THE PRINCIPLES of the celestial sun sight

THE PRINCIPLES of the celestial sun sight: Understanding the expression LOP (line of position) in three steps.

Please remember that the entire context of this website originates from the La Rochelle exercise. This exercise serves as the gateway leading you to an interactive worksheet that offers comprehensive, step-by-step guidance for both calculations and theoretical aspects.

Classic marine decorative image: message in a bottle

Introduction:

THE PRINCIPLES of the celestial sun sight, image observed height and calculated height
THE PRINCIPLES of the celestial sun sight, text of the principles 1
THE PRINCIPLES of the celestial sun sight, text of the principles 1

The St. Marcq Hilaire method involves comparing two entirely different methods:

THE PRINCIPLES of the celestial sun sight, image of true altitude circle (observed circle)

While a thread stretched between the Sun center and the Earth center strikes the Earth’s crust at the point GP.

GP stands for Geographical Position.

The three observers see the sun at the same angle (altitude).

The red circle is called the true or observed altitude circle after some corrections, which we will learn about on this website.


THE PRINCIPLES of the celestial sun sight

The required conditions are as follows: the estimated position must not have an uncertainty of more than 30 miles. The time of the measurement with the sextant must be equal to the time integrated into the calculation.

In this case, the two circles are close together with a horizontal difference on the Earth called the intercept.

The two circles Ho and Hc and the line of postion

The estimated position serves as the reference point for plotting the true altitude (observed) circle, locally associated with a straight line, called the line of position.

The method, which isn’t purely mathematical, involves two independent circles situated closely to each other with nearly identical characteristics; it’s also known as the intercept method.

Of course, it’s all about the observed altitude circle, taken with the sextant but it lacks a usable reference because the geographical position (GP) point, which lies in the center of your observed circle, is too far away and cannot be found on your nautical chart.

It is important to remember that this point (GP) is used in our mathematical spherical formulas.

THE PRINCIPLES of the celestial sun sight, image of the nautical almanac
As we will see, the GP (Geographical Position) point is defined by the nautical almanac using the sun’s declination and the Greenwich Hour Angle (GHA).
Marbella fishing boat author image: Hernán Piñera

The line of position

classic marine ancient decorative image of a telegraph on the bridge


A Line of Position (LOP) is a marked straight line on a nautical chart that represents the potential location of a vessel, determined using a sextant and relevant calculations.

Essentially, it signifies that the vessel is positioned somewhere along this line, yet it doesn’t provide an exact fix on its location.

Cloud Ocean And Moon, Author image: Jason Efstathiou

the solution

To accurately determine a vessel’s position, it is necessary to have the intersections of at least two LOPs. The process involves taking an initial observation with a sextant to measure the sun’s height above the horizon and calculate the first LOP.

Subsequently, a second observation is taken some time later as the sun changes its azimuth angle during its east-to-west movement. The second LOP is then calculated, and the intersection of these two lines reveals the vessel’s precise position.


beautiful sunrise. Author image: Praveenshashika

THE PRINCIPLES of the celestial sun sight in 3 steps:

1. Obtaining the observed circle (Ho) with the sextant.

3. Comparing them.

THE PRINCIPLES of the celestial sun sight: step 1
classic marine decorative image of a petrol lamp

Ho (observed height)

On our unknown but true position, we measure the height of the sun above the horizon with a sextant.

THE PRINCIPLES of the celestial sun sight, image of a sextant observation

After making all necessary sextant corrections (which will be explained later), we modify this height as if we were at the center of the earth and call it the observed altitude.(Ho)

THE PRINCIPLES of the celestial sun sight, image simplified corrections of the sextant altitude
simplified corrections of the sextant altitude
THE PRINCIPLES of the celestial sun sight, image apparent and true horizon
Attention: center earth, center sun

The sextant turned towards the point GP during the observation.

The (LOP) : line of position is a portion of the circle that is:

locally assimilated as a straight line!

The L.O.P is therefore perpendicular to the direction of the sun.


