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104-556: Most zones in UTM span 6 degrees of longitude , and each has a designated central meridian. The scale factor at the central meridian is specified to be 0.9996 of true scale for most UTM systems in use. The National Oceanic and Atmospheric Administration (NOAA) website states that the system was developed by the United States Army Corps of Engineers , starting in the early 1940s. However, a series of aerial photos found in

208-606: A = 6378.137 {\displaystyle a=6378.137} km and an inverse flattening of 1 / f = 298.257 223 563 {\displaystyle 1/f=298.257\,223\,563} . Let's take a point of latitude φ {\displaystyle \,\varphi } and of longitude λ {\displaystyle \,\lambda } and compute its UTM coordinates as well as point scale factor k {\displaystyle k\,\!} and meridian convergence γ {\displaystyle \gamma \,\!} using

312-678: A per-capita basis, Norway is the world's largest producer of oil and natural gas outside of the Middle East. The country has the fourth- and eighth-highest per-capita income in the world on the World Bank 's and IMF 's list, respectively. It has the world's largest sovereign wealth fund , with a value of US$ 1.3 trillion. Norway has two official names: Norge in Bokmål and Noreg in Nynorsk . The English name Norway comes from

416-413: A prime meridian , is mathematically related to time differences up to 12 hours by a factor of 15. Thus, a time differential (in hours) between two points is multiplied by 15 to obtain a longitudinal difference (in degrees). Historically, times used for calculating longitude have included apparent solar time , local mean time , and ephemeris time , with mean time being the one most used for navigation of

520-590: A resistance movement which incorporated civil disobedience and armed resistance including the destruction of Norsk Hydro 's heavy water plant and stockpile of heavy water at Vemork , which crippled the German nuclear programme . More important to the Allied war effort, however, was the role of the Norwegian Merchant Marine , the fourth-largest merchant marine fleet in the world. It was led by

624-407: A unitary state with a constitutional monarchy , Norway divides state power between the parliament , the cabinet , and the supreme court , as determined by the 1814 constitution . Norway has both administrative and political subdivisions on two levels: counties and municipalities . The Sámi people have a certain amount of self-determination and influence over traditional territories through

728-521: A central role in the peaceful separation of Norway from Sweden on 7 June 1905. A national referendum confirmed the people's preference for a monarchy over a republic. However, no Norwegian could legitimately claim the throne, since none of Norway's noble families could claim royal descent . The government then offered the throne of Norway to Prince Carl of Denmark, a prince of the Dano-German royal house of Schleswig-Holstein-Sonderburg-Glücksburg and

832-458: A conservative society. Life in Norway (especially economic life) was "dominated by the aristocracy of professional men who filled most of the important posts in the central government". There was no strong bourgeois class to demand a breakdown of this aristocratic control. Thus, even while revolution swept over most of the countries of Europe in 1848, Norway was largely unaffected. Marcus Thrane

936-665: A distant relative of Norway's medieval kings. Following the plebiscite, he was unanimously elected king by the Norwegian Parliament ; he took the name Haakon VII . Throughout the First World War , Norway remained neutral; however, diplomatic pressure from the British government meant that it heavily favoured the Allies . During the war, Norway exported fish to both Germany and Britain, until an ultimatum from

1040-457: A distinct national character. The movement covered all branches of culture, including literature ( Henrik Wergeland , Bjørnstjerne Bjørnson , Peter Christen Asbjørnsen , Jørgen Moe ), painting ( Hans Gude , Adolph Tidemand ), music ( Edvard Grieg ), and even language policy, where attempts to define a native written language for Norway led to today's two official written forms for Norwegian: Bokmål and Nynorsk . King Charles III John came to

1144-465: A false Easting of −500 000 meters is added to the central meridian. Thus a point that has an easting of 400 000 meters is about 100 km west of the central meridian. For most such points, the true distance would be slightly more than 100 km as measured on the surface of the Earth because of the distortion of the projection. UTM eastings range from about 166 000 meters to 834 000 meters at

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1248-637: A few of the more prevalent ones. Longitude is given as an angular measurement with 0° at the Prime Meridian , ranging from −180° westward to +180° eastward. 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 is divided into 60 seconds . A longitude is thus specified in sexagesimal notation as, for example, 23° 27′ 30″ E. For higher precision,

1352-658: A gross over-estimate (by about 70%) of the length of the Mediterranean. After the fall of the Roman Empire, interest in geography greatly declined in Europe. Hindu and Muslim astronomers continued to develop these ideas, adding many new locations and often improving on Ptolemy's data. For example al-Battānī used simultaneous observations of two lunar eclipses to determine the difference in longitude between Antakya and Raqqa with an error of less than 1°. This

