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The wikipedia article about frame dragging mentions the following fact about rotational frame dragging:

Another interesting consequence is that, for an object constrained in an equatorial orbit, but not in freefall, it weighs more if orbiting anti-spinward, and less if orbiting spinward. For example, in a suspended equatorial bowling alley, a bowling ball rolled anti-spinward would weigh more than the same ball rolled in a spinward direction. Note, frame dragging will neither accelerate nor slow down the bowling ball in either direction. It is not a "viscosity".

I would like to ask which one of the following situations is being described here, because the wording above is unclear:

1) The bowling ball weighs more in the sense that, if we imagine the suspended bowling alley covered with sensors, they register the ball to be heavier in anti-spinward (and lighter in the spinward) direction, compared to the case of an alley suspended above a non-rotating massive body.

2) The bowling ball weighs more in the sense that one requires more force to roll it in the antispinward direction (and less to roll it in the spinward direction) compared to the case of an alley suspended above a non-rotating massive body.

Of course, regardless of which one of the above interpretations is correct, I would expect that the same is valid also for an object of generic shape, even if the constraining surface is drag free.

The first case sounds analogous to what happens inside a rotating space station. Both of the above interpretations looks plausible to me.

I would also like to see the math justifying whichever interpretation is the correct one, since wikipedia doesn't provide any.

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The quote regards objects which are not in free fall, if you are in free fall your weight is 0 no matter what. To keep a constant distace while in free fall, you would have to be in a circular orbit.

To keep a constant distance while not in free fall, you would have to accelerate your rocket outwards or stand on a ground, in which case you will feel a force and therefore weight.

Frame dragging has the effect that the required local initial velocity to stay in a circular orbit is less in the prograde than in the retrograde direction.

With the same initial transverse velocity, you might need radial rocket support to keep your fixed distance on a retrograde orbit, while in the prograde direction the same initial velocity might be enough to stay on a free fall orbit with constant distance where you would need no extra forces.

The bowling ball analogy is of no use, if not outright misleading, at least in my humble opinion.

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  • $\begingroup$ Thank you for your answer. So, if I undestand corrrectly, the situation being described in the text above is n°1. $\endgroup$
    – Povel
    Feb 5, 2020 at 10:10
  • $\begingroup$ I wonder though, does the resistance offered by an object to being accelerated tangentially while sitting on a suspended (for example through rockets firing radially) equatorial platform inside the ergosphere depends on whether the object is being accelerated in the spinward or in the anti-spinward direction? Said differently, does the proper acceleration of the object for a given applied force depend on whether the applied force is the the prograde or retrograde direction? $\endgroup$
    – Povel
    Feb 5, 2020 at 10:24

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