Calculation: The conversion from apparent altitude (Ha) to observed altitude (Ho) of the sun requires correction for atmospheric refraction and compensation for the varying diameters and distances of both the Sun and the Earth throughout the year.
Sextant Corrections at a Glance:
Hs to Ha – THEORY page 1
Hs to Ha – CALCULATION page 2
Ha to Ho – THEORY page 3
Ha to Ho – CALCULATION “ON THIS PAGE 4.
And three complete exercises: Hs ⇒ Ho on this page.
Moreover, these adjustments collectively result in the final observed altitude, measured from the center of the Earth to the center of the Sun.
This page contributes to the primary objective of offering guidance and interactivity on the calculation and understanding of the Line of Position (LOP) using only a sextant and the sun, and then tracing this line on a plotting sheet. See recommendations.
Example of calculation apparent altitude to observed altitude (Ha to Ho)
sextant apparent to observed altitude:
Three entries:
1)Ha = 32°14′.5 (Apparent altitude.)
In fact, this apparent altitude was obtained in the blue section (Hs to Ha)
2) Date: Observation somewhere in JULY
3) lower limb of the sun
Tables for eye height up to 12 meters and measurement of the Sun’s lower limb only.
In fact, App altitude is about 32°, the observation between is April and September and we took the lower limb → altitude correction = 14′.4
Sextant apparent to observed altitude: solution example
Hs …………………. = _ _° _ _’. _
index error…….. = _ _° _ _’. _
Dip………………… = _ _° _ _’. _
_________________________ +
Ha………………….. = 32° 14′.5
sun correct LL …= 00° 14′.4
__________________________ +
Ho…………………….= 32° 28′.9
After all necessary corrections, a sextant reading taken on deck provides the geocentric altitude, that is, the angle measured from the Earth’s center to the Sun’s center.
This distinction is important, because the trigonometric formulas used to compute the calculated altitude are likewise derived from the centers of the celestial bodies.
Observed altitude = 32° 29′,0
Three exercises to calculate sextant altitude (Hs) to observed altitude (Ho)
See on this page the downloadable tables for eye height up to 12 meters and for measurements of the Sun’s lower limb only.
exercise 1:
Temps de l’année: March
lower limb
`eye height
Answer exercise 1 : Ho = 42° 27.2′
*Because of sextant reading accuracy and rounding in either my correction tables or the official Nautical Almanac tables, small differences may appear between my results and yours. These differences should not exceed 0.3′.
Exercise 2
Temps de l’année: September
sextant altitude(Hs)
lower limb
index error
Non adjustable error
eye height
Answer exercise 2 : Ho = 56° 29.9′
Exercise 3
Temps de l’année: June
sextant altitude (Hs)
lower limb
index error
Non adjustable error
eye height
Answer exercise 3 : Ho = 52° 33.4′