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Wikipedia actually goes into some detail regarding the components of Earth's gravitational force field. In the Wikipedia reference we do not have $J_{m,n}$ for $m>n>0$. Rather this term is broken up into a cosine component $C_n^m$ and a sine component $S_n^m$. This table gives results from one on a series of models called the JGM models, developed by ...


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Does J22 represent the rest of Earth's quadrupole moment? With a more usual notation ldegree, morder, there are the zonal l2m0, tesseral l2m1 and sectoral l2m2 spherical harmonics, but you probably already know. What does J22 look like? What is its shape and symmetry? Here's what I get for l2m2: For comparison, here's what I get for your "acceleration ...


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