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0 pointsstrainer9y ago0 comments

Come on it doesnt say "unknown reasons" it says the "It is possible the discrepancy is due to the limitation of javascripts 64bit FP numbers rather than subtle algorithmic or physics error"

70k km / a year (on a billion km long orbit) was a lot closer than I had hoped for, considering its a 64 bit newtonian model. But this is beside the fact that having worked on the project a fair bit, I understand that any model adjustments to conserve energy or momentum are non-physical 'fudges' to correct deficiencies of the model. There are no laws of physics dedicated to adjusting energy, momentum, information in order to conserve them. They are conserved by a mathematical correctness of every physical law - a proper account of that eludes me, but it is certainly explained somewhere.

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nonbel9y ago· 2 in thread

Right, you don't know how much error the floating point error accounts for. You also brought up loss of angular momentum to solar wind, etc. These are all just speculations. That may be fine for the purposes of your simulation, but not for predicting if asteroids will impact the earth or the influence of human activity on Earth's climate.

Also, I know you are supposed to use a symplectic integrator to ensure conservation of energy when doing these simulations, so it is not somehow hardcoded into the laws, eg: https://en.wikipedia.org/wiki/Leapfrog_integration

strainerOP9y ago

We could certainly calculate how much error was introduced by rounding, if we had the time and inclination. It is useful to understand that about numerical modelling, it should not be necessary to accept any indeterminable discrepancies.

Conservation of energy, momentum, information is hardcoded into all known laws of Physics. It is our integration algorithms which do not all ensure conservation of information - but that is carefully achievable with basic first order schemes, such as Verlet and leapfrog integration.

nonbel9y ago

>"Conservation of energy, momentum, information is hardcoded into all known laws of Physics. It is our integration algorithms which do not all ensure conservation of information - but that is carefully achievable with basic first order schemes, such as Verlet and leapfrog integration."

I am not sure about "conservation is encoded" part, but I can believe it. Either way, in practice the simulations will encounter issues along these lines if they are not careful. For example, I left your simulation running for what amounted to ~120 yrs and saturn lost all her moons. This is the best pic I could get, sorry (hopefully it is reproducible): https://i.imgur.com/C7emd28.png

Since you do not report anything about conservation of energy/momentum, how do we know that isn't the problem?

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petters9y ago

> There are no laws of physics dedicated to adjusting energy, momentum, information in order to conserve them. They are conserved by a mathematical correctness of every physical law

The physical laws guarantee conservation, yes. But not all numerical methods for solving differential equations do.

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