Longitude ( or ), identified by the
Greek letterThe Greek alphabet is a set of twenty-four letters that has been used to write the Greek language since the late 9th or early 8th century BCE. It is the first and oldest alphabet in the narrow sense that it notes each vowel and consonant with a separate symbol. It is as such in continuous use to...
lambdaLambda is the 11th letter of the Greek alphabet. In the system of Greek numerals it has a value of 30. It was derived from the Phoenician letter Lamed . Letters that arose from Lambda include the Roman L and the Cyrillic letter El . The ancient Grammarians and dramatists attest to a pronunciation...
(λ), is the geographic coordinate most commonly used in cartography and global navigation for east-west measurement. It is the angular distance measured east or west and usually expressed in degrees (or hours), minutes, and seconds, from the
prime meridianThe Prime Meridian is the meridian at which longitude is defined to be 0°.The Prime Meridian and its opposite the 180th meridian , which the International Date Line generally follows, form a great circle that divides the Earth into the Eastern and Western Hemispheres.Unlike the parallels of...
, defined to be at the
Royal Observatory, GreenwichThe Royal Observatory, Greenwich was commissioned in 1675 by King Charles II, with the foundation stone being laid on 10 August...
, in England, to the
meridianA meridian is an imaginary arc on the Earth's surface from the North Pole to the South Pole that connects all locations running along it with a given longitude. The position of a point on the meridian is given by the latitude. Each meridian is perpendicular to all circles of latitude at the...
passing through another position on the earth's surface. A location's position along a meridian is given by its
latitudeLatitude, usually denoted by the Greek letter phi gives the location of a place on Earth north or south of the equator. Lines of Latitude are the imaginary horizontal lines shown running east-to-west on maps that run either north or south of the equator...
. This is the angular distance of that place north or south of the equator, measured as an angle whose vertex is at the center of the earth.
History
Mariners and explorers for most of history struggled to determine precise longitude. Latitude was calculated by observing with
quadrantNot to be confused with quartileQuadrant may refer to:* Quadrant , a measuring instrument capable of measuring angles up to 90°* In science-fiction: Galactic quadrants...
or
astrolabeAn astrolabe is a historical astronomical instrument used by classical astronomers, navigators, and astrologers. Its many uses include locating and predicting the positions of the Sun, Moon, planets, and stars; determining local time given local latitude and vice-versa; surveying; and...
the inclination of the sun or of charted stars, but longitude presented no such manifest means of study.
Amerigo VespucciAmerigo Vespucci was an Italian explorer, navigator and cartographer. The continent of America is popularly believed to have derived its name from the feminized Latin version of his first name .-Expeditions:Amerigo Vespucci was born and brought up by his uncle in the Republic of Florence in what is...
was perhaps the first to proffer a solution, after devoting a great deal of time and energy studying the problem during his sojourns in the
New WorldThe New World is one of the names used for the non-Afro-Eurasian parts of the Earth, specifically the Americas and possibly Australia. When the term originated in the late 15th century, the Americas were new to the Europeans, who previously thought of the world as consisting only of Europe, Asia,...
:
As to longitude, I declare that I found so much difficulty in determining it that I was put to great pains to ascertain the east-west distance I had covered. The final result of my labors was that I found nothing better to do than to watch for and take observations at night of the conjunction of one planet with another, and especially of the conjunction of the moon with the other planets, because the moon is swifter in her course than any other planet. I compared my observations with an almanac. After I had made experiments many nights, one night, the twenty-third of August, 1499, there was a conjunction of the moon with Mars, which according to the almanac was to occur at midnight or a half hour before. I found that...at midnight Mars's position was three and a half degrees to the east.
By comparing the relative positions of the moon and Mars with their anticipated positions, Vespucci was able to crudely deduce his longitude. But this method had several limitations: First, it required the occurrence of a specific astronomical event (in this case, Mars passing through the same
right ascensionRight ascension is the astronomical term for one of the two coordinates of a point on the celestial sphere when using the equatorial coordinate system. The other coordinate is the declination.-Explanation:...
as the moon), and the observer needed to anticipate this event via an astronomical almanac. One needed also to know the precise time, which was difficult to ascertain in foreign lands. Finally, it required a stable viewing platform, rendering the technique useless on the rolling deck of a ship at sea.
Unlike latitude, which has the
equatorThe equator is the intersection of the Earth's surface with the plane perpendicular to the Earth's axis of rotation and containing the Earth's center of mass. In simpler language, it is an imaginary line on the Earth's surface equidistant from the North Pole and South Pole that divides the Earth...
as a natural starting position, there is no natural starting position for longitude. Therefore, a reference meridian had to be chosen. It was a popular practice to use a nation's capital as the starting point, but other significant locations were also used. While
BritishGreat Britain is an island lying to the northwest of Continental Europe. It is the ninth largest island in the world, and the largest European island. With a population of about 59.6 million people, it is the third most populated island on Earth. Great Britain is surrounded by over 1000 smaller...
cartographers had long used the Greenwich meridian in London, other references were used elsewhere, including:
El HierroEl Hierro, nicknamed Isla del Meridiano , is a Spanish island. It is the smallest and farthest south and west of the Canary Islands, in the Atlantic Ocean off the coast of Africa...
,
RomeRome is the capital of Italy and the country's largest and most populated municipality , with over 2.7 million residents in , while the population of the urban area is estimated by Eurostat to be 3.46 million. The metropolitan area of Rome is estimated by OECD to have a population of 3.7 million...
,
CopenhagenCopenhagen ; ) is the capital and largest city of Denmark, with an urban area with a population of 1,167,569 and a metropolitan area with a population of 1,875,179...
,
JerusalemJerusalem is the capital of Israel and its largest city in both population and area, with a population of 747,600 residents over an area of if disputed East Jerusalem is included...
,
Saint PetersburgSaint Petersburg is a city and a federal subject of Russia located on the Neva River at the head of the Gulf of Finland on the Baltic Sea. The city's other names were Petrograd and Leningrad...
,
PisaPisa is a city in Tuscany, central Italy, on the right bank of the mouth of the Arno River on the Ligurian Sea. It is the capital city of the Province of Pisa...
,
ParisParis is the capital of France and the country's most populous city. It is situated on the river Seine, in northern France, at the heart of the Île-de-France region...
,
PhiladelphiaPhiladelphia is the largest city in Pennsylvania and the sixth-most-populous city in the United States.In 2008, the population of the city proper was estimated to be over 1.4 million, while the metropolitan area's population of 5.8 million made it the country's fifth-largest...
, and Washington. In 1884, the
International Meridian ConferenceThe International Meridian Conference was a conference held in October 1884 in Washington, D.C., in the United States to determine the Prime Meridian of the world. The conference was held at the request of U.S. President Chester A...
adopted the Greenwich meridian as the
universal prime meridian or
zero point of longitude.
Noting and calculating longitude
Longitude is given as an
angular measurementIn geometry and trigonometry, an angle is the figure formed by two rays sharing a common endpoint, called the vertex of the angle...
ranging from 0° at the prime meridian to +180° eastward and −180° westward. The Greek letter λ (lambda), is used to denote the location of a place on Earth east or west of the prime meridian.
Each degree of longitude is sub-divided into 60
minutesA minute of arc or arcminute is a unit of angular measurement, equal to one sixtieth of one degree. Since one degree is defined as one three hundred sixtieth of a circle, 1 minute of arc is 1/21,600 of the amount of arc in a closed circle...
, each of which divided into 60 seconds. A longitude is thus specified in
sexagesimalSexagesimal is a numeral system with sixty as the base. It originated with the ancient Sumerians in the 2000s BCE, was transmitted to the Babylonians, and is still used—in modified form—for measuring time, angles, and geographic coordinates....
notation as
23° 27′ 30" E. For higher precision, the seconds are specified with a decimal fraction. An alternative representation uses degrees and minutes, where parts of a minute are expressed in decimal notation with a fraction, thus:
23° 27.500′ E. Degrees may also be expressed as a decimal fraction:
23.45833° E. For calculations, the angular measure may be converted to
radianThe radian is a unit of plane angle, equal to 180/π degrees, or about 57.2958 degrees, or about 57°17′45″. It is the standard unit of angular measurement in all areas of mathematics beyond the elementary level....
s, so longitude may also be expressed in this manner as a signed fraction of π (
piPi or π is a mathematical constant whose value is the ratio of any circle's circumference to its diameter in Euclidean space; this is the same value as the ratio of a circle's area to the square of its radius. The symbol π was first proposed by the Welsh mathematician William Jones in 1706...
), or an unsigned fraction of 2π.
For calculations, the West/East suffix is replaced by a negative sign in the
western hemisphereThe Western Hemisphere, also Western hemisphere or western hemisphere, is a geographical term for the half of the Earth that lies west of the Prime Meridian , the other half being the eastern hemisphere...
. Confusingly, the convention of negative for East is also sometimes seen. The preferred convention—that East be positive—is consistent with a right-handed
Cartesian coordinate systemA Cartesian coordinate system specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances from the point to two fixed perpendicular directed lines, measured in the same unit of length....
with the North Pole up. A specific longitude may then be combined with a specific latitude (usually positive in the
northern hemisphereThe Northern Hemisphere is the half of a planet that is north of the equator—the word hemisphere literally means 'half sphere'. It is also that half of the celestial sphere north of the celestial equator...
) to give a precise position on the Earth's surface.
Longitude at a point may be determined by calculating the time difference between that at its location and
Coordinated Universal TimeCoordinated Universal Time , ) is a time standard based on International Atomic Time with leap seconds added at irregular intervals to compensate for the Earth's slowing rotation...
(UTC). Since there are 24 hours in a day and 360 degrees in a circle, the sun moves across the sky at a rate of 15 degrees per hour (360°/24 hours = 15° per hour). So if the
time zoneA time zone is a region of the earth that has uniform standard time, usually referred to as the local time. By convention, time zones compute their local time as an offset from UTC . Local time is UTC plus the current time zone offset for the considered location.-Introduction:Time zones are...
a person is in is three hours ahead of UTC then that person is near 45° longitude (3 hours × 15° per hour = 45°). The word
near was used because the point might not be at the center of the time zone; also the time zones are defined politically, so their centers and boundaries often do not lie on meridians at multiples of 15°. In order to perform this calculation, however, a person needs to have a
chronometerA marine chronometer is a timekeeper precise enough to be used as a portable time standard; it can therefore be used to determine longitude by means of celestial navigation. When first developed in the eighteenth century it was a major technical achievement, as accurate knowledge of the time over a...
(watch) set to UTC and needs to determine local time by solar observation or astronomical observation. The details are more complex than described here: see the articles on
Universal TimeUniversal Time is a timescale based on the rotation of the Earth. It is a modern continuation of Greenwich Mean Time , i.e., the mean solar time on the meridian of Greenwich, and GMT is sometimes used loosely as a synonym for UTC. In fact the expression "Universal Time" is ambiguous, as there are...
and on the
equation of timeThe equation of time is the difference between apparent solar time and mean solar time, both taken at a given place at the same real instant of time....
for more details.
Plate movement and longitude
The surface layer of the Earth, the
lithosphereThe lithosphere is the rigid outermost shell of a rocky planet.- Earth's lithosphere :...
, is broken up into several
tectonic platesPlate tectonics is a theory which describes the large scale motions of Earth's lithosphere...
