Longitude by chronometer

Abstract: The automated repeating sextant (ARS) is a navigational instrument suitable for air, sea and land use. The ARS uses an electronic artificial horizon, an A/D conversion board and either microchips or a computer, with software, to read a celestial body's altitude above the horizon repeatedly in a brief period of time, and then compute a line of position from a statistically enhanced mean altitude; after a second or any successive line of position has been obtained the instrument either provides the latitude and longitude of the navigator, or combines the latitude and longitude with a graphic portrayal of the position on a simplified grid map. The instrument averages numerous individual observations and is relatively small, light and fast. The ARS may be embodied in a fully automated, continually-operating mode with a micro-computer, or may be embodied in a handheld version that is switched on and off. The body sighted by the ARS may be either a natural celestial body (sun, moon, navigational planet or navigational star) using light wave signals, or an artificial celestial body (manmade satellite), using radio frequency signals.

Abstract: : The object of celestial navigation is the determination of the latitude and longitude of a vessel at a specific time, through the use of observations of the altitudes of celestial bodies. Each observation defines a circle of position on the surface of the Earth, and the small segment of the circle that passes near the observer's estimated position is represented as a line of position (LOP). A position fix is located at the intersection of two or more LOPs. This construction works for a fixed observer or simultaneous observations. However, if the observer is moving, the LOPs from two consecutive observations do not necessarily intersect at a point corresponding to the observer's position at any time; if three or more observations are involved, there may be no common intersection. Since celestial navigation normally involves a single observer on a moving ship, something has to be done to account for the change in the observer's position during the time required to take a series of observations. This report reviews the methods used to deal with the observer's motion. A basic familiarity with the procedures, terminology, and notation of celestial navigation is assumed.

Abstract: This work presents a direct method for obtaining the latitude and longitude of an observer from the observed altitudes of two celestial bodies. No assumed position or dead-reckoned position or plotting is required. Starting with the Greenwich hour angles, declinations, and observed altitudes of each pair, the latitude and longitude of the two points from which the observations must have been made are directly computed. The algorithm is presented in the paper, along with its derivation. Two different, inexpensive, programmable pocket electronic calculators were programmed to execute the algorithm, and they do it in under 30 s. The algorithm was also programmed to run on a personal computer to examine the effect of the precision of the calculations on the error in the results. The findings show that the use of eight decimal places in the trigonometric computations provides acceptable results.

Abstract: A sight reduction apparatus includes a sextant, a processor, and a nautical almanac, preferably all provided in an unitary housing. The sextant includes a fixed telescope which is pointed at a known celestial body, and a radial arm is moved against an arc graduated in degrees until a mirror mounted on the sextant reflects an image of the horizon down the telescope to coincide with the known celestial body. The angular elevation of the celestial body, corrected for the exact time and date, gives the position of the user on an imaginary circle. The nautical almanac provides essential data for determining the location of a predetermined list of celestial bodies relative to a fixed location. The processor is programmed to determine the position of a user based upon measurements made with respect to two celestial bodies using the sextant and information provided in the nautical almanac and to further provide the position of a user in terms of latitude and longitude. Preferably, the processor includes a memory having a matrix of data and equations which enable the processor to create a perpetual nautical almanac.