Improving The Mathematical Method For Simulating Solar System Evolution
April 12, 2013

Scientists Zero In On The Creation And Evolution Of Our Solar System

John P. Millis, Ph.D. for — Your Universe Online

It seemed that that we had everything worked out. Astronomers modeled the creation and evolution as the collapse of a giant solar nebula. As the central star formed, the radiation then influenced the formation of the planets — rocky planets dominating the inner sanctum, while the larger gas giants naturally populated the orbits further out. All of this was then encased in a spherical swarm of icy bodies known as comets.

But during the last century, researchers have found that things are not so simple. Computational models indicate that creating a solar system, such as the one in which we live, has significant variables.

In fact, it seemed that reproducing the exact structure of our solar system was a challenge. Now, as more and more solar systems in our galaxy are found, we are discovering that there is significant variation in the way these systems arise and evolve.

Trying to create a model of solar evolution that would encompass all of these dynamic systems is difficult and complex. As a result, the computational methods take a significant amount of time to process, slowing the progress of investigation.

Recently, however, a team at the Computing Faculty at the University of the Basque Country (UPV/EHU) has developed methods that allow the simulations to be done faster and more accurately. Taking a unique, interdisciplinary approach, the team was able to leverage expertise across fields of mathematics, astrophysics and computer science to expedite these kinds of studies.

Mathematician Ander Murua explains, "At the Paris Observatory there is a well-known astronomer by the name of Jacques Laskar who is doing research into the evolution of the solar system. 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. When the astronomical information obtained by Laskar by means of these calculations and simulations is compared with geological data, it is possible to know how changes in the Earth's orbit are related to glaciations and warming, and this can help to predict what could happen in the future. Both the mathematical model of the solar system and the numerical methods used are important for carrying out these simulations."

Such innovations are important, because as the Universal clock is run back in these simulations, the interactions within the solar system become more chaotic, allowing many different evolutionary paths. So studying different scenarios, and being able to refine the mathematical models, is paramount. This is difficult when each simulation takes about a year to run. But using this new technique, the same work can be accomplished in a matter of weeks.

This work 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.