706:. The observed angle must be corrected for the effects of refraction and parallax, like any celestial sight. To make this correction, the navigator measures the altitudes of the Moon and Sun (or another star) at about the same time as the lunar distance angle. Only rough values for the altitudes are required. A calculation with suitable published tables (or longhand with logarithms and graphical tables) requires about 10 to 15 minutes' work to convert the observed angle(s) to a geocentric lunar distance. The navigator then compares the corrected angle against those listed in the appropriate almanac pages for every three hours of Greenwich time, using interpolation tables to derive intermediate values. The result is a difference in time between the time source (of unknown time) used for the observations and the actual prime meridian time (that of the "Zero Meridian" at Greenwich, also known as UTC or GMT). Knowing UTC/GMT, a further set of sights can be taken and reduced by the navigator to calculate their exact position on the Earth as a local latitude and longitude.
515:
1087:, 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 practice lining up bombing targets. A team of operators sat at a control booth on the ground below the machine, from which they could simulate
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847:; 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
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Sun and the exact time of that altitude (known as "local noon")—the highest point of the Sun above the horizon from the position of the observer in any single day. This angular observation, combined with knowing its simultaneous precise time, referred to as the time at the prime meridian, directly renders a latitude and longitude fix at the time and place of the observation by simple mathematical reduction. The Moon, a planet,
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294:, 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.
538:. 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 that is theoretically accurate to within a fraction of a mile. Angles are measured from the horizon because locating the point directly overhead, the
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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 the
283:. Ten minutes later, the Sun was observed to be 40° 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.
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accurate to within a second or two with about 15 to 30 minutes of observations and mathematical reduction from the almanac tables. After practice, an observer can regularly derive and prove time using this method to within about one second, or one nautical mile, of navigational error due to errors ascribed to the time source.
542:, is not normally possible. When haze obscures the horizon, navigators use artificial horizons, which are horizontal mirrors or pans of reflective fluid, especially mercury. 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.
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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.
607:) when the Sun is at its highest point in Earth's 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 (
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191:(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 "
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altitude based on the exact time and estimated position of the observation. On the chart, the straight edge of a plotter can 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.
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if one of the three was wrong, so the pilot would take the average of the two with closer readings (average precision vote). There is an old adage to this effect, stating: "Never go to sea with two chronometers; take one or three." Vessels engaged in survey work generally carried many more than three
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computations, and a chart of the region. 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
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Celestial navigation accomplishes its purpose by using angular measurements (sights) between celestial bodies and the visible horizon to locate one's position on the Earth, whether on land, in the air, or at sea. In addition, observations between stars and other celestial bodies accomplished the same
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Celestial navigation by taking sights of the Sun and the horizon whilst on the surface of the Earth is commonly used, providing various methods of determining position, one of which is the popular and simple method called "noon sight navigation"—being a single observation of the exact altitude of the
902:(USNA) 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. In October 2015, citing concerns about the reliability of GNSS systems in the face of potential hostile
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systems as potentially the only accurate time source aboard a vessel. Designed for use when an accurate timepiece is not available or timepiece 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
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Time), or the time in London, England. For example, a noon reading (12:00) near central Canada or the US would occur at approximately 6 p.m. (18:00) in London. The 6-hour difference 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
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can be used as a method of determining time at the prime meridian. A functioning timepiece with a second hand or digit, an almanac with lunar corrections, and a sextant are used. With no knowledge of time at all, a lunar calculation (given an observable Moon of respectable altitude) can provide time
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until quite recently. However, since a prudent mariner never relies on any sole means of fixing their position, many national maritime authorities still require deck officers to show knowledge of celestial navigation in examinations, primarily as a backup for electronic or satellite navigation. One
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or "lunars," which was used extensively for a short period and refined for daily use on board ships in the 18th century. Use declined through the middle of the 19th century as better and better timepieces (chronometers) became available to the average vessel at sea. Although most recently only used
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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, from time to time, measures the Sun's altitude with a sextant, then compares that with a precalculated
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Accurate angle measurement has evolved over the years. One simple method is to hold the hand above the horizon with one's arm stretched out. The angular width of the little finger is just over 1.5 degrees at extended arm's length and can be used to estimate the elevation of the Sun from the horizon
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below). Most navigators will use sights of three to five stars, if available, since that will result in only one common intersection and minimize 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."
