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# Longitude

Map of Earth showing curved lines of longitude

Longitude, sometimes denoted λ, describes the location of a place on Earth east or west of a north-south line called the Prime Meridian. Longitude is given as an angular measurement ranging from 0° at the Prime Meridian to +180° eastward and −180° westward. Unlike latitude, which has the equator as a natural starting position, there is no natural starting position for longitude. Therefore, a reference meridian had to be chosen. While British cartographers had long used the Greenwich meridian in London, other references were used elsewhere, including: Ferro, Rome, Copenhagen, Jerusalem, Saint Petersburg, Pisa, Paris, and Philadelphia. In 1884, the International Meridian Conference adopted the Greenwich meridian as the universal prime meridian.

Each degree of longitude is further sub-divided into 60 minutes, each of which divided into 60 seconds. A longitude is thus specified as 23° 27′ 30" E. For high accuracy, the seconds are specified with a decimal fraction. An alternative representation uses degrees and minutes, where parts of a minute are expressed as a decimal fraction, thus: 23&deg 27.500′ E. Degrees expressed as a decimal number is also used: 23.45833° E. Sometimes, the West/East suffix is replaced by a negative sign for West. Confusingly, the convention of negative for East is also sometimes seen. The preferred convention that East is positive is consistent with the right-handed x-axis in the Cartesian coordinate system.

A specific longitude may then be combined with a specific latitude to give a precise position on the Earth's surface.

As opposed to a degree of latitude, which always corresponds to about 111 km (69 mi), a degree of longitude corresponds to a distance from 0 to 111 km: it is 111 km times the cosine of the latitude, when the distance is laid out on a circle of constant latitude; if the shortest distance, on a great circle were used, the distance would be even a little less.

Longitude at a point may be determined by calculating the time difference between that at its location and Coordinated Universal Time (UTC). Since there are 24 hours in a day and 360 degrees in a circle, the sun moves 15 degrees per hour (360°/24 hours = 15° per hour). So if the time zone 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 chronometer (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 Time and on the Equation of time for more details.

A line of constant longitude is a meridian, and half of a great circle.

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### Measurement

This measurement is important to both cartography and navigation; the discovery of how to measure it accurately was among the important discoveries of the 1600s and 1700s. The first effective solution for mapmaking was achieved by Giovanni Domenico Cassini starting in 1681, using Galileo's method based on the satellites of Jupiter. For application without a professional astronomer at hand, and in particular measurement at sea, the problem was more difficult; see Dava Sobel's book: Longitude: The True Story of a Lone Genius Who Solved the Greatest Scientific Problem of His Time for a good historical overview. This genius was John Harrison, who eventually received the Longitude Prize with his timepiece which came to be known as the H-4.

### Longitude Act

The tragic wrecking of the fleet led by Sir Cloudesley Shovel led to the Longitude Act which created a prize for anyone who could devise a practical method of determining longitude at sea.

John Harrison's son led a voyage aboard a ship from Portsmouth, England to the Caribbean port city of Bridgetown, Barbados with his H4 aboard. Harrison discovered the present system of longitude by keeping the exact time of day for Britain, while using a process of triangulation to find the exact location of the island of Barbados in its distance from Britain.

## Ecliptic latitude and longitude

Ecliptic latitude and longitude are defined for the planets, stars, and other celestial bodies in a similar way to that in which the terrestrial counterparts are defined. The pole is the normal to the ecliptic nearest to terrestrial north, and the origin of longitude is the vernal equinox, generally as defined as a point in the J2000 reference frame; thus it is also the origin of celestial longitude . Ecliptic longitude is presumably the one referred to in the astrological context within the entry ephemeris.

## Longitude on bodies other than Earth

Planetary 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 crater. The north pole is that pole of rotation that lies on the north side of the invariable plane of the solar system (the ecliptic). 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 retrograde.

In the absence of other information, the axis of rotation is assumed to be normal to the mean orbital plane; Mercury 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 period. In the case of the giant planets, since their surface features are constantly changing and moving at various rates, the rotation of their magnetic fields is used as a reference instead. In the case of the Sun, 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. However, "planetocentric longitude" is measured positively to the east. Because of tradition, the Earth, Sun, and Moon do not conform with this definition: their rotations are prograde and longitudes run both east and west 180° instead of the usual 360°.

The reference surfaces for some planets (such as Earth and Mars) are ellipsoids of revolution for which the equatorial radius is larger than the polar radius. Smaller bodies (Io, Mimas, etc.) tend to be better approximated by triaxial ellipsoids; however, triaxial ellipsoids would render many computations more complicated, especially those related to map projections. 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-0 crater. [1]

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