Far out cosmology: instability of orbits (Introduction)

by David Turell , Tuesday, May 16, 2023, 18:51 (555 days ago) @ David Turell

Our planets have slightly shifting orbits. Can they crash?:

https://www.quantamagazine.org/new-math-shows-when-solar-systems-become-unstable-20230516/

"For centuries, ever since Isaac Newton formulated his laws of motion and gravity, mathematicians and astronomers have grappled with this issue. In the simplest model of the solar system, which considers only the gravitational forces exerted by the sun, the planets follow their elliptical orbits like clockwork for eternity. “It’s kind of a comforting picture,” said Richard Moeckel, a mathematician at the University of Minnesota. “It’s going to go on forever, and we’ll be long gone, but Jupiter will still be going around.”

"But once you account for gravitational attraction between the planets themselves, everything gets more complicated. You can no longer explicitly calculate the planets’ positions and velocities over long periods of time, and must instead ask qualitative questions about how they might behave. Might the effects of the planets’ mutual attraction accumulate and break the clockwork?

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"...in three papers that together exceed 150 pages, Guàrdia and two collaborators have proved for the first time that instability inevitably arises in a model of planets orbiting a sun.

“'The result is really very spectacular,” said Gabriella Pinzari, a mathematical physicist at the University of Padua in Italy. “The authors proved a theorem that is one of the most beautiful theorems that one could prove.” It could also help explain why our solar system looks the way it does.

***

"The new papers tackle a true n-body problem — showing that instability arises in a planetary system where three small bodies revolve around a much larger sun. Even though the size and shape of the orbits might spend a long time oscillating around fixed values, they will eventually change dramatically.

"This had been expected — it was widely believed that stability and instability coexist in this kind of model — but the mathematicians were the first to prove it.

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"The results provide a potential explanation for why the planets in our solar system have orbits that all lie nearly in the same plane. It shows that something as simple as a large angle of inclination can be a source of a great deal of instability, on multiple counts. “If you start with a situation where the mutual inclinations are quite big, then you will destroy the system quite ‘quickly,’” Chenciner said. “It would have been destroyed hundreds, thousands of centuries ago.”

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"Mathematicians now hope to use Clarke, Fejoz and Guàrdia’s techniques to prove instability in models that look more like our own solar system. These kinds of results are becoming particularly meaningful as astronomers uncover more and more exoplanets orbiting other stars, showcasing a broad range of configurations. “It’s like an open lab,” said Marian Gidea, a mathematician at Yeshiva University. “To understand on paper what types of evolutions of planetary systems can happen, and to compare that with what you are able to observe — it is very exciting. It gives a lot of information about the physics of our universe, and about how much of this our mathematics is able to capture through relatively simple models.”

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"The ultimate goal would be to prove instability in our own solar system. “I wake up in the middle of the night thinking about it,” Clarke said. “I would say that would be the real dream, but it would be a nightmare, wouldn’t it? Because we’d be screwed.”

Comment: stability within instability, and our planets stay in their orbits. Did this happen by chance? I think not.