Gravity g WGS84 84 at pole
09-28-2021, 03:21 PM
Post: #4
 Gil Member Posts: 202 Joined: Oct 2019
RE: Gravity g WGS84 84 at pole
RE: HP49-50G : —>g gravity calculation = g(latitude, height) with WGS84
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*é²*(q0´/q0))'
9.78032533482, from the above formulae
9.7803253359 official
—> almost equal value

j.p =
'GM/(a*a)*(1+m/3*é²*(q0´/q0))'
9.83218494001, from the above formulae
9.8321849378, official
—> almost equal value!

With
é² = sqrt (é²) =e'

And:

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

q0 =
'((1+3/é²)*ATAN(é²)-3/é²)/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
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 Messages In This Thread Gravity g WGS84 84 at pole - Gil - 09-28-2021, 08:53 AM RE: Gravity g WGS84 84 at pole - Albert Chan - 09-28-2021, 10:48 AM RE: Gravity g WGS84 84 at pole - Gil - 09-28-2021, 11:16 AM RE: Gravity g WGS84 84 at pole - Gil - 09-28-2021 03:21 PM

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