Celestial Navigation Basics Land Sea & Air – Course_d


In a previous post (Ref.1) I described how I developed an interest in Celestial Navigation and in my last posts (Ref.2, Ref.3) I explained what I believe to be the important points such as why CelNav is still relevant, the GP Geographic Position, the Navigation Triangle and it’s Trigonometric solution. In this post I will conclude by covering Sextant Measurements, Marcq St.Hilaire and NAO/AP3270. The On Line Course starts Feb 3rd.

Sextant Measurements – Hs, Ha, Ho, Hc

This past summer I spent a great deal of time at Toronto Harbourfront. It allowed me to forget about the pandemic and the horrible effect it was having on everyone. I shot a series of videos outlining sextant measurements and their reduction (Ref.4, Ref.5, Ref.6, Ref.7, Ref.8):

Hs = Sextant Altitude
Ha = Apparent Altitude = Hs +/- Instrument Error +/- I (Sextant Index Error) – D (Dip Error)
Ho = Observed Altitude = Ha – R + PA (Parallax in Altitude) +/- S (Semi Diameter for Sun/Moon)
Hc = Theoretical Altitude = Determine from GP/AP use Trig or NAO/AP3270
Intercept = Ho – Hc, Positive move toward GP, Negative move away from GP

The Hs or sextant altitude is the angle you actually measure with the sextant. Because your eye level is not exactly on the horizon, then you must subtract a dip angle plus adjust for any instrument errors to give Ha. This is where we see the Celestial Body in the sky. Next we adjust for refraction and parallax and this gives us Ho. If our measurement is perfect then Ho should be equal to Hc from our known position.

Marcq St.Hilaire & The Fix

Consider Figure 1. We are located at an unknown position D and we take two sextant measurements at different times giving us Ho1 & Ho2. Arc distance b1 = Zd1 = (90deg – Ho1). Similarly b2 = Zd2 = (90deg – Ho2). Thus our location is at the intersection of two great circle arcs emanating from GP1 & GP2. This can be solved by trigonometry and gives us our position or fix.

Fig.1 Two Altitude Solution

David Barrie’s book “The Sextant” (Ref.9/p.221) gives us insight into Marcq St.Hilaire and his intercept method (circa 1875). We don’t know where we are exactly, but we guess as best we can = AP. We need two measurements Ho1 & Ho2, and then we calculate Hc1/Az1 & Hc2/Az2 using the GP1/AP and GP2/AP. This was done with Nautical Almanac type tables as we shall see in the next section. Now we examine the intercepts:

Intercept1 = Ho1 – Hc1 if positive move along the Az1 a distance (Ho1-Hc1)*Re Km to AP’. Our position now lies along a Sumner line LOP1 perpendicular to the Az1.
Intercept2 = Ho2 – Hc2 if negative move away along the Az2 a distance (Ho2-Hc2)*Re Km to AP”. Our position now lies along a Sumner line LOP2 perpendicular to the Az2.
Position Fix = Intersection of LOP1 & LOP2

Fig.2 Marcq St.Hilaire Intercept Method


In order to solve the Intercept method manually with paper and pencil, we can use the Nautical Almanac NAO method or AP3270. The Nautical Almanac has tables that allow you to find the GP for the Sun/Moon/Planets & 57 Navigational stars for any hour of that particular year. There are also incremental tables for interpolation between hours to the second. It contains sight reduction procedures & tables to solve for Hc/Az given time & AP. It is a must as a first CelNav document to have. Figure 3 shows the completed form for Example 4 given on Page 285. We need to find the altitude Hc/Az for the Star Schedar on Feb 4th_2020 @ UT 06hrs 33min, EP = Lat 53deg N & Long = 5deg East. Four table look-ups are required, so you need to be alert! The advantage of NAO is that it’s all in one book.

Figure 4 shows the sight reduction form for the same problem using AP3270. The advantage of AP3270 is that only 2 table look-ups are required. Each method uses a slightly different approach and adjusts the EP to a different AP for whole number of degrees.
NAO: Hc =26deg 12min/Az = 27deg (AP = 53degN/5deg 15.4minE)
AP3270: Hc = 26deg 5min/Az = 26deg (AP = 53degN/4deg 52minE)

Fig.3 NAO Form for Nautical Almanac Solved Example 4 Page 285
Fig.4 AP3270 Form for Nautical Almanac Solved Example 4 Page 285

Celestial Navigation Basics & Equipment Course:

Fig.5 CelNav Course YouTube Video


#1. – “Celestial Navigation Basics Land Sea & Air – Course_a”

#2. – “Celestial Navigation Basics Land Sea & Air – Course_b”

#3. – “Celestial Navigation Basics Land Sea & Air – Course_c

#4. – “Celestial Navigation Basics – Hs Sextant Altitude”

#5. – “Celestial Navigation Basics – Ha Apparent Altitude”

#6. – “Celestial Navigation Basics – Ho Observed Altitude”

#7. – “Celestial Navigation Basics – Hc Calculated Altitude”

#8. – “Celestial Navigation Basics – Fix

#9. – “The Sextant: A Young Man’s Daring Sea Voyage and The Men Who Mapped The World’s Oceans”, David Barrie, ISBN 978-0062279354

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By Jeremy Clark

Jeremy Clark is a Senior Telecommunications Engineer and Advanced Amateur Radio Operator VE3PKC. He is the author of E-Books on Telecommunications, Navigation & Electronics.