Bulletin géodésique

, Volume 57, Issue 1, pp 374–381

New equations for meridional distance

Authors

  • B. R. Bowring
Article

DOI: 10.1007/BF02520940

Cite this article as:
Bowring, B.R. Bull. Geodesique (1983) 57: 374. doi:10.1007/BF02520940

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.

Notation

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

Copyright information

© Bureau Central de L'Association Internationale de Géodésie 1983