Sextant-Observed Altitude 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 altitude and its calculation.
Apparent height (Ha) to observed height (Ho)
RED section of the worksheet explained on this page
This step involves correcting for atmospheric refraction as well as compensating for the varying diameters and distances of both the Sun and the Earth throughout the year.
Consequently, these adjustments collectively yield the final observed altitude, as if measured from the center of the Earth to the center of the Sun.
Sextant-Observed Altitude of the Sun:
Introducing various astronomical phenomenas 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 altitude, it is necessary to account for various phenomenas, such as refraction, semi-diameter, and parallax.
Consequently, these adjustments collectively result in the final observed altitude (Ho).
Although taken on deck with the sextant, once all corrections are applied it represents the geocentric altitude — the angle that would be measured from the Earth’s center to the Sun’s center.
This geocentric form is the one required for the astronomical triangle formulas.
apparent altitude (Ha) to observed altitude (Ho):
In fact, the altitude correction table compiles the three errors mentioned above!
They are important to understand conceptually, but you don’t need to memorize them, since the correction tables already include them.
Furthermore, there is a small overview of these 3 phenomenas at the bottom of this page
Refraction, Parallax and semi-Diameter
Once more, the altitude correction table summarizes the three errors discussed earlier.
To illustrate, small overview of these 3 phenomenas:
Refraction of the atmosphere
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.
At sunset, you may still see about two-thirds of the Sun above the horizon… but the astronomer laughs: for them, it’s already bedtime — thanks to refraction!
Parallax
However the parallax is negligible for the sun but important for the moon
Semi-diameter of the sun
To clarify LL/UL (lower limb and upper limb):
In practice we measure mostly the lower limb of the sun and not the center
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 = 147100000 km
Semi-Diameter Angle = arctan ( 696350/147100000) = 16’.3
Distance at the beginning of July sun-earth = 152100000 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.
Observed sextant altitude 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.
The star and planet corrections, as well as the lower limb correction, appear on this page in the Nautical Almanac.
A simple altitude correction table for the Sun is given below.
All the above data were calculated by the author and owner of www.easysextant.com. The tables apply to eye heights up to 12 meters and to lower-limb Sun observations only.
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:
altitude correction = 13′,4
Therefore:
Ho = Ha + altitude corr. = 20°13′,4
Hence, 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 altitude of the sun:
Example: Calculation of Observed Altitude of the sun:
