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So, What is Actually the Distance from the Equator to the Pole? – Overview of the Meridian Distance Approximations

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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.
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  • Gdynia Maritime University, Gdynia, Poland
Bibliografia
  • [1] Adams, O.S., 1921. Latitude Developments Connected with Geodesy and Cartography. Washington, United States Coast and Geodetic Survey, Special Publication No. 67, p. 132.
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  • [11] Deakin, R.E., Hunter, M.N., 2010. Geometric Geodesy, Part A. School of Mathematical & Geospatial Science, RNIT University, Melbourne, Australia, January.
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  • [15] Karney, C.F.F., 2011. Geodesics on an ellipsoid of revolution. SRI International, Princeton, NJ, USA, 7 February, p. 29 -http://arxiv.org/pdf/1102.1215v1.pdf.
  • [16] Karney, C.F.F., 2013. Algorithms for geodesics. Journal of Geodesy, January, Volume 87, Issue 1, p. 43‐55.
  • [17] Kawase, K., 2011. A General Formula for Calculating Meridian Arc Length and its Application to Coordinate Conversion in the Gauss‐Krüger Projection. Bulletin of the Geospatial Information Authority of Japan, No. 59, pp. 1–13.
  • [18] Michon, G.P., 2012. Perimeter of an Ellipse. Final Answers. www.numericana.com/answer/ellipse.htm
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  • [20] Pallikaris, A., Tsoulos, L., Paradissis, D., 2009. New meridian arc formulas for sailing calculations in GIS, International Hydrographic Review.
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  • [22] Phythian, J.E., Williams, R., 1985. Cubic spline approximation to an integral function. Bulletin of the Institute of Mathematics and Its Applications, No. 21, p. 130‐131.
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  • [27] Weintrit, A. 2009. The Electronic Chart Display and Information System (ECDIS). An Operational Handbook. A Balkema Book. CRC Press, Taylor & Francis Group, Boca Raton – London ‐ New York ‐ Leiden, p. 1101.
  • [28] Weintrit, A., 2010. Jednostki miar wczoraj i dziś. Przegląd systemów miar i wag na lądzie i na morzu (in Polish) Akademia Morska w Gdyni, Gdynia.
  • [29] Weintrit, A., Kopacz, P., 2011. A Novel Approach to Loxodrome (Rhumb Line), Orthodrome (Great Circle) and Geodesic Line in ECDIS and Navigation in General. TransNav ‐ International Journal on Marine Navigation and Safety of Sea Transportation, Vol. 5, No. 4, p. 507‐517.
  • [30] Weintrit, A., Kopacz, P., 2012. On Computational Algorithms Implemented in Marine Navigation Electronic Devices and Systems. Annual of Navigation, No 19/2012, Part 2, Gdynia, p. 171‐182.
  • [31] Williams, E. 2002. Navigation on the spheroidal Earth,
  • [32] http://williams.best.vwh.net/ellipsoid/ellipsoid.html. Williams, R., 1996. The Great Ellipse on the surface of the spheroid, The Journal of Navigation, Vol. 49, No. 2, p. 229‐234.
Typ dokumentu
Bibliografia
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