Tumbling Venus -- equation needed

Hi all, back on 2-Sep-2011 I posted a speculation of Venus's rotation
titled "Tumbling Venus" (copied at bottom). As the Sun's magnetic
field has recently flipped, I'm reminded of the topic. The Earth's
magnetic field also flips every half-million years or so, and this is
presumably caused by the Earth's rotating inner core physically
flipping over and so turning the other way. I suspect a battery
action where electromagnetic energy builds up in the outer
(non-rotating) core until the force is so great as to impel the inner
(rotating) core to flip over -- then the built up energy drives the
inner core to rotate faster until the stored forces are consumed and
then it starts to build up with the opposite polarity, and so on, ad
rotundum.

My speculation on Venus is that the Venusian core comprises most of
the mass and inertia of the planet, so that when the time comes for
its (slowly-rotating) core to flip, it is the crust which flips and
not the core. Now in between such flips, the Venusian crust becomes
tidally locked to the Sun (the Venusian day has been measured to be
lengthening by 15 minutes in just the last few decades), so just prior
to the flip it will have a siderial day of 224.7 Earth-days equal to
its year. When the flip happens, since it is the crust that flips,
its siderial day would be 224.7 days going the other way, minus a
certain loss caused by the energy of the flip -- that is, some
rotational inertia is lost in the flip.

This is the equation that I need. I've got an impressive retinue of
reference books, but they don't say what happens when you take a
rotating sphere or spherical shell, and flip it upside-down. How much
rotational speed is lost in the process?

Wondering if anyone's encountered such an equation. Thanks,

Eric Flesch


When considering tumbling planets, we usually think of Uranus which
rolls along its orbit like a ball. However, this was surely due to a
primordial impact, because Uranus's moons' orbits are aligned with its
equator. Uranus has not truly tumbled.

A truly tumbled planet is Venus, and there is strong evidence for a
remarkable transformation. The evidence is
(1) Venus's siderial rotational period which is close to its orbital
period, although retrograde.
(2) Venus's axial tilt almost perfectly 90 degrees to the ecliptic.

These conditions can be replicated using a simple model. Suppose Venus
was a tidally bound planet, always showing the same face to the Sun.
In that scenario, both of the above conditions are required. Now
apply a force to turn Venus neatly upside-down. Observe the rotation
must slow slightly, similar to if you perform this action on a top --
there is some dissipation of the rotational inertia. The result:
Venus as it is today.

Of course, one could question where such a force could come from.
However, planets of our size are modelled to have a core which can
rotate differently than the mantle. We don't know what Venus's core
is doing. Earth's geologic record shows that our magnetic pole
periodically flips, and this is almost certainly related to what the
core is doing. Why should the core flip? We know nothing about the
process, but we can infer that it happens. If Venus has a large core,
heavier than the mantle, then when the core flips, it will be the
mantle which flips. And that would explain the Venus that we see
today.

Eric Flesch