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This kind of calculation requires few significant digits, and thus can be done with a slide rule. You can also time how much it takes by hand with pencil, as it was done in the old times, without a calculator and without a slide rule. However the main calculation which we do in CelNav, solving a spherical triangle, requires 5-6 digits, and this is not possible with a slide rule. Perhaps for this reason a slide rule is not in the list of standard equipment for a celestial navigator.