Celestial navigation

Celestial navigation, also known as astronavigation, is the ancient and modern practice of position fixing that enables a navigator to transition through a space without having to rely on estimated calculations, or dead reckoning, to know their position. Celestial navigation uses "sights", or angular measurements taken between a celestial body (e.g. the Sun, the Moon, a planet, or a star) and the visible horizon. The Sun is most commonly used, but navigators can also use the Moon, a planet, Polaris, or one of 57 other navigational stars whose coordinates are tabulated in the nautical almanac and air almanacs.

Celestial navigation is the use of angular measurements (sights) between celestial bodies and the visible horizon to locate one's position in the world, on land as well as at sea. At a given time, any celestial body is located directly over one point on the Earth's surface. The latitude and longitude of that point is known as the celestial body's geographic position (GP), the location of which can be determined from tables in the nautical or air almanac for that year.

The measured angle between the celestial body and the visible horizon is directly related to the distance between the celestial body's GP and the observer's position. After some computations, referred to as sight reduction, this measurement is used to plot a line of position (LOP) on a navigational chart or plotting work sheet, the observer's position being somewhere on that line. (The LOP is actually a short segment of a very large circle on Earth that surrounds the GP of the observed celestial body. An observer located anywhere on the circumference of this circle on Earth, measuring the angle of the same celestial body above the horizon at that instant of time, would observe that body to be at the same angle above the horizon.) Sights on two celestial bodies give two such lines on the chart, intersecting at the observer's position (actually, the two circles would result in two points of intersection arising from sights on two stars described above, but one can be discarded since it will be far from the estimated position—see the figure at example below). Most navigators will use sights of three to five stars, if available, since that will result in only one common intersection and minimizes the chance of error. That premise is the basis for the most commonly used method of celestial navigation, referred to as the 'altitude-intercept method'.

There are several other methods of celestial navigation that will also provide position-finding using sextant observations, such as the noon sight, and the more archaic lunar distance method. Joshua Slocum used the lunar distance method during the first recorded single-handed circumnavigation of the world. Unlike the altitude-intercept method, the noon sight and lunar distance methods do not require accurate knowledge of time. The altitude-intercept method of celestial navigation requires that the observer know exact Greenwich Mean Time (GMT) at the moment of his observation of the celestial body, to the second—since for every four seconds that the time source (commonly a chronometer or, in aircraft, an accurate "hack watch") is in error, the position will be off by approximately one nautical mile.

Marine sextant
A diagram of a nautical sextant, a tool used in celestial navigation


Sun Moon (annotated)

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 350 nautical miles (650 km) west of Madeira, or in South America, about 90 nautical miles (170 km) southwest of Asunción, 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

Using sextant swing
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.

Practical navigation

Practical celestial navigation usually requires a marine chronometer to measure time, a sextant to measure the angles, an almanac giving schedules of the coordinates of celestial objects, a set of sight reduction tables to help perform the height and azimuth computations, and a chart of the region.

Two ship's officers 'shoot' in one morning with the sextant, the sun altitude
Two nautical ship officers "shoot" in one morning with the sextant, the sun altitude

With sight reduction tables, the only calculations required are addition and subtraction. Small handheld computers, laptops and even scientific calculators enable modern navigators to "reduce" sextant sights in minutes, by automating all the calculation and/or 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 usually use celestial navigation in combination with satellite navigation to correct a dead reckoning track, that is, a course estimated from a vessel's position, course and speed. Using multiple methods helps the navigator detect errors, and simplifies procedures. When used this way, a navigator will from time to time measure the sun's altitude with a sextant, then compare that with a precalculated altitude based on the exact time and estimated position of the observation. On the chart, one will use the straight edge of a plotter to mark each position line. If the position line indicates a location more than a few miles from the estimated position, more observations can be taken to restart the dead-reckoning track.

In the event of equipment or electrical failure, taking sun lines a few times a day and advancing them by dead reckoning allows a vessel to get a crude running fix sufficient to return to port. One can also use the Moon, a planet, Polaris, or one of 57 other navigational stars to track celestial positioning.


