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

[Gil]

Note, please, that calculations here with Li & Götze closed formulae do not match (could not match) the calculations by Charles Karney with full theory according to Heiskanen & Moritz.

WGS84
According to Karney:
"gammay and gammaz are the
northerly and up components of gamma (up is in the direction of the normal to the WGS84 ellipsoid). gamma is the magnitude of the gravity.

As expected these results differ from L+G's results for
gamma_u (because this is neither the up component of the gravity nor its magnitude).

lat h gammay gammaz gamma
20 10000 -0.00005231628077462272 -9.75556773962467229537
9.75556773976495081667

lat h gammay gammaz gamma
80 5000 -0.00001391201648793046 -9.81521493778272672782
9.81521493779258612489."

To be compared with Li & Götze in Maxima
(& with HP49-50G):
9.755567739391774710519363610080945073955567777773578831194488706435195066202777​754390572703114008923
(with HP50G: 9.7555677283)

Li & Götze in Maxima (& with HP49-50G):
9.815214937766250073333365482033892183981119210801868284213419088307958628663215​851806608387826859838b0
(9.81521495521)