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Arc measurement,^[1] sometimes degree measurement^[2] (German: Gradmessung),^[3] is the astrogeodetic technique of determining of the radius of Earth – more specifically, the local Earth radius of curvature of the figure of the Earth – by relating the latitude difference (sometimes also the longitude difference) and the geographic distance (arc length) surveyed between two locations on Earth's surface. The most common variant involves only astronomical latitudes and the meridian arc length and is called meridian arc measurement; other variants may involve only astronomical longitude (parallel arc measurement) or both geographic coordinates (oblique arc measurement).^[1] Arc measurement campaigns in Europe were the precursors to the International Association of Geodesy (IAG).^[4]

History

The first known arc measurement was performed by Eratosthenes (240 BC) between Alexandria and Syene in what is now Egypt, determining the radius of the Earth with remarkable correctness. The French physician Jean Fernel measured the arc in 1528. The Dutch geodesist Snellius (~1620) repeated the experiment between Alkmaar and Bergen op Zoom using more modern geodetic instrumentation (Snellius' triangulation).

Later arc measurements aimed at determining the flattening of the Earth ellipsoid by measuring at different geographic latitudes. The first of these was the French Geodesic Mission, commissioned by the French Academy of Sciences in 1735–1738, involving measurement expeditions to Lapland (Maupertuis et al.) and Peru (Pierre Bouguer et al.).

Struve measured a geodetic control network via triangulation between the Arctic Sea and the Black Sea, the Struve Geodetic Arc. Bessel compiled several meridian arcs, to compute the famous Bessel ellipsoid (1841).

Nowadays, the method is replaced by worldwide geodetic networks and by satellite geodesy.

Other instances

Determination

Assume the astronomic latitudes of two endpoints, $\phi _{s}$ (standpoint) and $\phi _{f}$ (forepoint), are precisely determined by astrogeodesy, observing the zenith distances of sufficient numbers of stars (meridian altitude method). The radius of curvature at the midpoint of the meridian arc can then be calculated from:

R={\frac {{\mathit {\Delta }}'}{\vert \phi _{s}-\phi _{f}\vert }}

where ${\mathit {\Delta }}'$ is the arc length on mean sea level (MSL).

High precision land surveys can be used to determine the distance between two places at nearly the same longitude by measuring a baseline and a triangulation network linking fixed points. The meridian distance ${\mathit {\Delta }}$ from one end point to a fictitious point at the same latitude as the second end point is then calculated by trigonometry. The surface distance ${\mathit {\Delta }}$ is reduced to the corresponding distance at MSL, ${\mathit {\Delta }}'$ (see: Geographical distance#Altitude reduction).

Two arc measurements are different latitudinal bands serve to determine Earth's flattening.

References

^ ^a ^b Torge, W.; Müller, J. (2012). Geodesy. De Gruyter Textbook. De Gruyter. p. 5. ISBN 978-3-11-025000-8. Retrieved 2021-05-02.
^ Jordan, W., & Eggert, O. (1962). Jordan's Handbook of Geodesy, Vol. 1. Zenodo. http://doi.org/10.5281/zenodo.35314
^ Torge, W. (2008). Geodäsie. De Gruyter Lehrbuch (in German). De Gruyter. p. 5. ISBN 978-3-11-019817-1. Retrieved 2021-05-02.
^ Torge, Wolfgang (2015). "From a Regional Project to an International Organization: The "Baeyer-Helmert-Era" of the International Association of Geodesy 1862–1916". IAG 150 Years. International Association of Geodesy Symposia. Vol. 143. Springer, Cham. pp. 3–18. doi:10.1007/1345_2015_42. ISBN 978-3-319-24603-1.

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[Torge2012-1] Torge, W.; Müller, J. (2012). Geodesy. De Gruyter Textbook. De Gruyter. p. 5. ISBN 978-3-11-025000-8. Retrieved 2021-05-02.

[2] Jordan, W., & Eggert, O. (1962). Jordan's Handbook of Geodesy, Vol. 1. Zenodo. http://doi.org/10.5281/zenodo.35314

[Torge_2008_p._5-3] Torge, W. (2008). Geodäsie. De Gruyter Lehrbuch (in German). De Gruyter. p. 5. ISBN 978-3-11-019817-1. Retrieved 2021-05-02.

[4] Torge, Wolfgang (2015). "From a Regional Project to an International Organization: The "Baeyer-Helmert-Era" of the International Association of Geodesy 1862–1916". IAG 150 Years. International Association of Geodesy Symposia. Vol. 143. Springer, Cham. pp. 3–18. doi:10.1007/1345_2015_42. ISBN 978-3-319-24603-1.

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@@ Line 3: / Line 3: @@
 '''Arc measurement''',<ref name="Torge2012">{{cite book | last1=Torge | first1=W. | last2=Müller | first2=J. | title=Geodesy | publisher=De Gruyter | series=De Gruyter Textbook | year=2012 | isbn=978-3-11-025000-8 | url=https://books.google.com/books?id=RcfmBQAAQBAJ&pg=PA6 | access-date=2021-05-02 | page=5}}</ref> sometimes '''degree measurement'''<ref>[[Wilhelm Jordan (geodesist)|Jordan, W.]], & Eggert, O. (1962). Jordan's Handbook of Geodesy, Vol. 1. Zenodo. http://doi.org/10.5281/zenodo.35314</ref> ({{lang-de|Gradmessung}}),<ref name="Torge 2008 p. 5">{{cite book | last=Torge | first=W. | title=Geodäsie | publisher=De Gruyter | series=De Gruyter Lehrbuch | year=2008 | isbn=978-3-11-019817-1 | url=https://books.google.com/books?id=lsO2uz_5euIC&pg=PA5 | language=de | access-date=2021-05-02 | page=5}}</ref> is the [[astrogeodetic]] technique of determining of the [[radius of Earth]] – more specifically, the local [[Earth radius of curvature]] of the [[figure of the Earth]] – by relating the [[latitude]] difference (sometimes also the [[longitude]] difference) and the [[geographic distance]] ([[arc length]]) [[Surveying|surveyed]] between two locations on Earth's surface. The most common variant involves only [[astronomical latitude]]s and the [[meridian arc]] length and is called ''meridian arc measurement''; other variants may involve only [[astronomical longitude]] (''[[parallel of latitude|parallel]] arc measurement'') or both [[geographic coordinates]] (''oblique arc measurement'').<ref name="Torge2012"/>
+Arc measurement campaigns in Europe were the precursors to the [[International Association of Geodesy]] (IAG).<ref>{{Cite book|title=IAG 150 Years|volume = 143|last=Torge|first=Wolfgang|date=2015|publisher=Springer, Cham|pages=3–18|language=en|doi=10.1007/1345_2015_42|chapter = From a Regional Project to an International Organization: The "Baeyer-Helmert-Era" of the International Association of Geodesy 1862–1916|series = International Association of Geodesy Symposia|isbn = 978-3-319-24603-1}}</ref>
 ==History==

Revision as of 01:11, 3 January 2022

History

Other instances

Determination

See also

References