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The global liquid water subsurface ocean within Enceladus has been identified as being the primary source of material for Saturn's E-ring. Given that the moon is permanently ejecting large quantities of water to space through the south poles how long will this ocean continue to survive?

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No.
The approximate escape rate of water on Enceladus to space is $\rm \dot{m}_{\rm H2O}\approx 5000\; g\;s^{-1}$ (ref, with a factor 10 uncertainty in that number). Ganymedes icy mass $\rm m_{H2O}$, which I simply estimate at about 50% of its total mass would then need about $\rm m_{H2O}/\dot{m}_{H2O} \approx$ 400.000 billion years to escape, or about 30.000 times the age of the universe. In other words, Ganymedes water content at the current escape rates is stable.

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    $\begingroup$ The question asks about Enceladus. You first mention Enceladus & then discuss Ganymedes. Is there an error? $\endgroup$
    – Fred
    Commented Aug 8, 2023 at 5:50
  • $\begingroup$ @Fred Woops, it seems so.. when researching the material my thoughts must have jumped from one icy moon to another.. $\endgroup$ Commented Aug 8, 2023 at 13:05
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    $\begingroup$ Is that a decimal point, or a thousands separator? According to Wikipedia, Enceladus is losing water at a much higher rate than what you gave for Ganymede:~200 kg/s (it ejects ~250 kg/s of salty water, but much of the salt content falls back). $\endgroup$
    – PM 2Ring
    Commented Aug 9, 2023 at 12:37
  • $\begingroup$ @PM2Ring A thousands separator. The same calculation with Enceladus' mass and your quoted escape rate gives a total lifetime of 0.6 ages of the universe. So then the answer would be "Yes, but it's gonna take a while". $\endgroup$ Commented Aug 10, 2023 at 2:49

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