Map

From Wikipedia, the free encyclopedia

World map by Gerard van Shagen, Amsterdam, 1689

World map from 2016 CIA World Factbook

A map is a symbolic depiction emphasizing relationships between elements of some space, such as objects, regions, or themes.

Many maps are static, fixed to paper or some other durable medium, while others are dynamic or interactive. Although most commonly used to depict geography, maps may represent any space, real or imagined, without regard to context or scale, such as in brain mapping, DNA mapping, or computer network topology mapping. The space being mapped may be two dimensional, such as the surface of the earth, three dimensional, such as the interior of the earth, or even more abstract spaces of any dimension, such as arise in modeling phenomena having many independent variables.

Although the earliest maps known are of the heavens, geographic maps of territory have a very long tradition and exist from ancient times. The word "map" comes from the medieval Latin Mappa mundi, wherein mappa meant napkin or cloth and mundi the world. Thus, "map" became the shortened term referring to a two-dimensional representation of the surface of the world.

Geographic maps

A celestial map from the 17th century, by the cartographer Frederik de Wit

Cartography or map-making is the study and practice of crafting representations of the Earth upon a flat surface (see History of cartography), and one who makes maps is called a cartographer.

Road maps are perhaps the most widely used maps today, and form a subset of navigational maps, which also include aeronautical and nautical charts, railroad network maps, and hiking and bicycling maps. In terms of quantity, the largest number of drawn map sheets is probably made up by local surveys, carried out by municipalities, utilities, tax assessors, emergency services providers, and other local agencies. Many national surveying projects have been carried out by the military, such as the British Ordnance Survey: a civilian government agency, internationally renowned for its comprehensively detailed work.

In addition to location information maps may also be used to portray contour lines indicating constant values of elevation, temperature, rainfall, etc.

Orientation of maps

The Hereford Mappa Mundi from about 1300, Hereford Cathedral, England, is a classic "T-O" map with Jerusalem at centre, east toward the top, Europe the bottom left and Africa on the right.

The orientation of a map is the relationship between the directions on the map and the corresponding compass directions in reality. The word "orient" is derived from Latin oriens, meaning east. In the Middle Ages many maps, including the T and O maps, were drawn with east at the top (meaning that the direction "up" on the map corresponds to East on the compass). The most common cartographic convention is that north is at the top of a map.

Maps not oriented with north at the top:

• Maps from non-Western traditions are oriented a variety of ways. Old maps of Edo show the Japanese imperial palace as the "top", but also at the centre, of the map. Labels on the map are oriented in such a way that you cannot read them properly unless you put the imperial palace above your head.^{[citation needed]}
• Medieval European T and O maps such as the Hereford Mappa Mundi were centred on Jerusalem with East at the top. Indeed, prior to the reintroduction of Ptolemy's Geography to Europe around 1400, there was no single convention in the West. Portolan charts, for example, are oriented to the shores they describe.
• Maps of cities bordering a sea are often conventionally oriented with the sea at the top.
• Route and channel maps have traditionally been oriented to the road or waterway they describe.
• Polar maps of the Arctic or Antarctic regions are conventionally centred on the pole; the direction North would be towards or away from the centre of the map, respectively. Typical maps of the Arctic have 0° meridian towards the bottom of the page; maps of the Antarctic have the 0° meridian towards the top of the page.
• Reversed maps, also known as Upside-Down maps or South-Up maps, reverse the North is up convention and have south at the top.
• Buckminster Fuller's Dymaxion maps are based on a projection of the Earth's sphere onto an icosahedron. The resulting triangular pieces may be arranged in any order or orientation.
• Modern digital GIS maps such as ArcMap typically project north at the top of the map, but use math degrees (0 is east, degrees increase counter-clockwise), rather than compass degrees (0 is north, degrees increase clockwise) for orientation of transects. Compass decimal degrees can be converted to math degrees by subtracting them from 450; if the answer is greater than 360, subtract 360.

Scale and accuracy

A 'global view map' of Europe, Western Asia and Africa.

Many maps are drawn to a scale expressed as a ratio, such as 1:10,000, which means that 1 unit of measurement on the map corresponds to 10,000 of that same unit on the ground. The scale statement can be accurate when the region mapped is small enough for the curvature of the Earth to be neglected, such as a city map. Mapping larger regions, where curvature cannot be ignored, requires projections to map from the curved surface of the Earth to the plane. The impossibility of flattening the sphere to the plane without distortion means that the map cannot have constant scale. Rather, on most projections the best that can be attained is accurate scale along one or two paths on the projection. Because scale differs everywhere, it can only be measured meaningfully as point scale per location. Most maps strive to keep point scale variation within narrow bounds. Although the scale statement is nominal it is usually accurate enough for most purposes unless the map covers a large fraction of the earth. At the scope of a world map, scale as a single number is practically meaningless throughout most of the map. Instead, it usually refers to the scale along the equator.

Large scale maps, (e.g. 1:10,000), cover relatively small regions in great detail and small scale maps, (e.g. 1:10,000,000), cover large regions such as nations, continents and the whole globe. The large/small terminology arose from the practice of writing scales as numerical fractions: 1/10,000 is larger than 1/10,000,000. There is no exact dividing line between large and small but 1/100,000 might well be considered as a medium scale. Examples of large scale maps are the 1:25,000 maps produced for hikers; on the other hand maps intended for motorists at 1:250,000 or 1:1,000,000 are small scale.

It is important to recognize that even the most accurate maps sacrifice a certain amount of accuracy in scale to deliver a greater visual usefulness to its user. For example, the width of roads and small streams are exaggerated when they are too narrow to be shown on the map at true scale; that is, on a printed map they would be narrower than could be perceived by the naked eye. The same applies to computer maps where the smallest unit is the pixel. A narrow stream say must be shown to have the width of a pixel even if at the map scale it would be a small fraction of the pixel width.

Cartogram: The EU distorted to show population distributions.

Some maps, called cartograms, have the scale deliberately distorted to reflect information other than land area or distance. For example, this map (at the right) of Europe has been distorted to show population distribution, while the rough shape of the continent is still discernible.

