Abstract
If it were possible to determine the velocity of a vessel relative to the surface of the Earth, we would know its position at any instant by using the formulae of the previous section in all cases with a v constant.
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Notes
- 1.
Except in the case of the INERTIA NAVIGATION SYSTEMS. See appendix at the end of this section.
- 2.
In this chapter I merely want to state qualitatively the exact solution to a terrestrial fix by employing the angular distances outlined above.
- 3.
According to Joshua Slocum, there was at least one world leader in the 19th Century who still believed that the Earth was flat.
- 4.
The fact that the stars change their position on the Celestial Sphere will be explained and incorporated in the actual calculations in a later chapter.
- 5.
This fixed point, called Aries, is also a variable point as will be explained later.
- 6.
- 7.
To eliminate any ambiguity one must apply formulae (5) Sect. 2.2. rigorously which, in turn, makes it necessary to determine the sign and absolute value of he argument of cos−1 X to assure that ǀXǀ ≤ 1. (See appendix this section.) In addition, it is also necessary that the selected results meet all the criteria of the quadrant orientation diagram. The latter eliminates all the guess work.
- 8.
This analysis is explicitly provided in Sect. 2.6.
- 9.
In all cases where GHA S1(T1) < GHA S2(T2), the parallactic angle α becomes the angle at S2. By considering again all twelve relevant cases, we can again set up a box-diagram denoted by (S1, S2) = (S2, S1), and thereby reducing those cases to the previous ones. Example: (II, III) = (III, II).
- 10.
See Sect. 2.6 for an explicit error analysis.
- 11.
Note that whenever SHA S1 < SHA S2, it is possible that GHA S1(T1) > GHA S2(T2)—check.
- 12.
A prudent navigator always knows approximate latitude.
- 13.
A more realistic interpretation of the situation depicted in Fig. 2.8.3 results if one approximates all tangents to those circles by loxodromes that then appear as straight lines on the Mecator plotting sheets or charts.
- 14.
And bounded from above.
- 15.
The time is actually not required.
- 16.
In all cases where the vessel moves between the two culminations of the star during the period of 12h Sid. T. = 11h.96723467 Sol. M. T. the altitude of the first culmination in formula (1) has to be adjusted by either adding or subtracting the latitude made good by the vessel during that interval of time. This change in latitude can be easily calculated by using the corresponding formulae of Sect. 1.2 or 1.3.
- 17.
RA(CO) = [GHA\(\Upsilon\) − GHA(CO)]/15.
- 18.
When I practiced navigation onboard a chartered “DWOW” in the Bay of Bombay, India (now the Bay of Mumbai) back in 1974, I relied primarily on sunrise/set observations and also on low altitude observations executed with the help of an ancient Arabian “KAMEL”.
- 19.
Also see the evaluation of said danger in Chap. 3, Sect. 3.2.
- 20.
\( \begin{aligned} \upvarphi & = - \sin^{ - 1} \left( {\frac{\sin \updelta }{\text{C}}} \right) - \upalpha ,\upalpha = \tan^{ - 1} \left( {\frac{{\cos {\text{A}}_{\text{z}} }}{{\tan {\text{H}}}}} \right),{\text{with A}}_{\text{z}} = \sin^{ - 1} \left( {\frac{{\sin {\text{t cos}}\updelta }}{{\cos {\text{H}}^{ * } }}} \right) \\ {\text{C}} & = \left( {1 - \cos^{2} {\text{H}} \sin^{2} {\text{A}}_{\text{z}} } \right)^{{\frac{1}{2}}} \,{\text{and}}\,{\text{t}} = - \left({\uplambda + }{\text{GHA}} \right)\,{\text{or}}\,{\text{t}} = {\text{t}}_{ * } ( {\text{T}}_{0} ). \\ \end{aligned} \).
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Zischka, K.A. (2018). Astro-navigation. In: Astronavigation. Springer, Cham. https://doi.org/10.1007/978-3-319-47994-1_2
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DOI: https://doi.org/10.1007/978-3-319-47994-1_2
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