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> You make all of this sound like it's a difficult problem. It is a difficult problem. Consider all the elements of a solution on which space missions depend.

by lutusp 12y ago

> You make all of this sound like it's a difficult problem. It is a difficult problem. Consider all the elements of a solution on which space missions depend. All of them must be generated using numerical modeling methods, and for a solar system simulation in which most or all the candidate bodies are modeled, the computation load is quite high. > but you can still mathematically pick a parameter that generates something like a desired level of accuracy, instead of having to specify the parameter itself. This isn't true, or it's not assured to be true. The reason is that orbital systems with > 2 bodies meet the definition of a chaotic system, a system acutely sensitive to initial conditions. Everyone who works in this field understands that there's a time horizon past which we really cannot say what the solar system's configuration will be.

conistonwater 12y ago
> It is a difficult problem. Implementing an ODE solver good enough to use for designing spacecraft trajectories is a difficult problem. Implementing an ODE solver that can handle an n-body problem (with a fairly small n) without leaving user-visible magical parameters is not difficult. Introductory textbooks can explain how to do this. > The reason is that orbital systems with > 2 bodies meet the definition of a chaotic system, a system acutely sensitive to initial conditions. Even if you have a chaotic dynamical system, you can still solve it. You don't solve it in the sense that the trajectory you get is the correct one, because, as you rightly say, that is mathematically impossible for long time periods. But you can solve it in the sense that the solution you get "could" have originated from an initial condition close to the given initial condition. There are many interesting things you can do for complicated ODE problems. But writing ODE solvers of the level of complexity and accuracy we are talking about here is a solved problem.

by lutusp 12y ago

conistonwater 12y ago

> It is a difficult problem. Implementing an ODE solver good enough to use for designing spacecraft trajectories is a difficult problem. Implementing an ODE solver that can handle an n-body problem (with a fairly small n) without leaving user-visible magical parameters is not difficult. Introductory textbooks can explain how to do this. > The reason is that orbital systems with > 2 bodies meet the definition of a chaotic system, a system acutely sensitive to initial conditions. Even if you have a chaotic dynamical system, you can still solve it. You don't solve it in the sense that the trajectory you get is the correct one, because, as you rightly say, that is mathematically impossible for long time periods. But you can solve it in the sense that the solution you get "could" have originated from an initial condition close to the given initial condition. There are many interesting things you can do for complicated ODE problems. But writing ODE solvers of the level of complexity and accuracy we are talking about here is a solved problem.