My explorers will be using a torsion balance to weigh their new planet, which has no satellite, no magnetic field, and has a perpetual cloud cover. Is there a way to also use a torsion beam to determine the axis of rotation?
My assumption is that it could by "guessing" latitudinal and longitudinal orientation at 90° angles. Because the two attracting weights have three forces acting on them, and when the beam is aligned latitudinally, the force vector from centrifugal acceleration is working in opposite angles on the two weights relative to the beam center, except at the equator and the geographic poles. The beam aligned longitudinally will always have exactly the same centrifugal force vector on them, except at the geographic poles where they would be opposite. And if the weights are aligned vertically, they have different angular velocities. It would seem that in some arrangement or combination, the difference between the centrifugal force vector could be used to indicate the planet's axis of rotation and thereby point to the geographic poles.
I am not interested in alternatives to a torsion balance, this is the tool that they have.
Please let me know if there is any test or series of tests which can be done with a torsion balance that would allow the determination of their planet's axis of rotation.