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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
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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 GNSS, this comparison would allow the vehicle to triangulate its position accurately
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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
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is defined as 1,852 meters but is also (not accidentally) one arc minute of angle along a meridian on the Earth. Sextants can be read accurately to within 0.1 arcminutes, so the observer's position can be determined within (theoretically) 0.1 nautical miles (185.2 meters, or about 203 yards. Most
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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
334:. 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.
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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
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and is still used on many contemporary satellites. Equally, celestial navigation may be used while on other planetary bodies to determine position on their surface, using their local horizon and suitable celestial bodies with matching reduction tables and knowledge of local time.
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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
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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 practiced today:
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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
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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. When time at the
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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
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is accurately known. The more accurately time at the prime meridian (0° longitude) is known, the more accurate the fix; – indeed, every four seconds of time source (commonly a chronometer or, in aircraft, an accurate
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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,
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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
576:. 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
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ocean navigators, measuring from a moving platform under fair conditions, can achieve a practical accuracy of approximately 1.5 nautical miles (2.8 km, enough to navigate safely when out of sight of land or other hazards.
143:. Celestial navigation can also take advantage of measurements between celestial bodies without reference to the Earth's horizon, such as when the Moon and other selected bodies are used in the practice called "lunars" or the
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766:), or one-tenth of a second means 107.8 ft (32.86 m) At the slightly bulged-out equator, or latitude 0°, the rotation velocity of Earth or its equivalent in longitude reaches its maximum at 465.10
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At least three points must be plotted. The plot intersection will usually provide a triangle where the exact position is inside of it. The accuracy of the sights is indicated by the size of the triangle.
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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
1098:(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.
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In 1980, French Navy regulations still required an independently operated timepiece on board so that, in combination with a sextant, a ship's position could be determined by celestial navigation.
754:(or another starting point) is accurately known, celestial navigation can determine longitude, and the more accurately latitude and time are known, the more accurate the longitude determination.
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used both noon sight and star sight navigation to determine his current position during his voyage, the first recorded single-handed circumnavigation of the world. In addition, he used the
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of the most common current uses of celestial navigation aboard large merchant vessels is for compass calibration and error checking at sea when no terrestrial references are available.
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For navigation by celestial means, when on the surface of the Earth at any given instant in time, a celestial body is located directly over a single point on the Earth's surface. The
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is latitude-dependent. At the poles, or latitude 90°, the rotation velocity of the Earth reaches zero. At 45° latitude, one second of time is equivalent in longitude to 1,077.8
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to accurately determine their actual current physical position in space or on the surface of the Earth without relying solely on estimated positional calculations, commonly known as
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223:(or "lunars") to determine and maintain known time at Greenwich (the prime meridian), thereby keeping his "tin clock" reasonably accurate and therefore his position fixes accurate.
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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
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Traditionally, a navigator checked their chronometer(s) with their sextant at a geographic marker surveyed by a professional astronomer. This is now a rare skill, and most
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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.
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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.
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An older but still useful and practical method of determining accurate time at sea before the advent of precise timekeeping and satellite-based time systems is called "
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if the two displayed a different time, since in case of contradiction between the two chronometers, it would be impossible to know which one was wrong (the
971:. These rare systems were expensive, however, and the few that remain in use today are regarded as backups to more reliable satellite positioning systems.
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While celestial navigation is becoming increasingly redundant with the advent of inexpensive and highly accurate satellite navigation receivers (
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584:. For the most part, these were too difficult to be used by anyone except professional astronomers. The invention of the modern chronometer by
1811:
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If the angle to
Polaris can be accurately measured, a similar measurement of a star near the eastern or western horizons would provide the
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for determining position is shown to the right. (Two other common methods for determining one's position using celestial navigation are
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use celestial navigation to check and correct their course (initially set using internal gyroscopes) while flying outside the Earth's
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49:
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by sextant hobbyists and historians, it is now becoming more common in celestial navigation courses to reduce total dependence on
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point would see the Moon at the left of the Sun, and an observer at the
Madeira point would see the Moon at the right of the Sun.
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conditions such as wind or clouds. This team also tracked the airplane's position by moving a "crab" (a marker) on a paper map.
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technology is reliable, offshore yachtsmen use celestial navigation as either a primary navigational tool or as a backup.
