CelNav Seven - Noon Sun

[HenryC]

CelNav Seven

Throughout the year, the sun slowly travels north and south of the equator between the Tropics of Cancer and Capricorn.  It never leaves this equatorial zone, it's declination oscillating between roughly 23.5d N and S.  However, the earth spins around once a day so the sun's GHA goes through a complete 360d every 24 hours.  Every day, the sun will cross your local meridian, the imaginary line in the sky that goes from pole to pole  directly over your head.  How far above the horizon it appears to be at that moment depends entirely on how far N or S of the equator it, and you, are.

If you measure the sun's altitude at the moment of meridian crossing, your Local Apparent Noon (LAN), you can look up its declination and quickly determine how far away you are from its GP.  Since the sun's declination changes little over the course of a day, you don't even need to know the exact time this happens. All you have to do is catch the sun at its noon position, and make a rough guess (within a couple of hours), of your local time.  This will then give you a latitude, by simple addition or subtraction, without having to use any sight reduction. This is what Capt Aubrey is teaching his midshipmen in the sextant scene in the film Master and Commander.  A noon sun will give you a latitude, and it can be DR'd to a morning and/or afternoon sunline to give you a running fix.  Since it is easy, accurate, and requires no precise time or sight reduction, it belongs in every navigator's bag of tricks. 

At LAN, the sun's GHA will equal your Longitude, after you correct for whether you are in the E or W hemisphere).  At that time you will also know the sun's dec from the Almanac (it changes very slowly, so you don't need an exact time). The hard part is getting your shot when the sun crosses your meridian;  you have to start shooting a few minutes before local noon, and shoot continuously until the sun seems to stop climbing, and slowly starts to go back down in altitude. The exact moment is impossible to judge, but the altitude changes so gradually that you will be able to get a fairly good sextant reading of the high point.  When the sun is at its highest point, it must be on your meridian.You will know your angular distance from the sun, and you will know the latitude of the sun's GP (it's declination) so you should be able to calculate how far from the equator you must be (your latitude). The exact calculation depends on whether the sun is north or south of you,  and whether you and the sun are north or south of the equator. If the sun is S of you, you will be shooting it over the S horizon, if it is N of you, you will be shooting it over the N horizon.  The former is always the case N of the Tropic of Cancer.

There are only six possible combinations of the N to S order of ship, sun and equator at LAN; listed below. The latitude is calculated differently for each combination, depending on whether Lat and Dec are N or S (+ or -).  ZD is the Zenith Distance, the distance in degrees the sun is from your overhead point, ZD = 90 degrees - Ho.  ZD is always a positive number less than 90 degrees, it is also your distance from the sun's GP.

Ship, Sun, Equator      Lat =  Dec + ZD     
Ship, Equator, Sun      Lat =  Dec + ZD
Equator, Ship, Sun      Lat =  Dec + ZD

Equator, Sun, Ship      Lat =  Dec - ZD 
Sun, Equator, Ship      Lat =  Dec - ZD
Sun, Ship, Equator      Lat =  Dec - ZD   

Or reducing the rule to its simplest form, If the ship is N of the sun,  Lat = Dec + ZD.
If the ship is S of the sun, Lat = Dec - ZD. Let's do a couple  for practice:

If the sun is N of you at meridian passage and its Dec = -20d and the ZD = 10d, then
Lat = Dec - ZD = (-20) - 10 = 30S.

If the sun is S of you at meridian passage and its Dec = -20d and the ZD = 10d, then
Lat = Dec + ZD = (-20) + 10 = 10S.

That's the nooner, in a nutshell.  Unlike Lucky Jack Aubrey, you're not likely to be in the middle of the ocean these days with no source of accurate time, so the need for a noon sight as latitude is not very critical.  But even if you have the right UT available, there's a lot to be said for a noon sunline.  It is possible to have a high degree of accuracy because the horizon is generally sharp and refraction is minimal at noon, and the sun is changing elevation very slowly. 

Of course, determining  LAN is no problem if you know the UT (Universal Time, or Greenwich Mean Time, GMT) precisely. Just determine the Local Mean Time (LMT) of meridian passage  for that day to the nearest minute of time (look at the little box at the lower right corner of the right hand daily page).  On 1 Dec, 2011, LAN is at about 1149 LMT. Find what the UT is for 1149 LMT (because your chronometer is set to UT, not LMT, remember), and show up a few minutes early and shoot sun sights until it passes your meridian and starts falling again. 

LMT can be corrected to UT if you know your longitude, because it takes time for the sun to get from Greenwich to where you are.  The Conversion of Arc to Time table is on page i, the first of the "gray pages" in the back of the Almanac, right in front of the Increments and Corrections section we used to correct the GHA and Dec. So for example, if your Longitude is 38d 35'.5 W, the UT at 1149 LMT is 11h 49m UT + 2h 32m (from left hand table on page i) + 2m 22s (from right hand table on page i) = 14h 23m 22s.  So a little after 1415 UT you need to be out there getting ready for your observation. Write down your Hs and the UT for every shot until about 1430 and you should get a pretty good idea of the Sun's high point from your corrected Ho.

BY the way, don't confuse LMT with Local Standard Time (LST), what  our watches are set to for ordinary civil use. LMT is only good locally, for your exact longitude, it decreases to your W and increases to your east.  LST for an entire time Zone is the LMT of the central meridian of that Time zone, it is what we use in our ordinary life and set our home clocks to.  LST is of little use in navigation.

You should note that the sun is not always "overhead" at "high noon". It can be up to about a quarter of an hour early or late.  This is due to the fact the earth's orbit around the sun is an ellipse, not a perfect circle, and the earth moves slightly faster and slower at different parts of its orbit. As a result, the sun is often a few minutes early or late for its noontime appointment. So our clocks aren't really set to sun time, they are set to an imaginary average "Mean Sun" that travels in a perfectly uniform fashion.  That's why it's called Mean Time. The difference between Mean Sun and true sun is called the Equation of Time, and it is also printed for every day in the lower right hand corner of the daily pages of the Almanac, right next to the time of Meridian Passage.

Incidentally, the publishers of the Commercial edition no longer tint the gray pages gray, as of this year, no doubt to save money on ink. In the 2010 edition they were gray.

Oh, and BTW, you need not limit Latitude sights to the sun.  The moon works fine, day or night, and any star, with its slow rate of change of declination, can give you a good latitude at meridian passage.  You can also get a latitude off Polaris, see page 274 off the Almanac.