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## Example

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- Sun Moon (annotated).gif -
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An example illustrating the concept behind the intercept method for determining one's position is shown to the right. (Two other common methods for determining one's position using celestial navigation are the longitude by chronometer and ex-meridian methods.) In the adjacent image, the two circles on the map represent lines of position for the Sun and Moon at 1200 GMT on October 29, 2005. At this time, a navigator on a ship at sea measured the Moon to be 56 degrees above the horizon using a sextant. Ten minutes later, the Sun was observed to be 40 degrees above the horizon. Lines of position were then calculated and plotted for each of these observations. Since both the Sun and Moon were observed at their respective angles from the same location, the navigator would have to be located at one of the two locations where the circles cross.In this case the navigator is either located on the Atlantic Ocean, about {{convert|350|nmi|km}} west of Madeira, or in South America, about {{convert|90|nmi|km}} southwest of AsunciÃ³n, Paraguay. In most cases, determining which of the two intersections is the correct one is obvious to the observer because they are often thousands of miles apart. As it is unlikely that the ship is sailing across South America, the position in the Atlantic is the correct one. Note that the lines of position in the figure are distorted because of the map's projection; they would be circular if plotted on a globe.An observer at the Gran Chaco point would see the Moon at the left of the Sun, and an observer in the Madeira point would see the Moon at the right of the Sun.

## Angular measurement

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- Using sextant swing.gif -
Using a marine sextant to measure the altitude of the sun above the horizon
Accurate angle measurement evolved over the years. One simple method is to hold the hand above the horizon with one's arm stretched out. The width of the little finger is an angle just over 1.5 degrees elevation at extended arm's length and can be used to estimate the elevation of the sun from the horizon plane and therefore estimate the time until sunset. 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 and octant are most accurate because they measure angles from the horizon, eliminating errors caused by the placement of an instrument's pointers, and because their dual mirror system cancels relative motions of the instrument, showing a steady view of the object and horizon.Navigators measure distance on the globe in degrees, arcminutes and arcseconds. A nautical mile is defined as 1852 meters, but is also (not accidentally) one minute of angle along a meridian on the Earth. Sextants can be read accurately to within 0.2 arcminutes, so 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), enough to navigate safely when out of sight of land.{{citation needed|date=September 2011}}

### Latitude

Latitude was measured in the past either by measuring the altitude of the Sun at noon (the "noon sight"), or by measuring the altitudes of any other celestial body when crossing the meridian (reaching its maximum altitude when due north or south), and frequently by measuring the altitude of Polaris, the north star (assuming it is sufficiently visible above the horizon, which it is not in the Southern Hemisphere). Polaris always stays within 1 degree of the celestial north pole. If a navigator measures the angle to Polaris and finds it to be 10 degrees from the horizon, then he is about 10 degrees north of the equator. This approximate latitude is then corrected using simple tables or almanac corrections to determine a latitude theoretically accurate to within a fraction of a mile. Angles are measured from the horizon because locating the point directly overhead, the zenith, is not normally possible. When haze obscures the horizon, navigators use artificial horizons, which are horizontal mirrors of pans of reflective fluid, especially mercury historically. In the latter case, the angle between the reflected image in the mirror and the actual image of the object in the sky is exactly twice the required altitude.

### Longitude

#### Lunar distance

The older method, called "lunar distances", was refined in the 18th century and employed with decreasing regularity at sea through the middle of the 19th century. It is only used today by sextant hobbyists and historians, but the method is theoretically 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 the sun, or between the moon and one of several stars near the ecliptic. The observed angle must be corrected for the effects of refraction and parallax, like any celestial sight. To make this correction the navigator would measure the altitudes of the moon and sun (or star) at about the same time as the lunar distance angle. Only rough values for the altitudes were required. Then a calculation with logarithms or graphical tables requiring ten to fifteen minutes' work would convert the observed angle to a geocentric lunar distance. The navigator would compare the corrected angle against those listed in the almanac for every three hours of Greenwich time, and interpolate between those values to get the actual Greenwich time aboard ship. Knowing Greenwich time and comparing against local time from a common altitude sight, the navigator can work out his longitude.

#### Use of time

{{unreferenced section|date=April 2018}}The considerably more popular method was (and still is) to use an accurate timepiece to directly measure the time of a sextant sight. The need for accurate navigation led to the development of progressively more accurate chronometers in the 18th century (see John Harrison). Today, time is measured with a chronometer, a quartz watch, a shortwave radio time signal broadcast from an atomic clock, or the time displayed on a GPS.WEB,weblink How accurate is the TIME DISPLAY on my GPS?, Joe, Mehaffey, gpsinformation.net, 9 May 2018, no,weblink" title="web.archive.org/web/20170804120341weblink">weblink 4 August 2017, 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 checked his chronometer from his sextant, at a geographic marker surveyed by a professional astronomer. This is now a rare skill, and most harbourmasters cannot locate their harbour's marker.Traditionally, three chronometers were kept in gimbals in a dry room near the centre of the ship. They were used to set a hack watch for the actual sight, so that no chronometers were ever exposed to the wind and salt water on deck. Winding and comparing the chronometers was a crucial duty of the navigator. Even today, it is still logged daily in the ship's deck log and reported to the Captain before eight bells on the forenoon watch (shipboard noon). Navigators also set the ship's clocks and calendar.

The celestial line of position concept was discovered in 1837 by Thomas Hubbard Sumner when, after one observation, he computed and plotted his longitude at more than one trial latitude in his vicinity â€“ and noticed that the positions lay along a line. Using this method with two bodies, navigators were finally able to cross two position lines and obtain their position â€“ in effect determining both latitude and longitude. Later in the 19th century came the development of the modern (Marcq St. Hilaire) intercept method; with this method the body height and azimuth are calculated for a convenient trial position, and compared with the observed height. The difference in arcminutes is the nautical mile "intercept" distance that the position line needs to be shifted toward or away from the direction of the body's subpoint. (The intercept method uses the concept illustrated in the example in the â€œHow it worksâ€ section above.) Two other methods of reducing sights are the longitude by chronometer and the ex-meridian method.While celestial navigation is becoming increasingly redundant with the advent of inexpensive and highly accurate satellite navigation receivers (GPS), it was used extensively in aviation until the 1960s, and marine navigation until quite recently. However; since a prudent mariner never relies on any sole means of fixing his position, many national maritime authorities still require deck officers to show knowledge of celestial navigation in examinations, primarily as a backup for electronic/satellite navigation. One of the most common current usages of celestial navigation aboard large merchant vessels is for compass calibration and error checking at sea when no terrestrial references are available.The U.S. Air Force and U.S. Navy continued instructing military aviators on celestial navigation use until 1997, because:
• celestial navigation can be used independently of ground aids
• celestial navigation has global coverage
• celestial navigation can not be jammed (although it can be obscured by clouds)
• celestial navigation does not give off any signals that could be detected by an enemy U.S. Air Force Pamphlet (AFPAM) 11-216, Chapters 8â€“13

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## References

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