1456-550: A reference meridian of longitude λ 0 {\displaystyle \lambda _{0}} . By convention, in the northern hemisphere N 0 = 0 {\displaystyle N_{0}=0} km and in the southern hemisphere N 0 = 10000 {\displaystyle N_{0}=10000} km. By convention also k 0 = 0.9996 {\displaystyle k_{0}=0.9996} and E 0 = 500 {\displaystyle E_{0}=500} km. In

1560-418: A region of large north-south extent with low distortion. By using narrow zones of 6° of longitude (up to 668 km) in width, and reducing the scale factor along the central meridian to 0.9996 (a reduction of 1:2500), the amount of distortion is held below 1 part in 1,000 inside each zone. Distortion of scale increases to 1.0010 at the zone boundaries along the equator . In each zone the scale factor of

1664-634: A small group had left Norway following their king to Britain. This group included 13 ships, five aircraft, and 500 men from the Royal Norwegian Navy. By the end of the war, the force had grown to 58 ships and 7,500 men in service in the Royal Norwegian Navy, 5 squadrons of aircraft in the newly formed Norwegian Air Force, and land forces including the Norwegian Independent Company 1 and 5 Troop as well as No. 10 Commandos . During German occupation , Norwegians built

1768-686: A union between the two countries. In 1397, under Margaret I , the Kalmar Union was created between the three Scandinavian countries. She waged war against the Germans, resulting in a trade blockade and higher taxation on Norwegian goods, which led to a rebellion . However, the Norwegian Council of State was too weak to pull out of the union. Margaret pursued a centralising policy which inevitably favoured Denmark because of its greater population. Margaret also granted trade privileges to

1872-634: A united Norway. Harald's realm was mainly a South Norwegian coastal state. Fairhair ruled with a strong hand and according to the sagas, many Norwegians left the country to live in Iceland, the Faroe Islands , Greenland , and parts of Britain and Ireland. Haakon I the Good was Norway's first Christian king, in the mid-10th century, though his attempt to introduce the religion was rejected. Norse traditions were replaced slowly by Christian ones in

1976-553: Is 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 ellipsoid with a = 6 378 137 .0 m and b = 6 356 752 .3142 m . The distance between two points 1 degree apart on

2080-677: Is Oslo . Norway has a total area of 385,207 square kilometres (148,729 sq mi). The country shares a long eastern border with Sweden , and is bordered by Finland and Russia to the northeast. Norway has an extensive coastline facing the Skagerrak strait, the North Atlantic Ocean, and the Barents Sea . The unified kingdom of Norway was established in 872 as a merger of petty kingdoms and has existed continuously for 1,151–1,152 years. From 1537 to 1814, Norway

2184-415: Is considered to be the best that can be achieved with the methods then available: observation of the eclipse with the naked eye, and determination of local time using an astrolabe to measure the altitude of a suitable "clock star". In the later Middle Ages, interest in geography revived in the west, as travel increased, and Arab scholarship began to be known through contact with Spain and North Africa. In

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2288-454: Is little archaeological evidence dating to the early Iron Age (the last 500 years BC). The dead were cremated, and their graves contained few goods. During the first four centuries AD, the people of Norway were in contact with Roman-occupied Gaul ; about 70 Roman bronze cauldrons, often used as burial urns, have been found. Contact with countries farther south brought a knowledge of runes ; the oldest known Norwegian runic inscription dates from

2392-466: Is the Grid Convergence. Note: Hemi = +1 for Northern, Hemi = −1 for Southern First let's compute some intermediate values: The final formulae are: Longitude Longitude ( / ˈ l ɒ n dʒ ɪ tj uː d / , AU and UK also / ˈ l ɒ ŋ ɡ ɪ -/ ) is a geographic coordinate that specifies the east – west position of a point on the surface of

2496-764: The Earth , or another celestial body. It is an angular measurement , usually expressed in degrees and denoted by the Greek letter lambda (λ). Meridians are imaginary semicircular lines running from pole to pole that connect points with the same longitude. The prime meridian defines 0° longitude; by convention the International Reference Meridian for the Earth passes near the Royal Observatory in Greenwich , south-east London on

2600-584: The German invasion of France . King Haakon and the Norwegian government escaped to Rotherhithe in London. Throughout the war they sent radio speeches and supported clandestine military actions against the Germans. On the day of the invasion, the leader of the small National-Socialist party Nasjonal Samling , Vidkun Quisling , tried to seize power, but was forced by the German occupiers to step aside. Real power

