I've implemented the Earth harmonics calculation in JGM-3 model, using the coefficients from here
2 0 -0.10826360229840e-02 0.0
2 1 -0.24140000522221e-09 0.15430999737844e-08
2 2 0.15745360427672e-05 -0.90386807301869e-06
3 0 0.25324353457544e-05 0.0
Now, I want to switch to EGM2008, the coefficients are taken from here (Tide-free).
2 0 -0.484165143790815e-03 0.000000000000000e+00
2 1 -0.206615509074176e-09 0.138441389137979e-08
2 2 0.243938357328313e-05 -0.140027370385934e-05
3 0 0.957161207093473e-06 0.000000000000000e+00
There is a major difference. Probably, I should make some operations on the coefficients? For example, multiply $C_{20}$ by $\sqrt{5}$?
Multiplied all coefficients of EGM2008 by $\sqrt{2*degree+1}$, got
2 0 -1.082626173852220E-03 0.0000000000000E+00
2 1 -4.6200632349558E-10 3.0956435701202E-09
2 2 5.4546274930574E-06 -3.1311071889349E-06
3 0 2.5324105185677E-06 0.0000000000000E+00
Especially for $C_{21}$ and $C_{22}$ the difference is still major.
Extra
To calculate the Earth gravity potential in JGM-3, the equation was used: $U_{har}=\frac{\mu}{r}[1+\sum_{i=2}^d\sum_{j=0}^o (\frac{R_{eq}}{r})^iP_{ij}(\sin\phi)(S_{ij}\sin{j\lambda}+C_{ij}\cos{j\lambda})]$,
As you see, the argument of Lejendre polynom $P_{ij}$ is $sin\phi$.
However, here for EGM2008 it's said to use $cos\phi$. Is it specific for EGM2008 model?
0.15e-5
, but in EGM-2008 it's0.54E-05
. So major difference? May be it depends on order also? Added the coefficients to the question. $\endgroup$