Longitude
Longitude (/ˈlɒndʒɪtjuːd/ or /ˈlɒndʒɪtuːd/, Australian and
British also /ˈlɒŋɡɪtjuːd/),[1][2] is a geographic coordinate
that specifies the east-west position of a point on the Earth's
surface. It is an angular measurement, usually expressed in degrees
and denoted by the Greek letter lambda (λ). Meridians (lines running
from the
North Pole
North Pole to the South Pole) connect points with the same
longitude. By convention, one of these, the Prime Meridian, which
passes through the Royal Observatory, Greenwich, England, was
allocated the position of zero degrees longitude. The longitude of
other places is measured as the angle east or west from the Prime
Meridian, ranging from 0° at the
Prime Meridian
Prime Meridian to +180° eastward
and −180° westward. Specifically, it is the angle between a plane
containing the
Prime Meridian
Prime Meridian and a plane containing the North Pole,
South Pole
South Pole and the location in question. (This forms a right-handed
coordinate system with the z axis (right hand thumb) pointing from the
Earth's center toward the
North Pole
North Pole and the x axis (right hand index
finger) extending from Earth's center through the equator at the Prime
Meridian.)
A location's north–south position along a meridian is given by its
latitude, which is approximately the angle between the local vertical
and the plane of the Equator.
If the
Earth
Earth were perfectly spherical and homogeneous, then the
longitude at a point would be equal to the angle between a vertical
north–south plane through that point and the plane of the Greenwich
meridian. Everywhere on
Earth
Earth the vertical north–south plane would
contain the Earth's axis. But the
Earth
Earth is not homogeneous, and has
mountains—which have gravity and so can shift the vertical plane
away from the Earth's axis. The vertical north–south plane still
intersects the plane of the Greenwich meridian at some angle; that
angle is the astronomical longitude, calculated from star
observations. The longitude shown on maps and GPS devices is the angle
between the Greenwich plane and a not-quite-vertical plane through the
point; the not-quite-vertical plane is perpendicular to the surface of
the spheroid chosen to approximate the Earth's sea-level surface,
rather than perpendicular to the sea-level surface itself.
Contents
1 History
2 Noting and calculating longitude
2.1 Singularity and discontinuity of longitude
3 Plate movement and longitude
4 Length of a degree of longitude
5
Longitude
Longitude on bodies other than Earth
6 See also
7 References
8 External links
History[edit]
Main article:
History
History of longitude
Amerigo Vespucci's means of determining longitude
The measurement of longitude is important both to cartography and for
ocean navigation. Mariners and explorers for most of history struggled
to determine longitude. Finding a method of determining longitude took
centuries, resulting in the history of longitude recording the effort
of some of the greatest scientific minds.
Latitude
Latitude was calculated by observing with quadrant or astrolabe the
altitude of the sun or of charted stars above the horizon, but
longitude is harder.
Amerigo Vespucci
Amerigo Vespucci was perhaps the first European 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 had covered. The final result of my labours 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.[3]
John Harrison
John Harrison solved the greatest problem of his day.[4]
By comparing the positions of the moon and
Mars
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
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. See Lunar
distance (navigation).
In 1612
Galileo Galilei
Galileo Galilei demonstrated that with sufficiently accurate
knowledge of the orbits of the moons of Jupiter one could use their
positions as a universal clock and this would make possible the
determination of longitude, but the method he devised was
impracticable for navigators on ships because of their instability.[5]
In 1714 the British government passed the
Longitude Act
Longitude Act which offered
large financial rewards to the first person to demonstrate a practical
method for determining the longitude of a ship at sea. These rewards
motivated many to search for a solution.
Drawing of
Earth
Earth with longitudes but without latitudes.
John Harrison, a self-educated English clockmaker, invented the marine
chronometer, the key piece in solving the problem of accurately
establishing longitude at sea, thus revolutionising and extending the
possibility of safe long distance sea travel.[4] Though the Board of
Longitude
Longitude rewarded
John Harrison
John Harrison for his marine chronometer in 1773,
chronometers remained very expensive and the lunar distance method
continued to be used for decades. Finally, the combination of the
availability of marine chronometers and wireless telegraph time
signals put an end to the use of lunars in the 20th century.
