4 ms·

Notice that this is about new, particularly wild, solutions of the multi-body problem. By Kolmogorov-Arnold-Moser theorem, such unstable solutions form a negli

Notice that this is about new, particularly wild, solutions of the multi-body problem. By Kolmogorov-Arnold-Moser theorem, such unstable solutions form a negligible set among all possible initial conditions. The solar system is, still, stable with probability one.

londons_explore 3y ago
The article suggests around 1% of simulations show unstable behaviour...
TheOtherHobbes 3y ago
Perhaps you can explain why you think KAM somehow proves this while there are simulations - and this new work - which prove the opposite. Those models are all perfectly Newtonian. The solar system isn't. It's usefully Newtonian on the timescales we use to push things around it. But over much longer timescales planetary orbits are influenced by variations in the solar wind, visits from external objects, redistributions of mass in the Kuiper Belt and Oort cloud, and so on. These are mostly tiny influences, but enough to make claims of unconditional stability rather questionable.
- selimthegrim 3y ago
  If you read the paper that the article cites on Arnold diffusion KAM is certainly considered and discarded
- enriquto 3y ago
  [Disclaimer: not an expert on ODE, so I don't really know what I'm talking about] I was just astonished by the title of the article, because it seemed to contradict KAM. Yet, upon careful reading, you can interpret the title in that "a solar system model" is unstable, but not all of them. Which does not contradict KAM. If I understand it well, KAM is compatible with the following two sentences: (1) the set of stable initial conditions is of volume 1 in phase space (2) the set of unstable initial conditions is dense in phase space. Like the rationals are dense inside the reals, but still most reals are irrational. What is the case here? I'm not knowledgeable enough to read past the abstract of these publications.

londons_explore 3y ago

The article suggests around 1% of simulations show unstable behaviour...

TheOtherHobbes 3y ago

Perhaps you can explain why you think KAM somehow proves this while there are simulations - and this new work - which prove the opposite. Those models are all perfectly Newtonian. The solar system isn't. It's usefully Newtonian on the timescales we use to push things around it. But over much longer timescales planetary orbits are influenced by variations in the solar wind, visits from external objects, redistributions of mass in the Kuiper Belt and Oort cloud, and so on. These are mostly tiny influences, but enough to make claims of unconditional stability rather questionable.

selimthegrim 3y ago
If you read the paper that the article cites on Arnold diffusion KAM is certainly considered and discarded
enriquto 3y ago
[Disclaimer: not an expert on ODE, so I don't really know what I'm talking about] I was just astonished by the title of the article, because it seemed to contradict KAM. Yet, upon careful reading, you can interpret the title in that "a solar system model" is unstable, but not all of them. Which does not contradict KAM. If I understand it well, KAM is compatible with the following two sentences: (1) the set of stable initial conditions is of volume 1 in phase space (2) the set of unstable initial conditions is dense in phase space. Like the rationals are dense inside the reals, but still most reals are irrational. What is the case here? I'm not knowledgeable enough to read past the abstract of these publications.