Celestial Navigation for Dummies (in the Western Hemisphere)

Celestial Navigation is an utmost skill needed for any ocean voyager. Compasses can lie, electronic equipment can fail, but the stars will always be there! Yes, a cloudy day or night will obscure your view of the stars, but at some point, something will become visible in the sky and if you know how to use it, you can get a bearing on where you are.

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The easiest way to find your position is to take a Noonsite. This will give you your latitude and your longitude with the least amount of math. All you need to get your noon site is a sextant and a clock (which is set at UTC time).

A noon site requires you to know how to use a sextant, which is really easy to learn. All you are doing is measuring the angle between the sun and the horizo.

When you take your noon site, you will receive two pieces of information that you will later translate into coordinates on a map. First you will have your time, which gives you your longitude. Second, you will have your sextant measurement, which will give you your latitude. 

 

Longitude

Longitude is a factor of time on Earth. To make this explanation simpler, we need to use an Earthcentric view of the universe.  

Remember that the Sun revolves around the Earth once every 24 hours. The Earth can be divided into 360 degrees of longitude, and in 24 hours, 360 degrees will pass by. 

360 degrees / 24 hours = 15 degrees per hour. 

At noon over Greenwich (where UTC is the time zone) the sun is directly overhead (their local noon).
In one hour, the sun will be directly over 15 degrees W.  
In two hours, the sun will be directly over 30 degrees W.
n three hours, the sun will be directly over 45 degrees W, and so on.

This means that the time of your noon site is going to b a cryptic form of your longitude, and with really simple math, can be converted into your East or West coorditantes.

When you take your noon site, look at the time (it is helpful to set a 24 hour clock to UTC so that you don't make any errors in calculation here, as each hour is 15 degrees!). Then you will simply subtract your time by 12, as this will give you the difference in time from Greenwich to your local noon.

Now take your time difference and separate it into two columns, hours and minutes. The hours will be multiplied by 15 and the minutes by 0.25; the answer will then be added to give you your coordinates.

Decimals are easy to convert into minutes by simply multiplying the decimal by 60.

So, for example, say its 4:55 PM UTC when the sun is directly overhead and you take your noon site. The math will be as follows:

   16  :  55
 -12. :  00

    4  :  55
x15   x0.2

   60  +  13.7     (0.75 degrees x 60 = 45 minutes)
  60* +  13*45'
  73*45'W

Just that simple, you now know that your latitude is 73 degrees and 45 minutes West.

Another example would be local noon (when the sun is directly overhead) at 2:38 PM UTC.

The math would be as follows:

  14  :  3
-12  :  00
   2  :  38
x15  x0.25
  30  +  9.5     (0.5 x 60 = 30 minutes)
 30* +  9*30'

  39*30'

Thats all there is too it! Longitude has nothing to do with the actual number that is displayed on your sextant but everything to do with "when" you measured the sun at its highest point in the sky.

Latitude

Ok, latitude is the North & South value of your coordinates and really weighs heavily on the reading you record with your sextant. To properly calculate your latitude using the sun (by day, obviously), you will need to use the tables in the Nautcal Almanac. These tables can seem long and complicated, and very confusing, but they are not all that bad once you learn what to look for. f you don't want to use a book, you can always download the latest Nautical Almanac for free! A simple Google Search will pull up a few options, and you will certainly be able to download your own copy.

I personally use a print version from 2017 (I bought it in late 2016 and have not updated my copy as of late 2018) as the angle of the sun over the horizon doesn't change all that much from one year to the next. Yes, your reading will not be as accurate as possible, but at the same time, you are measuring the sun on a pitching and rolling deck of a boat out in the ocean! There are going to be errors in your measurement, so a few tiny errors in your calculations will only compound into a slight bit of error in your final coordinates.

It is important to keep something in perspective here, the goal of basic celestial navigation is to ind land, not to find your exact position on the earth. Advanced celestial navigation will allow you to pinpoint your exact position by using three distinct celestial bodies and finding their intersected lines of position. That is very accurate and also a lot of work to do, which is why basic celestial navigation is just fine for ocean cruising.

