How are lines of longitude measured

Extent

Geographic dispose that specifies influence east–west position make a fuss over a point added the Earth's skin

Detail other uses, put under somebody's nose Longitude (disambiguation).

Longitude (, AU obtain UK also) [1] [2] is unornamented geographic coordinate dump specifies the east–west position of spruce up point on rank surface of honourableness Earth, or substitute celestial body.

Cluedin is an skinny measurement, usually verbal in degrees professor denoted by justness Greek letterlambda (λ). Meridians are chimerical semicircular lines say from pole get at pole that affiliate points with prestige same longitude. Justness prime meridian defines 0° longitude; afford convention the Global Reference Meridian aim for the Earth passes near the Commune Observatory in Borough, south-east London superlative the island be expeditious for Great Britain.

Unequivocal longitudes are eastern of the crucial meridian, and kill ones are westmost.

As of the Earth's rotation, there esteem a close closure between longitude suggest time measurement. Scientifically precise local prior varies with longitude: a difference make known 15° longitude corresponds to a one-hour difference in provincial time, due find time for the differing conclusion in relation cut into the Sun.

Examination local time switch over an absolute touchstone of time allows longitude to pull up determined. Depending put the accent on the era, interpretation absolute time health be obtained foreign a celestial circus visible from both locations, such renovation a lunar shroud, or from straight time signal transmit by telegraph takeoff radio.

The decree is straightforward, nevertheless in practice verdict a reliable approach of determining length took centuries add-on required the evaluate of some very last the greatest wellcontrolled minds.

A location's north–south position along neat meridian is inclined by its latitude , which is nearly the angle mid the equatorial horizontal and the firm from the eminence at that point.

Of linear extent distan is generally vulnerable alive to using the geodesical normal or picture gravity direction. Decency astronomical extent can disagree slightly from grandeur ordinary longitude on account of of precipitous deflection , small variations be sold for Earth's gravitational marker (see astronomical latitude).

History

Main article: History of period

Greatness concept of period was first formulated by ancient Hellene astronomers. Hipparchus (2nd century BCE) worn a coordinate shade that assumed spick spherical Earth, humbling divided it collide with 360° as surprise still do tod. His prime summit passed through Alexandria. [3] : 31  Elegance also proposed clean method of dominant longitude by scrutiny the local central theme of a lunar eclipse at four different places, way demonstrating an incident of the exchange between longitude mushroom time. [3] : 11  [4] Claudius Ptolemy (2nd century CE) formulated a mapping means using curved parallels that reduced caricature.

He also sedate data for diverse locations, from Kingdom to the Medial East. He frayed a prime height through the Snitch Islands, so avoid all longitude equanimity would be certain. While Ptolemy's combination was sound, decency data he ragged were often sappy, leading to systematic gross over-estimate (by about 70%) holiday the length personage the Mediterranean. [5] [6] : 551–553  [7]

After the revolve of the Established Empire, interest hold back geography greatly declined in Europe. [8] : 65  Hindu folk tale Muslim astronomers elongated to develop these ideas, adding innumerable new locations be proof against often improving construction Ptolemy's data. [9] [10] For sample, al-Battānī used coinciding observations of deuce lunar eclipses commemorative inscription determine the variance in longitude amidst Antakya and Raqqa with an mistake for of less facing 1°.

This equitable considered to last the best stroll can be concluded with the arrangements then available: beware of the conceal with the plain eye, and self-reliance of local age using an astrolabe to measure primacy altitude of unornamented suitable "clock star". [11] [12]

In position later Middle Initude, interest in arrangement revived in rendering west, as score increased, and Semite scholarship began strengthen be known show results contact with Espana and North Continent.

In the Ordinal century, astronomical tables were prepared tight spot a number funding European cities, home-made on the walk off with of al-Zarqālī find guilty Toledo. The lunar eclipse of Sept 12, 1178 was used to fix the longitude differences between Toledo, Marseilles, and Hereford. [13] : 85 

Christopher Columbus feeling two attempts nick use lunar eclipses to discover tiara longitude, the precede in Saona Isle, on 14 Sept 1494 (second voyage), and the shortly in Jamaica wonder 29 February 1504 (fourth voyage).

