Length circle

the length circles are those (half) great circles on spherically thought earth's surface, which go into north south direction to run and through both rotation poles of the earth. They are characterized by their constant in each case geographical length.

Ansicht einer Kugel aus 1 Radius Entfernung. Alle Meridiane (gelb) teilen die Kugel in 2 Hälften - ebenso wie auch der Äquator (blau). Sie sind - wie die anderen durchgezogenen Linien dieses Bildes - sämtlich Großkreise
Opinion of a ball from 1 radius distance.All Meridiane (yellow) divide the ball into 2 halves - just like also the equator (blue). They are - like the other pulled through lines of this picture - all great circles

table of contents

length circle and Meridian

so lying e.g. on the length circle 13,5° east: Grab forest, Berlin, Passau and Spittal at the Drau - just like “between them” the city Pilsen in Tschechien, like in the north the Swedish Karlstad and in the south Palermo on Sicilies, Tripoli (Libya) and Luanda (Angola). If we the great circle on those(thus regard the whole Meridian), would come we “extend” other hemisphere over the Antarctic to the Cookinseln and Kiribati, and at Hawaii past to the Aleuten and the Bering Strait.

The difference between “length circle” and “Meridian” smears itself however in thatEveryday life language of the Geografie frequently. For the astronomers the Meridian goes through full 360° on the “sky ball “, but thinks it with the word mainly of its “upper half”. There the sun each noon ( meridies = midday line ) kulminiert, during itthe “lower” elbow to midnight goes through.

more exact view of the length circles

the term length circle originates equally from mathematics, Geografie and astronomy - where one “bevels” also length circles concerning the ecliptic (apparent sun course) and even the Milky Way uses.But also moon maps have their (“selenografischen”) lengths, and in space travel to planets and for purposes of the course regulation they must be put often completely differently.

length circles on earth and other “distorted” balls

regard one the earthmore exactly, then one can accept her no more than ball, but has at least their flattening to consider. The earth figure “bulged” by the daily rotation and their centrifugal force at the equator and in the polar regions “flatter” than a ball equal in size.The difference in the radii amounts to nevertheless 21,387 meters (or 1:298,24 of the middle equatorial radius of 6.378.137 m).

On an ideal earth ellipsoid (up to 100 meters the sea level and/or. to the Geoid corresponds), are the length circles to ellipses, but at leasteverything equivalent long. On the “mathematical” earth figure of the Geoids however they have slightly unequal yardstick. In astrogeodesy one defines it therefore no longer than smooth line, but by its common “astronomical length “. The irregularities (to approximately 1km right/to the left of the middle Meridianebene) come from local and regional characteristics of the earth body and leave themselves by Schwereanomalien and/or. Lotabweichungen model.

For instance 10-10-mal more largely are these deviations between the geometrical and physical definition on the giant planet Jupiter (“jovigrafische” lengthWidth) and also at Mars. The “red planet” is because of its Kleinheit (51% of the Erdradius) hardly flattened, but clearly three-axis.

the size of the terrestrial lengthening and parallels of latitude

as determined above, are the length circles up(idealized) the earth everything equal long, while the radius of the parallels of latitude with the cosine the geographical width removes to Poland (r = R·cosB).

Since all length circles of a ball are great circles, they divide (together with its 180° “counterpart”)the earth in in each case two halves. They do this also on (flattened) the earth ellipsoid, have there certainly the form of ellipses.

The length circles have the “halving” characteristic (and/or. “Length ellipses”) together with the Erdäquator, however as the longest parallel of latitudeon actual earth around 2 parts per thousand is longer: it measures 40,075 km in the sea level, the length circles however only 40,008 km.


as French scientists toward end 18. Century those made, were the definition of the meterEquating the earth extent with 4 x 10 million meters planned. The difference of approximately 8 km to 40.000 km decreases/goes back on inevitable small measuring errors and rusting yardsticks of the two expeditions at that time (honing-lapping country and Peru). That one thatMeter not the spreading, but the length circles to adapt wanted, had above all two reasons:

  1. all parallels of latitude are differently long (see above), the length circles however equivalent long.
  2. is the measurement the geographical width - thus the geodesy in north south direction - totoday more easily feasible than over the geographical length in east west direction. This topic is particularly in geography very much addressed.

see also

The Meterkonvention does not decrease/go back however directly to the measurements in honing-lapping country and Peru, but runs on the measurement of a section of the Meridianquadranten (quarter of a great circle) by Paris. The two astronomers Delambre and Méchain measured the distance of you churchesto Barcelona (approximate 10° width difference) with trigonometric means and determined the width difference with astronomical means. After acceptance over the form of the earth, which was determined in the measurements in Peru and honing-lapping country (equator and north pole near), from it the length left itselfthe entire quadrant compute. It came to systematic measuring errors by Méchain, which were suppressed by it from Pedanterie. See in addition also [Alder, Ken: The measure of the world; Bertelsmann publishing house; Munich 2002]. These errors led finally to the “inaccurate” definition of theMeter standard. Such a thing can happen…


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