**Quote from Mal on 09/24/08 at 17:07:18:**

What would be really interesting would be to see how these graphs would look for an asteroid belt in a different system, but I guess we're running into computational problems because there's no way even any current computer could handle running a simulation of 10,000 (never mind 400,000) asteroids before we die of old age... is there??

I think you're right .

But there may be a solution which can reduce the computing time.

Lets say we want to compute p bodies and add n asteroids ( p=10 , n=10000) .

The computing time goes up as : T = a. (n+p)*(n+p) , so kwadratic .

10 times more bodies gives 100 times longer run ...

But : if one runs the simulation once with the p bodies and stores the obtained data , then a separate program can calculate an additional body in a time T2= b*p . ( if the asteroid is small it has no influence upon the other bodies , so they don't have to be calculated ; their previous orbits which are known reman valid ) .

So if we run this program n times we have a total time of : T2 = n*b*p . This is the time to integrate the n asteroids .

T2/T gives : b*p/(a*n) , or if a=b then : T2/T = p/n .

If p=10 and n=10000 asteroids then the simulation in this way may be performed 10000/10 = 1000 times faster ...

Of course this requires a lot of reprogramming ....

I think jpl calculates orbits of asteroids in this way , assuming an asteroid doesn't influence the major bodies ...