Title:
Dynamical simulations of planetary systems
Abstract:
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 for planetary systems.