The Struve Geodetic Arc Index
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So, What Is Actually the Distance from the Equator to the Pole? – Overview of the Meridian Distance Approximations
the International Journal Volume 7 on Marine Navigation Number 2 http://www.transnav.eu and Safety of Sea Transportation June 2013 DOI: 10.12716/1001.07.02.14 So, What is Actually the Distance from the Equator to the Pole? – Overview of the Meridian Distance Approximations A. Weintrit Gdynia Maritime University, Gdynia, Poland ABSTRACT: In the paper the author presents overview of the meridian distance approximations. He would like to find the answer for the question what is actually the distance from the equator to the pole ‐ the polar distance. In spite of appearances this is not such a simple question. The problem of determining the polar distance is a great opportunity to demonstrate the multitude of possible solutions in common use. At the beginning of the paper the author discusses some approximations and a few exact expressions (infinite sums) to calculate perimeter and quadrant of an ellipse, he presents convenient measurement units of the distance on the surface of the Earth, existing methods for the solution of the great circle and great elliptic sailing, and in the end he analyses and compares geodetic formulas for the meridian arc length. 1 INTRODUCTION navigational receivers and navigational systems (ECDIS and ECS [Weintrit, 2009]) suggest the Unfortunately, from the early days of the necessity of a thorough examination, modification, development of the basic navigational software built verification and unification of the issue of sailing into satellite navigational receivers and later into calculations for navigational systems and receivers. electronic chart systems, it has been noted that for the The problem of determining the distance from the sake of simplicity and a number of other, often equator to the pole is a great opportunity to incomprehensible reasons, this navigational software demonstrate the multitude of possible solutions in is often based on the simple methods of limited common use. -
From Lacaille to Gill and the Start of the Arc of the 30 Meridian
From LaCaille to Gill and the start of the Arc of the 30th Meridian Jim R. SMITH, United Kingdom Key words: LaCaille. Maclear. Gill. Meridian Arcs. 30th Arc. SUMMARY If one looks at a map of European arcs of meridian and parallel at the beginning of the 20th century there will be seen to be a plethora them. Turning to Africa there was the complete opposite. Other than the arcs of Eratosthenes (c 300 BC) and the short arcs by LaCaille (1752) and Maclear (1841-48) the continent was empty. It was in 1879 that David Gill had the idea for a Cape to Cairo meridian arc but 1954 before it was completed. This presentation summaries the work of LaCaille and Maclear and then concentrates on a description of the 30th Meridian Arc in East Africa. The only other comparable arcs at the time were that through the centre of India by Lambton and Everest observed between 1800 and 1843; the Struve arc of 1816 to 1852 and the various arcs in France during the 18th century. The usefulness of such arcs was highlighted in 2005 with the inscription by UNESCO of the Struve Geodetic Arc on the World Heritage Monument list. A practical extension to the Struve Arc Monument is the 30th Meridian Arc since there is a connection between the two. At an ICA Symposium in Cape Town, 2003, Lindsay Braun gave a presentation that detailed the political machinations of the history of the 30th Arc; here it is hoped to fill in other aspects of this work including some facts and figures since that is what surveyors thrive upon. -
Struve Geodetic Arc Joins World Heritage List
ARTICLE Struve Geodetic Arc Joins World Heritage List 15th July, Durban, South Africa The World Heritage Committee chaired by Themba Wakashe, South Africa’s deputy director-general for Heritage and National Archives has inscribed seventeen cultural sites on the UNESCO World Heritage List. The nominations took place on 15th July at a meeting in Durban, South Africa. The World Heritage List now numbers 812 sites in total, including 628 cultural, 160 natural and 24 mixed sites, in 137 States. Bahrain, the Republic of Moldova and Bosnia and Herzegovina enter the List for the first time. The sites inscribed during the current session of the World Heritage Committee include three transboundary sites and extensions to six sites that were already on the List. The Struve Geodetic Arc is the first survey-site on the list. The countries hosting the Struve Geodetic Arc are Belarus, Estonia, Finland, Latvia, Lithuania, Norway, the Republic of Moldova, the Russian Federation, Sweden and Ukraine. The Struve Geo- detic Arc is a chain of survey triangulations stretching from Hammerfest in Norway to the Black Sea, through ten countries and over 2,820km. These are the points of a survey carried out between 1816 and 1855 by the astronomer Friedrich Georg Wilhelm Struve and represent the first accurate measuring of a long segment of a meridian. This helped establish the exact size and shape of our planet and marked an important step in the development of earth sciences and topographic mapping. It is an extraordinary example of scientific collaboration among scientists from different countries, and of collaboration between monarchs, for a scientific cause. -
