Longitude

Longitude, sometimes denoted by the Greek letter 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, Philadelphia and Washington. 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° 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.

History of the measurement of longitude

The search for a solution

The measurement of longitude is important to both cartography and navigation. Historically, the most important practical application of these was was to provide safe ocean navigation. Knowledge of both latitude and longitude was required. Whereas latitude was easy to determine by celestial navigation using the elevation of the pole star or of the sun at noon, for longitude early ocean navigators had to rely on dead reckoning. This was inaccurate on long voyages out of sight of land, and these voyages sometimes ended with shipwrecks.

The discovery of how to measure longitude 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.

The Longitude Act and Harrison's chronometer

The tragic wrecking of the British fleet led by Sir Cloudesley Shovell led to the British Longitude Act, which created the Longitude Prize for anyone who could devise a practical method of determining longitude at sea. This was eventually achieved by John Harrison with his chronometer; the timepiece in question was the one later known as H-4.

Harrison's son led a voyage aboard a ship from Portsmouth, England to the Caribbean port city of Bridgetown, Barbados with the H-4 aboard. Harrison demonstrated a method of determining longitude by keeping the exact time of day for Britain, while using astronomical observations to find the exact local time on the ship as it sailed to the island of Barbados. In this way he able to determine the position of the ship relative to Barbados whose longitude was known. The calculation of the ship's position was only 10 miles in error when it arrived.

Later developments

Exchanges of chronometers between observatories, to determine the precise differences in local time, used in conjunction with the observation of the transit of stars across the meridian became a standard way of determining longitude. Another method was the observation of occultations of stars at different observatories. From the mid 19th century, instead of exchanging chronometers, telegraph time signals were used; radio time signals followed in the early 20th century. Satellites were used for measurements from the 1970s and 1980s - see GPS.

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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