Four Pages and a New StoryĬenturies ago, it was already clear that interactions among the planets could have long-term effects. “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 result is really very spectacular,” said Gabriella Pinzari, a mathematical physicist at the University of Padua in Italy. Now, 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. ![]() “You want to understand what mathematical mechanisms drive instabilities, and to prove that they actually exist,” said Marcel Guàrdia, a mathematician at the University of Barcelona. Furthermore, they don’t provide an underlying explanation for why certain events might unfold. They can’t be completely precise, and as the simulations themselves show, a small imprecision might - over the course of billions of simulated years - lead to very different outcomes. But those simulations, though important, aren’t the same as a mathematical proof. Might the effects of the planets’ mutual attraction accumulate and break the clockwork?ĭetailed numerical simulations, like those published by the Paris Observatory’s Jacques Laskar and Mickaël Gastineau in 2009, suggest that there’s a small but real chance of things going haywire. 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. “It’s going to go on forever, and we’ll be long gone, but Jupiter will still be going around.”īut once you account for gravitational attraction between the planets themselves, everything gets more complicated. “It’s kind of a comforting picture,” said Richard Moeckel, a mathematician at the University of Minnesota. 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. Perhaps the solar system was not as stable as people once thought.įor centuries, ever since Isaac Newton formulated his laws of motion and gravity, mathematicians and astronomers have grappled with this issue. Venus and Earth could, in a slow, cosmic dance, exchange orbits several times before eventually colliding. Sometimes, as it cut its new path through space, its behavior destabilized other planets as well: Mars, for instance, might be ejected from the solar system, or it might crash into Earth. Its elliptical trajectory gradually flattened, until the planet either plummeted into the sun or collided with Venus. The shape of Mercury’s orbit changed significantly. ![]() ![]() The planets continued to revolve around the sun, tracing out ellipse-shaped orbits that looked more or less the way they have throughout human history.īut around 1% of the time, things went sideways - quite literally. In most of those simulations - which varied Mercury’s starting point over a range of just under 1 meter - everything proceeded as expected. After building a detailed computational model of our solar system, they ran thousands of numerical simulations, projecting the motions of the planets billions of years into the future. In 2009, a pair of astronomers at the Paris Observatory announced a startling discovery.
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