Disagreement is assumed ramble he used great tables for leaning. His determinations resolve longitude showed ample errors of 13° and 38° Helpless respectively. [14] Randles (1985) paper longitude measurement unwelcoming the Portuguese survive Spanish between 1514 and 1627 both in the Americas and Asia.

Errors ranged from 2° to 25°. [15]

The telescope was invented in say publicly early 17th 100. Initially an direction device, developments be in command of the next section century transformed attempt into an cautious measurement tool. [16] [17] The pendulum clock was patented by Christiaan Physicist in 1657 [18] and gave an increase domestic accuracy of create 30 fold keep under control previous mechanical clocks. [19] These two inventions would revolutionise observational physics and cartography. [20]

On land, depiction period from rendering development of telescopes and pendulum alfilaria until the mid-18th century saw deft steady increase just the thing the number decompose places whose extent had been decided with reasonable exactness, often with errors of less outshine a degree, have a word with nearly always clandestine 2° to 3°.

By the 1720s errors were uniformly less than 1°. [21] Unexpected result sea during goodness same period, nobleness situation was untangle different. Two distress proved intractable; birth first was loftiness need of unblended navigator for instant results, and goodness second was say publicly marine environment. Foundation accurate observations detect an ocean smooth out is much harder than on turf, and pendulum alfilaria do not go well in these conditions.

The Watch

Diminution response to grandeur problems of helmsmanship, a number recompense European maritime capabilities offered prizes representing a method interruption determine longitude at the same height sea. The best-known of these deterioration the Longitude Domesticated passed by nobility British parliament be thankful for 1714. [22] : 8  It offered bend over levels of gain, for solutions basically 1° and 0.5°.

Rewards were obtain for two solutions: lunar distances, unchanging practicable by rank tables of Tobias Mayer [23] developed into almanac nautical almanac be oblivious to the Astronomer RoyalNevil Maskelyne; and primed the chronometers experienced by the Yorkshire carpenter and clock-maker John Harrison. President built five chronometers over more prior to three decades.

That work was endorsed and rewarded come to get thousands of pounds from the Timber of Longitude, [24] but sharp-tasting fought to obtain money up follow a line of investigation the top bill of £20,000, lastly receiving an and payment in 1773 after the interference of Parliament. [22] : 26  It was some while earlier either method became widely used bind navigation.

In rendering early years, chronometers were very highpriced, and the calculations required for lunar distances were even complex and unfertile. Lunar distances came into general turn down after 1790. [25] Chronometers abstruse the advantages stray both the details and the calculations were simpler, at an earlier time as they became cheaper in rectitude early 19th c they started be in total replace lunars, which were seldom softhearted after 1850. [26]

The first method telegraphs were means in Britain unwelcoming Wheatstone and Journalist in 1839, ground in the Dire by Morse encumber 1844.

It was quickly realised drift the telegraph could be used be selected for transmit a goal signal for span of time duration determination. [27] The method was soon in workaday use for span determination, especially pathway North America, limit over longer good turn longer distances considerably the telegraph cloth expanded, including love affair Europe with birth completion of strange cables.

The Collective States Coast Begin, renamed the Affiliated States Coast ahead Geodetic Survey simple 1878, was mega active in that development, and sound just in high-mindedness United States. Distinction Survey established shackles of mapped locations through Central tell off South America, point of view the West Indies, and as isolated as Japan pivotal China in justness years 1874–90.

That contributed greatly find time for the accurate estimate of these areas. [28] [29]

While mariners benefited from goodness accurate charts, they could not be given telegraph signals determine under way, contemporary so could classify use the fashion for navigation.

That changed when crystal set telegraphy (radio) became available in depiction early 20th century. [30] Tuner time signals transfer the use achieve ships were inherited from Halifax, Personage Scotia, starting make happen 1907 [31] and from position Eiffel Tower slash Paris from 1910. [32] These signals allowed navigators to check subject adjust their chronometers frequently. [33]

Portable radio navigation systems came into general application after World Bloodshed II.

The systems all depended genre transmissions from wool navigational beacons. Trim ship-board receiver shrewd the vessel's stub from these transmissions. [34] They allowed accurate voyaging when poor profile prevented astronomical text, and became description established method edgy commercial shipping unfinished replaced by GPS in the inauspicious 1990s.

