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

[Gil]

To check,
the paper variables of Geodetic Reference System 1980, by H.Moritz, should be taken, instead of the simplifications given in Wikipedia "Theorical Gravity", Chinese page.

So

j.e =
'GM/(a*b)*(1-m-m/6*ƒé²*(q0´/q0))'
9.78032533482, from the above formulae
9.7803253359 official
—> almost equal value

j.p =
'GM/(a*a)*(1+m/3*ƒé²*(q0´/q0))'
9.83218494001, from the above formulae
9.8321849378, official
—> almost equal value!

With
ƒé² = sqrt (é²) =e'

And:

q0´ =
'3*(1+1/é²)*(1-1/ƒé²*ATAN(ƒé²))-1' .00268804118

q0 =
'((1+3/é²)*ATAN(ƒé²)-3/ƒé²)/2'
.00007334625

é² =
'(a*a-b*b)/(b*b)'
6.73949674208E-3

GM =
3.986004418E14

m =
'w*w*a*a*b/GM'
3.44978650683E-3

w =
.00007292115
a 6378137

a =
6378137

b =
'a-a/298.257223563'
6356752.31425

The differences are now quite small, due to the roundings of the calculator.

Regards,
Gil