A millimetre makes a world of difference when calculating planetary trajectories

Calculating the trajectories of two gravitating bodies is straightforward mathematics. But introducing even just one more variable into an orbital system can make its long-term trajectory impossible to predict. In 2009, two researchers at the University of California, Santa Cruz investigated just how difficult this mathematical phenomenon – known as the ‘N-body problem’ – makes forecasting the eventual fate of our own corner of space. The team ran 2,000 simulations of the solar system’s trajectory up to 5 billion years into the future, with the only variable being less than a millimetre difference in the distance between Mercury and the Sun. The simulations yielded a stunning array of results, including the possibility of Mercury careening into the Sun, colliding with Venus and destablising the entire inner solar system. This animation from TED-Ed breaks down the N-body problem with rich visuals and methodical clarity, and concludes with scientists’ efforts to minimise N-body unpredictability as humans press further into space.