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 can be measured in the same way. If the angle to Polaris can be accurately measured, 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 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 invention of the modern chronometer by John Harrison in 1761 vastly simplified longitudinal calculation.

The longitude problem took centuries to solve and was dependent on the construction of a non-pendulum clock (as pendulum clocks cannot function accurately on a tilting ship, or indeed a moving vehicle of any kind). Two useful methods evolved during the 18th century and are still practised today: lunar distance, which does not involve the use of a chronometer, and use of an accurate timepiece or chronometer.

Presently, lay-person calculations of longitude can be made by noting the exact local time (leaving out any reference for Daylight Saving Time) when the sun is at its highest point in the sky. The calculation of noon can be made more easily and accurately with a small, exactly vertical rod driven into level ground—take the time reading when the shadow is pointing due north (in the northern hemisphere). Then take your local time reading and subtract it from GMT (Greenwich Mean Time) or the time in London, England. For example, a noon reading (1200 hours) near central Canada or the US would occur at approximately 6 pm (1800 hours) in London. The six-hour differential is one quarter of a 24-hour day, or 90 degrees of a 360-degree circle (the Earth). The calculation can also be made by taking the number of hours (use decimals for fractions of an hour) multiplied by 15, the number of degrees in one hour. Either way, it can be demonstrated that much of central North America is at or near 90 degrees west longitude. Eastern longitudes can be determined by adding the local time to GMT, with similar calculations.

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

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.[1] 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.

Modern celestial navigation

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 – 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 – 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 “How it works” 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 [2]

The United States Naval Academy announced that it was discontinuing its course on celestial navigation (considered to be one of its most demanding non-engineering courses) from the formal curriculum in the spring of 1998.[3] In October 2015, citing concerns about the reliability of GPS systems in the face of potential hostile hacking, the USNA reinstated instruction in celestial navigation in the 2015–16 academic year.[4][5]

At another federal service academy, the US Merchant Marine Academy, there was no break in instruction in celestial navigation as it is required to pass the US Coast Guard License Exam to enter the Merchant Marine. It is also taught at Harvard, most recently as Astronomy 2.[6]

Celestial navigation continues to be used by private yachtsmen, and particularly by long-distance cruising yachts around the world. For small cruising boat crews, celestial navigation is generally considered an essential skill when venturing beyond visual range of land. Although GPS (Global Positioning System) technology is reliable, offshore yachtsmen use celestial navigation as either a primary navigational tool or as a backup.

Celestial navigation was used in commercial aviation up until the early part of the jet age; early Boeing 747s had a "sextant port" in the roof of the cockpit.[7] It was only phased out in the 1960s with the advent of inertial navigation and doppler navigation systems, and today's satellite-based systems which can locate the aircraft's position accurate to a 3-meter sphere with several updates per second.

A variation on terrestrial celestial navigation was used to help orient the Apollo spacecraft en route to and from the Moon. To this day, space missions such as the Mars Exploration Rover use star trackers to determine the attitude of the spacecraft.

As early as the mid-1960s, advanced electronic and computer systems had evolved enabling navigators to obtain automated celestial sight fixes. These systems were used aboard both ships and US Air Force aircraft, and were highly accurate, able to lock onto up to 11 stars (even in daytime) and resolve the craft's position to less than 300 feet (91 m). The SR-71 high-speed reconnaissance aircraft was one example of an aircraft that used a combination of automated celestial and inertial navigation. These rare systems were expensive, however, and the few that remain in use today are regarded as backups to more reliable satellite positioning systems.

Intercontinental ballistic missiles use celestial navigation to check and correct their course (initially set using internal gyroscopes) while flying outside the Earth's atmosphere. The immunity to jamming signals is the main driver behind this seemingly archaic technique.

