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Celestial navigation relies on the method of intercept lines to determine a vessel's position by calculating the difference between an estimated altitude and the true altitude of a celestial body.0:04 Navigators use a sextant to measure the true altitude above the horizon and a nautical almanac to determine the body's coordinates.0:22 By assuming an estimated position, a navigator calculates the expected altitude and azimuth using spherical trigonometry.3:42 The difference between the true and estimated altitude provides the distance to move from the estimated position to the line of position.3:30 Intersecting two such lines from different celestial bodies fixes the vessel's location.7:00 The derivation of these formulas involves the spherical law of cosines and the law of sines, which relate the sides and angles of a spherical triangle.11:52 While Spanish nautical almanacs often require electronic calculators to solve these equations, British tables utilize logarithms to perform the same calculations manually, maintaining independence from electronic systems.59:45 Understanding the mathematical derivation of these formulas clarifies the underlying principles of celestial navigation.

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