. Each plate moves in a different direction, at speeds of about 50 to 100 mm per year. As a result, for example, the longitudinal difference between a point on the equator in Uganda (on the
African PlateThe African Plate is a tectonic plate which includes the continent of Africa, as well as oceanic crust which lies between the continent and various surrounding ocean ridges....
) and a point on the equator in Ecuador (on the
South American PlateThe South American Plate is a tectonic plate covering the continent of South America and extending eastward to the Mid-Atlantic Ridge.The easterly side is a divergent boundary with the African Plate forming the southern part of the Mid-Atlantic Ridge. The southerly side is a complex boundary with...
) is increasing by about 0.0014 arcseconds per year.
If a global reference frame such as WGS84 is used, the longitude of a place on the surface will change from year to year. To minimize this change, when dealing exclusively with points on a single plate, a different reference frame can be used, whose coordinates are fixed to a particular plate, such as NAD83 for North America or ETRS89 for Europe.
Elliptic parameters
Because most planets (including Earth) are closer to
ellipsoids of revolution, or spheroids, rather than to
sphereA sphere is a perfectly round geometrical object in three-dimensional space, such as the shape of a round ball. Like a circle in two dimensions, a perfect sphere is completely symmetrical around its center, with all points on the surface lying the same distance r from the center point...
s, both the radius and the length of arc varies with latitude. This variation requires the introduction of elliptic parameters based on an ellipse's
angular eccentricityIn the study of ellipses and related geometry, various parameters in the distortion of a circle into an ellipse are identified and employed: Aspect ratio, flattening and eccentricity....
, (which equals , where and are the equatorial and polar radii; is the
first eccentricityIn mathematics, the eccentricity, denoted e or , is a parameter associated with every conic section. It can be thought of as a measure of how much the conic section deviates from being circular.In particular,* The eccentricity of a circle is zero....
squared, ; and or is the
flatteningThe flattening, ellipticity, or oblateness of an oblate spheroid is the "squashing" of the spheroid's pole, towards its equator.-First and second flattening:...
, ). Utilized in creating the integrands for
curvatureIn mathematics, curvature refers to any of a number of loosely related concepts in different areas of geometry. Intuitively, curvature is the amount by which a geometric object deviates from being flat, or straight in the case of a line, but this is defined in different ways depending on the context...
is the inverse of the principal elliptic integrand, :
-
Degree length
The length of an
arcdegreeA degree , usually denoted by ° , is a measurement of plane angle, representing 1⁄360 of a full rotation; one degree is equivalent to π/180 radians...
of north-south latitude difference, , is about 60 nautical miles, 111 kilometres or 69 statute miles at any latitude. The length of an arcdegree of east-west longitude difference, , is about the same at the equator as the north-south, reducing to zero at the poles.
In the case of a spheroid, a
meridianA meridian is an imaginary arc on the Earth's surface from the North Pole to the South Pole that connects all locations running along it with a given longitude. The position of a point on the meridian is given by the latitude. Each meridian is perpendicular to all circles of latitude at the...
and its anti-meridian form an
ellipseIn mathematics, an ellipse is the bounded case of a conic section, the geometric shape that results from cutting a circular conical or cylindrical surface with an oblique plane...
, from which an exact expression for the length of an arcdegree of latitude is:
This radius of arc (or "arcradius") is in the plane of a meridian, and is known as the
meridional radius of curvature, .
Similarly, an exact expression for the length of an arcdegree of longitude is:
The arcradius contained here is in the plane of the
prime verticalIn astronomy and astrology, the prime vertical is the vertical circle passing east and west through the zenith, and intersecting the horizon in its east and west points....
, the east-west plane perpendicular (or "
normalIn mathematics, two vectors are orthogonal if they are perpendicular, i.e., they form a right angle. The word comes from the Greek , meaning "straight", and , meaning "angle".- Definitions :...
") to both the plane of the meridian and the plane tangent to the surface of the ellipsoid, and is known as the
normal radius of curvature, .
