From: JamesL@Lugoj.com   
      
   Thomas Womack  wrote:   
   > Ian Stirling   wrote:   
   >   
   >>You of course need to pay attention to errors and rounding.   
   >   
   > Well, yes ... I'm slightly surprised to find that, if I put massless   
   > sample bodies in a variety of circular orbits around a point-mass   
   > Iapetus, not only do the far-out ones rapidly escape into independent   
   > Saturn orbits, but the closest-in ones [1000 to 2500km] have also left   
   > orbit, on classical petal patterns, within 10^8 seconds.   
   >   
   > Is this likely to be an integrator artefact?   
      
   Yes. Do you know what kind of intergrator you are using?   
      
   > I'm re-running with half   
   > the time step (I was using 1000 seconds, which seemed pretty   
   > conservative); I have no intuition about the N-body problem, but for   
   > lower orbits *around a point mass* to be less stable than higher ones   
   > seems implausible.   
      
   Energy needs to be conserved, and integration techniques like the simple   
   Euler method suffer from the kind of results you are seeing. Methods like   
   the Euler-Cromer or Verlet method do not have that problem in simple   
   central-body problems. There are many books on numerical methods that   
   describe many known methods along with their pros and cons - such as   
   "Numerical Recipes in X" by Press et al, where X is one of several   
   programming languages (I have one with X = C, and another where X =   
   Pascal).   
      
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