Demystifying Celestial Navigation: How the Sextant Actually Works

It is not black magic. It is just geometry. Understanding the difference between Ho and Hc.

For many sailors, the sextant is a symbol of mystery. It looks like a complex instrument reserved for the elite few who are good at advanced mathematics. At Sailing Munich, I tell my Yachtmaster Ocean students the truth: Celestial Navigation is simple geometry.

In a nutshell, we are simply comparing two angles.

The Concept: Ho vs. Hc

To find our position, we need to compare reality (what we see) with theory (what the books say).

1. The Observed Altitude (Ho) You stand on the deck and use your sextant to measure the angle between the horizon and a celestial body (Sun, Moon, Star, or Planet). After applying a few standard corrections (for height of eye, refraction, etc.), we call this final number Ho (Height Observed).

2. The Calculated Altitude (Hc) Since we do not know exactly where we are (otherwise you wouldn't have picked up your sextant, would you?), we guess. We pick a spot on the chart called the Assumed Position (AP). Using the Sight Reduction Tables, we look up what the angle of that star should be if we were standing exactly at that Assumed Position at that exact second. We call this theoretical angle Hc (Height Calculated).

The Intercept: The Magic Mile

Here is where the magic happens. You simply compare the two numbers. It is very unlikely that your measurement (Ho) equals the book's number (Hc). You are usually a different distance from the star than your Assumed Position.

• The Difference: The difference between Ho and Hc, expressed in minutes of a degree, is exactly how far away you are from your Assumed Position in Nautical Miles. This is called the Intercept.

• The Direction (Azimuth): The tables also tell you the direction of the star, called the Azimuth.

  
  

The Rule:

If your angle (Ho) is Greater than the table angle (Hc), you are closer Towards the star. If your angle (Ho) is Smaller, you are further Away.

Drawing the Chart

Once we have these numbers, the plotting is an architectural exercise:

1. Mark your Assumed Position (AP).

2. Draw the Azimuth line pointing to the star.

3. Measure the Intercept distance along that line (Towards or Away).

4. Draw a line perpendicular to the Azimuth. This is your Position Line.

You are somewhere on that line. To get a "Fix" (an exact spot), you simply repeat the process with a second star to get a crossing line. Or, if you are using the Sun, you wait a few hours for the sun to move, take a second shot, and advance your first line to cross the second one (a Running Fix).

Why the Course Takes 5 Days

If the principle is so simple, why is the Yachtmaster Ocean theory course five days long?

Because the devil is in the details. While the logic is simple, we need to learn how to apply corrections precisely. The earth turns, planets do not move at constant speeds, and we need to calculate exact times for Twilight (the only time you can see both the horizon and the stars).

I always explain to my participants that the first day is the hardest. After that, it gets easier. It is just "more of the same" logic applied to different bodies.

By the end of the week, you will be able to take a blank plotting sheet and find your way across the Atlantic without a GPS. And the feeling of satisfaction when those lines cross on the paper is one of the most rewarding moments in a sailor's life.

Fair winds,

Captain Leo Cunha