Along the equator (east-west), equals the equatorial radius. The radius of curvature at a
right angleIn geometry and trigonometry, a right angle is an angle of 90 degrees, corresponding to a quarter turn . It can be defined as the angle such that twice that angle amounts to a half turn, or 180°....
to the equator (north-south), , is 43 km shorter, hence the length of an arcdegree of latitude at the equator is about 1 km less than the length of an arcdegree of longitude at the equator. The radii of curvature are equal at the poles where they are about 64 km greater than the north-south equatorial radius of curvature
because the polar radius is 21 km less than the equatorial radius. The shorter polar radii indicate that the northern and southern hemispheres are flatter, making their radii of curvature longer. This flattening also 'pinches' the north-south equatorial radius of curvature, making it 43 km less than the equatorial radius. Both radii of curvature are perpendicular to the plane tangent to the surface of the ellipsoid at all latitudes, directed toward a point on the polar axis in the opposite hemisphere (except at the equator where both point toward Earth's center). The east-west radius of curvature reaches the axis, whereas the north-south radius of curvature is shorter at all latitudes except the poles.
The WGS84 ellipsoid, used by all
GPSThe Global Positioning System is a U.S. space-based global navigation satellite system. It provides reliable positioning, navigation, and timing services to worldwide users on a continuous basis in all weather, day and night, anywhere on or near the Earth.GPS is made up of three parts: between 24...
devices, uses an equatorial radius of 6378137.0 m and an inverse flattening, (1/f), of 298.257223563, hence its polar radius is 6356752.3142 m and its first eccentricity squared is 0.00669437999014. The more recent but little used
IERSIERS may refer to:* International Earth Rotation and Reference Systems Service* Independent Electricity Retail Solutions Pty Ltd* Information Exchange Requirements - used within MODAF and DODAF as the OV-3 view - called Information Exchange Matrix....
2003 ellipsoid provides equatorial and polar radii of 6378136.6 and 6356751.9 m, respectively, and an inverse flattening of 298.25642. Lengths of degrees on the WGS84 and IERS 2003 ellipsoids are the same when rounded to six significant digits. An appropriate calculator for any latitude is provided by the U.S. government's
National Geospatial-Intelligence AgencyThe National Geospatial-Intelligence Agency is an agency of the United States Government with the primary mission of collection, analysis, and distribution of geospatial intelligence in support of national security. NGA was formerly known as the National Imagery and Mapping Agency and is part of...
(NGA).
| Latitude |
N-S radius
of curvature
|
Surface distance
per 1° change
in latitude |
|
E-W radius
of curvature
|
Surface distance
per 1° change
in longitude |
| 0° |
6335.44 km |
110.574 km |
|
6378.14 km |
111.320 km |
| 15° |
6339.70 km |
110.649 km |
|
6379.57 km |
107.551 km |
| 30° |
6351.38 km |
110.852 km |
|
6383.48 km |
96.486 km |
| 45° |
6367.38 km |
111.132 km |
|
6388.84 km |
78.847 km |
| 60° |
6383.45 km |
111.412 km |
|
6394.21 km |
55.800 km |
| 75° |
6395.26 km |
111.618 km |
|
6398.15 km |
28.902 km |
| 90° |
6399.59 km |
111.694 km |
|
6399.59 km |
0.000 km |
Ecliptic latitude and longitude
EclipticThe ecliptic is the apparent path that the Sun traces out in the sky during the year, appearing to move eastwards on an imaginary spherical surface, the celestial sphere, relative to the fixed stars. More accurately, it is the intersection of the celestial sphere with the ecliptic plane, which is...
latitude and longitude are defined for the planets, stars, and other celestial bodies in a broadly similar way to that in which terrestrial latitude and longitude are defined, but there is a special difference.