Another example of distorted scale is the famous London Underground map. The basic geographical structure is respected but the tube lines (and the River Thames) are smoothed to clarify the relationships between stations. Near the center of the map stations are spaced out more than near the edges of map.

Further inaccuracies may be deliberate. For example, cartographers may simply omit military installations or remove features solely in order to enhance the clarity of the map. For example, a road map may not show railroads, smaller waterways or other prominent non-road objects, and even if it does, it may show them less clearly (e.g. dashed or dotted lines/outlines) than the main roads. Known as decluttering, the practice makes the subject matter that the user is interested in easier to read, usually without sacrificing overall accuracy. Software-based maps often allow the user to toggle decluttering between ON, OFF and AUTO as needed. In AUTO the degree of decluttering is adjusted as the user changes the scale being displayed.

Map types and projections

Map of large underwater features. (1995, NOAA)

Maps of the world or large areas are often either 'political' or 'physical'. The most important purpose of the political map is to show territorial borders; the purpose of the physical is to show features of geography such as mountains, soil type or land use including infrastructure such as roads, railroads and buildings. Topographic maps show elevations and relief with contour lines or shading.  Geological maps show not only the physical surface, but characteristics of the underlying rock, fault lines, and subsurface structures. Maps that depict the surface of the Earth also use a projection, a way of translating the three-dimensional real surface of the geoid to a two-dimensional picture. Perhaps the best-known world-map projection is the Mercator projection, originally designed as a form of nautical chart. Aeroplane pilots use aeronautical charts based on a Lambert conformal conic projection, in which a cone is laid over the section of the earth to be mapped. The cone intersects the sphere (the earth) at one or two parallels which are chosen as standard lines. This allows the pilots to plot a great-circle route approximation on a flat, two-dimensional chart.

• Azimuthal or Gnomonic map projections are often used in planning air routes due to their ability to represent great circles as straight lines.
• Richard Edes Harrison produced a striking series of maps during and after World War II for Fortune magazine. These used "bird's eye" projections to emphasise globally strategic "fronts" in the air age, pointing out proximities and barriers not apparent on a conventional rectangular projection of the world.

Electronic maps

A USGS digital raster graphic.

From the last quarter of the 20th century, the indispensable tool of the cartographer has been the computer. Much of cartography, especially at the data-gathering survey level, has been subsumed by Geographic Information Systems (GIS). The functionality of maps has been greatly advanced by technology simplifying the superimposition of spatially located variables onto existing geographical maps. Having local information such as rainfall level, distribution of wildlife, or demographic data integrated within the map allows more efficient analysis and better decision making. In the pre-electronic age such superimposition of data led Dr. John Snow to identify the location of an outbreak of cholera. Today, it is used by agencies of the human kind, as diverse as wildlife conservationists and militaries around the world.

Relief map Sierra Nevada

Even when GIS is not involved, most cartographers now use a variety of computer graphics programs to generate new maps.

Interactive, computerised maps are commercially available, allowing users to zoom in or zoom out (respectively meaning to increase or decrease the scale), sometimes by replacing one map with another of different scale, centered where possible on the same point. In-car global navigation satellite systems are computerised maps with route-planning and advice facilities which monitor the user's position with the help of satellites. From the computer scientist's point of view, zooming in entails one or a combination of:

1. replacing the map by a more detailed one
2. enlarging the same map without enlarging the pixels, hence showing more detail by removing less information compared to the less detailed version
3. enlarging the same map with the pixels enlarged (replaced by rectangles of pixels); no additional detail is shown, but, depending on the quality of one's vision, possibly more detail can be seen; if a computer display does not show adjacent pixels really separate, but overlapping instead (this does not apply for an LCD, but may apply for a cathode ray tube), then replacing a pixel by a rectangle of pixels does show more detail. A variation of this method is interpolation.

A world map in PDF format.

For example:

• Typically (2) applies to a Portable Document Format (PDF) file or other format based on vector graphics. The increase in detail is limited to the information contained in the file: enlargement of a curve may eventually result in a series of standard geometric figures such as straight lines, arcs of circles or splines.
• (2) may apply to text and (3) to the outline of a map feature such as a forest or building.
• (1) may apply to the text as needed (displaying labels for more features), while (2) applies to the rest of the image. Text is not necessarily enlarged when zooming in. Similarly, a road represented by a double line may or may not become wider when one zooms in.
• The map may also have layers which are partly raster graphics and partly vector graphics. For a single raster graphics image (2) applies until the pixels in the image file correspond to the pixels of the display, thereafter (3) applies.

Climatic maps

The maps that reflect the territorial distribution of climatic conditions based on the results of long-term observations are climatic maps. Climatic maps can be compiled both for individual climatic features (temperature, precipitation, humidity) and for combinations of them at the earth’s surface and in the upper layers of the atmosphere. Climatic maps afford a very convenient overview of the climatic features in a large region and permit values of climatic features to be compared in different parts of the region. Through interpolation the maps can be used to determine the values of climatic features in any particular spot.

Climatic maps generally apply to individual months and to the year as a whole, sometimes to the four seasons, to the growing period, and so forth. On maps compiled from the observations of ground meteorological stations, atmospheric pressure is converted to sea level. Air temperature maps are compiled both from the actual values observed on the surface of the earth and from values converted to sea level. The pressure field in free atmosphere is represented either by maps of the distribution of pressure at different standard altitudes—for example, at every kilometer above sea level—or by maps of baric topography on which altitudes (more precisely geopotentials) of the main isobaric surfaces (for example, 900, 800, and 700 millibars) counted off from sea level are plotted. The temperature, humidity, and wind on aeroclimatic maps may apply either to standard altitudes or to the main isobaric surfaces.