2704-867: The Kingdom of Norway , is a Nordic country in Northern Europe , situated on the Scandinavian Peninsula with a population of 5.5 million as of 2024. The remote Arctic island of Jan Mayen and the archipelago of Svalbard also form part of the Kingdom of Norway. Bouvet Island , located in the Subantarctic , is a dependency , and not a part of the Kingdom; Norway also claims the Antarctic territories of Peter I Island and Queen Maud Land . The capital and largest city in Norway

2808-485: The Labour Party held an absolute majority in the parliament. The government, led by prime minister Einar Gerhardsen , embarked on a programme inspired by Keynesian economics , emphasising state financed industrialisation and co-operation between trade unions and employers' organisations . Many measures of state control of the economy imposed during the war were continued, although the rationing of dairy products

2912-483: The Nordic welfare model with universal health care and a comprehensive social security system, and its values are rooted in egalitarian ideals. The Norwegian state has large ownership positions in key industrial sectors, having extensive reserves of petroleum, natural gas, minerals, lumber, seafood, and fresh water. The petroleum industry accounts for around a quarter of the country's gross domestic product (GDP). On

3016-593: The Old English word Norþweg mentioned in 880, meaning "northern way" or "way leading to the north", which is how the Anglo-Saxons referred to the coastline of Atlantic Norway. The Anglo-Saxons of Britain also referred to the kingdom of Norway in 880 as Norðmanna land . There is some disagreement about whether the native name of Norway originally had the same etymology as the English form. According to

3120-532: The Syttende mai (Seventeenth of May) holiday. Norwegian opposition to the decision to link Norway with Sweden caused the Norwegian–Swedish War to break out as Sweden tried to subdue Norway by military means. As Sweden's military was not strong enough to defeat the Norwegian forces outright, and Norway's treasury was not large enough to support a protracted war, and as British and Russian navies blockaded

3224-1322: The Sámi Parliament and the Finnmark Act . Norway maintains close ties with the European Union and the United States . Norway is a founding member of the United Nations , NATO , the European Free Trade Association , the Council of Europe , the Antarctic Treaty , and the Nordic Council ; a member of the European Economic Area , the WTO , and the OECD ; and a part of the Schengen Area . The Norwegian dialects share mutual intelligibility with Danish and Swedish . Norway maintains

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3328-587: The introduction of Protestantism in 1536, the archbishopric in Trondheim was dissolved; Norway lost its independence and effectually became a colony of Denmark. The Church's incomes and possessions were instead redirected to the court in Copenhagen. Norway lost the steady stream of pilgrims to the relics of St. Olav at the Nidaros shrine, and with them, much of the contact with cultural and economic life in

3432-474: The union with Sweden . Under this arrangement, Norway kept its liberal constitution and its own independent institutions, though it shared a monarch and foreign policy with Sweden. Following the recession caused by the Napoleonic Wars , economic development of Norway remained slow until 1830. This period also saw the rise of Norwegian romantic nationalism , as Norwegians sought to define and express

3536-542: The 12th century, astronomical tables were prepared for a number of European cities, based on the work of al-Zarqālī in Toledo . The lunar eclipse of September 12, 1178 was used to establish the longitude differences between Toledo, Marseilles , and Hereford . Christopher Columbus made two attempts to use lunar eclipses to discover his longitude, the first in Saona Island , on 14 September 1494 (second voyage), and

3640-656: The Abteilung für Luftbildwesen (Department for Aerial Photography). From 1947 onward the US Army employed a very similar system, but with the now-standard 0.9996 scale factor at the central meridian as opposed to the German 1.0. For areas within the contiguous United States the Clarke Ellipsoid of 1866 was used. For the remaining areas of Earth, including Hawaii , the International Ellipsoid

3744-602: The British government and anti-German sentiments as a result of German submarines targeting Norwegian merchantmen led to a termination of trade with Germany. 436 Norwegian merchantmen were sunk by the Kaiserliche Marine , with 1,150 Norwegian sailors killed. Norway once more proclaimed its neutrality during the Second World War , but was invaded by German forces on 9 April 1940. Although Norway

3848-600: The British parliament in 1714. It offered two levels of rewards, for solutions within 1° and 0.5°. Rewards were given for two solutions: lunar distances, made practicable by the tables of Tobias Mayer developed into an nautical almanac by the Astronomer Royal Nevil Maskelyne ; and for the chronometers developed by the Yorkshire carpenter and clock-maker John Harrison . Harrison built five chronometers over more than three decades. This work

3952-678: The Bundesarchiv-Militärarchiv (the military section of the German Federal Archives ) apparently dating from 1943–1944 bear the inscription UTMREF followed by grid letters and digits, and projected according to the transverse Mercator, a finding that would indicate that something called the UTM Reference system was developed in the 1942–43 time frame by the Wehrmacht . It was probably carried out by