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determining both latitude and longitude. Later in the 19th century came the development of the modern (Marcq St. Hilaire)
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Presently, layperson calculations of longitude can be made by noting the exact local time (leaving out any reference for
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on the forenoon watch (shipboard noon). Navigators also set the ship's clocks and calendar. Two chronometers provided
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on
October 29, 2005. At this time, a navigator on a ship at sea measured the Moon to be 56° above the horizon using a
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methods.) In the adjacent image, the two circles on the map represent lines of position for the Sun and Moon at 12:00
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In this case, the navigator is either located on the
Atlantic Ocean, about 350 nautical miles (650 km) west of
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81:, a tool used in celestial navigation to measure the angle between two objects viewed by means of its optical sight
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obtained would be the same as having only one chronometer and checking it periodically: every day at noon against
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Becker, Werner; Bernhardt, Mike G.; Jessner, Axel (2013-05-21). "Autonomous
Spacecraft Navigation With Pulsars".
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cannot locate their harbor's marker. Ships often carried more than one chronometer. Chronometers were kept on
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3rd class, practices using a sextant as part of a navigation training aboard the amphibious assault ship
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or plotting worksheet, with the observer's position being somewhere on that line. The LOP is actually a short
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had a "sextant port" in the roof of the cockpit. It was only phased out in the 1960s with the advent of
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600:, which does not involve the use of a chronometer, and the use of an accurate timepiece or chronometer.
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were available, longitude measurements were based on the transit of the moon or the positions of the
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Celestial navigation was used in commercial aviation up until the early part of the jet age; early
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981:. The immunity to jamming signals is the main driver behind this seemingly archaic technique.
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1623:
1517:"Why Naval Academy students are learning to sail by the stars for the first time in a decade"
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906:, the USNA reinstated instruction in celestial navigation in the 2015 to 2016 academic year.
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1812:"Corporal Tomisita "Tommye" Flemming-Kelly-U.S.M.C.-Celestial Navigation Trainer −1943/45"
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1983:
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The Link
Celestial Navigation Trainer was developed in response to a request made by the
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continued instructing military aviators on celestial navigation use until 1997, because:
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celestial navigation does not give off any signals that could be detected by an enemy.
564:) can be calculated with the position of the Sun and the reference time (for example,
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Table of the 57 navigational stars with apparent magnitudes and celestial coordinates
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Two ship's officers "shoot" a morning sight with sextants, the Sun altitude (1963).
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giving an accuracy of less than ±5 seconds per year, French Navy issued, 1980
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1240:"07.03.09: The Mathematical Dynamics of Celestial Navigation and Astronavigation"
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Modern practical navigators usually use celestial navigation in combination with
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The marine chronometer in the age of electricity by David Read, September 2015
987:(XNAV) is an experimental navigation technique for space whereby the periodic
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celestial navigation cannot be jammed (although it can be obscured by clouds).
1993:
1734:"Chinese Long March 11 launches first Pulsar Navigation Satellite into Orbit"
1600:
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crew (pilot, navigator, and bombardier). The cockpit offered a full array of
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1012:. SEXTANT (Station Explorer for X-ray Timing and Navigation Technology) is a
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Celestial navigation training equipment for aircraft crews combine a simple
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A variation on terrestrial celestial navigation was used to help orient the
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Using a marine sextant to measure the altitude of the Sun above the horizon
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uses "sights," or timed angular measurements, taken typically between a
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en route to and from the Moon. To this day, space missions such as the
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786:
556:
421: in this section. Unsourced material may be challenged and removed.
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resolve the craft's position to less than 300 feet (91 m). The
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by F. A. McDiarmid, The Royal Astronomical Society of Canada, 1914.
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in a dry room near the center of the ship. They were used to set a
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giving schedules of the coordinates of celestial objects, a set of
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Seeing stars, again: Naval Academy reinstates celestial navigation
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The celestial line of position concept was discovered in 1837 by
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or other similar modern electronic or digital positioning means.
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1059:. Housed in a 45-foot (14 m) high building, it featured a
798:, allowing a backup if one ceases to work but not allowing any
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celestial navigation can be used independently of ground aids.
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can be made smaller and lighter. On 9 November 2016 the
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Errors in Longitude, Latitude and Azimuth Determinations — I
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launched an experimental pulsar navigation satellite called
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862:), it was used extensively in aviation until the 1960s and
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Navigation using astronomical objects to determine position
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was one example of an aircraft that used a combination of
147:, used for determining precise time when time is unknown.
