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SUMMARY:Recent advances in algorithms for long term integrations of planet
 ary systems - Prof. Hanno Rein (Toronto)
DTSTART:20191111T140000Z
DTEND:20191111T150000Z
UID:TALK129202@talks.cam.ac.uk
CONTACT:Chris Hamilton
DESCRIPTION:\nAccurately predicting the motion of planets has kept astrono
 mers busy since antiquity. After Newton published his law of universal gra
 vitation in 1687\, it became clear that none of the planets' orbits were p
 erfectly periodic. This immediately leads to the question of whether the S
 olar System can remain stable over long timescales. By the end of the 18th
  century Lagrange and Laplace were able to formulate an analytic theory wh
 ich was in good agreement of observation\, but the question of stability r
 emained unanswered until a few decades ago. Only the advent of fast comput
 ers 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 fin
 ite chance of going unstable within the lifetime of the Sun. \nAlthough we
  have solved the question about the Solar System's stability\, the discove
 ry of thousands of other planetary systems beyond our own Solar System pre
 sents 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 neverth
 eless solve it. I will present some recent developments of numerical integ
 rators with very high accuracy.
LOCATION:MR14\,  Centre for Mathematical Sciences\, Wilberforce Road\, Cam
 bridge
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