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. It was a popular practice to use
a nation's capital as the starting point, but other locations were
also used. 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 D.C.
Washington D.C. In 1884 the International Meridian
Conference adopted the Greenwich meridian as the universal Prime
Meridian or zero point of longitude.
Noting and calculating longitude[edit]
Longitude
Longitude is given as an angular measurement ranging from 0° at the
Prime Meridian
Prime Meridian to +180° eastward and −180° westward. The Greek
letter λ (lambda),[6][7] is used to denote the location of a place on
Earth
Earth east or west of the Prime Meridian.
Each degree of longitude is sub-divided into 60 minutes, each of which
is 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° 27.5′ E. Degrees may also be expressed as a decimal
fraction: 23.45833° E. For calculations, the angular measure may
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
East suffix is replaced by a negative sign
in the western hemisphere. Confusingly, the convention of negative for
East
East is also sometimes seen. The preferred convention—that
East
East is
positive—is consistent with a right-handed Cartesian coordinate
system, with the
North Pole
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.
There is no other physical principle determining longitude directly
but with time.
Longitude
Longitude at a point may be determined by calculating
the time difference between that at its location and Coordinated
Universal Time
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
is 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 or astronomical observation. The details are more complex than
described here: see the articles on
Universal Time
Universal Time and on the equation
of time for more details.
Singularity and discontinuity of longitude[edit]
Note that the longitude is singular at the Poles and calculations that
are sufficiently accurate for other positions, may be inaccurate at or
near the Poles. Also the discontinuity at the ±180° meridian must be
handled with care in calculations. An example is a calculation of east
displacement by subtracting two longitudes, which gives the wrong
answer if the two positions are on either side of this meridian. To
avoid these complexities, consider replacing latitude and longitude
with another horizontal position representation in calculation.
Plate movement and longitude[edit]
The Earth's tectonic plates move relative to one another in different
directions at speeds on the order of 50 to 100mm per year.[8] So
points on the Earth's surface on different plates are always in motion
relative to one another. For example, the longitudinal difference
between a point on the
Equator
Equator in Uganda, on the African Plate, and a
point on the
Equator
Equator in Ecuador, on the South American Plate, is
increasing by about 0.0014 arcseconds per year. These tectonic
movements likewise affect latitude.
If a global reference frame (such as WGS84, for example) is used, the
longitude of a place on the surface will change from year to year. To
minimize this change, when dealing just 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.
Length of a degree of longitude[edit]
The length of a degree of longitude (east-west distance) depends only
on the radius of a circle of latitude. For a sphere of radius a that
radius at latitude φ is a cos φ, and the length of a one-degree (or
π/180 radian) arc along a circle of latitude is
Δ
l
o
n
g
1
=
π
180
∘
a
cos
ϕ
displaystyle Delta _ rm long ^ 1 = frac pi 180^ circ acos
phi
φ
Δ1
lat
Δ1
long
0°
110.574 km
111.320 km
15°
110.649 km
107.551 km
30°
110.852 km
96.486 km
45°
111.132 km
78.847 km
60°
111.412 km
55.800 km
75°
111.618 km
28.902 km
90°
111.694 km
0.000 km
When the
Earth
Earth is modelled by an ellipsoid this arc length
becomes[9][10]
Δ
l
o
n
g
1
=
π
a
cos
ϕ
180
∘
1
−
e
2
sin
2
ϕ
displaystyle Delta _ rm long ^ 1 = frac pi acos phi 180^
circ sqrt 1-e^ 2 sin ^ 2 phi
where e, the eccentricity of the ellipsoid, is related to the major
and minor axes (the equatorial and polar radii respectively) by
e
2
=
a
2
−
b
2
a
2
displaystyle e^ 2 = frac a^ 2 -b^ 2 a^ 2
An alternative formula is
Δ
l
o
n
g
1
=
π
180
∘
a
cos
ψ
where
tan
ψ
=
b
a
tan
ϕ
displaystyle Delta _ rm long ^ 1 = frac pi 180^ circ acos
psi quad mbox where tan psi = frac b a tan phi
Cos φ decreases from 1 at the equator to 0 at the poles, which
measures how circles of latitude shrink from the equator to a point at
the pole, so the length of a degree of longitude decreases likewise.
