Tides, rotations and spins

1. Jun 6, 2010

oldman

I want to ask here if tidal forces can in a sense be considered as the opposite of the centripetal forces that drive rotations or spins. I'd appreciate any web-accessible references about this.

First consider a uniform spherical cloud of non-interacting test masses falling radially toward a central mass. As it falls the sphere will become distorted by tidal accelerations that change
inter-particle separations, into an ellipsoid of revolution whose axis is radial, as described and
illustrated by Roger Penrose in The Road to Reality,Section 17.5, p.396,397.

If instead of a cloud of test particles the sphere were a isotropic solid, it would be strained by tidal forces (to a degree depending on its proximity to the central mass) into an ellipsoid of revolution, until internal stresses developed that were sufficient to balance tidal forces (or the solid became plastically deformed, or fractured).

The internal stresses that develop are compressions perpendicular to the ellipsoid axis and tensions along this axis. It looks to me that the radial compressive tidal forces are very like (but opposite in direction) the centripetal forces that would make the solid rotate about its radial axis (say spin about this axis), and that the tensile forces are very like (but opposite in direction) the centripetal forces that would make the solid rotate about any axis perpendicular to the solid’s radial axis. I’ll take the liberty of labeling these tidal forces anti-spin and anti-rotation forces because that's what they look like to me.

If the solid were to rotate with an appropriate angular velocity about an axis perpendicular to its radial ellipsoid-of-revolution axis, the centripetal accelerations generated by such rotation might exactly cancel the tensile tidal accelerations. In fact, since, as Penrose points out, the motion of the cloud or solid attracted by the central mass does not affect the nature of tidal forces, one might as well consider the cloud or solid to be in a circular orbit around the central mass, in which case the magnitude of the tidal forces would not vary.

I then wonder if the “appropriate angular velocity” above might not be one revolution per orbit, which would “freeze” the ellipsoid axis along the changing radial direction as it orbited, and also remove the tensile tidal distortion?

As in the case of The Moon presenting the same side to us as it orbits the Earth?

And might the anti-spin tidal forces cause a precession of the axis of rotation?