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# Latitude

Latitude, denoted φ, gives the location of a place on Earth north or south of the Equator.

A region's latitude has a great effect on its climate and weather.

Map of Earth showing lines of latitude. The lines of latitude are straight and horizontal on this map.

Latitude is an angular measurement ranging from 0° at the Equator to 90° at the poles. Other latitudes of particular importance are the Tropic of Cancer (latitude 23°27′ north), the Tropic of Capricorn (latitude 23°27′ south), the Arctic Circle (latitude 66°33′ north), and the Antarctic Circle (latitude 66°33′ south). Only at latitudes between the Tropics is it possible for the sun to be at the zenith. Only north of the Arctic Circle or south of the Antarctic Circle is the midnight sun possible.

All locations of a given latitude are collectively referred to as a line of latitude or parallel, because they are coplanar, and all such planes are parallel to the Equator. Lines of latitude other than the Equator are approximately small circles on the surface of the Earth; they are not geodesics since the shortest route between two points at the same latitude involves moving farther away from the equator.

Latitude more loosely determines tendencies in climate, polar auroras, prevailing winds, and other physical characteristics of geographic locations.

Each degree of latitude is further sub-divided into 60 minutes, each of which divided into 60 seconds. A latitude is thus specified as 13° 19′ 42" N. 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: 13&deg 19.717′ N. Degrees expressed as a decimal number are also used: 13.32861° N. Sometimes, the North/South suffix is replaced by a negative sign for South.

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

One minute of arc of latitude is approximately one nautical mile or 1852 metres.

Colatitude is the complement of latitude.

In common usage "latitude" refers to geodetic or geographic latitude φ and is the angle between a plumb line and the equatorial plane — because it originated as the angle between horizon and pole star. Because the Earth is slightly flattened by its rotation, cartographers refer to a variety of auxiliary latitudes to precisely adapt spherical projections according to their purpose.

The expressions following assume elliptical polar sections with eccentricity e, and that all sections parallel to the equatorial plane are circular. Geographic latitude (with longitude) then provides a Gauss map.

Geocentric latitude φg is probably what's generally thought to be meant by latitude. It is the angle between the plane of the equator and the radial line.

tanφg = (1 - e2)tanφ

For other planets such as Mars, geographic and geocentric latitude are called "planetographic" and "planetocentric" latitude, respectively. Most maps of Mars since 2002 use planetocentric coordinates.

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## Rectifying latitude

Rectifying latitude μ is the surface distance from the equator, scaled so the pole is "90°". Unfortunately, it is an incomplete elliptic integral:

$\mu=k\int_{x=0}^\phi(1-e^2\sin^2x)^{-3/2}dx$

Reduced or parametric latitude η is the latitude of the same radius on the sphere with the same equator.

$\tan\eta=\sqrt{1-e^2}\tan\phi$

Authalic latitude β gives an area-preserving transform to the sphere.

$\beta=\arcsin\left(\frac{Q(\phi)}{Q(\pi/2)}\right)$
where $Q(x)=\left|\frac{\sin x}{1-e^2\sin^2x}-\frac1{2e}\ln\left(\frac{1-e\sin x}{1+e\sin x}\right)\right|$

Conformal latitude χ gives an angle-preserving (conformal) transform to the sphere.

$\chi=2\arctan\sqrt{\frac{1+\sin\phi}{1-\sin\phi}\left(\frac{1-e\sin\phi}{1+e\sin \phi}\right)^e}-\frac\pi2$
Approximate difference from geographic latitude
φ reduced
φ − η
authalic
φ − β
rectifying
φ − μ
conformal
φ − χ
geocentric
φ − φg
0.00′ 0.00′ 0.00′ 0.00′ 0.00′
1.01′ 1.35′ 1.52′ 2.02′ 2.02′
10° 1.99′ 2.66′ 2.99′ 3.98′ 3.98′
15° 2.91′ 3.89′ 4.37′ 5.82′ 5.82′
20° 3.75′ 5.00′ 5.62′ 7.48′ 7.48′
25° 4.47′ 5.96′ 6.70′ 8.92′ 8.92′
30° 5.05′ 6.73′ 7.57′10.09′10.09′
35° 5.48′ 7.31′ 8.22′10.95′10.96′
40° 5.75′ 7.66′ 8.62′11.48′11.49′
45° 5.84′ 7.78′ 8.76′11.67′11.67′
50° 5.75′ 7.67′ 8.63′11.50′11.50′
55° 5.49′ 7.32′ 8.23′10.97′10.98′
60° 5.06′ 6.75′ 7.59′10.12′10.13′
65° 4.48′ 5.97′ 6.72′ 8.95′ 8.96′
70° 3.76′ 5.01′ 5.64′ 7.52′ 7.52′
75° 2.92′ 3.90′ 4.39′ 5.85′ 5.85′
80° 2.00′ 2.67′ 3.00′ 4.00′ 4.01′
85° 1.02′ 1.35′ 1.52′ 2.03′ 2.03′
90° 0.00′ 0.00′ 0.00′ 0.00′ 0.00′

