Bulletin

Issue: April 2005

Research in Action

Crunching Big Numbers for Space Missions

The mathematics behind lengthy space odysseys—like the current NASA Cassini-Huygens missions to Saturn and Titan—may be enhanced thanks to the work of La Trobe University Professor of Mathematics, Reinout Quispel.

With six other leading international academic mathematicians, Professor Quispel has received a $229,000 ARC Discovery grant over three years to work on an area of maths known as the numerical solution of differential equations.

This is a part of numerical analysis which is basically the mathematics of computer programs—although it had existed for more than a century before the computer was developed.

A century ago complex mathematical problems were solved by a room of people doing calculations—and they came to be known as computers. About a decade ago Professor Quispel was one of a group that developed a novel approach to numerical analysis.

Now that expanded group, Professor Quispel (Australia), Professor Arieh Iseries, Professor Ban Leimkuher and Dr Elizabeth Mansfield (all UK), Professor Robert McLachlan, (New Zealand), Professor Hans Munthe-Kaas (Norway) and Dr Mark Sofroniou (Italy), is intensifying its research.

All members of the group have worked for varying periods of time at La Trobe in recent years developing the new geometric approach or code.

‘We have developed a geometric approach to computer programs which basically means we use geometry to improve the programs and the new ARC Discovery grant enables us to progress these ideas,’ Professor Quispel said.

‘This project gives an important boost to Australia’s strength in the niche area of geometric numerical integration, in the face of strong international competition,’ he added.

‘The methods we are developing will enable more accurate computer calculations particularly applicable to the navigation of space craft on lengthy missions.

‘It will help to create new computer programs to improve calculations in dynamics with applications not only to distant space travel but in areas ranging from astronomy, through physics, chemistry, biology, meteorology and finance.

‘It will also lead to La Trobe being able to produce world class graduates and research training in this field,’ Professor Quispel said.

Part of the ARC grant will be used to support a post doctoral fellow, Dr Yajuan Sun from Beijing, who will work with Professor Quispel and Dr David McLaren at La Trobe for at least a year. Her work will complement that of Dr Volker Grimm, a German mathematician who has been at La Trobe for more than a year and will soon return to Germany. Dr Grimm’s presence at La Trobe was supported by a previous ARC grant.

While working at La Trobe, Dr Grimm has produced illustrations demonstrating the efficiency of the geometric code in computations of the orbits around the sun of the five outer planets in the solar system—Jupiter, Saturn, Uranus, Neptune and Pluto.

He produced two diagrams, the first illustrating the orbits as calculated by a traditional computer code and in the second, the same orbits as calculated using the geometric code.

‘Using the traditional code the planets seem to spiral in to the sun. This spiralling is not observed in practice, and is caused solely by the fact that the traditionally used code is inadequate. The geometric code suffers none of these drawbacks,’ Dr Grimm said.

Professor Quispel said that the inter-national group of three space agencies and 17 nations are using mathematics in the general area of computation of differential equations to navigate the Cassini space-craft which has sent back images of Saturn and later the Huygens space probe scheduled to examine the surface of Saturn’s moon, Titan. •

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