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 [Tony] calculation errors? (asteroid belts) (Read 10996 times)
 EDG Ultimate Member oh, crumbs!!! Posts: 611 Gender: Re: [Tony] calculation errors? (asteroid belts) Reply #1 - 10/12/08 at 10:13:22   Well I'm stumped. Here's a 60 year animation of the belt, but this time the asteroids have 0 mass and 0 radius, so they're massless points. And still the flicking is there (and it looks pretty much the same as the previous graph, so I doubt if it's anything to do with the asteroids perturbing eachother). To give an idea of scale, the eccentricity is varying between the order of 1e-5 and 1e-3 here.     Given that it's still happening with massless points (so they can have no gravitational influence at all on eachother), could this just be down to some kind of rounding/calculation error in the program? I can't think of anything else it could be, since gravity can't be the cause.     Though strangely enough, if you look at the animation, the flicking seems to go from left to right from the inner edge of the belt, but from right to left from the middle/far edge of the belt, and it seems to converge on 1 AU. Is that real or just an illusion of the animation? Could that signify anything? Back to top (formerly known as Mal)   IP Logged
 EDG Ultimate Member oh, crumbs!!! Posts: 611 Gender: Re: [Tony] calculation errors? (asteroid belts) Reply #2 - 10/12/08 at 10:14:02   Frank reckons this may be caused by the Euler algorithm itself:   Quote from frankuitaalst on 10/12/08 at 02:45:17:In my opnion this is due to the algoritm of integration of the Euler method . This method works very well , but induces some inaccurancies of the positions of the asteroids . The closer the objects come , ie as speed increases the error increases also . In the long term the effect is almost zero , but individual values tend to oscillate around the exact value . If you run the same at smaller timesteps the error should decrease also . I wonder how Tony interpretes this . Back to top (formerly known as Mal)   IP Logged
 EDG Ultimate Member oh, crumbs!!! Posts: 611 Gender: Re: [Tony] calculation errors? (asteroid belts) Reply #3 - 10/12/08 at 10:17:15   To try out Frank's idea, I ran the massless particle simulation again but at a 4k timestep. Sure enough, the oscillation is smaller (as shown below - the vertical axis is the same scale as before), so I think he's on to something. Again the scale of the oscillation is small, of the order 1e-3 to 1e-5.     If it is indeed a calculation issue, is there any way to reduce this at higher timesteps (sure, we can run the sims at lower timesteps, but then we'd never get anything done because it'd take forever to run them!)? Could this issue be introducing errors that are propagating into all the bodies in all the simulations? (e.g. if a given asteroid's eccentricity would only be pumped to higher values by another body if it was greater than zero, then these errors could be causing the orbits of bodies to evolve that shouldn't be evolving) Back to top (formerly known as Mal)   IP Logged