## Latitude and wealth

It is frequently observed that there is a distinct correlation between latitude and the wealth of nations. The continents along the equator, Africa and South America are the poorest. Even within Africa and South America this can be seen as the nations furthest from the equator are wealthier. In Africa the wealthiest nations are the three on the southern tip of the continent, South Africa, Botswana, and Namibia, and the countries of North Africa. Similarly in Latin America Argentina, Chile and Uruguay have long been the wealthiest. Within Asia, Indonesia, located on the equator, is among the poorest. The wealthiest nations of the world with the highest standard of living tend to be those at the northern extreme of areas open to human habitation, Canada, and the Nordic Countries. Within the wealthy continents, and even within large countries wealth increases with distance from the equator. Southern Europe has long been poorer as has the Southern United States.

There have been a number of explanations for this phenomenon. The first to describe and try to assess it was the French philosophe Montesquieu who proposed that cold weather means less blood in the extremities, which makes the flesh less elastic; this gives northerners more strength and makes them less able to relax. This forcing of the blood inward, according to Montesquieu also means more flows through the heart, increasing vitality. These findings have been wholly discredited by modern science.

Also discredited, but still current among some groups, is a racial explanation. Those near the equator tend to be dark skinned, better to cope with more direct sunlight. Some have alleged that darker skin colour is linked to lower intelligence. There is no evidence for this supposition.

Another explanation that is still widely held is that modern technologies and institutions were designed primarily in a small area of north western Europe. Thus agricultural techniques, machines, and medicines were designed to suit a temperate climate. These technologies and models readily spread to areas of similar climate, such as North America and Australia. As these areas also became centres of innovation this bias was further enhanced. Vastly less effort has been put into improving tropical agriculture than temperate because of this. Technologies, from automobiles to power lines are designed for colder drier regions and tend to work far worse in the tropics.

In simple words, the life in tropics doesn't create a strong natural urge for new technology development since life conditions in terms of basic body needs are comfortable enough. The colder the weather, the more life necessities are required for survival, which creates a strong motivation for ongoing innovative process. To make a comfortable life farther from tropics requires a more advanced technology. But once the life is comfortable enough, the 'innovation belt' is moving further from equator again.

This vicious cycle of technologies being designed for the wealthy, which makes them more wealthy and thus more able to fund technological development. One piece of evidence for this is that the far north has not always been the wealthiest latitude. Until only a few centuries ago, the wealthiest belt stretched from Southern Europe through the Middle East, northern India and southern China. A dramatic shift in technologies beginning with ocean going ships and culminating in the Industrial Revolution saw the most developed belt move north, in Europe, in China, and in the Americas. Northern Russia became a superpower while southern India became impoverished and colonized. Such dramatic changes argue that the current distribution of wealth is not due to immutable factors such as climate or race.

Linked to this explanation is that of disease. The tropics are far more prone to devastating diseases due to their temperature that makes life easier on vectors such as insects and rodents. There has long been a malarial belt spanning the globe; this made human life more difficult. Most notably it was almost impossible for most forms of northern livestock to thrive. These problems have been compounded by the wealth of the north: vastly more research money goes into curing the ailments of northerners.

Physiologist Jared Diamond, in his Pulitzer Prize-winning work Guns, Germs, and Steel, made the case that the Europe-Asia land mass is particularly favorable for the transition of societies from hunter-gatherer to farming communities. The continent stretches much further along the same lines of latitude than any of the other continents. As it is much easier to transfer a domesticated species along the same latitude than it is to move it to a warmer or colder climate, any species developed at a particular latitude will be transferred across the continent in a relatively short amount of time. Thus the inhabitants of this continent have a built-in advantage in terms of earlier development of farming, and a greater range of plants and animals from which to choose.

He also linked this progression to the development of diseases that were later to threaten the inhabitants of other continents. The close association of people in Europe-Asia with their domesticated animals provided a vector for the rapid transmission of diseases. Inhabitants of lands with few domesticated species were never exposed to the same range of diseases, and so, at least on the American continents, succumbed to diseases introduced from Europe.

• John P. Snyder Map Projections: a working manual USGS