## Correction Tables for Sextant Altitudes
The Altitude-Intercept method now generally used for Celestial Navigation,
is based on the comparison of an "observed altitude" (Ho) with a related
"computed altitude" (Hc). - The celestial bodies have no physical dimensions and observations are made from the center of the Earth.
- Light rays from celestial bodies come from infinitely far away and hence reach the Earth parallel to one another.
- The Earth has no atmosphere and air has no index of refraction.
These assumptions are not full-filled for observations made in the physical world.
In order to put the mathematically computed altitude and the "real world"
observed altitude on an alike basis of comparison,
some "corrections" must be applied to the measured sextant altitude.
The sextant altitude (Hs) corrected for index error (IE) and dip correction (dip) is called "apparent altitude" (Ha). This value is used as entry for further corrections (refraction (Refr) and parallax (Prlx) ).
## Correction Table for DipThe "dip correction" compensates for the fact that observations made by a navigator through a sextant are not performed on the "level of the horizon". The difference between the visible horizon - the line where the sky meets the sea - and the geodial horizon - the plane perpendicular to the zenith line in the location of the observer - is called "Dip of the Horizon". This "dip" (of the horizon) is not only caused by the elevation of the observer's eye above the plane of the geoidal horizon (He) but also by atmospheric refraction.
The correction for dip and the distance to the horizon can also be calculated with the following formulas: Correction_for_Dip ['] = 1.760 ['/sqrt(m)] * sqrt (He [m]) Distance_to_the_Horizon [Nm] = 2.075 [Nm/sqrt(m)] * sqrt(He [m]) These equations are empirical and include the effect of the curvation of the Earth as well as the effect of the atmospheric refraction on the dip of the horizon. A more detailed discussion on this can be found in the Notes on the Dip of the Horizon ## Correction Table for Refraction
Refraction is an optical characteristic of the Earth's atmosphere.
Light coming from outer space is deflected to the Earth's surface when it travels
through the atmosphere.
This is caused by the density gradient of the air in the atmosphere.
Air closer to the Earth's surface is denser that in the higher atmospheric layers.
The largest corrections for refraction occur at high pressure and low temperature.
Under these conditions the "air density" and thus refraction will obtain the highest
value. A simple empirical formula for calculating refraction from the apparent Altitude was developed by G.G. Bennett in 1982. The formula is used in the U.S. Naval Observatory's "Vector Astronomy Software" and is reported to be consistent with more complex algorithms within 0.07' over the full range of apparent Altitudes from horizon (0°) to Zenith (90°). Refr ['] = 1.0 ['] / tan(Ha [°] + 7.31 / (Ha [°] + 4.4) ) The formula is valid for so called atmospheric standard conditions for atmospheric pressure (1010 hPa) and air temperature (10°C), both measured at sea level. For conditions other than these, the value of 'Refr' should be be multiplied by the following (linear) correction factor: f = P [hPa] /(273+T [10°C] ) * 283/1010
The resulting refraction value for arbitrary temperature and air pressure is: Refr(P,T) = f * Refr. ## Tables for Parallax CorrectionParallax correction of apparent altitudes (Ha) is needed for celestial bodies which are "close" to the Earth. This applies to the Moon, which may have a parallax angle of more than 1°; but also the altitudes for the planets Venus and Mars may be corrected for parallax effects to obtain the best possible results.
The horizontal parallax angle (HP) and the "apparent altitude" corrected for
Refraction and Semi-Diameter (SD) are used as entries for the Parallax Correction
Tables. ## Tables for combined Parallax - Semi-Diameter CorrectionFor the Moon, both the corrections for Semi-Diameter and for
Parallax are significant and must be considered in the process of reducing
the measured topographic altitude at the surface of the Earth to the geographical
altitude as would be measured at the center of the Earth. |

Cover << Sail Away << Celestial Navigation << . | last updated: 08-Dec-2018 |