The plane of zero latitude for celestial objects is not parallel to the plane of the celestial and terrestrial equator: it is the plane of the ecliptic. This is inclined to the equator by the "obliquity of the ecliptic", currently about 23° 26'. The closest celestial counterpart to terrestrial latitude is
declinationIn astronomy, declination is one of the two coordinates of the equatorial coordinate system, the other being either right ascension or hour angle. Dec is comparable to latitude, projected onto the celestial sphere, and is measured in degrees north and south of the celestial equator...
, and the closest celestial counterpart to terrestrial longitude is
right ascensionRight ascension is the astronomical term for one of the two coordinates of a point on the celestial sphere when using the equatorial coordinate system. The other coordinate is the declination.-Explanation:...
. These celestial coordinates bear the same relationship to the celestial equator as terrestrial latitude and longitude do to the terrestrial equator, and they are also more frequently used in astronomy than celestial longitude and latitude.
The polar axis (relative to the celestial equator) is perpendicular to the plane of the equator, and parallel to the terrestrial polar axis. But the (north) pole of the ecliptic, relevant to the definition of ecliptic latitude, is the normal to the
eclipticThe ecliptic is the apparent path that the Sun traces out in the sky during the year, appearing to move eastwards on an imaginary spherical surface, the celestial sphere, relative to the fixed stars. More accurately, it is the intersection of the celestial sphere with the ecliptic plane, which is...
plane nearest to the direction of the celestial north pole of the equator, i.e. 23° 26' away from it.
Ecliptic latitude is measured from 0° to 90° north (+) or south (−) of the ecliptic. Ecliptic longitude is measured from 0° to 360° eastward (the direction that the Sun appears to move relative to the stars), along the ecliptic from the vernal equinox. The equinox at a specific date and time is a fixed equinox, such as that in the J2000 reference frame.
However, the equinox moves because it is the intersection of two planes, both of which move. The ecliptic is relatively stationary, wobbling within a 4° diameter circle relative to the fixed stars over millions of years under the gravitational influence of the other planets. The greatest movement is a relatively rapid gyration of Earth's equatorial plane whose pole traces a 47° diameter circle caused by the Moon. This causes the equinox to precess westward along the ecliptic about 50" per year. This moving equinox is called the
equinox of date. Ecliptic longitude relative to a moving equinox is used whenever the positions of the Sun, Moon, planets, or stars at dates other than that of a fixed equinox is important, as in
calendarA calendar is a system of organizing days for social, religious, commercial, or administrative purposes. This is done by giving names to periods of time, typically days, weeks, months, and years. The name given to each day is known as a date. Periods in a calendar are usually, though not...
s,
astrologyAstrology is a group of systems, traditions, and beliefs which hold that the relative positions of celestial bodies and related details can provide information about personality, human affairs, and other terrestrial matters. A practitioner of astrology is called an astrologer...
, or
celestial mechanicsCelestial mechanics is the branch of astronomy that deals with the motions of celestial objects. The field applies principles of physics, historically classical mechanics, to astronomical objects such as stars and planets to produce ephemeris data. Orbital mechanics is a subfield which focuses on...
. The 'error' of the
JulianThe Julian calendar, a reform of the Roman calendar, was introduced by Julius Caesar in 46 BC, and came into force in 45 BC . It was chosen after consultation with the astronomer Sosigenes of Alexandria and was probably designed to approximate the tropical year, known at least since Hipparchus...
or
Gregorian calendarThe Gregorian calendar is the internationally accepted civil calendar. It was first proposed by the Calabrian doctor Aloysius Lilius, and decreed by Pope Gregory XIII, after whom the calendar was named, on 24 February 1582 by the papal bull Inter gravissimas...
is always relative to a moving equinox. The years, months, and days of the
Chinese calendarThe Chinese calendar is lunisolar, incorporating elements of a lunar calendar with those of a solar calendar. It is not exclusive to China, but followed by many other Asian cultures. It is often referred to as the Chinese calendar because it was first perfected by the Chinese around 500 BCE...
all depend on the ecliptic longitudes
of date of the Sun and Moon. The 30° zodiacal segments used in astrology are also relative to a moving equinox. Celestial mechanics (here restricted to the motion of
solar systemThe Solar System consists of the Sun and those celestial objects bound to it by gravity, all of which formed from the collapse of a giant molecular cloud approximately 4.6 billion years ago...
bodies) uses both a fixed and moving equinox. Sometimes in the study of
Milankovitch cyclesMilankovitch Theory describes the collective effects of changes in the Earth's movements upon its climate, named after Serbian civil engineer and mathematician Milutin Milanković...
