What is longitude of point abcd respectively?

The lines running east to west are known as lines of latitude.  The lines running north to south are known as lines of longitude.

(Related: How to Remember the Difference Between Latitude and Longitude)

While lines of latitude run across a map east-west, the latitude indicates the north-south position of a point on earth.

Lines of latitude start at 0 degrees at the equator and end at 90 degrees at the North and South Poles (for a total to 180 degrees of latitude). Therefore, the higher the value of degree of latitude, the closer it is to the North or South Pole.

Everything north of the equator is known as the Northern Hemisphere and everything south of the equator is known as the Southern Hemisphere.

A location’s latitude is expressed in degrees (°), minutes (‘), and seconds (“).

A positive latitude value indicates a location in the Northern Hemisphere, while a negative value indicates a location in the Southern Hemisphere.

Lines of latitude are called parallels and in total there are 180 degrees of latitude.  The distance between each degree of latitude is about 69 miles (110 kilometers).

(Watch this video on YouTube: Latitude and Longitude)

A parallel is a named line connecting all points along the same line of latitude.

For example, the 49th parallel marked part of the border between Canada and the U.S. that was negotiated by the United States and Britain as part of the Treaty of 1818:

The five major parallels of latitudes from north to south are called: Arctic Circle, Tropic of Cancer, Equator, Tropic of Capricorn, and the Antarctic Circle.

On a map where the orientation of the map is either due north or due south, latitude appears as horizontal lines.

The equator divides the earth into the Northern Hemisphere and the Southern Hemisphere is marks the location of 0 degrees latitude.   Latitude represents an angular distance north or south of the equator.

The equator marks the locations on earth that are equidistance from the North and South Poles.  The Equator is the only line of latitude that is a great circle, all the other lines of latitude are small circles.

Related: What is at Zero Degrees Latitude and Zero Degrees Longitude?

The equator crosses 78.7% water and 21.3% land and is about 24,901 miles (40,075 km) long.

Here’s an interesting fact: the original definition of the length of a meter in 1793 was: one ten-millionth (10⁻⁷) of the distance between the equator and the North Pole along a great circle.

The current definition of a meter is: the distance traveled by light in 1/299,792,458 of a second in a vacuum.

(Source: Agnoli, P., & D’Agostini, G. (2004). Why does the meter beat the second?. arXiv preprint physics/0412078. arXiv:physics/0412078)

The Tropic of Cancer marks the location where the sun reaches the zenith at this latitude.  The exact latitude is not a fixed point and the latest measurement for 2014 is 23° 26′ 14.675″ (23° 26′ 16″).

The summer solstice, which occurs on either June 20 or 21 of each year, marks the day on which the sun shines vertically over this parallel.

Moving every year, the Tropic of Capricorn is the parallel line of latitude that is currently located at 23° 26′ 14.440″.

The winter solstice, which occurs on either December 21 or 22 of each year, marks the day on which the sun shines vertically over this line.

The Arctic and Antarctic Circles are the parallels of latitude that are roughly 66.5 degrees (66° 33′ 44″ (or 66.5622°).

The region above the Arctic Circle, which includes the North Pole, is known as the Arctic.

The region south of the Antarctic Circle, which includes the South Pole, is known as the Antarctic.

The Horse Latitudes are found at about 30 degrees North and South of the equator.

Horse latitudes represents areas in the subtopics where prevailing winds diverge and flow towards the poles (known as westerlies) or towards the Equator (known as trade winds).

The horses latitudes are characterized by high atmospheric pressure, weak winds, and generally calm, stable weather conditions. These areas are known for their clear skies and low precipitation, which contributes to the formation of deserts at these latitudes, such as the Sahara Desert in Africa and the Mojave Desert in North America.

Legend has it that the calm winds would stall sailing ships at these latitudes for days or even weeks. In desperation, sailors would toss horses and livestock being transported to the Americas over board in an attempt to preserve drinking water supplies. This is the suggested origin of the phrase “horse latitudes”.

Longitude are lines that run north-south and mark the position east-west of a point. Therefore, latitude is the angular distance east or west of the Prime Meridian, which passes through Greenwich, England.

Lines of longitude run from pole to pole, crossing the equator at right angles. All lines of longitude are equal in length. Each line of longitude also is one half of a great circle.

Unlike lines of latitude, which run parallel to the equator, lines of longitude (meridians) converge at the poles. This means that the distance between lines of longitude decreases as you move towards the poles, making them closer together than they are at the equator.

There are 360 degrees of longitude (+180° eastward and −180° westward.).

The longitude line of 0 degrees is known as the Prime Meridian and it divides the world into the Eastern Hemisphere and the Western Hemisphere.

A location’s longitude is expressed in degrees (°), minutes (‘), and seconds (“). A positive longitude value indicates a location in the Eastern Hemisphere, while a negative value indicates a location in the Western Hemisphere.

While lines of latitude are known as parallels, lines of longitude are known as meridians.

Distances that that are west of the Prime Meridian are noted with a – in front of the number (negative numbers) and distances that are east of the Prime Meridian are positive numbers (-180 degrees degrees of longitude west and 180 degrees of longitude east).

The distance between longitudes narrows the further away from the equator. As you move toward the poles, the distance between each line of longitude becomes smaller until the converge at the North and South Poles.

The distance between longitudes at the equator is the same as latitude, roughly 69 miles. At 45 degrees north or south, the distance between is about 49 miles (79 km).

The distance between longitudes reaches zero at the poles as the lines of meridian converge at that point.

Determining longitude accurately is crucial for navigation, particularly at sea.