Geodesy Methods Over Time
Geodesy methods over time GISC3325 - Lecture 4 Astronomic Latitude/Longitude • Given knowledge of the positions of an astronomic body e.g. Sun or Polaris and our time we can determine our location in terms of astronomic latitude and longitude. US Meridian Triangulation This map shows the first project undertaken by the founding Superintendent of the Survey of the Coast Ferdinand Hassler. Triangulation • Method of indirect measurement. • Angles measured at all nodes. • Scaled provided by one or more precisely measured base lines. • First attributed to Gemma Frisius in the 16th century in the Netherlands. Early surveying instruments Left is a Quadrant for angle measurements, below is how baseline lengths were measured. A non-spherical Earth • Willebrod Snell van Royen (Snellius) did the first triangulation project for the purpose of determining the radius of the earth from measurement of a meridian arc. • Snellius was also credited with the law of refraction and incidence in optics. • He also devised the solution of the resection problem. At point P observations are made to known points A, B and C. We solve for P. Jean Picard’s Meridian Arc • Measured meridian arc through Paris between Malvoisine and Amiens using triangulation network. • First to use a telescope with cross hairs as part of the quadrant. • Value obtained used by Newton to verify his law of gravitation. Ellipsoid Earth Model • On an expedition J.D. Cassini discovered that a one-second pendulum regulated at Paris needed to be shortened to regain a one-second oscillation. • Pendulum measurements are effected by gravity! Newton • Newton used measurements of Picard and Halley and the laws of gravitation to postulate a rotational ellipsoid as the equilibrium figure for a homogeneous, fluid, rotating Earth. -
Världsarvslistan
http://wimnell.com/omr91b.pdf • Tipasa • Kasbah of Algiers Världsarvslistan Andorra http://whc.unesco.org/en/list/ • Madriu-Perafita-Claror Valley Argentina The World Heritage List includes 936 properties forming part of the • Los Glaciares # cultural and natural heritage which the World Heritage Committee • Jesuit Missions of the Guaranis: San Ignacio Mini, Santa Ana, considers as having outstanding universal value. Nuestra Señora de Loreto and Santa Maria Mayor (Argentina), Ruins of Sao Miguel das Missoes (Brazil) * These include 725 cultural , 183 natural and 28 mixed properties in • Iguazu National Park 153 States Parties. As of November 2011, 188 States Parties have • Cueva de las Manos, Río Pinturas ratified the World Heritage Convention. • Península Valdés • Ischigualasto / Talampaya Natural Parks Afghanistan • Jesuit Block and Estancias of Córdoba • Quebrada de Humahuaca • Minaret and Archaeological Remains of Jam Armenia • Cultural Landscape and Archaeological Remains of the Bamiyan Valley • Monasteries of Haghpat and Sanahin Albania • Cathedral and Churches of Echmiatsin and the Archaeological Site of Zvartnots • Butrint • Monastery of Geghard and the Upper Azat Valley • Historic Centres of Berat and Gjirokastra Australia Algeria • Great Barrier Reef • Al Qal'a of Beni Hammad • Kakadu National Park • Djémila • Willandra Lakes Region • M'Zab Valley • Lord Howe Island Group • Tassili n'Ajjer # • Tasmanian Wilderness • Timgad • Gondwana Rainforests of Australia 1 • Uluru-Kata Tjuta National Park 2 • Qal’at al-Bahrain – Ancient Harbour -
The Struve Geodetic Arc and Its Possible Connections to the Arc of the 30Th Meridian in Africa
The Struve Geodetic Arc and Its Possible Connections to the Arc of the 30th Meridian in Africa James R SMITH, United Kingdom Keywords. Arc, Struve, 30th Arc, UNESCO SUMMARY This paper discusses the possible connections between the Struve Geodetic Arc and the Arc of the 39th Meridian in East Africa. Was the proposal by Otto Struve in 1868 carried out? If so, where are the results, if not, why not? Brief mention is made of the various later connections from the Struve Arc in Belarus to North Africa and hence a join in Egypt to the Arc of the 30th Meridian. Workshop – History of Surveying and Measurement 1/10 WSHS1 – History of Surveying and Measurement James Smith WSHS1.3 The Struve Geodetic Arc and Its Possible Connections to the Arc of the 30th Meridian in AfricaFIG Working Week 2004 Athens, Greece, May 22-27, 2004 The Struve Geodetic Arc and Its Possible Connections to the Arc of the 30th Meridian in Africa James R SMITH. United Kingdom 1. INTRODUCTION The Struve Geodetic Arc was from near North Cape in Northern Norway to near Ismail on the Black Sea was observed under the supervision of F G W Struve and Carl F de Tenner between 1816 and 1852. The Arc of the 30th Meridian from near Port Elizabeth in S Africa to near Cairo in Egypt was initiated by David Gill in South Africa in 1879 and was finally completed with the last section in the Sudan in 1954. The Struve Geodetic Arc has recently been submitted to UNESCO for possible recognition as a World Heritage Monument. -