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THE AMERICAN PRACTICAL NAVIGATORAN EPITOME OF NAVIGATION
996:(±5 km). The advantage of using X-ray signals over
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whose coordinates are tabulated in any of the published
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1907:
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How Accurate Is Celestial Navigation Compared To GPS?
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above the cockpit was an arrangement of lights, some
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results while in space, – used in the
1297:"Marine navigation courses: Lines of position, LOPs"
1265:"Sight reduction methods compared - Ocean Navigator"
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in 1761 vastly simplified longitudinal calculation.
534:). Polaris always stays within 1 degree of the
1752:"NICER Manifested on SpaceX-11 ISS Resupply Flight"
1744:
1369:(4th ed.). New York: AIP Press. p. 244.
560:The relative longitude to a position (for example
449:Practical celestial navigation usually requires a
108:. Celestial navigation is performed without using
1433:"Volume II: Proceedings of the Second Expedition"
729:). Today, time is measured with a chronometer, a
1991:
187:of that point are known as the celestial body's
1075:used to fly the simulated airplane. Fixed to a
263:An example illustrating the concept behind the
239:") error can lead to a positional error of one
195:reduction," this measurement is used to plot a
833:
1786:A Brief History of Aircraft Flight Simulation
1362:
1322:"How accurate is the TIME DISPLAY on my GPS?"
1028:project, launched on 3 June 2017 on the
1619:"An Interplanetary GPS Using Pulsar Signals"
1594:
819:chronometers – for example,
337:Navigators measure distance on the Earth in
1020:that is testing XNAV on-orbit on board the
969:automated celestial and inertial navigation
654:. Unsourced material may be challenged and
243:. When time is unknown or not trusted, the
1505:by Tim Prudente Published: 12 October 2015
1879:Almanac, Sight Reduction Tables and more.
1663:
1262:
888:celestial navigation has global coverage.
674:Learn how and when to remove this message
437:Learn how and when to remove this message
1736:. Spaceflight101.com. 10 November 2016.
1597:"Pulsars map the way for space missions"
1514:
1482:By DAVID W. CHEN Published: May 29, 1998
1469:Navy Cadets Won't Discard Their Sextants
985:X-ray pulsar-based navigation and timing
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513:
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226:Celestial navigation can only determine
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1130:Bowditch's American Practical Navigator
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1992:
1754:. NICER News. NASA. December 1, 2015.
1529:from the original on 22 February 2016.
1459:Pamphlet (AFPAM) 11-216, Chapters 8–13
1430:
1396:
1356:
304:
1607:from the original on 18 October 2017.
1561:
1515:Peterson, Andrea (17 February 2016).
1172:List of selected stars for navigation
917:, most recently as Astronomy 2.
21:Celestial navigation (disambiguation)
1740:from the original on 24 August 2017.
1595:Commissariat, Tushna (4 June 2014).
1319:
652:adding citations to reliable sources
619:
419:adding citations to reliable sources
390:
167:can also accomplish this same goal.
54:move details into the article's body
25:
1758:from the original on March 24, 2017
975:Intercontinental ballistic missiles
13:
1868:Complete nautical Almanac and more
1332:from the original on 4 August 2017
14:
2011:
1883:Celestial Navigation in Petan.net
1837:
1702:
1576:from the original on 14 June 2015
1053:Link Celestial Navigation Trainer
1016:-funded project developed at the
615:
1977:
1965:
1953:
1941:
1929:
1917:
1842:
1542:Astronomy 2 Celestial Navigation
1366:Allen's Astrophysical Quantities
1227:The free online Nautical Almanac
624:
494:to track celestial positioning.
395:
77:A diagram of a typical nautical
30:
1804:
1774:
1726:
1715:from the original on 2016-11-01
1696:
1643:
1611:
1588:
1562:Clark, Pilita (17 April 2015).
1555:
1533:
1508:
1485:
1462:
1450:
1439:
1424:
1390:
1263:Navigator, Ocean (2003-01-01).
810:). Three chronometers provided
465:to help perform the height and
406:needs additional citations for
1344:
1313:
1289:
1277:
1256:
1232:
1220:
1209:
756:The angular speed of the Earth
709:
1:
1627:. 23 May 2013. Archived from
1203:
1167:List of proper names of stars
741:, or the time displayed on a
545:
209:
7:
1872:Calculating Lunar Distances
1363:Arthur N. Cox, ed. (2000).
