<p>We start by calculating the moon Enceladus surface escape velocity <span class="math-container">$v_e$</span> as
<span class="math-container">$$v_e=\sqrt{\frac{2GM}{r}}$$</span>
where <span class="math-container">$G = 6.674×10^{-11}m^3kg^{-1}s^{-2}$</span> is the universal gravitational constant, <span class="math-container">$M=1.08×10^{20}kg$</span> is the moon mass, and <span class="math-container">$r=2.52×10^5m$</span> is the radius of the moon. Evaluation of the above equation gives us an escape velocity of about <span class="math-container">$239m/s$</span>.</p>
<p><a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5610430" rel="nofollow noreferrer">Perry et al.</a> provide high fidelity observations of Enceladus vapor plumes from the <a href="https://www.nasa.gov/mission_pages/cassini/main/index.html" rel="nofollow noreferrer">Cassini spacecraft</a>.</p>
<p><a href="https://i.sstatic.net/jrwvG.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/jrwvG.png" alt="enter image description here" /></a></p>
<p>The above graph is just for the high velocity plumes as described in the paper:</p>
<blockquote>
<p>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</p>
</blockquote>
<p>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.</p>
<p><a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5610430/" rel="nofollow noreferrer">Teolis et al.</a> agree:</p>
<blockquote>
<p>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.</p>
</blockquote>
<p>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.</p>

CC BY-SA 4.0
2021-01-07T05:49:17.973Z
2021-01-07T06:34:06.353Z
2021-01-07T06:34:06.353Z
Connor Garcia
<p>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?</p>

CC BY-SA 4.0
2020-07-19T15:23:14.020Z
somewhat related: [Enceladus; why use the words “geysers”, “jets”, and “plumes” interchangeably?](https://astronomy.stackexchange.com/q/19939/7982) and [How can “Geysers” on Europa reach heights of 100km?](https://astronomy.stackexchange.com/q/18496/7982) and [Is there an established distinction between a geyser and a cryovolcano in solar system bodies?](https://astronomy.stackexchange.com/q/19943/7982) and in Earth Science SE: [Why exactly is the feature on Io called a volcano, and the feature on Enceladus called a geyser?](https://earthscience.stackexchange.com/q/15436/6031)
uhoh
<escape-velocity><enceladus><geysers>
Do Enceladus' geysers fall back to its surface or do they achieve escape velocity?
Ioannes
# Do Enceladus' geysers fall back to its surface or do they achieve escape velocity?

(Asked by: username_0 on 2020-07-19)

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?

**Tags:** escape-velocity, enceladus, geysers
> **Comments:**
> **username_1**: somewhat related: [Enceladus; why use the words “geysers”, “jets”, and “plumes” interchangeably?](https://astronomy.stackexchange.com/q/19939/7982) and [How can “Geysers” on Europa reach heights of 100km?](https://astronomy.stackexchange.com/q/18496/7982) and [Is there an established distinction between a geyser and a cryovolcano in solar system bodies?](https://astronomy.stackexchange.com/q/19943/7982) and in Earth Science SE: [Why exactly is the feature on Io called a volcano, and the feature on Enceladus called a geyser?](https://earthscience.stackexchange.com/q/15436/6031)  

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## 1 answers

### Answer by username_2 on 2021-01-07. Score: 3

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.](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5610430) provide high fidelity observations of Enceladus vapor plumes from the [Cassini spacecraft](https://www.nasa.gov/mission_pages/cassini/main/index.html).

[![enter image description here](https://i.sstatic.net/jrwvG.png)](https://i.sstatic.net/jrwvG.png)

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.](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5610430/) 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.


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