4056-693: The Danish kingdom was on the losing side in 1814, it was forced by the Treaty of Kiel to cede Norway to Sweden, while the old Norwegian provinces of Iceland, Greenland, and the Faroe Islands remained with the Danish crown. Norway took this opportunity to declare independence, adopted a constitution based on American and French models, and elected the Crown Prince of Denmark and Norway, Christian Frederick , as king on 17 May 1814 – celebrated as

4160-407: The Earth into 60 zones, each 6° of longitude in width. Zone 1 covers longitude 180° to 174° W; zone numbering increases eastward to zone 60, which covers longitude 174°E to 180°. The polar regions south of 80°S and north of 84°N are excluded, and instead covered by the universal polar stereographic (UPS) coordinate system. Each of the 60 zones uses a transverse Mercator projection that can map

4264-569: The Hanseatic merchants of Lübeck in Bergen in return for recognition of her rule, and these hurt the Norwegian economy. The Hanseatic merchants formed a state within a state in Bergen for generations. The " Victual Brothers " launched three devastating pirate raids on the port (the last in 1427). Norway slipped ever more to the background under the Oldenburg dynasty (established 1448). There

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4368-591: The Norwegian coast, the belligerents were forced to negotiate the Convention of Moss . Christian Frederik abdicated the Norwegian throne and authorised the Parliament of Norway to make the necessary constitutional amendments to allow for the personal union that Norway was forced to accept. On 4 November 1814, the Parliament (Storting) elected Charles XIII of Sweden as king of Norway, thereby establishing

4472-617: The Norwegian shipping company Nortraship under the Allies throughout the war and took part in every war operation from the evacuation of Dunkirk to the Normandy landings . Every December Norway gives a Christmas tree to the United Kingdom as thanks for the British assistance during the war. Svalbard was not occupied by German troops, but Germany secretly established a meteorological station there in 1944. From 1945 to 1962,

4576-441: 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, some applications use another horizontal position representation . The length of a degree of longitude (east–west distance) depends only on

4680-416: The Sun. Comparing local time to an absolute measure of time allows longitude to be determined. Depending on the era, the absolute time might be obtained from a celestial event visible from both locations, such as a lunar eclipse, or from a time signal transmitted by telegraph or radio. The principle is straightforward, but in practice finding a reliable method of determining longitude took centuries and required

4784-512: The Universal Transverse Mercator/ Universal Polar Stereographic (UTM/UPS) coordinate system, which is a global (or universal) system of grid-based maps. The transverse Mercator projection is a variant of the Mercator projection , which was originally developed by the Flemish geographer and cartographer Gerardus Mercator , in 1570. This projection is conformal , which means it preserves angles and therefore shapes across small regions. However, it distorts distance and area. The UTM system divides

4888-411: The West Indies, and as far as Japan and China in the years 1874–90. This contributed greatly to the accurate mapping of these areas. While mariners benefited from the accurate charts, they could not receive telegraph signals while under way, and so could not use the method for navigation. This changed when wireless telegraphy (radio) became available in the early 20th century. Wireless time signals for

4992-453: The advantages that both the observations and the calculations were simpler, and as they became cheaper in the early 19th century they started to replace lunars, which were seldom used after 1850. The first working telegraphs were established in Britain by Wheatstone and Cooke in 1839, and in the US by Morse in 1844. It was quickly realised that the telegraph could be used to transmit a time signal for longitude determination. The method

5096-401: The boundaries between the UTM zones are approached. However, it is often convenient or necessary to measure a series of locations on a single grid when some are located in two adjacent zones. Around the boundaries of large scale maps (1:100,000 or larger) coordinates for both adjoining UTM zones are usually printed within a minimum distance of 40 km on either side of a zone boundary. Ideally,

5200-431: The central meridian reduces the diameter of the transverse cylinder to produce a secant projection with two standard lines , or lines of true scale, about 180 km on each side of, and about parallel to, the central meridian (Arc cos 0.9996 = 1.62° at the Equator). The scale is less than 1 inside the standard lines and greater than 1 outside them, but the overall distortion is minimized. The UTM zones are uniform across

5304-536: The coast, where the huge ice shelf of the last ice age first melted between 11,000 and 8000 BC. The oldest finds are stone tools dating from 9500 to 6000 BC, discovered in Finnmark ( Komsa culture ) in the north and Rogaland ( Fosna culture ) in the southwest. Theories about the two cultures being separate were deemed obsolete in the 1970s. Between 3000 and 2500 BC, new settlers ( Corded Ware culture ) arrived in eastern Norway . They were Indo-European farmers who grew grain and kept livestock, and gradually replaced

