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New equations for meridional distance

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Abstract

A simple equation to determine the distance on a meridian is developed using complex numbers. Very great accuracy is obtainable. Inverse and other forms are also presented.

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Abbreviations

a, b:

major, minor semiaxes of meridian ellipse

n:

(a-b)/(a+b)

A:

a(1+1/8n2)2/(1+n)

B:

9(1−3/8n2). k=−2/13B

B1 :

1−3/8n2

C:

1−9/16n2

E1, E2 :

errors. See (3) and (16)

F, G, H:

See (5)

M:

meridional distance from the equator

θ:

M/A

ϕ:

geodetic latitude

u:

parametric latitude

x, y:

Cartesian or complex number components

r, a:

polar representation

i:

(−1)1/2

Reference

  1. New Geodetic Tables for Clarke's Figure of 1880 with Transformations to Madrid 1924 and Other Figures. R.G.S. Technical Series No. 4. London 1927. p.x.

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Authors and Affiliations

  1. 9A The Shrubbery, Hook Road, KT6 5BJ, Surbiton, Surrey, England

    B. R. Bowring

Authors
  1. B. R. Bowring
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Bowring, B.R. New equations for meridional distance. Bull. Geodesique 57, 374–381 (1983). https://doi.org/10.1007/BF02520940

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  • DOI: https://doi.org/10.1007/BF02520940

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