Isolines are drawn on maps of such climatic features as the long-term mean values (of atmospheric pressure, temperature, humidity, total precipitation, and so forth) to connect points with equal values of the feature in question—for example, isobars for pressure, isotherms for temperature, and isohyets for precipitation. Isoamplitudes are drawn on maps of amplitudes (for example, annual amplitudes of air temperature—that is, the differences between the mean temperatures of the warmest and coldest month). Isanomals are drawn on maps of anomalies (for example, deviations of the mean temperature of each place from the mean temperature of the entire latitudinal zone). Isolines of frequency are drawn on maps showing the frequency of a particular phenomenon (for example, annual number of days with a thunderstorm or snow cover). Isochrones are drawn on maps showing the dates of onset of a given phenomenon (for example, the first frost and appearance or disappearance of the snow cover) or the date of a particular value of a meteorological element in the course of a year (for example, passing of the mean daily air temperature through zero). Isolines of the mean numerical value of wind velocity or isotachs are drawn on wind maps (charts); the wind resultants and directions of prevailing winds are indicated by arrows of different length or arrows with different plumes; lines of flow are often drawn. Maps of the zonal and meridional components of wind are frequently compiled for the free atmosphere. Atmospheric pressure and wind are usually combined on climatic maps. Wind roses, curves showing the distribution of other meteorological elements, diagrams of the annual course of elements at individual stations, and the like are also plotted on climatic maps.

Maps of climatic regionalization, that is, division of the earth’s surface into climatic zones and regions according to some classification of climates, are a special kind of climatic map.

Climatic maps are often incorporated into climatic atlases of varying geographic range (globe, hemispheres, continents, countries, oceans) or included in comprehensive atlases. Besides general climatic maps, applied climatic maps and atlases have great practical value. Aeroclimatic maps, aeroclimatic atlases, and agroclimatic maps are the most numerous.

Conventional signs

The various features shown on a map are represented by conventional signs or symbols. For example, colors can be used to indicate a classification of roads. Those signs are usually explained in the margin of the map, or on a separately published characteristic sheet.^[1]

Some cartographers prefer to make the map cover practically the entire screen or sheet of paper, leaving no room "outside" the map for information about the map as a whole. These cartographers typically place such information in an otherwise "blank" region "inside" the map—cartouche, map legend, title, compass rose, bar scale, etc. In particular, some maps contain smaller "sub-maps" in otherwise blank regions—often one at a much smaller scale showing the whole globe and where the whole map fits on that globe, and a few showing "regions of interest" at a larger scale in order to show details that wouldn't otherwise fit. Occasionally sub-maps use the same scale as the large map—a few maps of the contiguous United States include a sub-map to the same scale for each of the two non-contiguous states.

Labeling

To communicate spatial information effectively, features such as rivers, lakes, and cities need to be labeled. Over centuries cartographers have developed the art of placing names on even the densest of maps. Text placement or name placement can get mathematically very complex as the number of labels and map density increases. Therefore, text placement is time-consuming and labor-intensive, so cartographers and GIS users have developed automatic label placement to ease this process.^[2][3]

Non-geographical spatial maps

Maps exist of the Solar System, and other cosmological features such as star maps. In addition maps of other bodies such as the Moon and other planets are technically not geographical maps.

Topological maps

In a topological map, like this one showing inventory locations, the distances between locations is not important. Only the layout and connectivity between them matters.

Diagrams such as schematic diagrams and Gantt charts and treemaps display logical relationships between items, rather than geographical relationships. Topological in nature, only the connectivity is significant. The London Underground map and similar subway maps around the world are a common example of these maps.

General-purpose maps

General-purpose maps provide many types of information on one map. Most atlas maps, wall maps, and road maps fall into this category. The following are some features that might be shown on general-purpose maps: bodies of water, roads, railway lines, parks, elevations, towns and cities, political boundaries, latitude and longitude, national and provincial parks. These maps give a broad understanding of location and features of an area. The reader may gain an understanding of the type of landscape, the location of urban places, and the location of major transportation routes all at once.

Types of maps

• Atlas
• Climatic map
• Geologic map
• Physical map
• Political map
• Relief map
• Resource map
• Star map
• Street map
• Thematic map
• Topographical map
• Weather map
• World map
• Cadastral map

Legal regulation

Some countries required that all published maps represent their national claims regarding border disputes. For example:

• Within Russia, Google Maps shows Crimea as part of Russia.^[4]
• Both the Republic of India and the People's Republic of China require that all maps show areas subject to the Sino-Indian border dispute in their own favor.^[5]

In 2010, the People's Republic of China began requiring that all online maps served from within China be hosted there, making them subject to Chinese laws.^[6]

The Surprising Reason Why Neutron Stars Don't All Collapse To Form Black Holes

Ethan Siegel, Contributor,  Jun 13, 2018
Original link:  https://www.forbes.com/sites/startswithabang/2018/06/13/the-surprising-reason-why-neutron-stars-dont-all-collapse-to-form-black-holes/#468e0897159c

NASA

There are few things in the Universe that are as easy to form, in theory, as black holes are. Bring enough mass into a compact volume and it gets more and more difficult to gravitationally escape from it. If you were to gather enough matter in a single spot and let gravitation do its thing, you'd eventually pass a critical threshold, where the speed you'd need to gravitationally escape would exceed the speed of light. Reach that point, and you'll create a black hole.

But real, normal matter will very much resist getting there. Hydrogen, the most common element in the Universe, will fuse in a chain reaction at high temperatures and densities to create a star, rather than a black hole. Burned out stellar cores, like white dwarfs and neutron stars, can also resist gravitational collapse and stave off becoming a black hole. But while white dwarfs can reach only 1.4 times the mass of the Sun, neutron stars can get twice as massive. At long last, we finally understand why.

NASA, ESA and G. Bacon (STScI)

Sirius A and B, a normal (Sun-like) star and a white dwarf star. Even though the white dwarf is much lower in mass, its tiny, Earth-like size ensures its escape velocity is many times larger. For a neutron stars, masses can be even larger, with physical sizes in the tens of kilometers.

In our Universe, the matter-based objects we know of are all made of just a few simple ingredients: protons, neutrons, and electrons. Each proton and neutron is made up of three quarks, with a proton containing two up and one down quark, and a neutron containing one up and two downs. On the other hand, electrons themselves are fundamental particles. Although particles come in two classes — fermions and bosons — both quarks and electrons are fermions.

Contemporary Physics Education Project / DOE / NSF / LBNL

The Standard Model of particle physics accounts for three of the four forces (excepting gravity), the full suite of discovered particles, and all of their interactions. Quarks and leptons are fermions, which have a host of unique properties that the other (bosons) particles do not possess.