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5408-428: The control of Queen Margaret when the country entered into the Kalmar Union . After Sweden broke out of the Kalmar Union in 1521, Norway tried to follow suit, but the subsequent rebellion was defeated, and Norway remained in a union with Denmark until 1814. This period was by some referred to as the "400-Year Night", since all of the kingdom's intellectual and administrative power was centred in Copenhagen . With

5512-486: The convention of negative for east is also sometimes seen, most commonly in the United States ; the Earth System Research Laboratories used it on an older version of one of their pages, in order "to make coordinate entry less awkward" for applications confined to the Western Hemisphere . They have since shifted to the standard approach. The longitude is singular at the Poles and calculations that are sufficiently accurate for other positions may be inaccurate at or near

5616-513: The coordinates of each position should be measured on the grid for the zone in which they are located, but because the scale factor is still relatively small near zone boundaries, it is possible to overlap measurements into an adjoining zone for some distance when necessary. Latitude bands are not a part of UTM, but rather a part of the military grid reference system (MGRS). They are however sometimes included in UTM notation. Including latitude bands in UTM notation can lead to ambiguous coordinates—as

5720-476: The death of Haakon in 1379, his 10-year-old son Olaf IV acceded to the throne. As Olaf had already been elected to the throne of Denmark in 1376, Denmark and Norway entered a personal union . Olaf's mother and Haakon's widow, Queen Margaret, managed the foreign affairs of Denmark and Norway during Olaf's minority. Margaret was on the verge of achieving a union of Sweden with Denmark and Norway when Olaf IV suddenly died. Denmark made Margaret temporary ruler on

5824-434: The death of Olaf. On 2 February 1388, Norway followed suit and crowned Margaret. Queen Margaret knew that her power would be more secure if she were able to find a king to rule in her place. She settled on Eric of Pomerania , grandson of her sister. Thus at an all-Scandinavian meeting held at Kalmar, Erik of Pomerania was crowned king of all three Scandinavian countries, bringing the thrones of Norway, Denmark, and Sweden under

5928-421: The development of telescopes and pendulum clocks until the mid-18th century saw a steady increase in the number of places whose longitude had been determined with reasonable accuracy, often with errors of less than a degree, and nearly always within 2° to 3°. By the 1720s errors were consistently less than 1°. At sea during the same period, the situation was very different. Two problems proved intractable. The first

6032-409: The early 17th century. Initially an observation device, developments over the next half century transformed it into an accurate measurement tool. The pendulum clock was patented by Christiaan Huygens in 1657 and gave an increase in accuracy of about 30 fold over previous mechanical clocks. These two inventions would revolutionise observational astronomy and cartography. On land, the period from

6136-438: The economy, because of the loans the Hansa had made to the royals and the large debt the kings were carrying. The League's monopolistic control over the economy of Norway put pressure on all classes, especially the peasantry, to the degree that no real burgher class existed in Norway. From the 1040s to 1130, the country was at peace. In 1130, the civil war era broke out on the basis of unclear succession laws , which allowed

6240-556: The effort of some of the greatest scientific minds. A location's north–south position along a meridian is given by its latitude , which is approximately the angle between the equatorial plane and the normal from the ground at that location. Longitude is generally given using the geodetic normal or the gravity direction . The astronomical longitude can differ slightly from the ordinary longitude because of vertical deflection , small variations in Earth's gravitational field (see astronomical latitude ). The concept of longitude

6344-500: The end of the century. Throughout the High Middle Ages , the king established Norway as a sovereign state with a central administration and local representatives. In 1349, the Black Death spread to Norway and within a year killed a third of the population. Later plagues reduced the population to half the starting point by 1400. Many communities were entirely wiped out, resulting in an abundance of land, allowing farmers to switch to more animal husbandry . The reduction in taxes weakened

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6448-435: The equator is exactly 60 geographical miles or 111.3 kilometers, as there are 60 minutes in a degree. The length of 1 minute of longitude along the equator is 1 geographical mile or 1.855 km or 1.153 miles, while the length of 1 second of it is 0.016 geographical mile or 30.916 m or 101.43 feet. Norway in Europe  (green and dark grey) Norway ( Bokmål : Norge , Nynorsk : Noreg ), officially

6552-417: The equator. In the northern hemisphere positions are measured northward from zero at the equator. The maximum "northing" value is about 9 300 000 meters at latitude 84 degrees North, the north end of the UTM zones. The southern hemisphere's northing at the equator is set at 10 000 000 meters. Northings decrease southward from these 10 000 000 meters to about 1 100 000 meters at 80 degrees South,

