Physics and math behind flight through solar system: Where to start? I wrote a first program that simulates a solar system. I was able to calculate the locations for every planet on its elliptical route for any given time.
In a second program i managed to simulate newtonian gravitational behavior (n-body problem, time-step approach).  
But i'm wondering how it is possible to:
  (1) find routes (different possibilities) from a given location/planet to another
  (2) choose the best route according to duration or fuel cosumption
So where's a good place to start?
To be more exact: It's not about writing another simulation, its about understanding the physics behind it!  
Until now, i was not able to find any good resources on the internet.
 A: Just as calculating a lightwave's shortest path between points A and B where A is in air and B is in glass, you can put the actual functions of mediums then take the derivative. Just like the Snell's Law : http://en.wikipedia.org/wiki/Snell's_law. (but this time, medium is not constant, there are moving masses that change space and time)
There wont be a medium constant but instead you put space/time indexes where it will change near planets and stars.
Maybe you can use finite-element-approach instead. Just use a spherical(3D) wave(or circular 2D) generating point in the finite element matrix then watch every piece of wavefront. Which wavefront point reaches your target first, will be the spaceship.







A: I suggest looking at the Interplanetary Transport Network wikipedia page and this article (pdf). This is a way for interplanetary travel using very little propellant. 
The idea behind this is quite simple. It is well known that particles freely moving in the gravitational fields of several bodies exhibit chaotic motion, which means that nearby trajectories often exponentially diverge with time. So by using very little propellant the spacecraft can jump between such trajectories. The trick is to identify 'hubs' for such trajectories, like various Lagrange points, into which many trajectories to and from various destinations converge. Then the spacecraft using small 'nudges' jumps first onto path to such hub, then, once there, on a path to its next destination.
