A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Sean C
Date: 2019 Nov 10, 15:11 -0800
The calculated altitude is the geocentric altitude of the center of the body above the celestial horizon - without the effects of refraction or parallax in altitude. In other words, the Hc is what you would measure if you were at the center of the Earth and there was no atmosphere and you could perfectly measure the altitude of the center of the body above a fictitious horizon exactly 90° from the zenith of your orientation.
The sextant altitude (Hs) is corrected for index error and/or any systematic error and is then corrected for dip of the horizon (height of eye correction) to bring the measurement "up" from the visible [topocentric] horizon to the sensible horizon. The result is called the apparent altitude (Ha). The apparent altitude is then corrected for refraction of the atmosphere and, if necessary, parallax in altitude (which accounts for the difference between topocentric and geocentric measurements) and semi-diameter to obtain the observed altitude (Ho). Ideally, the observed altitude would match the calculated altitude - although this is rarely the case due to some unaccounted for error or using an assumed position other than the observer's actual position - which is usual practice. The stars (including the Sun) Jupiter and Saturn are all far enough away that the light rays coming from them are practically parallel. This means that there is no need for a parallax correction* because their altitude above the topocentric sensible horizon will be esentially the same as above the celestial horizon. And for CN purposes (using a common 3.5x magnification scope), all bodies except the Sun and Moon have no appreciable diameter, so no SD correction is needed for stars and planets. With a higher magnification scope, planets may have a barely visible diameter and it is advised to "split" the body on the horizon.
Hope that helps.
*I believe the Nautical Almanac accounts for the very small effect of the parallax of the Sun - either in its daily tabulated data or in the altitude correction table.