What is the escape velocity of Saturn at Enceladus distance?

Question

To what velocity would a spacecraft have to accelerate to launch from the surface of Enceladus into orbit around it? And from the orbital distance of Enceladus, what would be the escape velocity from Saturn, for a return journey to Earth?

My understanding is that a two-man craft the size and power of the Apollo LM ascent stage would have no problem leaving Enceladus or Ceres or most of the moons of Jupiter and Saturn (other than Titan with its thick atmosphere). I'm not so clear on whether a craft with the size and power of the Apollo CSM would be able to escape from the influence of Saturn, with or without a great deal more fuel than that used to escape our Moon during Apollo.

Answer 1

No, not even close. First, you wouldn't choose to escape directly from Enceladus distance. You would instead lower your perikrone to as close to Saturn as you can get (make sure you miss the rings on the way down!), and then do your escape burn there. You could use Titan to lower your perikrone.

Just escaping Saturn is not enough, since you would then be left stranded in a solar orbit much like Saturn's. You would have to also reduce your perihelion at least as far down as Jupiter, and then use a Jupiter gravity assist to get back to Earth.

The CSM had a total $\Delta V$ of about 2.8 km/s. (Much of which was used to get into lunar orbit.) Even if I ignore how in the heck you got there in the first place, and you have all that $\Delta V$ available in Enceladus orbit, you're still not getting back. You'd need 5.3 km/s to escape directly (your original question), 4.5 km/s to lower your perikrone to near Saturn directly, or 3.8 km/s to get up to Titan.

Even if by some swingby hijinks you find a way to get close to Saturn for an escape burn, at that point you will need 10 km/s to escape Saturn on a trajectory that will get you to Jupiter.

Finally, if you had found a magic elixir on Enceladus that multiplies the Isp of your engine by a factor of four, you are now on a ten-year journey home with a week or two of oxygen, water, food, and CO2 scrubbers.

Sorry, but you and your crew are screwed. You are living in your coffin. I don't know how you got there, but just make the best of your remaining time.