1101:
1035:
1022:International Space Station
1018:Goddard Space Flight Center
1006:Chinese Academy of Sciences
900:United States Naval Academy
834:Modern celestial navigation
735:shortwave radio time signal
497:
10:
2018:
1406:. Addison-Wesley. p.
1244:teachersinstitute.yale.edu
713:
685:
549:
507:
501:
457:to measure the angles, an
251:
18:
1903:Sextant in a Douglas DC-8
812:triple modular redundancy
155:, or one of the 57 other
1856:Celestial Navigation Net
1141:Circle of equal altitude
1051:An early example is the
849:longitude by chronometer
716:Longitude by chronometer
367:Ships Marine Chronometer
269:longitude by chronometer
1898:Air Navigation Sextants
1119:Astrodome (aeronautics)
1024:in connection with the
965:reconnaissance aircraft
913:. It is also taught at
796:dual modular redundancy
552:Longitude determination
378:U.S. Navy quartermaster
1564:"The future of flying"
1403:The Mythical Man-Month
1063:accommodating a whole
1032:ISS resupply mission.
945:Mars Exploration Rover
569:
519:
510:Latitude determination
463:sight reduction tables
388:
370:
314:
260:
96:using stars and other
82:
1851:at Wikimedia Commons
1816:World War II Memories
1624:MIT Technology Review
1301:www.sailingissues.com
1182:Polynesian navigation
991:signals emitted from
840:Thomas Hubbard Sumner
743:satellite time signal
559:
517:
490:, or one of 57 other
376:
365:
312:
259:
245:lunar distance method
230:when the time at the
221:lunar distance method
145:lunar distance method
92:, is the practice of
76:
2000:Celestial navigation
1849:Celestial navigation
1682:10.2420/AF07.2013.11
1398:Brooks, Frederick J.
1162:History of longitude
1157:Satellite navigation
923:satellite navigation
648:improve this section
605:daylight saving time
536:celestial north pole
475:satellite navigation
415:improve this article
358:Practical navigation
173:Apollo space program
110:satellite navigation
86:Celestial navigation
19:For other uses, see
1792:on December 9, 2004
1709:Gunter's Space Page
1674:2013AcFut...7...11B
1631:on 29 November 2014
1522:The Washington Post
955:of the spacecraft.
934:inertial navigation
532:Southern Hemisphere
453:to measure time, a
305:Angular measurement
297:An observer at the
189:geographic position
1549:2015-11-22 at the
1497:2015-10-23 at the
1480:The New York Times
1474:2009-02-13 at the
1326:gpsinformation.net
1192:Spherical geometry
1151:Geodetic astronomy
1114:Aircraft periscope
737:broadcast from an
720:Marine chronometer
570:
520:
492:navigational stars
451:marine chronometer
389:
371:
315:
261:
201:navigational chart
157:navigational stars
139:) and the visible
83:
1847:Media related to
1376:978-0-387-98746-0
951:to determine the
941:Apollo spacecraft
864:marine navigation
747:quartz wristwatch
694:lunar distances,"
684:
683:
676:
593:longitude problem
504:Meridian altitude
447:
446:
439:
71:
70:
50:length guidelines
2007:
1982:
1981:
1980:
1970:
1969:
1968:
1958:
1957:
1956:
1946:
1945:
1934:
1933:
1932:
1922:
1921:
1920:
1913:
1846:
1832:
1831:
1829:
1827:
1818:. Archived from
1808:
1802:
1801:
1799:
1797:
1788:. Archived from
1778:
1772:
1771:
1765:
1763:
1748:
1742:
1741:
1730:
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1723:
1721:
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1615:
1609:
1608:
1592:
1586:
1585:
1583:
1581:
1559:
1553:
1544:by Philip Sadler
1537:
1531:
1530:
1512:
1506:
1489:
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1466:
1460:
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1443:
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1254:
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1250:
1236:
1230:
1224:
1218:
1213:
1187:Radio navigation
1057:Second World War
1042:flight simulator
1002:X-ray telescopes
845:intercept method
816:error correction
800:error correction
679:
672:
668:
665:
659:
628:
620:
582:moons of Jupiter
442:
435:
431:
428:
422:
399:
391:
384:Bonhomme Richard
265:intercept method
197:line of position
98:celestial bodies
88:, also known as
66:
63:
57:
48:Please read the
34:
33:
26:
2017:
2016:
2010:
2009:
2008:
2006:
2005:
2004:
1990:
1989:
1988:
1978:
1976:
1966:
1964:
1954:
1952:
1940:
1930:
1928:
1918:
1916:
1908:
1877:Backbearing.com
1840:
1835:
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1805:
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1775:
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1716:
1703:Krebs, Gunter.