6656-408: The established method for commercial shipping until replaced by GPS in the early 1990s. The main conventional methods for determining longitude are listed below. With one exception (magnetic declination), they all depend on a common principle, which is to determine the time for an event or measurement and to compare it with the time at a different location. Longitude, being up to 180° east or west of

6760-423: The expense of Sweden and Russia. The famine of 1695–1696 killed roughly 10% of Norway's population. The harvest failed in Scandinavia at least nine times between 1740 and 1800, with great loss of life. After Denmark–Norway was attacked by the United Kingdom at the 1807 Battle of Copenhagen , it entered into an alliance with Napoleon , with the war leading to dire conditions and mass starvation in 1812. As

6864-418: The following formulas, the distances are in kilometers . First, here are some preliminary values: First we compute some intermediate values: The final formulae are: where E {\displaystyle E} is Easting, N {\displaystyle N} is Northing, k {\displaystyle k} is the Scale Factor, and γ {\displaystyle \gamma }

6968-402: The globe, except in two areas. On the southwest coast of Norway , zone 32 is extended 3° further west, and zone 31 is correspondingly shrunk to cover only open water. Also, in the region around Svalbard , the zones 32, 34 and 36 are not used, while zones 31 (9° wide), 33 (12° wide), 35 (12° wide), and 37 (9° wide) are extended to cover the gaps. Distortion of scale increases in each UTM zone as

7072-438: The hunting-fishing population of the west coast. From about 1500 BC, bronze was gradually introduced. Burial cairns built close to the sea as far north as Harstad and also inland in the south are characteristic of this period, with rock carving motifs that differ from those of the Stone Age , depicting ships resembling the Hjortspring boat , while large stone burial monuments known as stone ships were also erected. There

7176-403: The island of Great Britain . Positive longitudes are east of the prime meridian, and negative ones are west. Because of the Earth's rotation , there is a close connection between longitude and time measurement . Scientifically precise local time varies with longitude: a difference of 15° longitude corresponds to a one-hour difference in local time, due to the differing position in relation to

7280-433: The king's position, and many aristocrats lost the basis for their surplus. High tithes to church made it increasingly powerful and the archbishop became a member of the Council of State . The Hanseatic League took control over Norwegian trade during the 14th century and established a trading centre in Bergen . In 1380, Olaf Haakonsson inherited both the Norwegian (as Olaf IV) and Danish thrones (as Olaf II), creating

7384-419: The king's sons to rule jointly. The Archdiocese of Nidaros was created in 1152 and attempted to control the appointment of kings. The church inevitably had to take sides in the conflicts. The wars ended in 1217 with the appointment of Håkon IV Håkonsson , who introduced clear laws of succession. From 1000 to 1300, the population increased from 150,000 to 400,000, resulting both in more land being cleared and

7488-496: The kings of Sweden and of Denmark were elected to the throne by their respective nobles. Thus Sweden and Norway were united under King Magnus VII. In 1349, the Black Death killed between 50% and 60% of Norway's population and led to a period of social and economic decline. Although the death rate was comparable with the rest of Europe, economic recovery took much longer because of the small, scattered population. Even before

7592-516: The late 10th and early 11th centuries. This is largely attributed to the missionary kings Olaf I Tryggvasson and Olaf II Haraldsson (St. Olaf). Olaf Tryggvasson conducted raids in England, including attacking London. Arriving back in Norway in 995, Olaf landed in Moster where he built a church which became the first Christian church in Norway. From Moster, Olaf sailed north to Trondheim where he

7696-435: The letter "S" either refers to the southern hemisphere or a latitude band in the northern hemisphere—and should therefore be avoided. A position on the Earth is given by the UTM zone number and hemisphere designator and the easting and northing planar coordinate pair in that zone. The point of origin of each UTM zone is the intersection of the equator and the zone's central meridian. To avoid dealing with negative numbers,

7800-571: The ninth century when heading for the Faroe Islands , and eventually came across Vinland , known today as Newfoundland , in Canada. The Vikings from Norway were most active in the northern and western British Isles and eastern North America isles . According to tradition, Harald Fairhair unified them into one in 872 after the Battle of Hafrsfjord in Stavanger , thus becoming the first king of

7904-603: The northern hemisphere and one in the south; the non-ambiguous format is to specify the full zone and hemisphere designator, that is, "17N 630084 4833438". These formulae are truncated version of Transverse Mercator: flattening series , which were originally derived by Johann Heinrich Louis Krüger in 1912. They are accurate to around a millimeter within 3000 km of the central meridian. Concise commentaries for their derivation have also been given. The WGS 84 spatial reference system describes Earth as an oblate spheroid along north-south axis with an equatorial radius of

