Longitude

The longitude is an angular value, expression of positioning is - western of a point on Ground (or on another Planet). The longitude of reference is the Méridien of Greenwich.

Definition

All the of the same points longitude belong to a line marrying the terrestrial curve, cutting with right angle the equator and connecting the North pole to the South pole, this line is called Méridien . With the difference of the Latitude (Northern position - Southern) which profits from the equator and the poles like references, no natural reference exists for longitude. Longitude, generally noted λ, is thus an angular measurement on 360° compared to a meridian of reference , with an extent of +180° to -180° or 180° Is with 180° Western .

Calculation

The course of a motionless point on " Terre" (or on Sea) describing a circle (360°), that one calls a parallel (opposite with the meridian line), and a day comprising 24:00 by definition, one from of deduced that the Earth, and thus the point, turn of 15° per hour. It is thus enough to know local time in two different points in order to determine their difference in longitude (relative). From this way if one poses one of the points like reference, one will be able to deduce longitude (referred) from the second point. For example, if the hour UTC is the hour of the meridian line of Greenwich and if the local Time zone is three hours before UTC, the longitude of the place east of approximately Western 45° (3*15°).

Simple? not so sure. Because how to determine local time? If one has a GPS, it is enough to read posting. That is to say. But if one does not have which it, how to make? it is enough to identify, initially, the concept of local time at the solar hour by disregarding arbitrary choice of the states (shift compared to the sun). Then, the hour should be found solar. It is pointed out that the course of the sun in the sky is called ecliptic (or in a symmetrical way the plan of the orbit of the Earth) and that it depends on the latitude and the day of the year. This effect is due to the slope of 23°26' (angle called obliqueness of the ecliptic) of the axis of rotation of the Earth compared to that of the sun. It would thus be necessary to compare (to find a difference) the hour given (by a stop watch) to which the sun is in a precise position of its race in two different places. It is not very simple except in a point because there exists fortunately a privileged position which simplifies the procedure and which is defined when the sun reached its maximum height with the top of the horizon (culmination, not to confuse with zenith). In this position, it is midday, that is to say 12:00, and this in all the cases (whatever the latitude and whatever the day of the year). Thus, for example, in the case of a ship, it is enough to take the " top" at midday with its " and home port; to remake the point" at sea also at midday and to note the jet lag to finally deduce relative longitude from it (compared to the port) from the position of the ship at this time there. This way of preserving time gave its name to the first genuine sufficiently precise stop watches, the " Guard-temps".

Method to find midday : it is known that occurs when the sun is with the zenith (abuse language). To find this last, the simplest method consists in using a statement of shades. For that, one uses a horizontal small plank (sundial), provided with a " gnomon" (stick or vertical screw) and one notes the position of the end of his shade most frequently possible. And at midday, the length of the shade is minimal (because the sun is with its higher) and the shade gives the North-South axis. One then notes the hour given on the " Guard-temps" , for example 16:26, and 12:00 is withdrawn, which gives 4:26 of jet lag, that is to say a variation in longitude of 66,5° ((4 + 26/60) * 15°). Remark : if one continues measurements all the day one will be able to deduce (still) the North-South direction from it because it (also) is given by the axis of symmetry of the curve (connecting all the successive positions of the end of the shade of the gnomon).

History

The Astronome S British chose like prime meridian a Northern line - Southern passing by the royal observatory astronomical of Greenwich close to London to the the founded United Kingdom for the occasion. This meridian line is always used as meridian line of reference for the calculation of the time zones. Its French competitor, the Meridian of Paris, was definitively abandoned in 1884.

Need for the calculation of longitude

The measurement of longitude is fundamental for the Navigation, it gives the East-West position of the ship and makes it possible to locate it on the charts. The research of the best technique for its calculation was thus one of keenest and important of the 18th century.

In front of the number of maritime accidents due to the absence of sufficiently precise method to determine the East-West position of the ships, the British Parliament, under the pressure of the tradesmen and ship-owners, voted a law. In this law known as Longitude Act of 1714, Great Britain offered a price of 20  000 pounds sterling (several million Euro S of today) with any person able to conceive a means of determining longitude in a way practical, reliable, in any circumstance on board a building at sea.

Astronomical methods

The Astronome S British were persuaded that the solution could be only in the observation and the knowledge of the celestial mechanics, this one being of a high degree of accuracy. All the astronomers sought lengthily, while basing themselves on the observation of various stars, of planets and their satellites, and drew up tables of forecast of position of these celestial objects. But these methods have all the same weak point for a marin : they claim conditions difficult to join together on the buildings in open sea. Between the unforeseeable movements of the boats, the rare ideal atmospheric conditions and a complexity of various measurements and calculations, none thus satisfied the conditions enacted by the commission of Longitude act charged to examine the various projects and achievements in competition to gain the 20  000  £.

Use of the jet lag

Simplest consists in determining the difference between the hour (Solaire) local and the hour (solar) of a meridian line in reference. Only in order to carry out this calculation, it is necessary to know the specific time of the meridian line of reference, in addition to knowing exact local time.

The problems were of two orders:

• Technological: At that time, one called Chronomètre all rather precise Horloge. However no stop watch was able to function correctly at sea over a long life.
• Physical: The clocks with beam have one period which depends on G (value of the acceleration of the Pesanteur), but this one is not constant on the surface of the sphere and worse it is variable at sea where the swell causes parasitic decelerations and accelerations; the spring with spiral used for the pocket chronometer has one period dependant on the temperature.

The challenge was thus to succeed in manufacturing a sufficiently precise clock, of which the period is independent of the place geographical and being able to support the risks of a voyage on all the seas of the sphere.

This one was carried out and even several times improved, by John Harrison, Horloger Autodidacte in 1734. It put pursuant to work of Christian Huygens and of Robert Hooke on the spiral Ressort, it built a new type of mechanism. It used alloys of Laiton and Acier in order to control dilations. Its guard time of navy H4 1755 had a precision of ±4,5 second S over 10 days. The price promised by the law finishes by him being given afterwards many adventures in 1773.

Evolution

Currently this method of calculating of the longitude is always of topicality, in absence or, at the time of a failure of the systems of electronic positioning. The chronometers (clock) current are perfectly reliable.

For a few decades the system GPS, associating several satellite S with a Receiving portable Calculator, has made it possible to know its position  instantaneously;: longitude, latitude and altitude, like its rate of travel.

Wikipedia bonds

To insert Latitude S or longitudes in an article of Wikipedia, it is recommended to use models pre-establish

External bonds

• concrete Methods to find the latitude and longitude

To find the position geographical exact of a place
• Geocoordinates from Wikipedia for Google Earth

Longitude and latitude of cities and villages of the world

• German Database of S.à.r.l Heavens-Above GMBH, specialized in astronomy
• Second Bond

For France

• Form of search for L '''' national geographical Institute (IGN) ''', only authority on the matter, for the longitude and the latitude, expressed in degrees (°), minutes (') and seconds ("), coordinates corresponding to those of the town hall of the commune.
• Longitude and latitude of an address in Maporama France - Note: do not give, for the communes not having plan of city (either vast majority of the communes of France) that coordinates corresponding to the town hall of the commune, and those being able to appreciably differ (about a few seconds, as well in latitude as in longitude) from those which are given by the geographical institute National (IGN)

Sources

• Dava Sobel, Longitude , Threshold Points Science, 1998 ISBN 2020338580

Nds-nl: Lengtegraod Zh-min-nan: Keng-tō͘

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