Journal of Geodesy

, Volume 73, Issue 11, pp 603–610

Fast transform from geocentric to geodetic coordinates

  • T. Fukushima

DOI: 10.1007/s001900050271

Cite this article as:
Fukushima, T. Journal of Geodesy (1999) 73: 603. doi:10.1007/s001900050271


 A new iterative procedure to transform geocentric rectangular coordinates to geodetic coordinates is derived. The procedure solves a modification of Borkowski's quartic equation by the Newton method from a set of stable starters. The new method runs a little faster than the single application of Bowring's formula, which has been known as the most efficient procedure. The new method is sufficiently precise because the resulting relative error is less than 10−15, and this method is stable in the sense that the iteration converges for all coordinates including the near-geocenter region where Bowring's iterative method diverges and the near-polar axis region where Borkowski's non-iterative method suffers a loss of precision.

Key words. Coordinate transformation Geocentric coordinates Geodetic coordinates Newton method 

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • T. Fukushima
    • 1
  1. 1.National Astronomical Observatory, 2-21-1, Ohsawa, Mitaka, Tokyo 181-8588, Japan e-mail:; Tel.: +81 422 41 3613; Fax: +81 422 41 3793JP

Personalised recommendations