Would a torsion balance be able to determine the poles of a planet which has no magnetic field?

Question

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.

Answer 1

This is eminently doable, because gravity varies as you describe.

The gravity of Earth varies slightly by location, and you may have seen images like the top image from the Wikipedia article above. Note that the scale of this figure's legend goes from -50 to +50 milligals, where a "gal" is a totally unnecessary synonym for m/s^2. But also notice that such gravity variations are made relative to a "reference ellipsoid" that takes the bulge of the Earth's equator and the centrifugal force into account. By contrast, the gravity of Earth ranges from "9.780 m/s2 at the Equator to about 9.832 m/s2 at the poles" to quote Wikipedia's figures. The difference is 0.052 m/s, which is roughly comparable to the other deviations.

A torsion balance was used, even a century ago, to prospect for underground ores. So you can certainly make the measurements with sufficient sensitivity. Distinguishing between local geographic influences and latitudinal effects simply takes a lot of measurements.

Answer 2

No. A torsion balance is entirely the wrong tool for that purpose.

A simple stick in the ground will suffice. Or, if for some reason tracking shadows isn't your thing, a gyrocompass will do it.

Incidentally, even if a planet has a magnetic field, there is no guarantee that a magnetic compass will point reasonably close to the rotational poles like they do on Earth.

Answer 3

Is there a way to use a torsion beam to determine the axis of rotation?

You will need to suspend the balls from a great spaceship gently accelerating away from the planet. Then you could measure the torsion relative to the movement on the planet and record F1 and F3 as variables of the same function.

F2 is negligible and can be left out.

This is what it might look like:

Answer 4

Let's see, you want to find the North pole of a planet that has no magnetic field and thus, no magnetic North pole... Huh?

Whatever, let's say you want to find the geographic pole—the place from where your planet's vector of rotation (w rad/s) exits. If you initially placed your torsion balance mildly close to the position East-West, you wouldn't be able to tell.

It's better to use a Foucault pendulum if you must use the centripetal force.

If you want to do it the hard way:

• Just make a Foucault pendulum and see in which way it turns. That way you could determine in which hemisphere you are, if it rotates clockwise, then you are on the northen hemisphere.

• Maybe you could measure how hard is the "centripetal" force with some maths and the foucault pendulum, this way you could calculate your latitude.

• Also, you can do the experiment of waiting for the shortest length of shade of a stick in the ground to determine which is the North-South axis and which way is the closest pole (where the shortest shade pointed).

• Together these two experiments will tell you in which hemisphere you are and in which way is the closest pole.

If you want to do it the lazy way:

• Stick a stick in the ground, wait for the shortest shade to pass.
• Place yourself looking to the way the shade pointed and extend your arms to the sides.
• If the Sun is now moving towards your left side, you are on the North Hemisphere and you are looking to the North.
• Else, you are on the South Hemisphere and you are looking to the South.

Because the Sun always sets on the West.

Even if it's always cloudy, you should be able to tell which way is the sun if you made a little hole in the wall of a dark room. Wherever the spot of light ends is the oposite direction of where the sun is.

Or you could use a parabolic mirror or an helliograph: