Reference Ellipsoid and the Geodetic Coordinate System - Geodesy: Introduction to Geodetic Datum and Geodetic Systems - page 187

Fig. 5.12 Endpoint trace of
N

Fig. 5.13 Endpoint trace of
M

Table 5.3 The law of changes in the radius of curvature of the meridian (M) with latitude (B)
B M Note

8
<
:

B ﾼ 0º a 1 e 2 ð Þ At the equator, M is less than the equatorial radius a

c

M 0 ﾼ

3
2

1 þ e 0 2

0º < B < 90º a(1 e 2 ) < M < cMincreases with the increasing latitude, its value ranging
from a(1 e 2 )toc

8
<
:

a
1

B ﾼ 90º At the poles, M coincides with the polar radius of curvature

c

p

M 90 ﾼ e 2

c

arbitrary direction varies with the azimuth A with a cycle of 180 . Meanwhile, in
( 5.30 ), the only term related to the direction is cos 2 A and therefore the radii of
curvature R A at a given point in the direction of A, (180 A), (180 + A),

(360 A) are the same. Hence, R A changes over a cycle period of 180 and is

symmetrical with respect to the meridian and the prime vertical.