8008-440: The plague, the population was only about 500,000. After the plague, many farms lay idle while the population slowly increased. However, the few surviving farms' tenants found their bargaining positions with their landlords greatly strengthened. King Magnus VII ruled Norway until 1350, when his son, Haakon, was placed on the throne as Haakon VI . In 1363, Haakon married Margaret , daughter of King Valdemar IV of Denmark . Upon

8112-454: 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 When the Earth is modelled by an ellipsoid this arc length becomes where e , the eccentricity of the ellipsoid, is related to the major and minor axes (the equatorial and polar radii respectively) by An alternative formula

8216-489: The reign of Charles III John brought some significant social and political reforms. In 1854, women won the right to inherit property. In 1863, the last trace of keeping unmarried women in the status of minors was removed. Furthermore, women were eligible for different occupations, particularly the common school teacher. By mid-century, Norway's democracy was limited; voting was limited to officials, property owners, leaseholders and burghers of incorporated towns. Norway remained

8320-478: The relationship between longitude and time. Claudius Ptolemy (2nd century CE) developed a mapping system using curved parallels that reduced distortion. He also collected data for many locations, from Britain to the Middle East. He used a prime meridian through the Canary Islands, so that all longitude values would be positive. While Ptolemy's system was sound, the data he used were often poor, leading to

8424-418: The rest of Europe. Eventually restored as a kingdom (albeit in legislative union with Denmark) in 1661, Norway saw its land area decrease in the 17th century with the loss of the provinces Båhuslen , Jemtland , and Herjedalen to Sweden, as the result of a number of disastrous wars with Sweden. In the north, its territory was increased by the acquisition of the northern provinces of Troms and Finnmark , at

8528-414: 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) therefore a degree of longitude along

8632-428: The sea. See also the equation of time for details on the differences. With the exception of magnetic declination, all proved practicable methods. Developments on land and sea, however, were very different. Several newer methods for navigation, location finding, and the determination of longitude exist. Radio navigation , satellite navigation , and Inertial navigation systems , along with celestial navigation , are

8736-568: The second in Jamaica on 29 February 1504 (fourth voyage). It is assumed that he used astronomical tables for reference. His determinations of longitude showed large errors of 13° and 38° W respectively. Randles (1985) documents longitude measurement by the Portuguese and Spanish between 1514 and 1627 both in the Americas and Asia. Errors ranged from 2° to 25°. The telescope was invented in

8840-473: The seconds are specified with a decimal fraction . An alternative representation uses degrees and minutes, and parts of a minute are expressed in decimal notation, 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 2 π . For calculations,

8944-527: The south end of the UTM zones. Therefore, no point has a negative northing value. For example, the CN Tower is at 43°38′33.24″N 79°23′13.7″W  /  43.6425667°N 79.387139°W  / 43.6425667; -79.387139  ( CN Tower ) , which is in UTM zone 17, and the grid position is 630 084  m east, 4 833 438  m north. Two points in Zone 17 have these coordinates, one in

9048-543: The subdivision of farms. While in the Viking Age farmers owned their own land, by 1300, seventy per cent of the land was owned by the king, the church, or the aristocracy, and about twenty per cent of yields went to these landowners. The 14th century is described as Norway's golden age , with peace and increase in trade, especially with the British Islands, although Germany became increasingly important towards

9152-582: The third century. By the time of the first historical records of Scandinavia, about the 8th century, several small political entities existed in Norway. It has been estimated that there were nine petty realms in Western Norway during the early Viking Age . Archaeologist Bergljot Solberg on this basis estimates that there would have been at least 20 in the whole country. In the Viking period, Norwegian Viking explorers discovered Iceland by accident in

9256-452: The throne of Norway and Sweden in 1818 and reigned to 1844. He protected the constitution and liberties of Norway and Sweden during the age of Metternich . As such, he was regarded as a liberal monarch. However, he was ruthless in his use of paid informers, secret police and restrictions on the freedom of the press to put down public movements for reform—especially the Norwegian national independence movement. The Romantic Era that followed

9360-498: The traditional dominant view, the first component was originally norðr , a cognate of English north , so the full name was Norðr vegr , "the way northwards", referring to the sailing route along the Norwegian coast, and contrasting with suðrvegar "southern way" (from Old Norse suðr ) for (Germany), and austrvegr "eastern way" (from austr ) for the Baltic . The earliest traces of human occupation in Norway are found along

9464-658: The use of ships were transmitted from Halifax, Nova Scotia , starting in 1907 and from the Eiffel Tower in Paris from 1910. These signals allowed navigators to check and adjust their chronometers frequently. Radio navigation systems came into general use after World War II . The systems all depended on transmissions from fixed navigational beacons. A ship-board receiver calculated the vessel's position from these transmissions. They allowed accurate navigation when poor visibility prevented astronomical observations, and became