Why should you care? It turns out that these classification properties are vitally important when it comes to the question of black hole formation. Fermions have a few properties that bosons don't, including:

• they have half-integer (e.g., ±1/2, ±3/2, ±5/2, etc.) spins as opposed to integer (0, ±1, ±2, etc.) spins,
• they have antiparticle counterparts; there are no anti-bosons,
• and they obey the Pauli Exclusion Principle, whereas bosons don't.

That last property is the key to staving off collapse into a black hole.

PoorLeno / Wikimedia Commons

The energy levels and electron wavefunctions that correspond to different states within a hydrogen atom. Because of the spin = 1/2 nature of the electron, only two (+1/2 and -1/2 states) electrons can be in any given state at once.

The Pauli exclusion principle, which only applies to fermions, not bosons, states, explicitly, that in any quantum system, no two fermions can occupy the same quantum state. It means that if you take, say, an electron and put it in a particular location, it will have a set of properties in that state: energy levels, angular momentum, etc.

If you take a second electron and add it to your system, however, in the same location, it is forbidden from having those same quantum numbers. It must either occupy a different energy level, have a different spin (+1/2 if the first was -1/2, for example), or occupy a different location in space. This principle explains why the periodic table is arranged as it is.

This is why atoms have different properties, why they bind together in the intricate combinations that they do, and why each element in the periodic table is unique: because the electron configuration of each type of atom is unlike any other.

APS/Alan Stonebraker

The three valence quarks of a proton contribute to its spin, but so do the gluons, sea quarks and antiquarks, and orbital angular momentum as well. The electrostatic repulsion and the attractive strong nuclear force, in tandem, are what give the proton its size.

Protons and neutrons are similar. Despite being composite particles, made up of three quarks apiece, they behave as single, individual fermions themselves. They, too, obey the Pauli Exclusion Principle, and no two protons or neutrons can occupy the same quantum state. The fact that electrons are fermions is what keeps white dwarf stars from collapsing under their own gravity; the fact that neutrons are fermions prevents neutron stars from collapsing further. The Pauli exclusion principle responsible for atomic structure is responsible for keeping the densest physical objects of all from becoming black holes.

CXC/M. Weiss

A white dwarf, a neutron star or even a strange quark star are all still made of fermions. The Pauli degeneracy pressure helps hold up the stellar remnant against gravitational collapse, preventing a black hole from forming.

And yet, when you look at the white dwarf stars we have in the Universe, they cap out at around 1.4 solar masses: the Chandrasekhar mass limit. The quantum degeneracy pressure arising from the fact that no two electrons can occupy the same quantum state is what prevents black holes from forming until that threshold is crossed.

In neutron stars, there should be a similar mass limit: the Tolman-Oppenheimer-Volkoff limit. Initially, it was anticipated that this would be about the same as the Chandrasekhar mass limit, since the underlying physics is the same. Sure, it's not specifically electrons that are providing the quantum degeneracy pressure, but the principle (and the equations) are pretty much the same. But we now know, from our observations, that there are neutron stars much more massive than 1.4 solar masses, perhaps rising as high as 2.3 or 2.5 times the mass of our Sun.

ESO/Luís Calçada

A neutron star is one of the densest collections of matter in the Universe, but there is an upper limit to their mass. Exceed it, and the neutron star will further collapse to form a black hole.

And yet, there are reasons for the differences. In neutron stars, the strong nuclear force plays a role, causing a larger effective repulsion than for a simple model of degenerate, cold gases of fermions (which is what's relevant for electrons). For the past 20+ years, calculations of the theoretical mass limit for neutron stars have varied tremendously: from about 1.5 to 3.0 solar masses. The reason for the uncertainty has been the unknowns surrounding the behavior of extremely dense matter, like the densities you'll find inside an atomic nucleus, are not well known.

Or rather, these unknowns plagued us for a long time, until a new paper last month changed all of that. With the publication of their new paper in Nature, The pressure distribution inside the proton, coauthors V. D. Burkert, L. Elouadrhiri, and F. X. Girod may have just achieved the key advance needed to understand what's happening inside neutron stars.

Brookhaven National Laboratory

A better understanding of the internal structure of a proton, including how the "sea" quarks and gluons are distributed, has been achieved through both experimental improvements and new theoretical developments in tandem. These results apply to neutrons as well.

Our models of nucleons like protons and neutrons have improved tremendously over the past few decades, coincident with improvements in both computational and experimental techniques. The latest research uses an old technique known as Compton scattering, where electrons are fired at the internal structure of a proton to probe its structure. When an electron interacts (electromagnetically) with a quark, it emits a high-energy photon, along with a scattered electron and leads to nuclear recoil. By measuring all three products, you can calculate the pressure distribution experienced by the quarks inside the atomic nucleus. In a shocking find, the average peak pressure, near the center of the proton, comes out to 10³⁵ pascals: a greater pressure than neutron stars experience anywhere.

The quark-confinement-induced pressure distribution in the proton by V.D. Burkert, L. Elouadrhiri, and F.X. Girod

At large distances, quarks are confined within a nucleon. But at short distances, there's a repulsive pressure that prevents other quarks-and-nuclei from getting too close to each individual proton (or, by extension, neutron).

In other words, by understanding how the pressure distribution inside an individual nucleon works, we can calculate when and under what conditions that pressure can be overcome. Although the experiment was only done for protons, the results should be analogous for neutrons, too, meaning that, in the future, we should be able to calculate a more exact limit for the masses of neutron stars.

LIGO-Virgo/Frank Elavsky/Northwestern

The masses of stellar remnants are measured in many different ways. This graphic shows the masses for black holes detected through electromagnetic observations (purple); the black holes measured by gravitational-wave observations (blue); neutron stars measured with electromagnetic observations (yellow); and the masses of the neutron stars that merged in an event called GW170817, which were detected in gravitational waves (orange). The result of the merger was a neutron star, briefly, that swiftly became a black hole.

