= Solution
Rotation rate, oblateness and measured external gravitational multipoles provide constraints beyond <mass> and <radius>; spin-axis precession/nutation and satellite dynamics can add moment-related information. For a giant planet the deep rotation rate and <hydrostatic approximation> matter. These measurements require an interior model or supplementary constraints for an accurate moment: a <spherically symmetric> body's exterior monopole alone cannot reveal its radial <density> distribution. An exact moment cannot generally be inferred just by labeling a measured $J_2$ as $C$.
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