Great Elliptic Arc Distance1
GREAT ELLIPTIC ARC DISTANCE1 R. E. Deakin School of Mathematical & Geospatial Sciences, RMIT University, GPO Box 2476V, MELBOURNE VIC 3001, AUSTRALIA email: [email protected] January 2012 ABSTRACT These notes provide a detailed derivation of series formula for (i) Meridian distance M as a function of latitude φ and the ellipsoid constant eccentricity-squared e2, and φ and the ellipsoid constant third flattening n; (ii) Rectifying latitude µ as functions of φ,e2 and φ,n; and (iii) latitude φ as functions of µ,e2 and µ,n These series can then be used in solving the direct and inverse problems on the ellipsoid (using great elliptic arcs) and are easily obtained using the Computer Algebra System Maxima. In addition, a detailed derivation of the equation for the great elliptic arc on an ellipsoid is provided as well as defining the azimuth and the vertex of a great elliptic. And to assist in the solution of the direct and inverse problems the auxiliary sphere is introduced and equations developed. INTRODUCTION In geodesy, the great elliptic arc between P1 and P2 on the ellipsoid is the curve created by intersecting the ellipsoid with the plane containing P1 , P2 and O (the centre of the ellipsoid) and these planes are great elliptic planes or sections. Figure 1 shows P on the great elliptic arc between P1 and P2 . P is the geocentric latitude of P and P is the longitude of P. There are an infinite number of planes that cut the surface of the ellipsoid and contain the chord PP12 but only one of these will contain the centre O. -
Pskov from Wikipedia, the Free Encyclopedia Coordinates: 57°49′N 28°20′E
Create account Log in Article Talk Read Edit View history Pskov From Wikipedia, the free encyclopedia Coordinates: 57°49′N 28°20′E Pskov (Russian: Псков; IPA: [pskof] ( listen), ancient Russian spelling "Плѣсковъ", Pleskov) is Navigation Pskov (English) a city and the administrative center of Pskov Oblast, Russia, located about 20 kilometers Псков (Russian) Main page (12 mi) east from the Estonian border, on the Velikaya River. Population: 203,279 (2010 [1] Contents Census);[3] 202,780 (2002 Census);[5] 203,789 (1989 Census).[6] - City - Featured content Current events Contents Random article 1 History Donate to Wikipedia 1.1 Early history 1.2 Pskov Republic 1.3 Modern history Interaction 2 Administrative and municipal status Help 3 Landmarks and sights About Wikipedia 4 Climate Community portal 5 Economy Recent changes 6 Notable people Krom (or Kremlin) in Pskov Contact Wikipedia 7 International relations 7.1 Twin towns and sister cities Toolbox 8 References 8.1 Notes What links here 8.2 Sources Related changes 9 External links Upload file Special pages History [edit] Location of Pskov Oblast in Russia Permanent link Page information Data item Early history [edit] Cite this page The name of the city, originally spelled "Pleskov", may be loosely translated as "[the town] of purling waters". Its earliest mention comes in 903, which records that Igor of Kiev married a [citation needed] Print/export local lady, St. Olga. Pskovians sometimes take this year as the city's foundation date, and in 2003 a great jubilee took place to celebrate Pskov's 1,100th anniversary. Create a book Pskov The first prince of Pskov was Vladimir the Great's younger son Sudislav. -
The Meridian Arc Measurement in Peru 1735 – 1745
The Meridian Arc Measurement in Peru 1735 – 1745 Jim R. SMITH, United Kingdom Key words: Peru. Meridian. Arc. Triangulation. ABSTRACT: In the early 18th century the earth was recognised as having some ellipsoidal shape rather than a true sphere. Experts differed as to whether the ellipsoid was flattened at the Poles or the Equator. The French Academy of Sciences decided to settle the argument once and for all by sending one expedition to Lapland- as near to the Pole as possible; and another to Peru- as near to the Equator as possible. The result supported the view held by Newton in England rather than that of the Cassinis in Paris. CONTACT Jim R. Smith, Secretary to International Institution for History of Surveying & Measurement 24 Woodbury Ave, Petersfield Hants GU32 2EE UNITED KINGDOM Tel. & fax + 44 1730 262 619 E-mail: [email protected] Website: http://www.ddl.org/figtree/hsm/index.htm HS4 Surveying and Mapping the Americas – In the Andes of South America 1/12 Jim R. Smith The Meridian Arc Measurement in Peru 1735-1745 FIG XXII International Congress Washington, D.C. USA, April 19-26 2002 THE MERIDIAN ARC MEASUREMENT IN PERU 1735 – 1745 Jim R SMITH, United Kingdom 1. BACKGROUND The story might be said to begin just after the mid 17th century when Jean Richer was sent to Cayenne, S. America, to carry out a range of scientific experiments that included the determination of the length of a seconds pendulum. He returned to Paris convinced that in Cayenne the pendulum needed to be 11 lines (2.8 mm) shorter there than in Paris to keep the same time. -
