Observed sextant height of the sun

Observed sextant height of the sun: On this self-instruction platform, you’ll discover the significance of sextant corrections through a series of eight identical exercises, commencing with the LA ROCHELLE exercise.

On this page, we explore the theory behind determining the observed height of the sun. If you’ve been following the course, you’ve already learned about apparent height and its calculation.

Observed sextant height of the sun: Apparent height (Ha) to observed height (Ho)

Altitude = Height

This step involves correcting for atmospheric refraction as well as  compensation for the varying diameters and distances of both the Sun and the Earth throughout the year.

These adjustments collectively result in the final observed height, measured from the center of the Earth to the center of the Sun.


Big waves at Los Hervideros, Lanzarote. Author image: IDS.photos from Tiverton UK

Observed sextant height of the sun:

RED section of the worksheet explained on this page

Introducing various astronomical phenomena that can affect the accuracy of observing the Sun.

After correcting errors specific to the sextant and the height of the eye above the horizon to obtain the apparent height, it is necessary to account for various phenomena, such as refraction, semi-diameter, and parallax.

This process ensures the accurate measurement of the center of the Earth to the center of the sun, and is referred to as the observed height.

Observed sextant height of the sun, image la hauteur observée
observed height Ho

apparent height (Ha) to observed height (Ho):

The altitude correction table compiles the three errors mentioned above! They are interesting, but you don’t need to remember them!!

There is a small overview of these 3 phenomenas at the bottom of this page


Sea Cliff Bridge (Clifton). Looking towards Coalcliff. Author image: Coalcliff

Observed sextant height of the sun:

Refraction, Parallax and semi-Diameter

While these errors are fascinating, there’s no requirement to memorize them!

Once more, the altitude correction table summarizes the three errors discussed earlier.

Small overview of these 3 phenomena:

Refraction of the atmosphere
Observed sextant height of the sun, image refraction of the atmoshere

In fact the refraction formula is:   

⎼ ( 55,7 ✕ Tan (90° ⎼ altitude sight)) / 60 (always negative)

 The effect is that the sun appears to be higher above the horizon than it actually is.

Parallax
Observed sextant height of the sun, image parallax

However the parallax is negligible for the sun but important for the moon

Semi-diameter of the sun
Observed sextant height of the sun, image semi diameter

To clarify LL/UL (lower limb and upper limb):

To clarify in practice we mesure mostly the lower limb of the sun and not the center

apparent height (Ha) to observed height (Ho):

the distance between the earth and sun changes over the year, so the semi diameter correction angle will change also a little

The term “semi-diameter” is commonly used in astronomy and geodesy to refer to half of the apparent or angular diameter of an object in the sky, such as a planet or star. This is because the apparent size of these objects is usually measured in angular units, such as degrees, minutes, and seconds of arc.

The semi-diameter of the sun  696350 km 

Distance at the beginning of January sun-earth = 147,100,000 km

Semi-Diameter Angle = arc Tan ( 696350/147100000) = 16’,3

Distance at the beginning of July sun-earth = 152,100,000 km

Semi-Diameter Angle = arcTAN ( 696350/152100000) = 15’,7

To summarize in the permanent Altitude correction tables from Nautical Almanac, this change in the semi-diameter results in two different correction periods:

The period from October to March, and the period from April to September.

In conclusion, using the altitude correction table is relatively easy.

It compiles the three errors mentioned above.


Storm clouds pouring rain down on nearby Bora Bora. Author image: Peter Gill

Observed sextant height of the sun:

The use of the altitude correction tables

10°-90° SUN, STARS, PLANETS

Permanent table of the Nautical Almanac

An example how to use the altitude corrections tables:

  • As an example, suppose that the apparent altitude (Ha) of the sun is 20°
  • We observed the lower limb of the sun.
  • The date of the sight is sometime in June.
Observed sextant height of the sun, image altitude correction tables
Simplified altitude correction tables from Nautical Almanac (here for sun only)

You can find a more elaborate altitude correction table below.

So now we look in the altitude correction table and then we find in the period april-sept. with Ha = 20° and using the lower limb of the sun:

Ho = 13′,4


How it was calculated 😆 :

During the period from April to September, the average semi-diameter is 15,9 minutes.

Taking into account the refraction of ⎼2′,5 minutes (calculated as ⎼(55.7*tan(90⎼20)/60)).

The final result is ( 15′,9 + ⎼2′,5 ) = 13′,4

Undoubtedly it’s worth noting that the parallax of the sun can be disregarded in this context.


Observed sextant height of the sun:

Example: Calculation of Observed Sextant Height of the sun:


Looking east at American Marram Grass. Author image: Royalbroil