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They probably are using a tool like this to analyze possible trajectories... these tools do use numerical optimization libraries to pick paths between targets and destinations. Just guessing based on what was said in the summary, they are using the Saturn-Titan Lagrange points to alter their trajectories without using much fuel. You can do some pretty crazy maneuvers around these points.

different three-body systems

It is a multi-body problem. Generally solved using a whole bunch of pieces of software, just to check ;~)

I've never heard of using multiple 3-body systems. I did this stuff in college not to long ago, so, while I'm not saying it isn't done.... ;~) (*NOT* a Masters degree, just bachelors. Which is like working the McDonalds grill for a year and then trying to get a job as a master chef).

The way we did it (again, as undergrads) was some pretty raw itterative brute force. We did a lot of happy math, don't get me wrong, but the body of the work is done by progs like STK (http://www.stk.com/) from analytical graphics.

It is possible to get a ball park using some happy math tricks. Not enough to really model the trajectory, but enough to say 'oh, I'm going to need a deltaV of 'x' km/s' and you will have a good idea of your error margin (e.g. 'x' +/- 5%). We did these for a number of trajectories as homework problems; a few hours each, pencil paper only. Well, some of use ;~) I abused my TI-89 horribly :~)

check out STK, http://www.stk.com/ from AGI. It's pratically an industry standard.

Want to plan a trip to Mars? no problem using the Astrogator plug-in you're in buisness. However it will set you back several thousands of dollars....

Satellite Took Kit - http://www.stk.com

The concept seems so simple, but the reality is much more complex. IANARS (I am not a rocket scientist), but orbital mechanics just don't work at all like you're used to things working on earth (or in Star [Trek|Wars]).

Agreed, but with products like STK, and Kalman Filtering techniques, it's not out of the real of possibility to hand over ops to University Engineering departments. In many cases, this is the source for the theories and sensors onboard the spacecraft.

However, Hughes, the company who built the satellite then figure out a way to use some of the station keeping fuel and gravity assist from the Moon to kick it into a geostationary orbit. The downside of this is a shorter operational lifetime as the station keeping fuel is what keeps the satellite at the equator and not wandering North-South on a 12 hour cycle.

A reference to this can be found on the Satellite Toolkit (STK) website http://www.stk.com/press/display.cfm?id=24

D.

This is obviously a richly researched topic with lots of published papers. Some of them talk about new algorithms for tackling the complex dynamics you're talking about. And of course there's always Moore's Law; the computers used for Apollo missions were about as powerful as (or maybe much less than?) Palm Pilots.

It's probably quite feasible to give the L1 station a radio link to an orbital mechanics cluster on the ground, which can be as big as is needed, and could run equations of motion for a couple dozen nearby orbits in faster-than-real-time.

It's difficult, but not unreasonable, because we do have precise coordinates. Want to have a pretty good idea of where the ISS is right now? Here is a state vector, and this or this software will let you propagate that vector. The really difficult part in the whole process isn't tracking, it's getting escape velocity out of your nerf.

Just want to take the moment to gloat and be proud that the Company I work for, Analytical Graphics, is playing a huge role in assisting in the deorbit. We also have a Mir De-Orbit Video that shows how Mir will most likely burn up upon re-entry.

Just want to take the moment to gloat and be proud that the Company I work for, Analytical Graphics, is playing a huge role in assisting in the deorbit. We also have a Mir De-Orbit Video that shows how Mir will most likely burn up upon re-entry.

If you are not familiar with NORAD 2-line elements, look at celestrak's documentation. You can also look at celestrak's software archive.

Paper: An Operational and Performance Overview of the IRIDIUM Low Earth Orbit Satellite System -
Stephen R. Pratt, Richard A. Raines, Carl E. Fossa Jr., and Michael A. Temple Department of Electrical and Computer Engineering, Air Force Institute of Technology

If you are really interested in playing around with looking at the constellation, take a look at one of the best product's around for visualization and prediction, AGI's STK . You can download a modelling limited version of their software for free from their "Resources" tab.

I'm sure people with the proper tools, such as the Satellite Tool Kit orbit calculator or Orbital Mechanics CDROM, can make some interesting launches by using the Earth and Moon to redirect trajectories.