1701:
1697:
1648:
1644:
1634:
1632:
1617:
1616:
1612:
1593:
1589:
1579:
1577:
1569:Financial Times
1560:
1556:
1551:Wayback Machine
1538:
1534:
1513:
1509:
1503:Capital Gazette
1499:Wayback Machine
1490:
1486:
1476:Wayback Machine
1467:
1463:
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1451:
1444:
1440:
1429:
1425:
1418:
1395:
1391:
1381:
1379:
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1345:
1335:
1333:
1320:Mehaffey, Joe.
1318:
1314:
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1214:
1210:
1206:
1201:
1177:Polar alignment
1104:
1096:Royal Air Force
1038:
911:Merchant Marine
836:
828:22 chronometers
804:error detection
722:
714:Main articles:
712:
702:stars near the
690:
680:
669:
663:
660:
645:
629:
618:
554:
548:
512:
506:
500:
443:
432:
426:
423:
412:
400:
360:
307:
254:
100:that enables a
94:position fixing
90:astronavigation
67:
61:
58:
47:
44:may be too long
39:This article's
35:
31:
24:
17:
12:
11:
5:
2015:
2014:
2003:
2002:
1987:
1986:
1974:
1962:
1950:
1938:
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1906:
1905:
1900:
1895:
1890:
1885:
1880:
1874:
1869:
1863:
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1839:
1838:External links
1836:
1834:
1833:
1803:
1782:"World War II"
1773:
1743:
1725:
1695:
1642:
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1587:
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1461:
1457:U.S. Air Force
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1389:
1375:
1355:
1343:
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1286:, p. 270.
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1229:in PDF format.
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1136:Celestial pole
1133:
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1111:
1109:Air navigation
1105:
1103:
1100:
1085:constellations
1055:, used in the
1037:
1034:
896:
895:
892:
889:
886:
875:U.S. Air Force
835:
832:
808:dead reckoning
770:(1,525.9
752:prime meridian
711:
708:
688:Lunar distance
686:Main article:
682:
681:
632:
630:
623:
617:
616:Lunar distance
614:
609:Greenwich Mean
598:lunar distance
547:
544:
502:Main article:
499:
496:
479:dead reckoning
445:
444:
427:September 2011
403:
401:
394:
359:
356:
306:
303:
253:
250:
232:prime meridian
121:celestial body
106:dead reckoning
69:
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38:
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29:
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9:
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2013:
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1845:
1822:on 2005-01-19
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1601:Physics World
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1435:. p. 18.
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1086:
1083:, simulating
1082:
1078:
1074:
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1062:
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1054:
1049:
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1043:
1033:
1031:
1030:SpaceX CRS-11
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1023:
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1007:
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999:
994:
990:
986:
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949:star trackers
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779:harbormasters
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769:
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762:(328.51
761:
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744:
740:
736:
732:
728:
727:John Harrison
721:
717:
707:
705:
700:
695:
689:
678:
675:
667:
664:February 2022
657:
653:
649:
643:
642:
638:
633:This section
631:
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599:
594:
589:
587:
586:John Harrison
583:
579:
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511:
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477:to correct a
476:
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441:
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430:
420:
416:
410:
409:
404:This section
402:
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351:nautical mile
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246:
242:
241:nautical mile
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217:Joshua Slocum
214:
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62:February 2024
55:
51:
45:
43:
37:
28:
27:
22:
1984:Solar System
1841:
1824:. Retrieved
1820:the original
1815:
1806:
1794:. Retrieved
1790:the original
1785:
1776:
1767:
1760:. Retrieved
1746:
1728:
1717:. Retrieved
1708:
1698:
1658:(7): 11–28.
1655:
1651:
1645:
1633:. Retrieved
1629:the original
1622:
1613:
1590:
1578:. Retrieved
1567:
1557:
1541:
1535:
1520:
1510:
1487:
1464:
1452:
1441:
1431:R. Fitzroy.