The measurements of the enormous pressure inside the proton, as well as the distribution of that pressure, show us what's responsible for preventing the collapse of neutron stars. It's the internal pressure inside each proton and neutron, arising from the strong force, that holds up neutron stars when white dwarfs have long given out. Determining exactly where that mass threshold is just got a great boost. Rather than solely relying on astrophysical observations, the experimental side of nuclear physics may provide the guidepost we need to theoretically understand where the limits of neutron stars actually lie.

Astrophysicist and author Ethan Siegel is the founder and primary writer of Starts With A Bang! His books, Treknology and Beyond The Galaxy, are available wherever books are sold.

Navigation

From Wikipedia, the free encyclopedia

Table of geography, hydrography, and navigation, from the 1728 Cyclopaedia

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.^[1] The field of navigation includes four general categories: land navigation, marine navigation, aeronautic navigation, and space navigation.^[2]

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.^[2] In this sense, navigation includes orienteering and pedestrian navigation.^[2]

History

In the European medieval period, navigation was considered part of the set of seven mechanical arts, none of which were used for long voyages across open ocean. Polynesian navigation is probably the earliest form of open ocean navigation, it was based on memory and observation recorded on scientific instruments like the Marshall Islands Stick Charts of Ocean Swells. Early Pacific Polynesians used the motion of stars, weather, the position of certain wildlife species, or the size of waves to find the path from one island to another.
Maritime navigation using scientific instruments such as the mariner's astrolabe first occurred in the Mediterranean during the Middle Ages. Although land astrolabes were invented in the Hellenistic period and existed in classical antiquity and the Islamic Golden Age, the oldest record of a sea astrolabe is that of Majorcan astronomer Ramon Llull dating from 1295.^[3] The perfecting of this navigation instrument is attributed to Portuguese navigators during early Portuguese discoveries in the Age of Discovery.^[4][5] The earliest known description of how to make and use a sea astrolabe comes from Spanish cosmographer Martín Cortés de Albacar's Arte de Navegar (The Art of Navigation) published in 1551,^[6] based on the principle of the archipendulum used in constructing the Egyptian pyramids.

Open-seas navigation using the astrolabe and the compass started during the Age of Discovery in the 15th century. The Portuguese began systematically exploring the Atlantic coast of Africa from 1418, under the sponsorship of Prince Henry. In 1488 Bartolomeu Dias reached the Indian Ocean by this route. In 1492 the Spanish monarchs funded Christopher Columbus's expedition to sail west to reach the Indies by crossing the Atlantic, which resulted in the Discovery of America. In 1498, a Portuguese expedition commanded by Vasco da Gama reached India by sailing around Africa, opening up direct trade with Asia. Soon, the Portuguese sailed further eastward, to the Spice Islands in 1512, landing in China one year later.

The first circumnavigation of the earth was completed in 1522 with the Magellan-Elcano expedition, a Spanish voyage of discovery led by Portuguese explorer Ferdinand Magellan and completed by Spanish navigator Juan Sebastián Elcano after the former's death in the Philippines in 1521. The fleet of seven ships sailed from Sanlúcar de Barrameda in Southern Spain in 1519, crossed the Atlantic Ocean and after several stopovers rounded the southern tip of South America. Some ships were lost, but the remaining fleet continued across the Pacific making a number of discoveries including Guam and the Philippines. By then, only two galleons were left from the original seven. The Victoria led by Elcano sailed across the Indian Ocean and north along the coast of Africa, to finally arrive in Spain in 1522, three years after its departure. The Trinidad sailed east from the Philippines, trying to find a maritime path back to the Americas, but was unsuccessful. The eastward route across the Pacific, also known as the tornaviaje (return trip) was only discovered forty years later, when Spanish cosmographer Andrés de Urdaneta sailed from the Philippines, north to parallel 39°, and hit the eastward Kuroshio Current which took its galleon across the Pacific. He arrived in Acapulco on October 8, 1565.

Etymology

The term stems from the 1530s, from Latin navigationem (nom. navigatio), from navigatus, pp. of navigare "to sail, sail over, go by sea, steer a ship," from navis "ship" and the root of agere "to drive".^[7]

Basic concepts

Map of Earth
Longitude (λ)
Lines of longitude appear vertical with varying curvature in this projection, but are actually halves of great ellipses, with identical radii at a given latitude.
Latitude (φ)
Lines of latitude appear horizontal with varying curvature in this projection; but are actually circular with different radii. All locations with a given latitude are collectively referred to as a circle of latitude.
The equator divides the planet into a Northern Hemisphere and a Southern Hemisphere, and has a latitude of 0°.

Latitude

Roughly, the latitude of a place on Earth is its angular distance north or south of the equator.^[8] Latitude is usually expressed in degrees (marked with °) ranging from 0° at the Equator to 90° at the North and South poles.^[8] The latitude of the North Pole is 90° N, and the latitude of the South Pole is 90° S.^[8] Mariners calculated latitude in the Northern Hemisphere by sighting the North Star Polaris with a sextant and using sight reduction tables to correct for height of eye and atmospheric refraction. The height of Polaris in degrees above the horizon is the latitude of the observer, within a degree or so.

Longitude

Similar to latitude, the longitude of a place on Earth is the angular distance east or west of the prime meridian or Greenwich meridian.^[8] Longitude is usually expressed in degrees (marked with °) ranging from 0° at the Greenwich meridian to 180° east and west. Sydney, for example, has a longitude of about 151° east. New York City has a longitude of 74° west. For most of history, mariners struggled to determine longitude. Longitude can be calculated if the precise time of a sighting is known. Lacking that, one can use a sextant to take a lunar distance (also called the lunar observation, or "lunar" for short) that, with a nautical almanac, can be used to calculate the time at zero longitude (see Greenwich Mean Time).^[9] Reliable marine chronometers were unavailable until the late 18th century and not affordable until the 19th century.^[10][11][12] For about a hundred years, from about 1767 until about 1850,^[13] mariners lacking a chronometer used the method of lunar distances to determine Greenwich time to find their longitude. A mariner with a chronometer could check its reading using a lunar determination of Greenwich time.^[10][14]

Loxodrome

In navigation, a rhumb line (or loxodrome) is a line crossing all meridians of longitude at the same angle, i.e. a path derived from a defined initial bearing. That is, upon taking an initial bearing, one proceeds along the same bearing, without changing the direction as measured relative to true or magnetic north.

