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

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. http://www.transnav.eu the International Journal on Marine Navigation and Safety of Sea Transportation Volume 7 Number 2

Comparison of main geometric characteristics of deformed sphere and standard spheroid

“…Let us identify the semi-major axis a and the quarter-meridian length (defined as the arc length along the meridian between the Equator and North Pole) m P of the spheroid ( 7) with the equatorial radius R and the quarter-meridian length m λ of the λ -sphere, i.e., R ≡ a and m λ ≡ m P , where (see, e.g., [7,8,15])…”