Reference Ellipsoid and the Geodetic Coordinate System - Geodesy: Introduction to Geodetic Datum and Geodetic Systems - page 172

1 1

1

e 0 2

1 e 2 ﾼ

e 0 2 ,1

þ ﾼ

e 2 ,

1 þ

e 0 2 e 2 ð 5 : 13 Þ

e 0 2 , e 0 2

e 2

ﾼ ﾼ

e 2 , 1

1 þ

p

1 e

p

e 0 , e 0 e 2 e 02 e ﾼ ﾼ 1 þ :

Relationship Between a and c

It follows from ( 5.9 ) and ( 5.11 ) that:

q

1 c

p

e 0 2 a ﾼ 1 e 2 , c ﾼ a þ : ð 5 : 14 Þ

Relationship Between f and e

From ( 5.9 ) and ( 5.11 ) one also obtains:

p

1 , e 2 f 2 f ﾼ 1 e 2 ﾼ 2f : ð5:15Þ

Relationship Between W and V

From ( 5.10 ) one gets:

e 0 2 e 0 2 cos 2 B

1

ﾼ

V 2

1 þ

W 2 e 2 sin 2 B cos 2 B ﾼ 1 ﾼ 1 1 ﾼ

e 0 2 : e 0 2 e 0 2

1 þ þ 1 þ

Hence:

q

1

V

p

e 0 2 e 2

W ﾼ 1 , and V ﾼ W þ : ð 5 : 16 Þ

The above parameters, signs, and basic expressions of relationship will always
be used hereafter in the derivations of formulae.