X-ray pulsar-based navigation and timing (XNAV) is an experimental navigation technique whereby the periodic X-ray signals emitted from pulsars are used to determine the location of a vehicle, such as a spacecraft in deep space. A vehicle using XNAV would compare received X-ray signals with a database of known pulsar frequencies and locations. Similar to GPS, this comparison would allow the vehicle to triangulate its position accurately (±5 km). The advantage of using X-ray signals over radio waves is that X-ray telescopes can be made smaller and lighter.[8][9][10] On 9 November 2016 the Chinese Academy of Sciences launched an experimental pulsar navigation satellite called XPNAV 1.[11][12] SEXTANT (Station Explorer for X-ray Timing and Navigation Technology) is a NASA-funded project developed at the Goddard Space Flight Center that is testing XNAV on-orbit on board the International Space Station in connection with the NICER project, launched on 3 June 2017 on the SpaceX CRS-11 ISS resupply mission.[13]

Celestial navigation trainer

Celestial navigation trainers for aircraft crews combine a simple flight simulator with a planetarium.

An early example is the Link Celestial Navigation Trainer, used in the Second World War.[14][15] Housed in a 45 feet (14 m) high building, it featured a cockpit accommodating a whole bomber crew (pilot, navigator and bombardier). The cockpit offered a full array of instruments which the pilot used to fly the simulated aeroplane. Fixed to a dome above the cockpit was an arrangement of lights, some collimated, simulating constellations from which the navigator determined the plane's position. The dome's movement simulated the changing positions of the stars with the passage of time and the movement of the plane around the earth. The navigator also received simulated radio signals from various positions on the ground. Below the cockpit moved "terrain plates" – large, movable aerial photographs of the land below – which gave the crew the impression of flight and enabled the bomber to practise lining up bombing targets. A team of operators sat at a control booth on the ground below the machine, from which they could simulate weather conditions such as wind or cloud. This team also tracked the aeroplane's position by moving a "crab" (a marker) on a paper map.

The Link Celestial Navigation Trainer was developed in response to a request made by the Royal Air Force (RAF) in 1939. The RAF ordered 60 of these machines, and the first one was built in 1941. The RAF used only a few of these, leasing the rest back to the US, where eventually hundreds were in use.

See also


  1. ^ Mehaffey, Joe. "How accurate is the TIME DISPLAY on my GPS?". gpsinformation.net. Archived from the original on 4 August 2017. Retrieved 9 May 2018.
  2. ^ U.S. Air Force Pamphlet (AFPAM) 11-216, Chapters 8–13
  3. ^ Navy Cadets Won't Discard Their Sextants Archived 2009-02-13 at the Wayback Machine, The New York Times By DAVID W. CHEN Published: May 29, 1998
  4. ^ Seeing stars, again: Naval Academy reinstates celestial navigation Archived 2015-10-23 at the Wayback Machine, Capital Gazette by Tim Prudente Published: 12 October 2015
  5. ^ Peterson, Andrea (17 February 2016). "Why Naval Academy students are learning to sail by the stars for the first time in a decade". Washington Post. Archived from the original on 22 February 2016.
  6. ^ Astronomy 2 Celestial Navigation by Philip Sadler Archived 2015-11-22 at the Wayback Machine
  7. ^ Clark, Pilita (17 April 2015). "The future of flying". Financial Times. Archived from the original on 14 June 2015. Retrieved 19 April 2015.
  8. ^ Commissariat, Tushna (4 June 2014). "Pulsars map the way for space missions". Physics World. Archived from the original on 18 October 2017.
  9. ^ "An Interplanetary GPS Using Pulsar Signals". MIT Technology Review. 23 May 2013.
  10. ^ Becker, Werner; Bernhardt, Mike G.; Jessner, Axel (2013-05-21). "Autonomous Spacecraft Navigation With Pulsars". arXiv:1305.4842. doi:10.2420/AF07.2013.11.
  11. ^ Krebs, Gunter. "XPNAV 1". Gunter's Space Page. Archived from the original on 2016-11-01. Retrieved 2016-11-01.
  12. ^ "Chinese Long March 11 launches first Pulsar Navigation Satellite into Orbit". Spaceflight101.com. 10 November 2016. Archived from the original on 24 August 2017.
  13. ^ "NICER Manifested on SpaceX-11 ISS Resupply Flight". NICER News. NASA. December 1, 2015. Archived from the original on March 24, 2017. Retrieved June 14, 2017. Previously scheduled for a December 2016 launch on SpaceX-12, NICER will now fly to the International Space Station with two other payloads on SpaceX Commercial Resupply Services (CRS)-11, in the Dragon vehicle's unpressurized Trunk.
  14. ^ "World War II". A Brief History of Aircraft Flight Simulation. Archived from the original on December 9, 2004. Retrieved January 27, 2005.
  15. ^ "Corporal Tomisita "Tommye" Flemming-Kelly-U.S.M.C.-Celestial Navigation Trainer −1943/45". World War II Memories. Archived from the original on 2005-01-19. Retrieved January 27, 2005.

