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Recent advances in algorithms for long term integrations of planetary systems

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Accurately predicting the motion of planets has kept astronomers busy since antiquity. After Newton published his law of universal gravitation in 1687, it became clear that none of the planets’ orbits were perfectly periodic. This immediately leads to the question of whether the Solar System can remain stable over long timescales. By the end of the 18th century Lagrange and Laplace were able to formulate an analytic theory which was in good agreement of observation, but the question of stability remained unanswered until a few decades ago. Only the advent of fast computers made it possible to calculate the motion of planets accurately enough to find that the Solar System is on the brink of instability and has a finite chance of going unstable within the lifetime of the Sun. Although we have solved the question about the Solar System’s stability, the discovery of thousands of other planetary systems beyond our own Solar System presents new challenges for fast and reliable numerical integration methods. We need these tools to validate and characterise planetary systems as well as to understand their formation history. After a historical overview of the subject at the beginning of my talk, I will discuss why this is such a hard problem from a mathematical point of view, and how one can nevertheless solve it. I will present some recent developments of numerical integrators with very high accuracy.

This talk is part of the DAMTP Astrophysics Seminars series.

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