This contrasts with the small (1%) increase in the length of a degree
of latitude (north-south distance), equator to pole. The table shows
both for the
WGS84
WGS84 ellipsoid with a =
7006637813700000000♠6378137.0 m and b =
7006635675231420000♠6356752.3142 m. Note that the distance
between two points 1 degree apart on the same circle of latitude,
measured along that circle of latitude, is slightly more than the
shortest (geodesic) distance between those points (unless on the
equator, where these are equal); the difference is less than
0.6 m (2 ft).
A geographical mile is defined to be the length of one minute of arc
along the equator (one equatorial minute of longitude), so a degree of
longitude along the equator is exactly 60 geographical miles, as there
are 60 minutes in a degree.
Longitude
Longitude on bodies other than Earth[edit]
See also:
Prime meridian
Prime meridian (planets)
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
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
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. 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
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
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
Earth and 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, 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
Mars (since about 2002) is to use
planetocentric coordinates. The meridian of
Mars
Mars is located at Airy-0
crater.[11]
Tidally-locked bodies have a natural reference longitude passing
through the point nearest to their parent body: 0° the center of the
primary-facing hemisphere, 90° the center of the leading hemisphere,
180° the center of the anti-primary hemisphere, and 270° the center
of the trailing hemisphere.[12] 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[edit]
American Practical Navigator
Cardinal direction
Ecliptic
Ecliptic longitude
Geodesy
Geodetic system
Geographic coordinate system
Geographical distance
Geotagging
Great-circle distance
History
History of longitude
Island of the
Day
Day Before
Latitude
List of cities by longitude
Meridian arc
Natural Area Code
Navigation
Orders of magnitude
Right ascension
Right ascension on celestial sphere
World Geodetic System
References[edit]
^ "Definition of LONGITUDE". www.merriam-webster.com. Retrieved 14
March 2018.
^ Oxford English Dictionary
^ 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.
^ a b "
Longitude
Longitude clock comes alive". BBC. March 11, 2002.
^ Denny, Mark (2012), The Science of Navigation: From Dead Reckoning
to GPS, Johns Hopkins University Press, p. 105,
ISBN 9781421405605, in 1610, Galileo thought he might win the
Spanish longitude prize with his idea of measuring time by observing
the moons of Jupiter ... The trouble with the method was in making
accurate measurements of the four moons while on the deck of a moving
ship at sea. This problem proved intractable, and the method was
therefore not adopted .
^ "Coordinate Conversion". colorado.edu. Retrieved 14 March
2018.
^ "λ =
Longitude
Longitude east of Greenwich (for longitude west of Greenwich,
use a minus sign)."
John P. Snyder,
Map
Map Projections, A Working Manual,
USGS
USGS Professional
Paper 1395, page ix
^ Read HH, Watson Janet (1975). Introduction to Geology. New York:
Halsted. pp. 13–15.
^ Osborne, Peter (2013). "Chapter 5: The geometry of the ellipsoid".
The Mercator Projections: The Normal and Transverse Mercator
Projections on the
Sphere
Sphere and the
Ellipsoid
Ellipsoid with Full Derivations of
all Formulae (PDF). Edinburgh. doi:10.5281/zenodo.35392.
^ Rapp, Richard H. (April 1991). "Chapter 3: Properties of the
Ellipsoid". Geometric
Geodesy
Geodesy Part I. Columbus, Ohio.: Department of
Geodetic Science and Surveying, Ohio State University.
^ Where is zero degrees longitude on Mars? – Copyright 2000 – 2010
© European
Space
Space Agency. All rights reserved.
^ First map of extraterrestrial planet – Center of Astrophysics.
External links[edit]
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Elements of the Planets and Satellites
"
Longitude
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.
Board of
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Longitude Collection, Cambridge Digital Library – complete
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