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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.

Torsion Balance force vectors

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.

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    $\begingroup$ This sounds like more of a physics question than a question about building your fictional world. $\endgroup$
    – sphennings
    Aug 15, 2020 at 1:28
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    $\begingroup$ As long as you can see the stars at night, and map their arcs across the sky as the world turns, and know the planet is spherical, and its radius, working out where the poles are is doable with basic trigonometry. $\endgroup$
    – notovny
    Aug 15, 2020 at 1:56
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    $\begingroup$ Real world questions are on-topic so long as they are asked in a worldbuilding context - which this question is. However, the four stream-of-consciousness questions don't make for a high-quality question. Please remember, Vogon, that SE's model is one-specific-question/one-best-answer. Try to keep things focused. Thanks. $\endgroup$ Aug 15, 2020 at 3:42
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    $\begingroup$ @AlexP - this is not earth. How exactly would you observe a star or the sun on a completely cloud-covered planet??? $\endgroup$
    – Vogon Poet
    Aug 15, 2020 at 7:59
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    $\begingroup$ " . . . using a torsion balance to weigh their new planet . . .. Is there a way to also use a torsion beam to determine the axis of rotation??" Are they trying to weigh the planet or are they trying to determine the axis of rotation? $\endgroup$
    – Daron
    Mar 4 at 14:23

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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.

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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.

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    $\begingroup$ Technically this doesn't meet the hard-science mandate because it doesn't explain with the appropriate citations, etc., why "no" is the best answer. Can you explain why the torsion balance is "entirely the wrong tool for that purpose"? $\endgroup$ Aug 15, 2020 at 3:43
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    $\begingroup$ 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. In fact I believe Earth is the only planet with a magnetic field so far with the magnetic poles close to the geographical ones. The gas giants don't even seem to have their magnetic axes intersecting their rotational axes at all. Adding this to the answer could make it more in line with hard-science :) $\endgroup$ Aug 17, 2020 at 0:49
  • $\begingroup$ Would this work with perpetual cloud cover? $\endgroup$
    – Daron
    Mar 4 at 14:54
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    $\begingroup$ @Daron A gyrocompass will. $\endgroup$ Mar 4 at 17:38
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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:

rightangle

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  • $\begingroup$ That would certainly find it if such a ship could ascend smoothly. I’m not sure we could pull that off today. But you are right, the $\Delta$ between F1 and F3 would increase as the beam’s altitude increased. The rocket also must remain on a perfect vertical vector relative to the launch pad. Could a mechanical apparatus - an elevator get enough difference? Maybe set it up on a tall cliff, and measure top and bottom variances? A skyscraper? $\endgroup$
    – Vogon Poet
    Mar 4 at 2:18
  • $\begingroup$ Yes that's exactly what the spaceship has to do. Since a cliff or an elevator are both attached to the planet, you have the same problem as above. All you've really got then is a really long pendulum $\endgroup$
    – Devio52
    Mar 4 at 2:49
  • $\begingroup$ Now two very careful measurements at maybe a 20km altitude difference (mountaintop to valley), the suspended beam will become slightly less level at the higher altitude when oriented longitudinally (due to higher F3), and show no difference at all when aligned latitudinally. Is this the same basic test without moving? $\endgroup$
    – Vogon Poet
    Mar 4 at 3:40
  • $\begingroup$ It would have to be a Foucault Pendulum. Then the explorers could determine the axis and speed of rotation, as long as they know in advance their exact position on the ball $\endgroup$
    – Devio52
    Mar 4 at 13:58
  • $\begingroup$ Hey great picture -- love the rocket! But I can see this totally radical rocket has a window. Couldn't we just look out the window to find the poles? No need for the giant steel testicle apparatus. $\endgroup$
    – Daron
    Mar 4 at 14:26
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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.

Foucault Pendulum

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: Heliograph photo, from ebay

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  • $\begingroup$ I'm pretty sure the question is talking about the geographic North pole, not a magnetic one? Everything that rotates has two poles at the ends of their axial rotation. In the question, there is no visible sunlight (constant cloud cover). $\endgroup$
    – Vogon Poet
    Mar 4 at 17:06
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    $\begingroup$ No, a ball rotating doesn't have a north and a south pole, nor does a cilinder rotating nor does a wheel. $\endgroup$ Mar 4 at 17:18
  • $\begingroup$ Geographic pole is the word we chose to use to describe "the place from where a planet's vector of rotation (w rad/s) exits." But whatever you prefer to call it, it seems you figured it out. $\endgroup$
    – Vogon Poet
    Mar 4 at 17:29

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