Maths (very very frightening)

[GoSlash27]

Streetwind,

 Plusck's clearly got this well in hand, but maybe I can explain it in a way that helps it click.

 "Excess velocity" is what I denoted as Vxs and he referred to as V_∞. It is simply this:

 Suppose you are in orbit around the sun. You are not within Kerbin's SoI, you just happen to be the same distance from the sun. You wish to set up a Hohmann transfer to Duna's distance from the sun.

 It's easy to sort out how much DV that burn would take, right? You just use the vis-viva and calculate it like any other altitude change. Well... that DV *is* your excess velocity. You see, a hyperbole from Kerbin's perspective is actually just a parabola from the sun's perspective.

 

So that's how you do it. You figure out the Vxs as above. Then you figure out the velocity you'd need to escape Kerbin, which is simply your current orbital velocity times sqrt(2). Instead of linearly adding these values, you add them Pythagorean style (because the shortest distance between 2 points is a straight line, not "go that way and hang a right"). Finally, you subtract your initial orbital velocity about Kerbin (yay Oberth) and you have your answer.

HTHs,
-Slashy