9568-471: The utility of grid-based conformal maps by mapping their territory during the interwar period . Calculating the distance between two points on these maps could be performed more easily in the field (using the Pythagorean theorem ) than was possible using the trigonometric formulas required under the graticule-based system of latitude and longitude . In the post-war years, these concepts were extended into

9672-472: The west/east suffix is replaced by a negative sign in the western hemisphere . The international standard convention ( ISO 6709 )—that east is 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 (positive in the northern hemisphere ) to give a precise position on the Earth's surface. Confusingly,

9776-631: Was a Utopian socialist who in 1848 organised a labour society in Drammen . In just a few months, this society had a membership of 500 and was publishing its own newspaper. Within two years, 300 societies had been organised all over Norway, with a total membership of 20,000 drawn from the lower classes of both urban and rural areas. In the end, the revolt was easily crushed; Thrane was captured and jailed. In 1898, all men were granted universal suffrage , followed by all women in 1913. Christian Michelsen , Prime Minister of Norway from 1905 to 1907, played

9880-400: Was first developed by ancient Greek astronomers. Hipparchus (2nd century BCE) used a coordinate system that assumed a spherical Earth, and divided it into 360° as we still do today. His prime meridian passed through Alexandria . He also proposed a method of determining longitude by comparing the local time of a lunar eclipse at two different places, thus demonstrating an understanding of

9984-408: Was one revolt under Knut Alvsson in 1502. Norway took no part in the events which led to Swedish independence from Denmark in the 1520s. Upon the death of King Haakon V in 1319, Magnus Eriksson , at just three years old, inherited the throne as King Magnus VII. A simultaneous movement to make Magnus King of Sweden proved successful (he was a grandson of King Magnus Ladulås of Sweden), and both

10088-468: Was part of Denmark–Norway , and, from 1814 to 1905, it was in a personal union with Sweden. Norway was neutral during the First World War , and in the Second World War until April 1940 when it was invaded and occupied by Nazi Germany until the end of the war. Harald V of the House of Glücksburg is the current King of Norway . Jonas Gahr Støre has been Prime Minister of Norway since 2021. As

10192-634: Was proclaimed King of Norway by the Eyrathing in 995. One of the most important sources for the history of the 11th century Vikings is the treaty between the Icelanders and Olaf II Haraldsson, king of Norway circa 1015 to 1028. Feudalism never really developed in Norway or Sweden, as it did in the rest of Europe. However, the administration of government took on a very conservative feudal character. The Hanseatic League forced royalty to cede to them greater and greater concessions over foreign trade and

10296-685: Was soon in practical use for longitude determination, especially in North America, and over longer and longer distances as the telegraph network expanded, including western Europe with the completion of transatlantic cables. The United States Coast Survey, renamed the United States Coast and Geodetic Survey in 1878, was particularly active in this development, and not just in the United States. The Survey established chains of mapped locations through Central and South America, and

10400-569: Was supported and rewarded with thousands of pounds from the Board of Longitude, but he fought to receive money up to the top reward of £20,000, finally receiving an additional payment in 1773 after the intervention of parliament. It was some while before either method became widely used in navigation. In the early years, chronometers were very expensive, and the calculations required for lunar distances were still complex and time-consuming. Lunar distances came into general use after 1790. Chronometers had

10504-483: Was the need of a navigator for immediate results. The second was the marine environment. Making accurate observations in an ocean swell is much harder than on land, and pendulum clocks do not work well in these conditions. In response to the problems of navigation, a number of European maritime powers offered prizes for a method to determine longitude at sea. The best-known of these is the Longitude Act passed by

10608-455: Was unprepared for the German surprise attack (see: Battle of Drøbak Sound , Norwegian Campaign , and Invasion of Norway ), military and naval resistance lasted for two months. Norwegian armed forces in the north launched an offensive against the German forces in the Battles of Narvik , but were forced to surrender on 10 June after losing British support which had been diverted to France during

10712-490: Was used. The World Geodetic System WGS84 ellipsoid is now generally used to model the Earth in the UTM coordinate system, which means current UTM northing at a given point can differ up to 200 meters from the old. For different geographic regions, other datum systems can be used. Prior to the development of the Universal Transverse Mercator coordinate system, several European nations demonstrated

10816-582: Was wielded by the leader of the German occupation authority, Josef Terboven . Quisling, as minister president , later formed a collaborationist government under German control . Up to 15,000 Norwegians volunteered to fight in German units, including the Waffen-SS . Many Norwegians and persons of Norwegian descent joined the Allied forces as well as the Free Norwegian Forces . In June 1940,

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