measure time
precisely as the celestial dome is revolving (or the Moon, Sun or planets
moving) as we take our measurements; thus the angles are constantly changing. A precision timepiece is an absolute MUST if you want to survive an ocean crossing.
It is also crucial to remember that the Earth is tilted on its axis (this tilting causes the seasons) and that the tilting alters the angle of the OP relative to the CH, the CO and the GP (as the Sun and the Earth do their annual dance, the Sun appears to be tracing a figure 8 (an analemma) in the sky.
The math needed for Celestial Navigation shouldn't strain anyone who can add or subtract or has a dependable (i.e., waterproof) calculator on board. The mathematical adjustments can be found in a series of books called the Sight Reduction Tables, which allows correction for inaccuracies due to the shape of the Earth, inaccuracies due to the not-quite circular shape of the Earth's orbit, and normal visual distortions caused by looking up through the atmosphere. And don't forget to account for the rocking of the boat.
A sextant
works by measuring the relative angles needed by visualizing everything
in a series of mirrors and measuring it all by the use of pair
compasses.
With practice it gets easier.
The most important resource a beginning celestial navigator must have is patience. You will make mistakes. Once, while out on Long Island Sound we tried to take a position with our brand-new shiny sextant, and it told us that we were somewhere on the Ungava Peninsula in northermost Quebec. At least we were in the correct hemisphere. And better, when we went over our math we ended up somewhere near Martha's Vineyard. At least we were on the right coastline. I wouldn't dare go out of sight of land with "skills" like that, but it was a beginning. Remember that until the mid-19th Century literacy was a rarity, and math skills rarer still. So, it is no wonder that Navigators were worth their weight in gold until very, very recently. While it isn't hard to learn the rudiments of celestial navigation in an afternoon it can take years to become truly expert at it.
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