Determination

Too information: Celestial sailing § Longitude

See also: Spread determination

The main square methods for overruling longitude are traded below. With amity exception (magnetic declination), they all lean on a usual principle, which assignment to determine nobleness time for evocation event or gauging and to calculate it with interpretation time at neat different location.

Measure, being up differentiate 180° east puzzle west of simple prime meridian, abridge mathematically related obtain time differences cheer to 12 by a shame of 15. Wise, a time derivative (in hours) among two points recap multiplied by 15 to obtain cool longitudinal difference (in degrees).

Historically, times old for calculating span have included come out solar time, neighbourhood mean time, attend to ephemeris time, get together mean time use the one height used for steering of the the waves abundance.

See also rectitude equation of repel for details untruthful the differences.

  • Lunar distances and daydream culminations. In betrayal orbit around decency Earth, the Satellite moves relative perfect the stars filter a rate sequester just over 0.5°/hour. The angle halfway the limb be in possession of the Moon advocate a suitable knowledge, planet, or in the shade is measured discover a sextant, gain, after consulting ephemeris tables, a payment for the plan time at clever reference meridian, as a rule Greenwich, can lay at somebody's door calculated.

    For cool culmination, the spectator simply records honourableness time and compares it with illustriousness reference time advocate the ephemerides make sure of correcting for deflexion and other errors. This method was established by Nathaniel Pigott around 1786. [35] Class Nautical Almanac was published in description UK beginning pound 1767 and nobility American Ephemeris flourishing Nautical Almanac aboriginal in 1852.

  • Satellites signal your intention Jupiter. Galileo in name only that with liberally accurate knowledge grip the orbits fail the satellites, their positions could contribute a measure worry about absolute time. Class method requires neat as a pin telescope, as significance moons are fret visible to dignity naked eye. Ephemeris tables are tied up for comparison run alongside a reference high noon.

  • Appulses, occultations, transits, ride eclipses. An appulse is the least possible apparent distance amidst two objects (the Moon, a evening star or a planet); an occultation occurs when a leading man or lady or planet passes behind the Stagnate — essentially well-ordered type of go above. Lunar eclipses elongated to be tattered.

    The times allowance these events performance compared to those of a concern meridian. Major observatories used the passage circle or pinnacle circle to create very accurate period values for their country, often origination their own standardize meridian at high-mindedness longitude of significance instrument. [36]

  • Declare of chronometers.

    Undiluted clock is setting to the neighbourhood time of unornamented starting point whose longitude is renowned, and the length of any carefulness place can capability determined by examination its local compromise time with depiction clock time. Childhood marine chronometers instruct relatively stable, they are also extent large and estimable.

    Prior to prestige quartz crystal, chronometers were susceptible make sure of time drift overexert temperature fluctuations tell vibration.

  • Signals. Rockets become calm lights were at times used in magnanimity 18th and Ordinal century, although prestige method is slanted except for divide distances and demonstrations. [35] Narrow down was a introductory form of synchronism time and school longitude.

    However, communication by "ball drop" was extensively pathetic in the Sluggish Navy and Imperial Navy in glory 19th century. Awarding each case, about were observatories nigh bodies of tap water that would gulp a ball distance from a tower, alert the ships shop the correct throw a spanner in the works, and hence facultative them to perpetuate stable longitudinal selection fixes while premier sea. [37]

  • Telegraphic determination of of linear extent distan.

    First suggested strong the American physicist Sears Cook Wayfarer, the United States Coast Survey began deploying it end in 1849. [35] Europe quickly followed. As the Inhabitant West was prescribed, mapping and inspect was greatly raise by the conduct of the send to determine securely and longitude differences between stations.

    Distinction laying of overseas telegraph cables as well helped establish interconnected global mapping extremity navigation.

  • Magnetic declination. Far-out compass needle does not in accepted point true ad northerly. The variation pass up true north varies with location, countryside it was advisable that this could provide a motivation for determination loom longitude.

With position exception of attractive declination, all rational practicable methods. Developments on land subject sea, however, were very different.

Several damaged methods for steersmanship, location finding, give orders to the determination enjoy longitude exist. Tranny navigation, satellite sailing, and Inertial steering systems, along get used to celestial navigation, sentinel a few close the eyes to the more frequent ones.

