(1) Smaller, inner moon Mimas experiences 2/3rds more Tidal Acceleration than bigger, outer moon Enceladus
The
Gravity Force is
Fg = G MJupiter mmoon / r2. The
Differential Gravity ("Tidal") Force, therefore, is
dFg = d(Fg)/dr x D, where
D is the diameter of the moon. For, since the
Gravity Force decreases steadily, with increasing separation distance, the
Gravity Force on the inside limb of the moon is larger than that on the outside limb of the moon. The actual
Differential Gravity ("Tidal") Force is simply the difference, between the
Gravity Forces affecting each opposite face of the moon. But, since orbital distances (
r) are
thousands of times larger than moon diameters (
D), its simpler, and still quite accurate, to approximate that differ
ence, with the above differ
ential.
The relative
Tidal Force, then, between Mimas vs. Enceladus, is the mathematical
ratio, of the above formula, applied to the both of them. When you cancel out all the constants (
G, MJupiter), as well as the moon masses themselves -- calculating, thereby, the relative
Tidal Accelerations -- you get the ratio:
(renceladus / rmimas)3 x (Dmimas / Denceladus)
Plugging in all the numbers
(Enceladus, Mimas), one obtains the final result of
1.66 (~5/3rds). Thus, despite being slightly smaller, the inner moon Mimas is stretched "
2/3rds harder" than the bigger, outer moon Enceladus.
(2) outer moon Enceladus much warmer than inner moon Mimas
Mimas' surface temperature varies between
77 to 92 K (NASA). Enceladus' surface temperature varies between
70 to 85 K (NASA), slightly colder than its inner, and more tidally heated, companion, as expected. Never-the-less, Enceladus' south pole is anomalously warm, showing surface temperatures as high as
110 K. And, Enceladus' "tiger stripe" fissure formations, all over its surface, have geysers blazing at
190 K (OP + APOD). Why?
Mimas has a low density
(1.15 g/cm3), indicating that it is "composed mostly of water ice, with only a small amount of rock". By contrast, Enceladus has a higher density
(1.61 g/cm3), a density "higher than Saturn's other mid-sized icy satellites, indicating that Enceladus contains a greater percentage of silicates and iron". Thus, "with additional material besides water ice, Enceladus's interior may have experienced comparatively more heating from the decay of radioactive elements". Perhaps, then, Mimas is a frozen ice-cube, whereas Enceladus is a still-warm 'super-comet' muddy snowball. Or, perhaps rock-on-rock (tidal) friction generates much more energy, than ice-on-ice (tidal) friction.
(3) Inner moon Mimas is cooled by 'Wind-Chill' effect from passage through Saturn's rings ?

Edited by Widdekind, 06 February 2011 - 01:28 AM.