External links

Media related to Celestial navigation at Wikimedia Commons


An almucantar (also spelled almucantarat or almacantara) is a circle on the celestial sphere parallel to the horizon. Two stars that lie on the same almucantar have the same altitude.

The term was introduced into European astronomy by monastic astronomer Hermann Contractus of Reichenau, Latinized from the Arabic word al-muqanṭarah ("the almucantar, sundial", plural: al-muqanṭarāt), derived from qanṭarah ("arch, bridge")

Celestial Navigation (novel)

Celestial Navigation is a 1974 novel by Anne Tyler. This was her 5th novel.

Circle of equal altitude

The circle of equal altitude also called circle of position, CoP, is the real line of position in celestial navigation. It is defined as the locus of the Earth on which an observer sees a star, at a given time, with the same observed altitude. It was discovered by the American sea-captain Thomas Hubbard Sumner.


In astronomy and celestial navigation, an ephemeris (plural: ephemerides) gives the trajectory of naturally occurring astronomical objects as well as artificial satellites in the sky, i.e., the position (and possibly velocity) over time. The etymology is from Latin ephemeris, meaning 'diary' and from Greek, Modern εφημερίς (ephemeris), meaning 'diary, journal'. Historically, positions were given as printed tables of values, given at regular intervals of date and time. The calculation of these tables was one of the first applications of mechanical computers. Modern ephemerides are often computed electronically, from mathematical models of the motion of astronomical objects and the Earth. However, printed ephemerides are still produced, as they are useful when computational devices are not available.

The astronomical position calculated from an ephemeris is given in the spherical polar coordinate system of right ascension and declination. Some of the astronomical phenomena of interest to astronomers are eclipses, apparent retrograde motion/planetary stations, planetary ingresses, sidereal time, positions for the mean and true nodes of the moon, the phases of the Moon, and the positions of minor celestial bodies such as Chiron.

Ephemerides are used in celestial navigation and astronomy. They are also used by some astrologers.

Fernanda D'Agostino

Fernanda (Nanda) D'Agostino is an artist who, "has integrated personal, societal and environmental concerns into many installations and large-scale public art projects" in her 30-year career. Her new media works frequently incorporate technically sophisticated interactive elements.D'Agostino was awarded a Bonnie Bronson Fellowship in 1995, a Flintridge Foundation Award for visual artists in 2002, and an Oregon Arts Commission Fellowship in 2016 among other honors.Monographs on D'Agostino's work have been published twice by The Art Gym, Offering: An installation in 1989 and Method of Loci in 2013. Her work is held in the collections of the Houston Museum of Fine Art, the Yellowstone Art Museum, and the Missoula Museum of the Arts.

Hour angle

In astronomy and celestial navigation, the hour angle is one of the coordinates used in the equatorial coordinate system to give the direction of a point on the celestial sphere. The hour angle of a point is the angle between two planes: one containing Earth's axis and the zenith (the meridian plane), and the other containing Earth's axis and the given point (the hour circle passing through the point).

The angle may be expressed as negative east of the meridian plane and positive west of the meridian plane, or as positive westward from 0° to 360°. The angle may be measured in degrees or in time, with 24h = 360° exactly.

In astronomy, hour angle is defined as the angular distance on the celestial sphere measured westward along the celestial equator from the meridian to the hour circle passing through a point. It may be given in degrees, time, or rotations depending on the application.

In celestial navigation, the convention is to measure in degrees westward from the prime meridian (Greenwich hour angle, GHA), from the local meridian (local hour angle, LHA) or from the first point of Aries (sidereal hour angle, SHA).

The hour angle is paired with the declination to fully specify the location of a point on the celestial sphere in the equatorial coordinate system.

List of selected stars for navigation

Fifty-eight selected navigational stars are given a special status in the field of celestial navigation. Of the approximately 6,000 stars visible to the naked eye under optimal conditions, the selected stars are among the brightest and span 38 constellations of the celestial sphere from the declination of −70° to +89°. Many of the selected stars were named in antiquity by the Babylonians, Greeks, Romans, and Arabs.

The star Polaris, often called the "North Star", is treated specially due to its proximity to the north celestial pole. When navigating in the Northern Hemisphere, special techniques can be used with Polaris to determine latitude or gyrocompass error. The other 57 selected stars have daily positions given in nautical almanacs, aiding the navigator in efficiently performing observations on them. A second group of 115 "tabulated stars" can also be used for celestial navigation, but are often less familiar to the navigator and require extra calculations.

For purposes of identification, the positions of navigational stars — expressed as declination and sidereal hour angle — are often rounded to the nearest degree. In addition to tables, star charts provide an aid to the navigator in identifying the navigational stars, showing constellations, relative positions, and brightness.

Lunar distance (navigation)

In celestial navigation, lunar distance is the angular distance between the Moon and another celestial body. The lunar distances method uses this angle, also called a lunar, and a nautical almanac to calculate Greenwich time. That calculated time can be used in solving a spherical triangle. The method was published in 1763 and used until about 1850 when it was superseded by the marine chronometer. A similar method uses the positions of the Galilean moons of Jupiter.

Mariner's astrolabe

The mariner's astrolabe, also called sea astrolabe, was an inclinometer used to determine the latitude of a ship at sea by measuring the sun's noon altitude (declination) or the meridian altitude of a star of known declination. Not an astrolabe proper, the mariner's astrolabe was rather a graduated circle with an alidade used to measure vertical angles. They were designed to allow for their use on boats in rough water and/or in heavy winds, which astrolabes are ill-equipped to handle. In the sixteenth century, the instrument was also called a ring.

Nautical almanac

A nautical almanac is a publication describing the positions of a selection of celestial bodies for the purpose of enabling navigators to use celestial navigation to determine the position of their ship while at sea. The Almanac specifies for each whole hour of the year the position on the Earth's surface (in declination and Greenwich hour angle) at which the sun, moon, planets and first point of Aries is directly overhead. The positions of 57 selected stars are specified relative to the first point of Aries.

In Great Britain, The Nautical Almanac has been published annually by HM Nautical Almanac Office, ever since the first edition was published in 1767.

In the United States, a nautical almanac has been published annually by the US Naval Observatory since 1852. It was originally titled American Ephemeris and Nautical Almanac. Since 1958, the USNO and HMNAO have jointly published a unified nautical almanac, the Astronomical Almanac for use by the navies of both countries. Almanac data is now available online from the US Naval Observatory.Also commercial almanacs were produced that combined other information. A good example would be Brown's — which commenced in 1877 – and is still produced annually, its early twentieth century subtitle being "Harbour and Dock Guide and Advertiser and Daily Tide Tables". This combination of trade advertising, and information "by permission... of the Hydrographic Department of the Admiralty" provided a useful compendium of information. More recent editions have kept up with the changes in technology – the 1924 edition for instance had extensive advertisements for coaling stations. Meanwhile, the Reeds Nautical Almanac, published by Adlard Coles Nautical, has been in print since 1932, and in 1944 was used by landing craft involved in the Normandy landings.The "Air Almanac" of the United States and Great Britain tabulates celestial coordinates for 10-minute intervals for use in aerial navigation. The Sokkia Corporation's annual "Celestial Observation Handbook and Ephemeris" tabulated daily celestial coordinates (to a tenth of an arcsecond) for the Sun and nine stars; it was last published for 2008.

To find the position of a ship or aircraft by celestial navigation, the navigator measures with a sextant the apparent height of a celestial body above the horizon, and notes the time from a marine chronometer. That height is compared with the height predicted for a trial position; the arcminutes of height difference is how many nautical miles the position line is from the trial position.


