From: schillin@spock.usc.edu   
      
   Ian Stirling  writes:   
      
   >tribolumen  wrote:   
   >> Does anyone know of a method, or a piece of software, for calculating (or at   
   >> least approximating) low-thrust interplanetary trajectories?  Most of what   
   >> I've found so far is PhD theses about using calculus of variations for fun   
   >> and profit.  While I can handle a little math (my undergrad degree is in   
   >> physics), I'd rather not deal with that level of it if I don't have to.   
      
   >With the advent of PCs that can do hundreds of millions, or billions   
   >of calculations per second at high precision, simply ignoring all of this   
   >fancy calculus stuff, and calculating forces acting on the spacecraft, and   
   >the resultant accellerations and positions, every minute, for a decade long   
   >mission is not a big problem.   
      
   Yes, but how do you know what the mission *is*?  That's the problem you're   
   trying to solve in the first place, not the initial condition that you can   
   plug into the equation solver, and it has to be defined in rather more   
   detail than "get from Earth to Jupiter" if your methodology is to compute   
   the trajectory every minute of the way.   
      
      
   >No, it's by no means the best way to do it, and can be a problem if you want   
   >software that tries out millions of possibile trajectories between   
   >mouse-clicks.   
      
   Millions?  *Millions*?   
      
   For a decade-long mission being computed at one-minute intervals, even   
   assuming we crudely control the spacecraft to +/- 10% in thrust and   
   +/- 15 degrees in heading, there are approximately four hundred fifty   
   million trillion trillion (insert the word "trillion" 1,476,524 times   
   here) trillion possible missions your spacecraft could fly.  Of these,   
   assuming you had enough thrust and propellant to reach Jupiter in the   
   first place, only one in every sixteen hundred trillion trillion (inser   
   the word "trillion" 738,261 times here) trillion will end up within a   
   million kilometers of Jupiter.  And only one will be the optimum course   
   for reaching your desired destination.   
      
   And you think you're going to sort through those 4.5E+17718332 possible   
   missions at a rate of a few measly *million* per mouse click?   
      
   Sorry, no.  Even solving this problem numerically requires a great deal   
   of knowledge, insight, and computational cleverness be applied to the   
   question of which vanishingly small fraction of the possible range of   
   trajectories should be investigated.   
      
      
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