This method is a practical procedure to reduce celestial sights with the needed accuracy, without using electronic tools such as calculator or a computer. And it could serve as a backup in case of malfunction of the positioning system aboard.
Doniol The first approach of a compact and concise method was published by R. Doniol in 1955 and involved
haversines. The altitude is derived from \sin (Hc) = n - a \cdot (m + n), in which n = \cos (Lat - Dec), m = \cos (Lat + Dec), a = \operatorname{hav}(LHA). The calculation is:
n = cos(
Lat −
Dec)
m = cos(
Lat +
Dec)
a = hav(
LHA)
Hc = arcsin(
n −
a ⋅ (
m +
n))
Ultra compact sight reduction A practical and friendly method using only
haversines was developed between 2014 and 2015, and published in NavList. A compact expression for the altitude was derived using haversines, \operatorname{hav}(), for all the terms of the equation: \operatorname{hav}(ZD) = \operatorname{hav}(Lat - Dec) + \left( 1 - \operatorname{hav}(Lat - Dec) - \operatorname{hav}(Lat + Dec) \right) \cdot \operatorname{hav}(LHA) where ZD is the
zenith distance, Hc = (90^\circ - ZD) is the calculated altitude. The algorithm if
absolute values are used is: For the azimuth a diagram was developed for a faster solution without calculation, and with an accuracy of 1°. This diagram could be used also for star identification. An ambiguity in the value of azimuth may arise since in the diagram 0^\circ \leqslant Z \leqslant 90^\circ. Z is E↔W as the name of the meridian angle, but the N↕S name is not determined. In most situations azimuth ambiguities are resolved simply by observation. When there are reasons for doubt or for the purpose of checking the following formula should be used: \operatorname{hav}(Z) = \frac{\operatorname{hav}(90^\circ \pm \vert Dec\vert) - \operatorname{hav}(\vert Lat\vert - Hc)}{1 - \operatorname{hav}(\vert Lat\vert - Hc) - \operatorname{hav}(\vert Lat \vert + Hc)} The algorithm if
absolute values are used is: This computation of the altitude and the azimuth needs a haversine table. For a precision of 1
minute of arc, a four figure table is enough.
An example == See also ==