, the
invariable planeThe invariable plane of a planetary system, also called Laplace's invariable plane, is the plane passing through its barycenter which is perpendicular to its angular momentum vector. In the solar system, about 98% of this effect is contributed by the orbital angular momenta of the four jovian...
of the solar system is substituted for the moving ecliptic. Longitude may be denominated from 0 to radians in either case.
Longitude on bodies other than Earth
PlanetA planet , is a celestial body orbiting a star or stellar remnant that is massive enough to be rounded by its own gravity, is not massive enough to cause thermonuclear fusion, and has cleared its neighbouring region of planetesimals.The term planet is ancient, with ties to history, science,...
ary co-ordinate systems are defined relative to their mean axis of rotation and various definitions of longitude depending on the body. The longitude systems of most of those bodies with observable rigid surfaces have been defined by references to a surface feature such as a
craterIn the broadest sense, the term impact crater can be applied to any depression, natural or manmade, resulting from the high velocity impact of a projectile with a larger body...
. The
north poleThe North Pole, also known as the Geographic North Pole or Terrestrial North Pole, is, subject to the caveats explained below, defined as the point in the northern hemisphere where the Earth's axis of rotation meets the Earth's surface...
is that pole of rotation that lies on the north side of the invariable plane of the solar system (near the
eclipticThe ecliptic is the apparent path that the Sun traces out in the sky during the year, appearing to move eastwards on an imaginary spherical surface, the celestial sphere, relative to the fixed stars. More accurately, it is the intersection of the celestial sphere with the ecliptic plane, which is...
). The location of the prime meridian as well as the position of body's north pole on the celestial sphere may vary with time due to precession of the axis of rotation of the planet (or satellite). If the position angle of the body's prime meridian increases with time, the body has a direct (or prograde) rotation; otherwise the rotation is said to be
retrogradeRetrograde motion is in the direction opposite to the movement of something else, and is the contrary of direct or prograde motion. The idea of retrograde or prograde motion is useful in three contexts: for describing the orbits of celestial bodies, for describing the rotations of celestial...
.
In the absence of other information, the axis of rotation is assumed to be normal to the mean
orbital planeThe orbital plane of an object orbiting another is the geometrical plane in which the orbit is embedded. Three non-colinear points in space suffice to define the orbital plane...
;
MercuryFor the liquid metallic element, see Mercury .Mercury is the innermost and smallest planet in the Solar System, orbiting the Sun once every 87.969 days. The orbit of Mercury has the highest eccentricity of all the Solar System planets, and it has the smallest axial tilt. It completes three...
and most of the satellites are in this category. For many of the satellites, it is assumed that the rotation rate is equal to the mean
orbital periodThe orbital period is the time taken for a given object to make one complete orbit about another object.When mentioned without further qualification in astronomy this refers to the sidereal period of an astronomical object, which is calculated with respect to the stars.There are several kinds of...
. In the case of the
giant planetsA gas giant is a large planet that is not primarily composed of rock or other solid matter. There are four gas giants in our Solar System: Jupiter, Saturn, Uranus, and Neptune...
, since their surface features are constantly changing and moving at various rates, the rotation of their
magnetic fieldMagnetic fields surround magnetic materials and electric currents and are detected by the force they exert on other magnetic materials and moving electric charges...
s is used as a reference instead. In the case of the
SunThe Sun is the star at the center of the Solar System. The Earth and other matter orbit the Sun, which by itself accounts for about 99.86% of the Solar System's mass....