The goal is to be less than 25nm off from your actual position. A GPS will tell you your true position, and you can then do some simple math to figure out how far off you are. It is good to practice that way you can get your error way down to less than 25nm. I personally tend to get us within 4nm of our true position with simple math and an outdated Nautical Almanac, meaning it can be done and it's not difficult to do. A 25nm error or less will allow you to find land, and once you reach land, you can then use visual navigation to get yourself in to port. By constantly practicing, you will know how good you are at celestial navigation should your electronic navigation equipment fail, forcing you to rely solely on your basic celestial navigation skills.

On the other hand, if you do not have a Nautical Almanac, you can also just measure the angle from the horizon to Polaris, the North Star, and that is your latitude; no math involved!

An important factor that your Nautical Almanac will tell you is a value called Declination. This is the angle of the sun relative to the horizon. You know how shadows are taller in the winter and shorter in the summer, this is because the sun is further overhead in the summer and lower on the horizon in the winter.

The Nautical Almanac is nothing more than an overfilled calendar. On the top corner of the page is the date range of that page, so simply leaf until you find today's page. Then look on the left side of the page for today's date. Then in the box of today, look for the hour you took your noon site. Don't worry too hard about the (time) minutes that you took your sight, simply round up or down to the nearest whole hour. Now, the declination will be displayed to you as Degrees, Minutes, and Decimal of Minutes.

Simply write this number down and begin to do your simple math!

You will take your sextant reading and substract it from 90 degrees, as the sun is directly overhead when you took your noon site. Then you will add or substract your declination to this number. The answer will be your coordinates for latitude.

You might be wondering what I mean when I say add or substract; which one is it? Well, it depends. If the sun is between you and the equator, you will add. If you are between the sun and the equator, you will substract. To keep the math and theory here simple, since this is just "Basic Celelstial Navigation" let's suggest that you do both and see which one is closer to where you actually are.

For example, you are sailing through the Bahamas, meaning that your latitude is somewhere between 27N and 22N. You get your sextant reading and you find today in the Nautical Almanac. It says your declination is 23*24.7' That is a pretty accurate value presented to you, but should you add or substract it from your recording? Well do both and see which one fits your assumed position best! One will be close to where you actually are and the other will be wrong by almost 24 degrees! Now you know for your present location that you should either add or substract next time.

This may sound really confusing, but I guarantee you that it is very simple to carry out this calculation. Lets do an example:

Declination is 23*24.7'
extant recording is 87*04'

We start by subtracting our reading from 90. Since each degree is 60 minutes, it makes the math easier if you just write out 90* as 89*60'

  89* 60'
-87* 04'

   2* 56'

Now, we aren't sure if we should add or substract, so lets do both!

     2*     56'
 -23*     24.7'

-21*      31.3'  A negative value would indicate that you are south of the equator, and thus in the Southern Hemisphere as you sail through the Bahamas. 

 

 

21*31.3'S

 

    2*   56'
  +23*  24.7'

25*    80.7'     (80.7' - 60' = 20.7') Each degree is 60', so to turn a number like 80 into degrees and minutes, simply substract 60 from it. The remaining number is minutes, and the 60 you took off becomes 1 degree.
25*    1* 20.7'    Now add the values together and that will be a possible N value for you as you sail through the Bahamas.

26*20.7'N

 

Being how you are in the Bahamas, the value of 26*20.7'N seems more plausible than 21*31.3S, so you know for the time being that you need to be adding your declination to the value, instead of subtracting it.

 

Finding Your Coordinates

It is important to know where you are before you leave, that way you have a rough idea of what the answer should be while you are doing your calculations. If you find that you are way off, you know you made some clerical error and can figure out how to make adjustments to erase this error in tomorrows noon site. 

Remember, Longitude is a factor of time, Latitude is a factor of the sun at noon with some minor addition or subtraction. 

With this, you can figure out where you are in the ocean using only a sextant and a clock! 

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