Inertial Navigation on Earth... and Beyond

Notes

In the absolutely general case, this problem is unsolvable - but fortunately we don't have to navigate in an arbitrary gravity field. The inertial navigator knows the direction and magnitude of the force opposing gravity (the buoyant force) at the start of the trip quite well - and updates to that direction and magnitude can be calculated from a model of the earth as a rotating oblate spheroid (and deviations from that model can be corrected in part by use of gravity maps).

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