Re: [Paddlewise] Longitude and astronomy

On Wed, Jul 28, 2010 at 2:15 AM, PeterO <rebyl_kayak_at_energysustained.com>wrote:

>
> I've often wondered just how the astronomers did their calculation and it
> sounds as if you have insight into how this might have worked. I'd be glad
> of any suggestions you might have for understanding  the method better?
>
> Before we had "computers" it was a career path for mathematically inclined
people who were employed by universities and scientific organizations to
undertake the tedious calculations required by science experimenters. They
were employed as "computers" to... well... compute. These computations often
found their way into tables  that were published and collected to make the
math easier. Sine tables, cosine tables, log tables, etc. were all part and
parcel of an engineer's or scientist's life not more than two generations
ago (along with slide rules).

The idea of celestial navigation revolves around the concept that a
celestial body is directly above some point on the earth at some point in
time. The pesky habit the earth has of rotating every 24 hours introduces
some complications. So "computers" were employed to calculate the point on
the earth a celestial body would be above at every second of time.

When you know the time accurately you can use the navigational tables to
determine the geographic location that your celestial body is directly above
and then use a sextant to determine just how far away from that geographic
position you happen to be using relatively simple trigonometry. (There are
tables for spherical trig calculations, too.)

Unfortunately the result of this procedure turns out not to be a point on
the map but a circle. Much like simply taking the height of a streetlamp to
determine how far you are away from its base. It tell you nothing about
which direction you are away from the base but only how far.

This is called, in navigational terms, a "line of position".

In order to get an accurate idea of where you really are you need to 'cross"
that first sighting with a second one that is, preferably, 90 degrees or so
offset from it. So that the two lines of position intersect where you happen
to be. If the two celestial bodies are not far enough apart you can get some
significant confusion in the accuracy.

This causes navigators to do what we like to call a "round of stars" and is
why the second officer of a ship (traditionally the "navigational officer)
has watches that make it easier to take star sights as well as a couple of
sun sights. (The position using the sun is treated slightly differently from
that of a star sigh.)

In the old days the science and art of navigation was highly prized amongst
mariners and we often collected and practiced various methods of reducing
celestial sights to geographical positions. Space and weight was not a
factor for ship navigators but aviators and yachtsmen discovered that 48
volumes of navigational tables were somewhat bulky. At some point in time
the British Home Office (which kindly published many of these tables) came
out with H.O. 249 which had a limited number of navigational stars but was
only in a couple volumes. This, along with a nautical almanac, a good
timepiece, and a sextant was all one would need to navigate a vessel or
aircraft around the world.

This, in a nutshell, is how celestial navigation works (more or less). But
the actual method for calculating the data was outside my expertise. So I
probably did not answer your question. But maybe answered questions others
had on this subject.


Craig Jungers
Moses Lake, WA
www.nwkayaking.net
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