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I found contradictory sources for what's considered in geoid and can't decide on either side because the sources seem about equally reliable. In particular, the question I'm asking is whether acceleration or acceleration due to earth's gravitational force is the same for every point on the surface geoid defines (centrifugal force being considered in the first case but not in the second one).

Furthermore: Let's consider a position http://quicklatex.com/cache3/b2/ql_4f7c7ba7a94c1766ba4e245f67c10db2_l3.png in spherical coordinates. Is there a functional relation http://quicklatex.com/cache3/df/ql_fc5885a7200cf4c05395096db67d04df_l3.png mapping a position in spherical coordinates without the radius to the radius? There should be for geoid to make sense but given earth not being made of a homogeneous material, I can't really imagine there to be a perfect mapping just considering either acceleration or acceleration due to earth's gravitational force. Are the values of http://quicklatex.com/cache3/5b/ql_dbe323ab303f7a84fac2f523dad32f5b_l3.png required to be continuous? Because then it's obvious it works.

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