Navigation is a field of study that focuses on the process of monitoring and controlling the movement of a craft or vehicle from one place to another. The field of navigation includes four general categories: land navigation, marine navigation, aeronautic navigation, and space navigation.It is also the term of art used for the specialized knowledge used by navigators to perform navigation tasks. All navigational techniques involve locating the navigator's position compared to known locations or patterns.

Navigation, in a broader sense, can refer to any skill or study that involves the determination of position and direction. In this sense, navigation includes orienteering and pedestrian navigation.

Navigational algorithms

Navigational Algorithms is a web site whose purpose is to make available the scientific part of the art of navigation, containing specialized articles and software that implements the various procedures of calculus. The topics covered are:

Celestial navigation: Sight reduction, circle of equal altitude, Line Of Position, Fix...

Positional astronomy: RA, GHA, Dec

Coastal navigation: Range, Bearing, Horizontal angles, IALA...

Sailings: Rhumbs, Loxodromic, Orthodromic, Meridional parts...

Weather, tides

Software PC- PDA: Nautical Almanac, Sailings, Variation, Sextant corrections

Navigational instrument

Navigational instruments refers to the instruments used by nautical navigators and pilots as tools of their trade. The purpose of navigation is to ascertain the present position and to determine the speed, direction etc. to arrive at the port or point of destination.

Octant (instrument)

The octant, also called reflecting quadrant, is a measuring instrument used primarily in navigation. It is a type of reflecting instrument.


A sextant is a doubly reflecting navigation instrument that measures the angular distance between two visible objects. The primary use of a sextant is to measure the angle between an astronomical object and the horizon for the purposes of celestial navigation. The estimation of this angle, the altitude, is known as sighting or shooting the object, or taking a sight. The angle, and the time when it was measured, can be used to calculate a position line on a nautical or aeronautical chart—for example, sighting the Sun at noon or Polaris at night (in the Northern Hemisphere) to estimate latitude. Sighting the height of a landmark can give a measure of distance off and, held horizontally, a sextant can measure angles between objects for a position on a chart. A sextant can also be used to measure the lunar distance between the moon and another celestial object (such as a star or planet) in order to determine Greenwich Mean Time and hence longitude. The principle of the instrument was first implemented around 1731 by John Hadley (1682–1744) and Thomas Godfrey (1704–1749), but it was also found later in the unpublished writings of Isaac Newton (1643–1727). Additional links can be found to Bartholomew Gosnold (1571–1607) indicating that the use of a sextant for nautical navigation predates Hadley's implementation. In 1922, it was modified for aeronautical navigation by Portuguese navigator and naval officer Gago Coutinho.

Star tracker

A star tracker is an optical device that measures the positions of stars using photocells or a camera.

As the positions of many stars have been measured by astronomers to a high degree of accuracy, a star tracker on a satellite or spacecraft may be used to determine the orientation (or attitude) of the spacecraft with respect to the stars. In order to do this, the star tracker must obtain an image of the stars, measure their apparent position in the reference frame of the spacecraft, and identify the stars so their position can be compared with their known absolute position from a star catalog. A star tracker may include a processor to identify stars by comparing the pattern of observed stars with the known pattern of stars in the sky.

Sun sensor

A sun sensor is a navigational instrument used by spacecraft to detect the position of the sun. Sun sensors are used for attitude control, solar array pointing, gyro updating, and fail-safe recovery.In addition to spacecraft, sun sensors find use in ground-based weather stations and sun-tracking systems, and aerial vehicles including balloons and UAVs.

The West Wing (season 1)

The first season of the American political drama television series The West Wing aired in the United States on NBC from September 22, 1999 to May 17, 2000 and consisted of 22 episodes.

X-ray pulsar-based navigation

X-ray pulsar-based navigation and timing (XNAV) or simply pulsar navigation is a navigation technique whereby the periodic X-ray signals emitted from pulsars are used to determine the location of a vehicle, such as a spacecraft in deep space. A vehicle using XNAV would compare received X-ray signals with a database of known pulsar frequencies and locations. Similar to GPS, this comparison would allow the vehicle to triangulate its position accurately (±5 km). The advantage of using X-ray signals over radio waves is that X-ray telescopes can be made smaller and lighter.

Experimental demonstrations have been reported in 2018.

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