The History of Geodesy Told Through Maps
The History of Geodesy Told through Maps Prof. Dr. Rahmi Nurhan Çelik & Prof. Dr. Erol KÖKTÜRK 16 th May 2015 Sofia Missionaries in 5000 years With all due respect... 3rd FIG Young Surveyors European Meeting 1 SUMMARIZED CHRONOLOGY 3000 BC : While settling, people were needed who understand geometries for building villages and dividing lands into parts. It is known that Egyptian, Assyrian, Babylonian were realized such surveying techniques. 1700 BC : After floating of Nile river, land surveying were realized to set back to lost fields’ boundaries. (32 cm wide and 5.36 m long first text book “Papyrus Rhind” explain the geometric shapes like circle, triangle, trapezoids, etc. 550+ BC : Thereafter Greeks took important role in surveying. Names in that period are well known by almost everybody in the world. Pythagoras (570–495 BC), Plato (428– 348 BC), Aristotle (384-322 BC), Eratosthenes (275–194 BC), Ptolemy (83–161 BC) 500 BC : Pythagoras thought and proposed that earth is not like a disk, it is round as a sphere 450 BC : Herodotus (484-425 BC), make a World map 350 BC : Aristotle prove Pythagoras’s thesis. 230 BC : Eratosthenes, made a survey in Egypt using sun’s angle of elevation in Alexandria and Syene (now Aswan) in order to calculate Earth circumferences. As a result of that survey he calculated the Earth circumferences about 46.000 km Moreover he also make the map of known World, c. 194 BC. 3rd FIG Young Surveyors European Meeting 2 150 : Ptolemy (AD 90-168) argued that the earth was the center of the universe. -
B10.Pdf (774.2Kb)
Page 1 Coordinates Series B, No. 10 The History of Cartography in a Nutshell Persistent URL for citation: http://purl.oclc.org/ coordinates/b10.pdf Vladimiro Valerio Vladimiro Valerio (e-mail: [email protected]) is full Professor of Projective Geometry at the Date of Publication: 06/03/08 Department of History of Architecture at the University IUAV of Venice. His publications include "Cartography in the Kingdom of Naples During the Early Modern Period" in vol. 3 of The History of Cartography (University of Chicago Press). Abstract This is a very short history of cartography. Notes and links to images are included at the end. Keywords: maps, cartography, history, portolan charts, map projections, Claudius Ptolemy, Gerardus Mercator, Fra Mauro, Peutinger Table, C.F. Cassini de Thury Editor’s Note: About five years ago Professor Valerio was asked to prepare a short article on the history of cartography for a multimedia presentation by the Istituto e Museo di Storia della Scienza of Florence. He was astounded to learn that his article could only be thirteen lines long, but he nonetheless complied. The following is a translation of that article. Most of us are familiar with much longer accounts of this subject, such as the multi-volume History of Cartography being published by the University of Chicago Press, or the single volume edited by James R. Akerman and Robert W. Karrow, Jr., Maps: Finding Our Place in the World (Chicago: University of Page 2 Chicago Press, 2007). But, as the Reader’s Digest has taught us, there are few limits to condensation. Prof. -
Meridian Distance.Pdf
MERIDIAN DISTANCE R.E.Deakin School of Mathematical & Geospatial Sciences, RMIT University, GPO Box 2476V, MELBOURNE, Australia email: [email protected] March 2006 ABSTRACT These notes provide a detailed derivation of the equations for computing meridian distance on an ellipsoid of revolution given ellipsoid parameters and latitude. Computation of meridian distance is a requirement for geodetic calculations on the ellipsoid, in particular, computations to do with conversion of geodetic coordinates φλ, (latitude, longitude) to Universal Transverse Mercator (UTM) projection coordinates E,N (East,North) that are used in Australia for survey coordination. The "opposite" transformation, E,N to φλ, requires latitude given meridian distance and these note show how series equations for meridian distances are "reversed" to give series equations for latitude. The derivation of equations follow methods set out in Lehrbuch Der Geodäsie (Baeschlin, 1948), Handbuch der Vermessungskunde (Jordan/Eggert/Kneissl, 1958), Geometric Geodesy (Rapp, 1982) and Geodesy and Map Projections (Lauf, 1983) and some of the formula derived are used in the Geocentric Datum of Australia Technical Manual (ICSM, 2002) – an on-line reference manual available from Geoscience Australia. An understanding of the methods introduced in the following pages, in particular the solution of elliptic integrals by series expansion and reversion of a series, will give the student an insight into other geodetic calculations. MATLAB functions for computing (i) meridian distance given