## Thursday, April 22, 2010

I attended a celestial navigation course at Windworks over the April 10th weekend.  Everybody knows that celestial navigation is used to figure out where you are when your at sea, right?  You use the sextant to measure an angle and then do a bunch of math and voila, now you know where you are!

I understood that overview but never really understood what was really going on.  Now I know!

A general overview of celestial navigation is really pretty easy.  Don't be confused by my description - its probably much easier than it sounds!

All sailors should know how to do simple navigation.  One of the easy things to do when sailing around coastlines is to get a fix for where you are by taking three bearings to landmarks.  For example, if you know roughly where you are, look at a chart to pick three things you will be able to see.  A lighthouse, a radio tower and the end of a point of land.  Go onto deck with a hand bearing compass and record the bearings to each of these three marks.  Then go back to your chart and draw lines from the marks along the bearings you measured and the three lines will cross in some small area - that's where you are.

Celestial navigation is basically the same thing.  The most basic form is where you pick three stars which will be visible and arranged around the horizon roughly equally.  Then you go up on deck with your sextant and take a measurement and record the time.  With some basic math (addition and subtraction) and table lookups, you can then end up with three lines of position (LOPs) which will intersect in a small area.  The area of intersection is where you are.  Its the same as for taking a fix with a compass but with more math.

Its pretty cool.

For a star, the basic idea is that the stars have well known positions in the sky at any particular time.  This can all be found by looking it up in tables and doing a little math.  After doing this math you end up with the geographic position of the star at that exact time - essentially the point on earth which is directly below the star right then.  The next step is to assume that you are at some point, your assumed position.  This can be done by estimating where you think you are by dead reckoning.  If you're far out its ok, that will be fixed a little bit later.  Now comes the magic of the sight reduction tables.  Given the geographic position of a star, and your assumed position you can easily calculate a bearing to the star and its exact expected height above your horizon.  That part of the calculation is mainly done as table lookups and is a little magic.

So what you do is pick a star (or three) from the tables which you want to measure.  Then go onto deck and find the star and then measure the angle between it and the horizon with the sextant.  A sextant really only does one thing - it measures angles very precisely.  When you measure the angle you also record the time.  Then you make an assumption for where you think you are and do the calculation to find where the star was expected to be at that exact time.  Once that is done, you have two angles: the height of the star where it was expected to be and the height of the star in reality.  The difference between these two angles relates to how far away from your assumed point you are.

Hold your arm up for this next part: if the height of the star was expected to be 45 deg above the horizon (hold your arm out at 45 degrees) but was measured to be 30 degrees (slide your arm down to 30 degrees) then: are you closer or further away from the geographic position of the star?  After a bit of thought and repeated arm gestures, the answer comes: you are further away!  If the angle measured was greater than the expected angle then you are closer to the star's geographic position than you thought.

So almost done now.  You have an assumed position and a bearing to the star at the exact time you measured the star.  Draw a line on a chart from where you are to the star.  Now adjust your assumed point toward or away from the star by the amount corresponding to the difference in the two angles (the computed angle and the measured angle.)  Make a mark on the chart at that point.  For example, given your assumed position, the bearing to the star (its azimuth) might be 230 degrees and you are 3.5 miles further away - so put a new mark at that point.  You aren't at that point, that would be too easy.  So what does that point indicate?

To understand what you just did, think of a streetlight.  The geographic position of the streetlight is the point just below the light (for a star its the point directly below the star, for a streetlight, the point directly below the streetlight.)  Now pretend you measured an angle of 45 degrees from where you are to the streetlight.  If all you know is where the streetlight is and that angle, what it tells you is that you can be anywhere on a circle of a calculated radius out from the streetlight.  The one angle won't tell you where you are, but you can draw a circle around the light and you are somewhere on that circle.  If you do the same thing again for a second streetlight you will have two circles which intersect.  If you add a third streetlight and measure the angle to it, compute the radius you have three circles which intersect in a small area - that's where you are!  That's what's going on with our star sights - we use three stars, measure the angles, calculate their position and expected heights and then figure out where we are.

So back to the mark on the chart we made.  We moved toward or away from our assumed position by the amount corresponding to the difference in the computed and measured angle.  That gave us a point on the chart.  Now draw a perpendicular line, a line at a right angle to that point and azimuth and draw a new line.  We are somewhere along this line, the line is a line of position.  To be exact, we should draw a small portion of a circle with the stars geographic position at its center - but that circle is so large for us that on the chart in front of us the little portion of the circle looks like a line.  So just draw a line.

So we have a line on the chart and we're somewhere along that line.  This is exactly the same as the coastal situation where we took a bearing to a lighthouse, drew that line on the chart and knew we were somewhere along that line.  If you do the same thing two more times with two more stars you get two more lines of position which will intersect in a small triangle, and that will be our fix.  We used the stars to figure out where we were on earth.  Cool!

You can also use the sun, moon or four of the planets for the fixes.

Celestial navigation is simply to use these bodies to calculate lines of position on a chart.  If you draw three lines of position you have a fix and know where you are.  In hindsight this all seems pretty obvious.  Everybody knows that's how it works, right?

Something you might not know: there are only 57 stars used for navigation out of all the billions and billions of stars out there.  Something you do know: stars are really pretty to look at.  Something you might not know: the names and positions of the 57 navigation stars.

I don't yet know where the 57 stars are.  But now I can figure out where any of them will be at some point in time, walk outside, look in that direction and height above the horizon and there it will be.  And that's pretty neat!

I'll be keeping my GPS.