Re: escape velocity Io, also escape velocity jovian system from Io

Hi John,

Several good questions there. Obviously, in the future of space exploration 
we need bases in locations where energy or energetic materials can be 
found, that are conveniently placed to launch material to other locations. 
This requires a low gravitational potential well and a favourable 
environment.

Let's look at the figures:

To calculate escape velocity (according to my physics book) we need to know 
 the mass of the attracting body, and our distance from it. If we are 
already in orbit about the body we have half of the escape velocity 
already. The actual sum is Ve = sqrt(2*G*M/R) where G is the universal 
gravitational constant, M is the central mass and R is the radius.

For example, for Earth escape velocity from the surface is Ve = sqrt 
(6.67e-11 * 5.98e24 / 6.371e6)    [e24 means times ten to the power 24, and 
all units are in the MKS system] The answer for Earth is 11.2 km/sec.

For Io, taking it in isolation, we have a much smaller mass and about 1/4 
the radius. Here, Ve = sqrt(6.67e-11 * 8.93e22 / 1.82e6) i.e. Ve = 2.56 
km/sec, - less than 1/4 of that for Earth - so we could easily escape from 
Io with simple chemical rockets, or some sort of volcanic/geothermal 
powered steam catapult, as you suggest.

However, this then leaves us rather close to Jupiter, the most massive body 
in the Solar System. Escape velocity from Io's orbital distance around 
Jupiter is Ve = sqrt(6.67e-11 * 1.9 e27 / 4.22e8) i.e. Ve = 24.5 km/sec. 
Now as I said before, we already have half this velocity if we're in a 
stable orbit, so we would only need 12.25km/sec to escape Jupiter orbit 
(I'm not 100% sure how those two velocities add, but it seems logical that 
if we launch from Io in the "forwards" direction of its orbit, we would 
need to add the two escape velocities, giving about 14.81km/sec)

Therefore, it is more expensive and difficult to Launch from Io to 
Non-Jovian orbits than it is to do the same from Earth (although I'm 
ignoring the gravity field of the Sun which adds to the required deltaV to 
get from Earth to the remoter outer planets)

To do these calculations properly needs a lot of maths and a full computer 
simulation of the orbits of the body you are leaving and heading for, plus 
anything you pass "near" on the way, especially the Sun and Jupiter. For 
now, however, you can see that it isn't an easy ride from Io because 
Jupiter is so huge and not very far away.

In fact, that's why Io is so volcanically active. The gravity field of 
Jupiter is so strong that its tidal flexing on Io is enough to melt the 
planet's interior. Tides come from the gradient of gravity, or an even 
higher derivative so they are usually very weak. Jupiter is so massive that 
its tidal influence on Io is severe.

There's one other point you need to be aware of, and which you allude to in 
your question. Jupiter has enormous magnetic fields and active radiation 
belts. Anywhere in near-Jovian space is an unfriendly environment for men 
or computers (look at the trouble the Galileo probe is having with 
radiation-induced resets of its computer)

For more info see Bill Arnett's excellent Nine Planets Tour
http://seds.lpl.arizona.edu/nineplanets/nineplanets/

The Galileo homepage
http://galileo.ivv.nasa.gov/index.html

And a tutorial on orbits and escape velocity
http://www.usafa.af.mil/dfp/cockpit-phys/cp_gp3.htm

Keep up the thinking and the learning, and one day it could be your name on 
those NASA websites!

Nick