, even this criterion fails (because its magnetosphere is very complex and does not really rotate in a steady fashion), and an agreed-upon value for the rotation of its equator is used instead.
For
planetographic longitude, west longitudes (i.e., longitudes measured positively to the west) are used when the rotation is prograde, and east longitudes (i.e., longitudes measured positively to the east) when the rotation is retrograde. In simpler terms, imagine a distant, non-orbiting observer viewing a planet as it rotates. Also suppose that this observer is within the plane of the planet's equator. A point on the equator that passes directly in front of this observer later in time has a higher planetographic longitude than a point that did so earlier in time.
However,
planetocentric longitude is always measured positively to the east, regardless of which way the planet rotates.
East is defined as the counter-clockwise direction around the planet, as seen from above its north pole, and the north pole is whichever pole more closely aligns with the Earth's north pole. Longitudes traditionally have been written using "E" or "W" instead of "+" or "−" to indicate this polarity. For example, the following all mean the same thing:
The reference surfaces for some planets (such as Earth and
MarsMars is the fourth planet from the Sun in the Solar System. The planet is named after Mars, the Roman god of war. It is also referred to as the "Red Planet" because of its reddish appearance, due to iron oxide prevalent on its surface....
) are
ellipsoidAn ellipsoid is a type of quadric surface that is a higher dimensional analogue of an ellipse. The equation of a standard axis-aligned ellipsoid body in an xyz-Cartesian coordinate system is...
s of revolution for which the equatorial radius is larger than the polar radius; in other words, they are oblate spheroids. Smaller bodies (
IoIo is the innermost of the four Galilean moons of the planet Jupiter and, with a diameter of 3,642 kilometres, the fourth-largest moon in the Solar System. It was named after Io, a priestess of Hera who became one of the lovers of Zeus.With over 400 active volcanoes, Io is the most...
,
MimasMimas is a moon of Saturn which was discovered in 1789 by William Herschel. It is named after Mimas, a son of Gaia in Greek mythology, and is also designated Saturn I....
, etc.) tend to be better approximated by triaxial ellipsoids; however, triaxial ellipsoids would render many computations more complicated, especially those related to
map projectionA map projection is any method of representing the surface of a sphere or other shape on a plane. Map projections are necessary for creating maps. All map projections distort the surface in some fashion...
s. Many projections would lose their elegant and popular properties. For this reason spherical reference surfaces are frequently used in mapping programs.
The modern standard for maps of Mars (since about 2002) is to use planetocentric coordinates. The meridian of Mars is located at
Airy-0Airy-0 is a crater on Mars whose location defines the position of the prime meridian of that planet. Airy-0 is about 0.5 kilometers across and lies within the larger crater Airy in the region Sinus Meridiani....
crater.
Tidally-locked bodies have a natural reference longitude passing through the point nearest to their parent body. However,
librationIn astronomy libration refers to the various orbital conditions which make it possible to see more than 50% of the moon's surface over time, even though the front of the Moon is tidally locked to always face towards Earth...
due to non-circular orbits or axial tilts causes this point to move around any fixed point on the celestial body like an
analemmaIn astronomy, an analemma is a curve representing the angular offset of a celestial body from its mean position on the celestial sphere as viewed from another celestial body...
.
External links
- Resources for determining your latitude and longitude
- Worldwide Index - Tageo.com – contains 2,700,000 coordinates of places including US towns
- for each city it gives the satellite map location, country, province, coordinates (dd,dms), variant names and nearby places.
- IAU/IAG Working Group On Cartographic Coordinates and Rotational Elements of the Planets and Satellites
- Average Latitude & Longitude of Countries
- "Longitude forged": an essay exposing a hoax solution to the problem of calculating longitude, undetected in Dava Sobel's Longitude, from TLS, November 12, 2008.
- How to find and convert Latitude & Longitude