Great circle sailing

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SLIDE 15.3. When using sight reduction tables, substitute your departure latitude for the AP latitude; the destination latitude for the declination; and subtract the altitude from 90° to get the distance. The value of Zn, obtained from the tables, is the departure course.

SLIDE 15.4. It’s a bit more complicated to understand how to use tables for great-circle distances greater than 90°. We start by thinking of altitudes below the horizon, and antipodes: The antipode of a location on earth is the point directly on the opposite side of the earth. A straight line drawn from a point through the center of the earth connects to its antipode on the other side of the earth. Each point is the antipode of the other. The above figure is drawn in the plane of the departure, the destination, and the destination’s antipode. It shows that a body with an altitude H below the horizon has an antipode with the same altitude H which is above the horizon. Thus in the above figure, the great-circle distance from the departure to the destination is equal to 90° plus the altitude of its antipode which is above the horizon, and therefore is listed in the sight reduction tables.

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