# Do Enceladus' geysers fall back to its surface or do they achieve escape velocity?

Enceladus, a moon of Saturn, has a very low surface gravity at 0.114 m/s² or 0.012 g. It has a subsurface ocean of liquid water and is ejecting plumes of it. Does the ejected water eventually fall/rain down to the surface or does it (or some of it) achieve escape velocity due to Enceladus' very low mass and gravity? If so, is Enceladus losing mass and will eventually run out of water?

• – uhoh Jul 19 '20 at 15:23

We start by calculating the moon Enceladus surface escape velocity $$v_e$$ as $$v_e=\sqrt{\frac{2GM}{r}}$$ where $$G = 6.674×10^{-11}m^3kg^{-1}s^{-2}$$ is the universal gravitational constant, $$M=1.08×10^{20}kg$$ is the moon mass, and $$r=2.52×10^5m$$ is the radius of the moon. Evaluation of the above equation gives us an escape velocity of about $$239m/s$$.

Perry et al. provide high fidelity observations of Enceladus vapor plumes from the Cassini spacecraft. The above graph is just for the high velocity plumes as described in the paper:

The H2O neutrals measured during E8 had a Mach-4 distribution centered on 1.2 km/s with a width of ±300 m/s, which corresponds to a temperature of 65K

Since the average high speed plume velocity of 1.2km/s is about five times greater than our calculated escape velocity of 239m/s, we can conclude that some of Enceladus's plumes certainly achieve escape velocity.

Teolis et al. agree:

The expression assumes radial expansion of the gas from the surface sources at constant speed, neglecting gravity since the mean molecular speed in the jets significantly exceeds (by at least a factor two) the 240 m/s Enceladus escape speed.

Enceladus is losing mass through it's (mostly water) jets. I couldn't find a conclusive analysis of mass loss rate. Eventually I would expect that enough water will be lost that the current mechanism for creating the jets under the 10 km ice crust will no longer be in effect, but this is just my intuition. I don't have a credible source or calculation to back this up.