Everything about Longitude totally explained
Longitude, symbolized by the
Greek character
lambda (λ), is the east-west (Side to Side)
geographic coordinate measurement most commonly used in cartography and global navigation. A line of longitude is a
meridian and half of a
great circle.
History
Mariners and
explorers for most of history struggled to determine precise longitude.
Latitude was calculated by observing with
quadrant or
astrolabe the inclination of the
sun or of charted
stars, but longitude presented no such manifest means of study.
Amerigo Vespucci 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 World.
"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'd 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 [analmanac]. After I'd 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 ascension 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
equator as a natural starting position, there's 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:
El Hierro,
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 or
zero point of longitude.
Noting and calculating longitude
Longitude is given as an
angular measurement 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
minutes, each of which divided into 60
seconds. A longitude is thus specified in
sexagesimal 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 usually must be converted to
radians, so longitude may also be expressed in this manner as a signed fraction of π (
pi), or an unsigned fraction of 2π.
For calculations, the West/East suffix is replaced by a negative sign in the
western 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 system with the
North Pole up. A specific longitude may then be combined with a specific
latitude (usually positive in the
northern hemisphere) 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 Time (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 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 don't 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.
Elliptic parameters
Because most planets (including Earth) are
ellipsoids of revolution, or
spheroids, rather than
spheres, 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 eccentricity,
(which equals
radians in either case.
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 (near 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's 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 doesn't 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 (for example, longitudes measured positively to the west) are used when the rotation is prograde and east longitudes (for example, 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 don't 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.
Tidally-locked bodies have a natural reference longitude passing through the point nearest to their parent body. However,
libration due to non-circular orbits or axial tilts causes this point to move around any fixed point on the celestial body like an
analemma.
Further Information
Get more info on 'Longitude'.
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