Modern technique

Most modern navigation relies primarily on positions determined electronically by receivers collecting information from satellites. Most other modern techniques rely on crossing lines of position or LOP.^[15] A line of position can refer to two different things, either a line on a chart or a line between the observer and an object in real life.^[16] A bearing is a measure of the direction to an object.^[16] If the navigator measures the direction in real life, the angle can then be drawn on a nautical chart and the navigator will be on that line on the chart.^[16]

In addition to bearings, navigators also often measure distances to objects.^[15] On the chart, a distance produces a circle or arc of position.^[15] Circles, arcs, and hyperbolae of positions are often referred to as lines of position.

If the navigator draws two lines of position, and they intersect he must be at that position.^[15] A fix is the intersection of two or more LOPs.^[15]

If only one line of position is available, this may be evaluated against the Dead reckoning position to establish an estimated position.^[17]

Lines (or circles) of position can be derived from a variety of sources:

• celestial observation (a short segment of the circle of equal altitude, but generally represented as a line),
• terrestrial range (natural or man made) when two charted points are observed to be in line with each other,^[18]
• compass bearing to a charted object,
• radar range to a charted object,
• on certain coastlines, a depth sounding from echo sounder or hand lead line.

There are some methods seldom used today such as "dipping a light" to calculate the geographic range from observer to lighthouse.

Methods of navigation have changed through history.^[19] Each new method has enhanced the mariner's ability to complete his voyage.^[19] One of the most important judgments the navigator must make is the best method to use.^[19] Some types of navigation are depicted in the table.

Modern navigation methods

Illustration	Description	Application
	Dead reckoning or DR, in which one advances a prior position using the ship's course and speed. The new position is called a DR position. It is generally accepted that only course and speed determine the DR position. Correcting the DR position for leeway, current effects, and steering error result in an estimated position or EP. An inertial navigator develops an extremely accurate EP.[19]	Used at all times.
	Pilotage involves navigating in restricted waters with frequent determination of position relative to geographic and hydrographic features.[19]	When within sight of land.
	Celestial navigation involves reducing celestial measurements to lines of position using tables, spherical trigonometry, and almanacs.	Used primarily as a backup to satellite and other electronic systems in the open ocean.[19]

Electronic navigation covers any method of position fixing using electronic means, including:
	Radio navigation uses radio waves to determine position by either radio direction finding systems or hyperbolic systems, such as Decca, Omega and LORAN-C.	Losing ground to GPS.
	Radar navigation uses radar to determine the distance from or bearing of objects whose position is known. This process is separate from radar's use as a collision avoidance system.[19]	Primarily when within radar range of land.
	Satellite navigation uses artificial earth satellite systems, such as GPS, to determine position.[19]	Used in all situations.

The practice of navigation usually involves a combination of these different methods.^[19]

Mental navigation checks

By mental navigation checks, a pilot or a navigator estimates tracks, distances, and altitudes which will then help the pilot avoid gross navigation errors.

Piloting

Manual navigation through Dutch airspace

Piloting (also called pilotage) involves navigating an aircraft by visual reference to landmarks,^[20] or a water vessel in restricted waters and fixing its position as precisely as possible at frequent intervals.^[21] More so than in other phases of navigation, proper preparation and attention to detail are important.^[21] Procedures vary from vessel to vessel, and between military, commercial, and private vessels.^[21]

A military navigation team will nearly always consist of several people.^[21] A military navigator might have bearing takers stationed at the gyro repeaters on the bridge wings for taking simultaneous bearings, while the civilian navigator must often take and plot them himself.^[21] While the military navigator will have a bearing book and someone to record entries for each fix, the civilian navigator will simply pilot the bearings on the chart as they are taken and not record them at all.^[21]

If the ship is equipped with an ECDIS, it is reasonable for the navigator to simply monitor the progress of the ship along the chosen track, visually ensuring that the ship is proceeding as desired, checking the compass, sounder and other indicators only occasionally.^[21] If a pilot is aboard, as is often the case in the most restricted of waters, his judgement can generally be relied upon, further easing the workload.^[21] But should the ECDIS fail, the navigator will have to rely on his skill in the manual and time-tested procedures.^[21]

Celestial navigation

A celestial fix will be at the intersection of two or more circles.

Celestial navigation systems are based on observation of the positions of the Sun, Moon, Planets and navigational stars. Such systems are in use as well for terrestrial navigating as for interstellar navigating. By knowing which point on the rotating earth a celestial object is above and measuring its height above the observer's horizon, the navigator can determine his distance from that subpoint. A nautical almanac and a marine chronometer are used to compute the subpoint on earth a celestial body is over, and a sextant is used to measure the body's angular height above the horizon. That height can then be used to compute distance from the subpoint to create a circular line of position. A navigator shoots a number of stars in succession to give a series of overlapping lines of position. Where they intersect is the celestial fix. The moon and sun may also be used. The sun can also be used by itself to shoot a succession of lines of position (best done around local noon) to determine a position.^[22]

Marine chronometer

In order to accurately measure longitude, the precise time of a sextant sighting (down to the second, if possible) must be recorded. Each second of error is equivalent to 15 seconds of longitude error, which at the equator is a position error of .25 of a nautical mile, about the accuracy limit of manual celestial navigation.

