Learn more about "Longitude"

Longitude

History

"''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 (astronomy and astrology)|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 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 degree (angle)|degrees to the east.''" Vespucci, Amerigo. "Letter from Seville to Lorenzo di Pier Francesco de' Medici, 1500." Pohl, Frederick J. '''Amerigo Vespucci: Pilot Major'''. New York: Columbia University Press, 1945. 76-90. Page 80.

Noting and calculating longitude

Plate movement and longitude

Elliptic parameters

Degree length

Similarly, an exact expression for the length of an arcdegree of longitude is:
- :$\backslash frac\{\backslash pi\}\{180^\backslash circ\}\backslash cos(\backslash phi)N(\backslash phi).\backslash ;\backslash !$ The arcradius contained here is in the plane of the prime vertical, the east-west plane perpendicular (or "Orthogonality|normal") 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'', $N\backslash ;\backslash !$.The Math ForumJohn P. Snyder, ''Map Projections—A Working Manual'' (1987) 24-25 Along the equator (east-west), $N\backslash ;\backslash !$ equals the equatorial radius. The radius of curvature at a right angle to the equator (north-south), $M\backslash ;\backslash !$, 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 Global Positioning System|GPS 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.NIMA TR8350.2 page 3-1. The more recent but little used IERS 2003 ellipsoid provides equatorial and polar radii of 6378136.6 and 6356751.9 m, respectively, and an inverse flattening of 298.25642.IERS Conventions (2003) (Chp. 1, page 12) 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 Agency (NGA).Length of degree calculator - National Geospatial-Intelligence Agency

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 the celestial north pole. 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 calendars, astrology, or celestial mechanics. The 'error' of the Julian calendar|Julian or Gregorian calendar is always relative to a moving equinox. The years, months, and days of the Chinese calendar 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 system bodies) uses both a fixed and moving equinox. Sometimes in the study of Milankovitch cycles, the invariable plane of the solar system is substituted for the moving ecliptic. Longitude may be denominated from 0 to $\backslash begin\{matrix\}2\backslash pi\backslash end\{matrix\}$ 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 Impact crater|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 Prograde and retrograde motion|retrograde. In the absence of other information, the axis of rotation is assumed to be normal to the mean orbital plane; Mercury (planet)|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 gas giant|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. 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:
- −91°
- 91°W
- +269°
- 269°E. The reference surfaces for some planets (such as Earth and Mars (planet)|Mars) are ellipsoids of revolution for which the equatorial radius is larger than the polar radius; in other words, they are oblate spheroids. Smaller bodies (Io (moon)|Io, Mimas (moon)|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.Where is zero degrees longitude on Mars? Tidal lock|Tidally-locked bodies have a natural reference longitude passing through the point nearest to their parent body.First map of extraterrestial planet. 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.

See also

- American Practical Navigator
- Cardinal direction
- Geotagging
- Geodetic system
- Geographic coordinate system
- Great-circle distance
- History of longitude
- Latitude
- Lunar distance (navigation)
- Sextant
- World Geodetic System

Notes

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
- Latitude and longitude converter – Convert latitude and longitude from degree, decimal form to degree, minutes, seconds form and vice versa. Also included a farthest point and a distance calculator.
- Average Latitude & Longitude of Countries
- Latitude / Longitude Converter – convert latitude / longitude between DMS and decimal formats. Category:Lines of longitude|* Category:Navigation zh-min-nan:Keng-tō͘ be-x-old:Даўгата nds-nl:Lengtegraod

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