Enceladus Tidal Heating and Plume

What is modelled

Enceladus is squeezed and relaxed by Saturn as it moves on a slightly eccentric orbit. The flexing dissipates energy as heat. The ice shell conducts heat to space, and where the balance sits sets how thick the shell can stay. Gas and ice grains leave the south-polar fractures: the gas speed is a setting, the grains are slowed by their inertia (big grains lag the gas), and a grain escapes if its speed is above the escape speed of the moon.

Equations

• Tidal heating E = (21/2)(k2/Q) G MS² R&sup5; n e² / a&sup6;.
• Shell conduction P = k ΔT / H · 4 π R²; balance at H = k ΔT 4 π R² / E.
• Grain speed v = vgas / (1 + r / rc) with a fixed coupling radius r_c of 2 µm.
• Apex rmax = 1 / (1/R − v²/2GM), escape speed √(2GM/R).
• Grain sizes follow a log-normal spread of width 0.5.

Checks run in the page

• An inverse-square orbit integration against the apex formula.
• Grains just below and just above the escape speed.
• The two equivalent forms of the heating law and the e² scaling.
• The flight time of a slow grain against constant gravity.

Honest simplifications

The real k2/Q of Enceladus is poorly known, the shell is not a uniform slab, heat is produced in the core as well, and the grain-gas coupling here is a one-parameter heuristic, not a plume model. The mass flux is a fixed illustrative number. The page shows the physics scale, not a calibrated reconstruction of Cassini data.

• Press Circular orbit and see the heating collapse, because it scales with the square of the eccentricity.
• Press Slow gas, big grains and watch almost every grain fall back.
• Thin the shell to see the conduction loss rise above the heating.