The spring-driven marine chronometer is a precision timepiece used aboard ship to provide accurate time for celestial observations.^[22] A chronometer differs from a spring-driven watch principally in that it contains a variable lever device to maintain even pressure on the mainspring, and a special balance designed to compensate for temperature variations.^[22]

A spring-driven chronometer is set approximately to Greenwich mean time (GMT) and is not reset until the instrument is overhauled and cleaned, usually at three-year intervals.^[22] The difference between GMT and chronometer time is carefully determined and applied as a correction to all chronometer readings.^[22] Spring-driven chronometers must be wound at about the same time each day.^[22]

Quartz crystal marine chronometers have replaced spring-driven chronometers aboard many ships because of their greater accuracy.^[22] They are maintained on GMT directly from radio time signals.^[22] This eliminates chronometer error and watch error corrections.^[22] Should the second hand be in error by a readable amount, it can be reset electrically.^[22]

The basic element for time generation is a quartz crystal oscillator.^[22] The quartz crystal is temperature compensated and is hermetically sealed in an evacuated envelope.^[22] A calibrated adjustment capability is provided to adjust for the aging of the crystal.^[22]

The chronometer is designed to operate for a minimum of 1 year on a single set of batteries.^[22] Observations may be timed and ship's clocks set with a comparing watch, which is set to chronometer time and taken to the bridge wing for recording sight times.^[22] In practice, a wrist watch coordinated to the nearest second with the chronometer will be adequate.^[22]

A stop watch, either spring wound or digital, may also be used for celestial observations.^[22] In this case, the watch is started at a known GMT by chronometer, and the elapsed time of each sight added to this to obtain GMT of the sight.^[22]

All chronometers and watches should be checked regularly with a radio time signal.^[22] Times and frequencies of radio time signals are listed in publications such as Radio Navigational Aids.^[22]

The marine sextant

The marine sextant is used to measure the elevation of celestial bodies above the horizon.

The second critical component of celestial navigation is to measure the angle formed at the observer's eye between the celestial body and the sensible horizon. The sextant, an optical instrument, is used to perform this function. The sextant consists of two primary assemblies. The frame is a rigid triangular structure with a pivot at the top and a graduated segment of a circle, referred to as the "arc", at the bottom. The second component is the index arm, which is attached to the pivot at the top of the frame. At the bottom is an endless vernier which clamps into teeth on the bottom of the "arc". The optical system consists of two mirrors and, generally, a low power telescope. One mirror, referred to as the "index mirror" is fixed to the top of the index arm, over the pivot. As the index arm is moved, this mirror rotates, and the graduated scale on the arc indicates the measured angle ("altitude").

The second mirror, referred to as the "horizon glass", is fixed to the front of the frame. One half of the horizon glass is silvered and the other half is clear. Light from the celestial body strikes the index mirror and is reflected to the silvered portion of the horizon glass, then back to the observer's eye through the telescope. The observer manipulates the index arm so the reflected image of the body in the horizon glass is just resting on the visual horizon, seen through the clear side of the horizon glass.

Adjustment of the sextant consists of checking and aligning all the optical elements to eliminate "index correction". Index correction should be checked, using the horizon or more preferably a star, each time the sextant is used. The practice of taking celestial observations from the deck of a rolling ship, often through cloud cover and with a hazy horizon, is by far the most challenging part of celestial navigation.^{[citation needed]}

Inertial navigation

Inertial navigation system is a dead reckoning type of navigation system that computes its position based on motion sensors. Once the initial latitude and longitude is established, the system receives impulses from motion detectors that measure the acceleration along three or more axes enabling it to continually and accurately calculate the current latitude and longitude. Its advantages over other navigation systems are that, once the starting position is set, it does not require outside information, it is not affected by adverse weather conditions and it cannot be detected or jammed. Its disadvantage is that since the current position is calculated solely from previous positions, its errors are cumulative, increasing at a rate roughly proportional to the time since the initial position was input. Inertial navigation systems must therefore be frequently corrected with a location 'fix' from some other type of navigation system. The US Navy developed a Ships Inertial Navigation System (SINS) during the Polaris missile program to ensure a safe, reliable and accurate navigation system for its missile submarines. Inertial navigation systems were in wide use until satellite navigation systems (GPS) became available. Inertial Navigation Systems are still in common use on submarines, since GPS reception or other fix sources are not possible while submerged.

Electronic navigation

Radio navigation

A radio direction finder or RDF is a device for finding the direction to a radio source. Due to radio's ability to travel very long distances "over the horizon", it makes a particularly good navigation system for ships and aircraft that might be flying at a distance from land.
RDFs works by rotating a directional antenna and listening for the direction in which the signal from a known station comes through most strongly. This sort of system was widely used in the 1930s and 1940s. RDF antennas are easy to spot on German World War II aircraft, as loops under the rear section of the fuselage, whereas most US aircraft enclosed the antenna in a small teardrop-shaped fairing.

In navigational applications, RDF signals are provided in the form of radio beacons, the radio version of a lighthouse. The signal is typically a simple AM broadcast of a morse code series of letters, which the RDF can tune in to see if the beacon is "on the air". Most modern detectors can also tune in any commercial radio stations, which is particularly useful due to their high power and location near major cities.

Decca, OMEGA, and LORAN-C are three similar hyperbolic navigation systems. Decca was a hyperbolic low frequency radio navigation system (also known as multilateration) that was first deployed during World War II when the Allied forces needed a system which could be used to achieve accurate landings. As was the case with Loran C, its primary use was for ship navigation in coastal waters. Fishing vessels were major post-war users, but it was also used on aircraft, including a very early (1949) application of moving-map displays. The system was deployed in the North Sea and was used by helicopters operating to oil platforms.

The OMEGA Navigation System was the first truly global radio navigation system for aircraft, operated by the United States in cooperation with six partner nations. OMEGA was developed by the United States Navy for military aviation users. It was approved for development in 1968 and promised a true worldwide oceanic coverage capability with only eight transmitters and the ability to achieve a four-mile (6 km) accuracy when fixing a position. Initially, the system was to be used for navigating nuclear bombers across the North Pole to Russia. Later, it was found useful for submarines.[1] Due to the success of the Global Positioning System the use of Omega declined during the 1990s, to a point where the cost of operating Omega could no longer be justified. Omega was terminated on September 30, 1997 and all stations ceased operation.

LORAN is a terrestrial navigation system using low frequency radio transmitters that use the time interval between radio signals received from three or more stations to determine the position of a ship or aircraft. The current version of LORAN in common use is LORAN-C, which operates in the low frequency portion of the EM spectrum from 90 to 110 kHz. Many nations are users of the system, including the United States, Japan, and several European countries. Russia uses a nearly exact system in the same frequency range, called CHAYKA. LORAN use is in steep decline, with GPS being the primary replacement. However, there are attempts to enhance and re-popularize LORAN. LORAN signals are less susceptible to interference and can penetrate better into foliage and buildings than GPS signals.

