(49g 50g) Theoretical Earth gravity g = g(latitude, height), WGS84, GRS80/67

[Gil]

New version 12b

Minor changes ("nice to have"),
above all relative to gE (g at Equator), gE.STR, gP (g at Pole), gP.STR, k and k.STR values in GRS80 and WGS84 directory.

I'm particularly indebted to Charles Karney for his patience and insight regarding some of the formulae and results in relation to the above and to the topic in general.

Version 11f

With latitude and height h, calculates automatically
g2C67 g8C67 gS67 g2C80 g8C80 gS80 gS84 gSFR g±SFR gClFR.

g 2C67: g
2C67: 
g
ravity result
g
2
C67: 
2
nd order appro
g2
C
67: 
C
hebyshev
g2C
67
: GRS
67

g
8
C80: 
8
th order appro
g8C
80
: GRS
80 ±S S
modif

g
S
84 : 
S
omigliana
gS
84 
: WGS
84 
g
µ
:g
Mean

g
FR(EE)
:g
your FREE 
ellips
Cl : closed form for g calculation, without having to introduce gE / GP (self calculated)

As previously, you can calculate your own FREE ellipsoid, changing the values of GM w f a in FREE Dir (no need to look for g at Equator or at Pole).
Two methods automatically calculated : closed form or modified Somigliana's.

J2.CAL: is to get a close value of J2 in GRS67 WGS84 and FREE.
It is not used, however, to further calculations (seemingly to many rounding intermediate errors).

F.CAL: is to get a close value of f in WGS80.
It is not used, however, to further calculations (seemingly to many rounding intermediate errors).
Only f and f.STR values (more accurate) are used instead for further calculations.

Many self-explaining NOTES at the end of each directory.