How exactly are space probes trajectories calculated?

After answering a question a few minutes ago about the location of Voyager 1, and playing around with Celestia, I started wondering -- how exactly are these "gravitational slingshot" trajectories set up anyway? We have numerous examples of those. For example, the 6-year-long voyage of the Messenger probe to Mercury had some 6 or 7 such maneuvers to gradually lose energy and allow it to enter an orbit around Mercury. This has to be very carefully planned, otherwise too much fuel is spent in course correction, or the probe gets ejected or even passes too close to the atmosphere of a planet and crashes. So, while at first it might be "eyeballed" when preparing the orbit solution for a mission, in the end it has to be selected exactly -- at what instant to make an attitude correction so it passes at the closest approach at a certain minute and thusly picks up/loses delta-V. My question is specifically if, on these moments the interaction is treated as a 2-body interaction, or something more complicated. For example, the Celestia simulator shows Voyager 1 making a pass near Titan en route to Saturn, and after passing near Saturn it gets ejected towards the northern celestial hemisphere. To me, this suggests some careful planning prior to launch -- they knew how to plan the orbit. And given that computers have limited digit precision (which might not matter in face of some tiny uncertainties such as radiation pressure), there is always some room for uncertainty in the orbits. Does anyone know of comprehensive textbooks detailing this subject? Whether more sophisticated approaches than mere 2-body approximations (a la Newton law of gravitation) is done? Whether relativistic corrections are considered ("turned on") or ignored ("turned off") when the trajectory crosses some boundary distance to the Sun? Whether cutoffs are applied at some instances (for example, radiation pressure is ignored up until some point and then used in the calculations beyond a certain distance from the Sun)?

Asked By: Satan Claws - 12/24/2012
Best Answer - Chosen by Asker
The calculations are way beyond 2-body interactions. First, the engineers start with a high-precision ephemeris of the plants, such at JPL's DE-421. Then they add in the ephemeris of any moons (or asteroids) the probe will come close to. That gives a gravity map of the solar system... More
Answered By: Morningfox - 12/24/2012
Additional Answers (4) More
Answered By: MarkG - 12/24/2012
When we did simpler problems like this in my Celestial Mechanics class, we worked backwards from where we wanted to end up. We had no zippy little computers in the classroom, so we just set them up, no graphics, no fun little dotted line trajectories... boo hoo.
Answered By: Faesson - 12/24/2012
Try this: More
Answered By: quantumclaustrophobe - 12/24/2012
Textbooks... More
Answered By: oklatonola - 12/24/2012
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