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<blockquote style="position: relative; padding-left: 55px;"><section><a href="https://mastodon.social/users/hannorein/statuses/114824027259648031">Hanno Rein (hannorein@mastodon.social)'s status on Sunday, 13-Jul-2025 07:04:57 JST</a><a href="https://mastodon.social/@hannorein" title="hannorein@mastodon.social"><img src="https://gnusocial.jp/avatar/297401-48-20241118004232.webp" width="48" height="48" alt="Hanno Rein" style="position: absolute; left: 0; top: 0;">Hanno Rein</a><div><a href="https://mastodon.social/@hannorein/114795388419993266" rel="in-reply-to">in reply to</a></div></section><article><p>💫🌎 My group's new paper is now on the arXiv. We do something really simple that I'm surprised nobody has done before: a convergence study of N-body simulations of the Solar System. We find that timesteps can be ridiculously large and still yield physical results. Specifically, the timestep can be as large as 1/3 of Mercury's orbital period, or ~32days. This works because the Solar System is chaotic and secular, not mean-motion resonances are driving the evolution. <a href="https://arxiv.org/abs/2507.04987" rel="nofollow">https://arxiv.org/abs/2507.04987</a></p></article><footer><a rel="bookmark" href="https://gnusocial.jp/conversation/5343396#notice-10482512">In conversation</a><time datetime="2025-07-13T07:04:57+09:00" title="Sunday, 13-Jul-2025 07:04:57 JST">about a year ago</time> <span>from <span><a href="https://mastodon.social/@hannorein/114824027259648031" rel="external" title="Sent from mastodon.social via ActivityPub">mastodon.social</a></span></span><a href="https://mastodon.social/@hannorein/114824027259648031">permalink</a><h4>Attachments</h4><ol><li><article><header><div>Domain not in remote thumbnail source whitelist: arxiv.org</div><h5><a href="https://arxiv.org/abs/2507.04987">On the convergence of N-body simulations of the Solar System</a></h5><div></div></header><div>Most direct N-body integrations of planetary systems use a symplectic integrator with a fixed timestep. A large timestep is desirable because simulations run fast. However, simulations yield unphysical results if the timestep is too large. Surprisingly, no systematic convergence study has been performed on long (Gyr) timescales. In this paper we present numerical experiments to determine the minimum timestep one has to use in long-term integrations of the Solar System in order to recover the system's fundamental secular frequencies and instability rate. We find that timesteps of up to 32 days, i.e. a third of Mercury's orbital period, yield physical results in 5 Gyr integrations. We argue that the chaotic diffusion that drives the Solar System's long-term evolution dominates over numerical diffusion and timestep resonances. Our results bolster confidence that most simulations in the literature are indeed converged and provide guidance on how to run time and energy efficient simulations while making sure results can be trusted.</div><footer></footer></article></li></ol></footer></blockquote>

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Hanno Rein (hannorein@mastodon.social)'s status on Sunday, 13-Jul-2025 07:04:57 JST Hanno Rein
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💫🌎 My group's new paper is now on the arXiv. We do something really simple that I'm surprised nobody has done before: a convergence study of N-body simulations of the Solar System. We find that timesteps can be ridiculously large and still yield physical results. Specifically, the timestep can be as large as 1/3 of Mercury's orbital period, or ~32days. This works because the Solar System is chaotic and secular, not mean-motion resonances are driving the evolution. https://arxiv.org/abs/2507.04987
In conversationabout a year ago from mastodon.socialpermalink
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1. Domain not in remote thumbnail source whitelist: arxiv.org
  On the convergence of N-body simulations of the Solar System
  Most direct N-body integrations of planetary systems use a symplectic integrator with a fixed timestep. A large timestep is desirable because simulations run fast. However, simulations yield unphysical results if the timestep is too large. Surprisingly, no systematic convergence study has been performed on long (Gyr) timescales. In this paper we present numerical experiments to determine the minimum timestep one has to use in long-term integrations of the Solar System in order to recover the system's fundamental secular frequencies and instability rate. We find that timesteps of up to 32 days, i.e. a third of Mercury's orbital period, yield physical results in 5 Gyr integrations. We argue that the chaotic diffusion that drives the Solar System's long-term evolution dominates over numerical diffusion and timestep resonances. Our results bolster confidence that most simulations in the literature are indeed converged and provide guidance on how to run time and energy efficient simulations while making sure results can be trusted.

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