Havelock Island, Andaman Islands, India. Author image: Vyacheslav Argenberg

decorative image of a life buoy

Hc (calculated height)

At our dead reckoning position, we use the exact time of the observation, the nautical almanac, and the spherical trigonometry formulas to calculate the height of the sun, which is referred to as the calculated height (Hc).

simplified worksheet

That is to say Center Earth, Center Sun.

To summarize these spherical trigonometry formulas will always calculate from Center Earth, Center Sun, or Center Star, Moon, or Planets.

At the same time we also calculate with the spherical trigonometry formulas the direction of the sun. (azimuth)

The calculated height (Hc) also has its own position circle.


Islands of the Andaman sea. Author image: Jukka from HELSINKI, Finland

THE PRINCIPLES of the celestial sun sight: step 3
decorative image: sea bird

compare Ho et Hc:

The Ho and Hc values are completely independent of each other.

Naturally, the calculated height includes the exact time of the observation with the sextant

THE PRINCIPLES of the celestial sun sight, text difference between Ho and Hc

While our dead reckoning (estimated position) is not too far off from our true position, we can compare the circle of positions Ho with Hc.

To clarify we can estimate that the circle of position Ho is parallel to the circle of position Hc, since the two circles are close.

It is preferable that the dead reckoning uncertainty does not exceed more than 30 miles.

In other words using dead reckoning on the map and the direction of the sun, we can draw a Line of Position Hc perpendicular to the direction of the sun that passes over our dead reckoning position.

That’s our reference!


The distance between the two lines of positions is called the intercept and we adopt Ho – Hc = intercept.

THE PRINCIPLES of the celestial sun sight, image intercept
THE PRINCIPLES of the celestial sun sight, image both calculated and observed circle
THE PRINCIPLES of the celestial sun sight, image circle Ho and Hc
circle Hc and Ho On a nautical chart, this circle is drawn as a straight line.
The outcome and the manner in which we mark the ultimate line of position.

In practice, neither the Line of Position (L.O.P.) for our Dead Reckoning (D.R.) position nor the circles are plotted or drawn.

THE PRINCIPLES of the celestial sun sight, image Ho and Hc and intercept
THE PRINCIPLES of the celestial sun sight

Hence, imagine that your estimated position based on dead reckoning is actually your true position.

While, at this moment, you use a sextant to measure the height of the sun and calculate its height using your formulas.

In this scenario, the observed height will be equal to the calculated height.

THE PRINCIPLES of the celestial sun sight, image Ho from center earth
THE PRINCIPLES of the celestial sun sight, image Ho from center eartc

Now, the intercept will be zero, and the two lines of positions join as they pass over the dead reckoning position perpendicular to the sun’s direction.


Classic marine image: barrel.
Firstly how to calculate the intercept?
THE PRINCIPLES of the celestial sun sight, image intercept between Ho and Hc
THE PRINCIPLES of the celestial sun sight, image intercept between Ho and Hc
Additionally to better understand the 1′.5 nautical mile see the definition “nautical mile”

THE PRINCIPLES of the celestial sun sight

To clarify if the intercept is positive or negative:
Intercept (+) Ho> Hc
THE PRINCIPLES of the celestial sun sight, image intercept +

+ “towards the sun”


Intercept( -) Hc > Ho
THE PRINCIPLES of the celestial sun sight, image intercept -

– “away from the sun”


THE PRINCIPLES of the celestial sun sight: How to draw the LOP on the map:
decorative image: seaman's hat

In conclusion four examples

+ “towards the sun” (positif)

– “away from the sun” (negatif)

THE PRINCIPLES of the celestial sun sight, four examples azimuth and intercept
the triangle symbol is the dead reckoning position on our map

In fact we will learn how to construct a map ourself.


THE PRINCIPLES of the celestial sun sight: Additional Knowledge:

Concerning the time interval between two Lines of Position (LOPs), the process of transferring a LOP, and understanding the uncertainty area associated with a LOP

Sun’s LOP running fix and the uncertainty zone.

Day planning with the two sun LOP’s

As a matter of fact, using the local apparent noon sight latitude with the sun is a widely adopted technique in maritime navigation.

Undoubtedly, it offers a straightforward and swift approach for determining latitude.

Local apparent noon sight latitude

Calculate Local Apparent Noon Time