Celestial navigation

Celestial navigation is a position fixing technique that was the first system devised to help sailors locate themselves on a featureless ocean. Celestial navigation uses angular measurements (sights) between the horizon and a common celestial object. The Sun is most often measured. Skilled navigators can use the Moon, planets or one of 57 "navigational stars" that are described in nautical almanacs. Sights on the moon, planet and stars allow navigation to occur at night or when clouds obscure other objects.

Celestial navigation works because at any given instant of time, any particular celestial object (e.g. Spica, the Moon, Jupiter) will be directly over a particular geographic position on the Earth. That is it will have an exact latitude and longitude. The actual angle to the celestial object locates the navigator on a circle on the surface of the Earth. Every location on the circle has the same angle to the celestial object. The circle will be centered on the celestial object's latitude and longitude. Two or three sights on different objects, or at different times establish that the navigator is at the intersection of several such circles. The sights are reduced to positions by simple methods that add and subtract logarithms of trigonometric values taken from tables.

Accurate angle measurement evolved over the years. One simple method is to hold the hand above the horizon with your arm stretched out. The width of a finger is an angle just over 1.5 degrees. The need for more accurate measurements led to the development of a number of increasingly accurate instruments, including the kamal, astrolabe, octant and sextant. The sextant is the most accurate because it measures angles from the horizon, eliminating errors caused by the placement of an instrument's pointers, and because its dual mirror system cancels relative motions of the instrument, showing a steady view of the star and horizon.

Navigators measure distance on the globe in degrees, minutes and seconds. A nautical mile is defined as 1852 meters, but is also (not accidentally) about one minute of angle on the globe. Sextants can be read accurately to within 0.2 minutes. So, with two sights, the correct time to within a second and the estimated position of the observer, the observer's position can be determined within (theoretically) 0.2 miles, about 400 yards (370 m). Most ocean navigators, shooting from a moving platform, can achieve a practical accuracy of 1.5 miles (2.8 km), more than close enough to see a harbor or city.

Practical celestial navigation usually requires a chronometer to measure time, a sextant to measure the angles, an almanac giving angular schedules of celestial objects, a set of sight reduction tables to help perform the math, and a chart of the region. With sight reduction tables, the only math required is addition and subtraction. Small handheld computers and laptops enable modern navigators to "reduce" sextant sights in minutes, by automating all the calculation and data lookup steps. Most people can master simpler celestial navigation procedures after a day or two of instruction and practice, even using manual calculation methods.

Modern practical navigators nearly always use celestial navigation in combination with satellite navigation to correct a dead-reckoning track, that is, a course estimated from a vessel's position, angle and speed. Using multiple methods helps the navigator to detect errors, and simplifies procedures. When used this way, a navigator will from time to time take the sun's altitude with the sextant, then compare that with a precalculated altitude based on the time and estimated position of the observation. On the chart, one will use a compass to mark where the arc of each measurement intersects the dead-reckoning line. If the arc shows one to be more than a few miles from the estimated position, one may take more observations to restart the dead-reckoning track.

In the event of equipment or electrical failure, one can get to a port by simply taking sun lines a few times a day and advancing them by dead reckoning to get a crude running fix.

Latitude. Latitude was measured in the past either at noon (the "noon sight") or from Polaris, the north star. Polaris stays within 1 degree of always being over the north pole. If a navigator measures the angle to Polaris and finds it to be 10 degrees from the horizon, then he is on a circle at about 10 degrees of geographic latitude. Angles are measured from the horizon because locating the point directly overhead, the zenith, is difficult. When haze obscures the horizon, navigators use artificial horizons, which are bubble levels reflected into a sextant.

Latitude can also be determined by the direction in which the stars travel over time. If the stars rise out of the east and travel straight up you are at the equator, but if they drift south you are to the north of the equator. The same is true of the day-to-day drift of the stars due to the movement of the Earth in orbit around the Sun; each day a star will drift approximately one degree. In either case if the drift can be measured accurately, simple trigonometry will reveal the latitude.

Longitude can be measured in the same way. If one can accurately measure the angle to Polaris, a similar measurement to a star near the eastern or western horizons will provide the longitude. The problem is that the Earth turns 15 degrees per hour, making such measurements dependent on time. A measure only a few minutes before or after the same measure the day before creates serious navigation errors. Before good chronometers were available, longitude measurements were based on the transit of the moon, or the positions of the moons of Jupiter. For the most part, these were too difficult to be used by anyone except professional astronomers.

The solution to the longitude problem took many years to solve. Two useful methods evolved during 1700-1900 CE, and are still practiced today: lunar distance, which does not rely on a timepiece, and use of an accurate timepiece, or chronometer.

Lunar Distance. The older method, called "lunar distances", was refined in the 18th century. It is only used today by sextant hobbyists and historians, but the method is sound, and can be used when a timepiece is not available or its accuracy is suspect during a long sea voyage. The navigator precisely measures the angle between the moon and a body like the sun or a selected group of stars lying along the ecliptic. That angle, after it is corrected for various errors, is the same at any place on the surface of the earth facing the moon at a unique instant of time. Old almanacs used to list angles in tables. The navigator could thumb through the almanac to find the angle he or she measured, and thus know the time at Greenwich. Modern handheld and laptop calculators can perform the calculation in minutes, allowing the navigator to use other acceptable celestial bodies than the old nine. Knowing Greenwich time, the navigator can work out longitude.

Accurate Timepieces. The considerably more popular method was (and is) to use an accurate timepiece to directly indicate the time of a sextant sight. The need for accurate navigation led to the development of progressively more accurate chronometers in the 18th century. Time is measured with a chronometer, a quartz watch, or a short wave radio broadcast from an atomic clock. A quartz wristwatch normally keeps time within a half-second per day. If it is worn constantly, keeping it near body heat, its rate of drift can be measured with the radio, and by compensating for this drift, a navigator can keep time to better than a second per month. Traditionally, a navigator set his chronometer from his sextant, at a geographic marker surveyed by a professional astronomer. This is now a rare skill, and most harbor masters cannot locate their harbor's marker.

Traditionally, three chronometers were kept in gimbals in a dry room near the center of the ship. They were used to set a watch for the actual sight, so that no chronometers were ever risked to the wind and salt water on deck. Winding the chronometers was a crucial duty of the navigator, logged as "chron. wound." for checking by line officers. Navigators also set the ship's clocks and calendar.

Modern Celestial Navigation. Modern celestial navigation methods, developed in the 19th century, allow navigators to measure latitude as part of a fix, by sighting 2 or 3 bodies within a few minutes of each other. When the celestial line of position concept was discovered in 1837, leading to the modern mathematical "intercept method" of reducing sextant sights later in the 19th century, navigators were finally able to obtain both latitude and longitude at once from their celestial observations, giving them a position "fix", rather than viewing these two properties as separate entities. At the turn of the 21st century, advanced electronic and computer systems had evolved enabling navigators to obtain automated celestial sight fixes. These rare systems are regarded mainly as potential backups to the more reliable satellite positioning systems, but could play a role in future spaceship travel.

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