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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.

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    $\begingroup$ (not enough for a full answer but...) You should have a good understanding of energy (like the Oberth effect) and different types of transfer orbits. From there you can construct a decently efficient path piece-wise. (There are some good articles on this based around the popular video game "kerbal space program") And then there are the magical things I know little about: lh6.googleusercontent.com/-Pz-3360uNoA/UTthQF-SdQI/AAAAAAAAdnM/… and maths.manchester.ac.uk/~jm/Choreographies $\endgroup$ – user12029 Jun 27 '13 at 20:23
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    $\begingroup$ A related question that you might find interesting: physics.stackexchange.com/q/26148/16660. $\endgroup$ – Wouter Jun 27 '13 at 20:23
  • $\begingroup$ This looks like a good place to start: en.wikipedia.org/wiki/Interplanetary_spaceflight $\endgroup$ – Keep these mind Jun 27 '13 at 20:33
  • $\begingroup$ joe, the first thing to know in real-life space flight is that planets' trajectories are not elliptical. The second and third stops on your way are Lambert's problem and patched conics. Fourth: what propulsion do you use? Fifth: there are loads of resources on the Net and in libraries... $\endgroup$ – Deer Hunter Jun 27 '13 at 20:36
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    $\begingroup$ And regarding point (2), you want to look into optimization theory for the math behind selecting the "best" of "something" given whatever criteria you provide. $\endgroup$ – tpg2114 Jun 27 '13 at 20:52
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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.

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  • $\begingroup$ Actually a very interesting answer! Upvoted. Currently i have no idea how to model this in a piece of program. What's the math behind it? $\endgroup$ – joe Jun 29 '13 at 13:32
  • $\begingroup$ Just some diffusion algorithm like any FEM, plus you already have the nbody thing right? Maybe a flux/velocity solver can be needed on top of the diffusion as "advect" solver. Any wave propagation algorithm should work. $\endgroup$ – huseyin tugrul buyukisik Jun 29 '13 at 13:33
  • $\begingroup$ Well, i'm not a physicist.... $\endgroup$ – joe Jun 29 '13 at 13:38
  • $\begingroup$ You like math? If so, you may look at Navier-Stokes equations and Poisson differential equations. This is even more embarrasingly-parallel than nbody algorithm so you can use gpu better. $\endgroup$ – huseyin tugrul buyukisik Jun 29 '13 at 13:41
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    $\begingroup$ Work hard, have fun. $\endgroup$ – huseyin tugrul buyukisik Jun 30 '13 at 14:16
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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.

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