From: jrfrank@ibm-pc.borg.retro.com   
      
   Alain Fournier  wrote in   
   news:r8W4d.31291$0f.17792@charlie.risq.qc.ca:   
      
   > You can accelerate your computations by using the   
   > exact equation of an orbit around a single mass point (elliptical   
   > orbits) and then use RK4 to model the perturbations. So you would   
   > compute a new elliptical orbit at each RK4 step, compute where the   
   > orbit would bring you at the end of the step, then use RK4 to compute   
   > how the perturbations will change that. Such a method will allow you   
   > to use larger steps which makes computations run faster.   
      
   Good point. David might be able to search for the algorithms more easily if   
   we give him the names of the methods.   
      
   The method David is planning to use (numerical integration of the perturbed   
   equations of motion) is called "Cowell's Method."   
      
   The method you describe (analytical solution of a "reference orbit" plus   
   numerical integration of the perturbations) is called "Encke's Method." The   
   tricky part is that David will have to update ("rectify") the reference   
   orbit periodically as the perturbations grow. As we both have said, this   
   may be a bit clumsy to implement in a spreadsheet.   
      
   Since David has already implemented the analytical solution as a cross-   
   check on his numerical solution, he's already partway there.   
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   JRF   
      
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