Radar navigation

Radar ranges and bearings can be very useful navigation.

When a vessel is within radar range of land or special radar aids to navigation, the navigator can take distances and angular bearings to charted objects and use these to establish arcs of position and lines of position on a chart.^[23] A fix consisting of only radar information is called a radar fix.^[24]

Types of radar fixes include "range and bearing to a single object,"^[25] "two or more bearings,"^[25] "tangent bearings,"^[25] and "two or more ranges."^[25]

Parallel indexing is a technique defined by William Burger in the 1957 book The Radar Observer's Handbook.^[26] This technique involves creating a line on the screen that is parallel to the ship's course, but offset to the left or right by some distance.^[26] This parallel line allows the navigator to maintain a given distance away from hazards.^[26]

Some techniques have been developed for special situations. One, known as the "contour method," involves marking a transparent plastic template on the radar screen and moving it to the chart to fix a position.^[27]

Another special technique, known as the Franklin Continuous Radar Plot Technique, involves drawing the path a radar object should follow on the radar display if the ship stays on its planned course.^[28] During the transit, the navigator can check that the ship is on track by checking that the pip lies on the drawn line.^[28]

Smartphone navigation

In the modern era, smartphones act as personal GPS navigators for any civilian.

Satellite navigation

Global Navigation Satellite System or GNSS is the term for satellite navigation systems that provide positioning with global coverage. A GNSS allow small electronic receivers to determine their location (longitude, latitude, and altitude) to within a few metres using time signals transmitted along a line of sight by radio from satellites. Receivers on the ground with a fixed position can also be used to calculate the precise time as a reference for scientific experiments.

As of October 2011, only the United States NAVSTAR Global Positioning System (GPS) and the Russian GLONASS are fully globally operational GNSSs. The European Union's Galileo positioning system is a next generation GNSS in the initial deployment phase, scheduled to be operational by 2013. China has indicated it may expand its regional Beidou navigation system into a global system.

More than two dozen GPS satellites are in medium Earth orbit, transmitting signals allowing GPS receivers to determine the receiver's location, speed and direction.

Since the first experimental satellite was launched in 1978, GPS has become an indispensable aid to navigation around the world, and an important tool for map-making and land surveying. GPS also provides a precise time reference used in many applications including scientific study of earthquakes, and synchronization of telecommunications networks.

Developed by the United States Department of Defense, GPS is officially named NAVSTAR GPS (NAVigation Satellite Timing And Ranging Global Positioning System). The satellite constellation is managed by the United States Air Force 50th Space Wing. The cost of maintaining the system is approximately US$750 million per year,^[29] including the replacement of aging satellites, and research and development. Despite this fact, GPS is free for civilian use as a public good.

Navigation processes

Ships and similar vessels

Day's work in navigation

The Day's work in navigation is a minimal set of tasks consistent with prudent navigation. The definition will vary on military and civilian vessels, and from ship to ship, but takes a form resembling:^[30]

1. Maintain a continuous dead reckoning plot.
2. Take two or more star observations at morning twilight for a celestial fix (prudent to observe 6 stars).
3. Morning sun observation. Can be taken on or near prime vertical for longitude, or at any time for a line of position.
4. Determine compass error by azimuth observation of the sun.
5. Computation of the interval to noon, watch time of local apparent noon, and constants for meridian or ex-meridian sights.
6. Noontime meridian or ex-meridian observation of the sun for noon latitude line. Running fix or cross with Venus line for noon fix.
7. Noontime determination the day's run and day's set and drift.
8. At least one afternoon sun line, in case the stars are not visible at twilight.
9. Determine compass error by azimuth observation of the sun.
10. Take two or more star observations at evening twilight for a celestial fix (prudent to observe 6 stars).

Passage planning

Poor passage planning and deviation from the plan can lead to groundings, ship damage and cargo loss.

Passage planning or voyage planning is a procedure to develop a complete description of vessel's voyage from start to finish. The plan includes leaving the dock and harbor area, the en route portion of a voyage, approaching the destination, and mooring. According to international law, a vessel's captain is legally responsible for passage planning,^[31] however on larger vessels, the task will be delegated to the ship's navigator.^[32]

Studies show that human error is a factor in 80 percent of navigational accidents and that in many cases the human making the error had access to information that could have prevented the accident.^[32] The practice of voyage planning has evolved from penciling lines on nautical charts to a process of risk management.^[32]

Passage planning consists of four stages: appraisal, planning, execution, and monitoring,^[32] which are specified in International Maritime Organization Resolution A.893(21), Guidelines For Voyage Planning,^[33] and these guidelines are reflected in the local laws of IMO signatory countries (for example, Title 33 of the U.S. Code of Federal Regulations), and a number of professional books or publications. There are some fifty elements of a comprehensive passage plan depending on the size and type of vessel.

The appraisal stage deals with the collection of information relevant to the proposed voyage as well as ascertaining risks and assessing the key features of the voyage. This will involve considering the type of navigation required e.g. Ice navigation, the region the ship will be passing through and the hydrographic information on the route. In the next stage, the written plan is created. The third stage is the execution of the finalised voyage plan, taking into account any special circumstances which may arise such as changes in the weather, which may require the plan to be reviewed or altered. The final stage of passage planning consists of monitoring the vessel's progress in relation to the plan and responding to deviations and unforeseen circumstances.

Land navigation

Navigation for cars and other land-based travel typically uses maps, landmarks, and in recent times computer navigation ("satnav", short for satellite navigation), as well as any means available on water.

Computerized navigation commonly relies on GPS for current location information, a navigational map database of roads and navigable routes, and uses algorithms related to the shortest path problem to identify optimal routes.

Integrated bridge systems

Electronic integrated bridge concepts are driving future navigation system planning.^[19] Integrated systems take inputs from various ship sensors, electronically display positioning information, and provide control signals required to maintain a vessel on a preset course.^[19] The navigator becomes a system manager, choosing system presets, interpreting system output, and monitoring vessel response.^[19]