As shown in the following diagram, the observer measures the altitude in relation to the visible horizon from his position at O on the Earth’s surface. So, the observed altitude is the angle HOX. However, the true altitude is measured from the Earth’s centre in relation to the celestial horizon and is the angle RCX.
Point O will be approximately 6367 Km. from the centre of the Earth and so it would seem that the visible horizon is bound to be slightly offset from the celestial horizon. Because of the vast distances of the stars and the planets from the Earth, we can assume that, in their cases, the celestial horizon and the visible horizon correspond with very little error. However, in the cases of the Sun and the Moon, which are relatively near, a correction called Parallax must be added.
Parallax. We measure the altitude of a celestial body from our position in relation to our visible horizon; this is known as the observed altitude. However, when calculating the true altitude, measurements are made from the Earth’s centre in relation to the celestial horizon. The displacement between the observed position of an object and the true position is known as parallax.
Parallax corrections for stars and planets. Because the stars and the planets are at such great distances from the Earth, we can assume that, in their cases, the celestial horizon and the visible horizon correspond with very little error. However, in certain cases when extreme accuracy is needed, parallax corrections for Mars and Venus are required and these are listed in the altitude correction tables.
Parallax corrections for the Sun and the Moon. Because the Sun and the Moon are relatively close to the Earth, parallax will be significant and so a correction has to be made. These corrections are included in the altitude correction tables and therefore do not have to be applied separately.
Horizontal Parallax. Parallax error is greatest when the celestial body is close to the horizon and decreases to zero as the altitude approaches 90o. It is negligible except in the case of the Moon which is close to the Earth in comparison with the other celestial bodies. Because horizontal parallax is significant in the case of the Moon, a separate correction (abbreviated to HP) has to be applied.
Links: Altitude Correction for Dip Altitude Correction For Semi-Diameter
(A thorough treatment of this topic can be found in the book Astro Navigation Demystified).
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