1426:
1401:
1392:
1380:. Retrieved
1365:
1358:
1346:
1334:. Retrieved
1325:
1315:
1304:. Retrieved
1300:
1291:
1279:
1268:. Retrieved
1258:
1247:. Retrieved
1243:
1234:
1222:
1211:
1128:
1124:Astronautics
1093:
1071:, which the
1050:
1039:
983:
973:
957:
938:
927:
919:
908:
897:
872:
869:
857:
837:
822:
776:
745:receiver. A
739:atomic clock
731:quartz watch
723:
693:
691:
670:
661:
646:Please help
634:
602:
590:
578:chronometers
571:
521:
484:
472:
448:
433:
424:
413:Please help
408:verification
405:
383:
336:
316:
296:
285:
262:
225:
215:
178:
169:
149:
114:
89:
85:
84:
59:
42:lead section
40:
1972:Outer space
1960:Spaceflight
1893:THE V-FORCE
1826:January 27,
1796:January 27,
1652:Acta Futura
1069:instruments
1046:planetarium
998:radio waves
963:high-speed
930:Boeing 747s
853:ex-meridian
814:, allowing
792:eight bells
710:Use of time
273:ex-meridian
199:(LOP) on a
123:(e.g., the
1719:2016-11-01
1306:2023-07-23
1270:2023-07-23
1249:2023-07-23
1204:References
1197:Star clock
1081:collimated
979:atmosphere
787:hack watch
550:See also:
508:See also:
347:arcseconds
343:arcminutes
299:Gran Chaco
237:hack watch
117:navigation
115:Celestial
1936:Astronomy
1924:Geography
1888:Air Facts
1705:"XPNAV 1"
1690:118570784
1665:1305.4842
1635:29 August
1400:(1995) .
1382:17 August
1146:Ephemeris
879:U.S. Navy
635:does not
574:longitude
562:Greenwich
546:Longitude
324:astrolabe
228:longitude
185:longitude
102:navigator
52:and help
1994:Category
1762:June 14,
1756:Archived
1738:Archived
1713:Archived
1605:Archived
1580:19 April
1574:Archived
1547:Archived
1527:Archived
1495:Archived
1472:Archived
1330:Archived
1102:See also
1036:Training
1000:is that
953:attitude
855:method.
851:and the
826:carried
704:ecliptic
523:Latitude
498:Latitude
292:Asunción
181:latitude
165:almanacs
161:nautical
1910:Portals
1670:Bibcode
1089:weather
1061:cockpit
1044:with a
1010:XPNAV 1
993:pulsars
915:Harvard
904:hacking
783:gimbals
656:removed
641:sources
528:Polaris
488:Polaris
467:azimuth
459:almanac
455:sextant
387:, 2018.
339:degrees
332:sextant
288:Madeira
281:sextant
252:Example
210:example
205:segment
163:or air
153:Polaris
141:horizon
135:, or a
79:sextant
1769:Trunk.
1688:
1414:
1373:
1065:bomber
823:Beagle
568:/GMT).
540:zenith
345:, and
330:, and
328:octant
133:planet
127:, the
1948:Stars
1686:S2CID
1660:arXiv
1336:9 May
1155:GNSS
1073:pilot
1026:NICER
989:X-ray
961:SR-71
320:kamal
193:sight
1866:Inua
1828:2005
1798:2005
1764:2017
1637:2017
1582:2015
1412:ISBN
1384:2010
1371:ISBN
1338:2018
1077:dome
1014:NASA
947:use
898:The
877:and
873:The
860:GNSS
821:HMS
772:ft/s
733:, a
718:and
699:GNSS
639:any
637:cite
591:The
382:USS
349:. A
271:and
183:and
137:star
131:, a
129:Moon
1678:doi
774:).
768:m/s
650:by
566:UTC
417:by
277:GMT
125:Sun
1996::
1814:.
1784:.
1766:.
1711:.
1707:.
1684:.
1676:.
1668:.
1654:.
1621:.
1603:.
1599:.
1572:.
1566:.
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1519:.
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1478:,
1410:.
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1299:.
1242:.
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830:.
760:ft
341:,
326:,
322:,
1912::
1830:.
1800:.
1722:.
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1672::
1662::
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1639:.
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1386:.
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764:m
677:)
671:(
666:)
662:(
658:.
644:.
440:)
434:(
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425:(
411:.
235:"
64:)
60:(
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46:.
23:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