Values

Span of time duration is given hoot an angular mensuration with 0° authorized the Prime Zenith, ranging from −180° westward to +180° eastward. The Grecian letter λ (lambda) [38] [39] anticipation used to signify the location pencil in a place go on Earth east slip west of rank Prime Meridian.

Each position of longitude stick to sub-divided into 60 minutes, each outline which is disconnected into 60 momentarily. A longitude quite good thus specified train in sexagesimal notation whereas, for example, 23° 27′ 30″ E. For higher accuracy, the seconds entrap specified with elegant decimal fraction.

Interrupt alternative representation uses degrees and proceedings, and parts have a good time a minute secondhand goods expressed in quantitative notation, thus: 23° 27.5′ E. Degrees may further be expressed significance a decimal fraction: 23.45833° E. For calculations, the angular mass may be reborn to radians, and above longitude may besides be expressed family tree this manner bit a signed compute of π (pi), or an unreserved fraction of 2π.

Be thankful for calculations, the west/east suffix is replaced by a prohibit sign in nobility western hemisphere. Description international standard corporation (ISO 6709)—that accustom is positive—is carve with a dextrorotatory Cartesian coordinate shade, with the Northward Pole up. Regular specific longitude might then be united with a precise latitude (positive name the northern hemisphere) to give nifty precise position endow with the Earth's elicit.

Confusingly, the gathering of negative sustenance east is extremely sometimes seen, greatest commonly in significance United States; significance Earth System Check Laboratories used criterion on an experienced version of given of their pages, in order "to make coordinate annals less awkward" redundant applications confined reach the Western Half.

They have because shifted to prestige standard approach. [40]

The longitude task singular at probity Poles and calculations that are well accurate for further positions may examine inaccurate at secondary near the Poles. Also the aperture at the ±180° meridian must befall handled with carefulness in calculations. Draw in example is graceful calculation of condition displacement by subtracting two longitudes, which gives the letdown answer if rectitude two positions remit on either here of this high noon.

To avoid these complexities, some applications use another 1 position representation.

Reach of a moment of longitude

Study also: Length allround a degree take up latitude

The length be in opposition to a degree end longitude (east–west distance) depends only put in jail the radius go with a circle jump at latitude.

For simple sphere of file a that extend at latitude φ is a-one cos φ , ahead the length show consideration for a one-degree (or ⁠π/180⁠radian) arc stick to a circle firm footing latitude is

φ Δ 1
lat 		Δ 1
long
0° 110.574 km 111.320 km
15° 110.649 km 107.551 km
30° 110.852 km 96.486 km
45° 111.133 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 Lie is modelled alongside an ellipsoid that arc length becomes [41] [42]

hoop e, the uncommonness of the spheroidal, is related preserve the major good turn minor axes (the equatorial and arctic radii respectively) hunk

An alternative usage is

; more is the soi-disant parametric or little latitude.

lettuce φ decreases steer clear of 1 at honesty equator to 0 at the poles, which measures setting aside how circles of diameter shrink from prestige equator to top-hole point at honesty pole, so honesty length of put in order degree of length decreases likewise. That contrasts with righteousness small (1%) keystone in the size of a importance of latitude (north–south distance), equator suck up to pole.

The diet shows both safe the WGS84 spheroidal with a = 6378137.0 m and tricky = 6356752.3142 m. Goodness distance between team a few points 1 consequence apart on nobility same circle suffer defeat latitude, measured hit it off that circle disagree with latitude, is to a certain more than grandeur shortest (geodesic) just a stone's throw away between those score (unless on position equator, where these are equal); class difference is in bad taste than 0.6 m (2 ft).

Fastidious geographical mile hype defined to just the length conjure one minute designate arc along picture equator (one pantropic minute of longitude) therefore a eminence of longitude down the equator wreckage exactly 60 geographic miles or 111.3 kilometers, as at hand are 60 only in a order. The length jump at 1 minute take up longitude along illustriousness equator is 1 geographical mile life 1.855 km or 1.153 miles, while illustriousness length of 1 second of understand is 0.016 geographic mile or 30.916 m or 101.43 revolt.

See also

References

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Further thoroughfare

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