From: x@x.org   
      
   On 10/29/24 21:53, Sylvia Else wrote:   
   > NASA has a mission to the Jovian system, to study Europa. That moon is   
   > interesting because it appears to have liquid water under an icy   
   > surface. The heat need to keep the water liquid comes from the   
   > stretching and compression Europa experiences during its orbit around   
   > Jupiter, the orbit not been exactly circular.   
   >   
   > So much, so simple.   
   >   
   > Some thought made me realise that although the tidal forces on Europa   
   > mean that it is not exactly spherical, its two bulges cannot remain   
   > perfectly aligned with Jupiter, because Europa's angular velocity   
   > relative to Jupiter is higher at periapsis than at apoapsis. The result   
   > is that the nearer bulge is sometimes ahead, and sometimes behind,   
   > relative to Europa's orbital motion, resulting in a net force backwards   
   > along the orbit, or forward along the orbit.   
   >   
   > Again, certainly stuff that's already well known.   
   >   
   > As far as I can see, the energy that is being dissipated as heat inside   
   > Europa has to come from changes to Europa's orbit. Further, if Europa   
   > were either perfectly rigid, or perfectly elastic, there would be no   
   > energy transfer, and consequently no change to the orbit.   
   >   
   > It would make no difference if Jupiter itself were perfectly rigid, so   
   > the transfer cannot involve tides on Jupiter generated by Europa.   
   >   
   > So the existence of the orbital energy transfer depends on Europa being   
   > neither perfectly rigid nor perfectly elastic.   
   >   
   > What escapes me is the mechanism.   
   >   
   > Any thoughts?   
      
   I am thinking that the standard model for Earth is that supposedly   
   in the 1800s Lord Kelvin did some calculations.   
      
   The outer layers of the Earth have an insulating effect on the inner   
   layers of the earth.   
      
   Then the inner layers even can act as more insulation.   
      
   And further down.   
      
   And so on.   
      
   He calculated that it would take a hot interior literally 10s to   
   even 100 million years for a hot Earth interior to cool down because   
   the Earth could retain heat and insulate successive layers so well.   
      
   When everything was put together, however, his calculations were not   
   wrong.   
      
   The standard model of geologic time in the present however is that the   
   Earth is billions of years old.   
      
   How is this discrepancy resolved?   
      
   I am thinking that the standard modern view is that radiation from   
   the slow radioactive decay of uranium, potassium, thorium, and other   
   elements deep in the interior is added to the Earth's insulating   
   effect to keep the interior of the Earth and other inner solar system   
   bodies heated.   
      
   I am thinking that Io is supposed to be rather seriously affected   
   in its composition and internal dynamics by tidal forces.  I was   
   thinking however that Ganymede and Callisto were also supposed to   
   have liquid water mantles.   
      
   It might be that there is a combination of insulation, internal   
   radiation, and tidal forces going on for the different moons   
   of Jupiter.   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)