Historically, accurate timekeeping was the key to measuring longitude, as the difference in time between a known location (usually the Prime Meridian) and the local time at an unknown location could be used to calculate the east-west distance between the two points.

In 1714, the British government established the Longitude Prize, which awarded £20,000 to anyone who could develop a practical method for accurately determining a ship’s longitude.

John Harrison, a self-taught clockmaker, eventually won the prize in 1765 with his marine chronometer, a highly accurate clock that could be used to measure longitude at sea.

The development of precise marine chronometers and, later, Global Positioning System (GPS), revolutionized the determination of longitude, making it easier for navigators and geographers to pinpoint locations on Earth.

The line of longitude where the degree is zero is known as the Prime Meridian.  Passing through the Royal Observatory, Greenwich, England, it is also known as the Greenwich Meridian and divides Earth into two equal halves known as the Eastern Hemisphere and the Western Hemisphere.

Related: The Prime Meridian isn’t Where You Think it is

The line on Earth where one calendar day becomes the next is known as the International Date Line (IDL) which passes through the Pacific Ocean.

The line is generally found 180 degrees from the Prime Meridian but the line circumvents some regions and islands to avoid dividing contiguous pieces of regions and countries into two separate days.

There are 23 one-hour slices and two 30 minutes slices that divide the world up into different time zones.  Traveling from east to west over the International Date Line advances the calendar by one day.

More: Geography of the International Date Line

To provide a geographic location using latitude and longitude, a pair of numbers known as coordinates are used.

Coordinates are composed of degrees, minutes, and seconds (DMS). When providing coordinates, Latitude is always written first.

To provide the location of the United States Capitol building using latitude and longitude would be: 38° 53′ 35″ N, 77° 00′ 32″ W.

Decimal Degrees, which converts the minutes and seconds portion of the coordinates, is another way to write coordinates. In stead of noting the cardinal directions (N,S,W, or W) in decimal degrees, points that are west of the Prime Meridian and south of equator are preceded by a negative sign.

Therefore, the United States Capitol’s coordinates (the absolute location) in decimal degrees are 38.889722°, -77.008889°.

Many mapping programs such as Google Maps use DD.

This article was first written on January 2, 2016 and has since been updated.

Longitude (/ˈlɒndʒɪtjuːd/, AU and UK also /ˈlɒŋɡɪ-/)[1][2] is a geographic coordinate that specifies the east–west position of a point on the surface of 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 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 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 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 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.[3]: 31  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 the relationship between longitude and time.[3]: 11 [4] 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 a gross over-estimate (by about 70%) of the length of the Mediterranean.[5][6]: 551–553 [7]

After the fall of the Roman Empire, interest in geography greatly declined in Europe.[8]: 65  Hindu and Muslim astronomers continued to develop these ideas, adding many new locations and often improving on Ptolemy's data.[9][10] 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 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".[11][12]

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 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.[13]: 85

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 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.[14] 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°.[15]

The telescope was invented in the early 17th century. Initially an observation device, developments over the next half century transformed it into an accurate measurement tool.[16][17] The pendulum clock was patented by Christiaan Huygens in 1657[18] and gave an increase in accuracy of about 30 fold over previous mechanical clocks.[19] These two inventions would revolutionise observational astronomy and cartography.[20]

On land, the period from 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°.[21] At sea during the same period, the situation was very different. Two problems proved intractable. The first 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 the British parliament in 1714.[22]: 8  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[23] 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 was supported and rewarded with thousands of pounds from the Board of Longitude,[24] 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[22]: 26 . 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.[25] Chronometers had 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.[26]

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.[27] The method 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 US Coast Survey 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 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.[28][29]

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.[30] Wireless time signals for the use of ships were transmitted from Halifax, Nova Scotia, starting in 1907[31] and from the Eiffel Tower in Paris from 1910.[32] These signals allowed navigators to check and adjust their chronometers frequently.[33]

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.[34] They allowed accurate navigation when poor visibility prevented astronomical observations, and became the established method for commercial shipping until replaced by GPS in the early 1990s.

The main methods for determining longitude are listed below. With one exception (magnetic declination) they all depend on a common principle, which was to determine an absolute time from an event or measurement and to compare the corresponding local time at two different locations.

With the exception of magnetic declination, all proved practicable methods. Developments on land and sea, however, were very different.

There is no other physical principle determining longitude directly but with time.[clarification needed] 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 a location's time zone is three hours ahead of UTC then that location is near 45° longitude (3 hours × 15° per hour = 45°). The word near is used because the point might not be at the centre of the time zone; also the time zones are defined politically, so their centres and boundaries often do not lie on meridians at multiples of 15°. In order to perform this calculation, however, one needs 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 and on the equation of time for more details.

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)[35][36] 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, 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 2π.

For calculations, 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, the convention of negative for East is also sometimes seen, most commonly in the United States; the Earth System Research Laboratory 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.[37]

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.

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

When the Earth is modelled by an ellipsoid this arc length becomes[38][39]

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 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 = 6378137.0 m and b = 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) therefore a degree of longitude along 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.

For an error-free plotted traverse:

ΣL = 0, ΣD = 0

ΣL = Algebraic sum of Latitudes of all the sides

ΣD = Algebraic sum of departure of all the sides

For a segment AB

Latitude = L cos θ & Departure = L sin θ

In whole circle bearing, Bearings are taken w.r.t North Direction

Calculation:

As  Latitude is +ve & Departure is - ve

The line AB lies in 4 th quadrant ( > 270 ° )

From the figure

\(\tan \theta = \frac{{\sum D}}{{\sum L}} = \frac{{-45.1}}{{78}}\)

∴ θ =  - 30°

The whole circle bearing of the line AB is