Posted: Apr 16, 2013 
Speeding up research into the evolution of the solar system

(Nanowerk News) Logging the evolution of the solar system sounds like a job which could take just as long as it took for its planets to form. This hasn't stopped scientists from trying, however, and their work has led to the development of numerical mathematical methods and simulations which have so far been able to look 250 million years back into the history of the solar system.

In an attempt to obtain a comprehensive picture of the solar system's evolution in a much shorter time, mathematicians at the Computing Faculty of the University of the Basque Country (UPV/EHU) have developed new numerical methods which enable simulation calculations to be done faster and more accurately.

The team at UPV/EHU have harnessed the research potential of interdisciplinary collaboration by cooperating with mathematicians, computer scientists, physicists and astronomers at the Universities of Valencia and Castellon and the Paris Observatory.

'There is a wellknown astronomer by the name of Jacques Laskar at the Paris Observatory who is doing research into the evolution of the solar system,' says Ander Murua, a mathematician at UPV/EHU. 'Among other things, Laskar has developed precise mathematical models of the solar system and by using numerical methods in powerful computers he has made calculations to find out how the solar system has evolved over millions of years.'

Laskar's team did their latest simulation about three years ago and went back 250 million years. It took the computers a whole year to do it. Nevertheless, according to Laskar, even though the results obtained for the last 50 million years are reliable, those from further back lose reliability because of the chaotic behaviour of the system.

'Apparently, the next time Laskar does a simulation, he would like to achieve a reliability of the results for a period of 70 million years, by finetuning the mathematical model and improving the numerical methods to do the calculations,' says Murua.

Laskar issued a challenge via mutual acquaintances to the mathematicians at UPV/EHU to develop faster and more accurate simulations. This led to wider collaboration and brought Murua and computer scientists Joseba Makazaga and Mikel Antoņana together at the UPV/EHU's Computing Faculty where they began working to refine Laskar's approach.

'We responded to the challenge issued by Laskar and we have improved the numerical methods used in the simulation,' Murua says. 'Our team has largely been responsible for developing numerical methods that are more effective those known so far. First, we have achieved greater accuracy and secondly we have considerably reduced the time needed to do the calculations.'

In fact, they have carried out many experiments to verify the validity of their new numerical methods and have seen that the simulation can be done ten times faster than with previous methods. 'We don't know when Laskar is planning to do the simulation again, but when he does, we won't have to wait a year for the results, the work will be completed in a matter of weeks,' according to Murua.

In the meantime, an explanation of the numerical methods developed has been published in the scientific journal Applied Numerical Mathematics in an article entitled 'New families of symplectic splitting methods for numerical integration in dynamical astronomy'.

In addition, Murua has announced that they will also be publishing the results of the comparison between the new methods and the previous ones in the journal Celestial Mechanics and Dynamical Astronomy.
