The Rosetta spacecraft, owned and operated by the European Space Agency (ESA), passed the Lutetia asteroid at close range in summer 2010. The asteroid was measured to be more than 100 kilometres in diameter. The new research results on the asteroid, published in the journal Science, were acquired through international cooperation, and the analysis was based on a mathematical method developed by Professor Mikko Kaasalainen. The analysis conducted at Tampere University of Technology is part of the research of the Finnish Centre of Excellence in Inverse Problems Research, and is being funded by the Academy of Finland.

The density of the Lutetia asteroid was determined by calculating its mass from changes along the flight path of the spacecraft, and its volume from a model of the entire asteroid. The model was constructed mathematically, even though the spacecraft originally viewed only about half of the surface of the asteroid while flying past. Using Kaasalainen's method, developed specifically for spacecraft fly-bys, it is possible to combine ground-based light-curve measurements and adaptive-optical imaging with images taken by the space probe. "This method enabled us to create a reliable model of the part of Lutetia that wasn't visible to the spacecraft, and thereby, to calculate Lutetia's density, which proved to be much larger than the values that we've been able to get for other asteroids," Kaasalainen explains.

Mathematics in space research

"Lutetia's history was constructed much like a puzzle; research groups from different fields all around the world contributed their input to create the final result," says Kaasalainen. "The high density, large number of old impact traces, and other surface characteristics led geologists to conclude that Lutetia likely has a metallic core surrounded by a more porous outer layer. Despite its dents and knocks, Lutetia has remained nearly in its original shape, unlike the majority of asteroids, which mostly have come together from a number of impact fragments. Targets such as Lutetia are extremely valuable, because they provide us with information about the conditions that existed at the dawn of our solar system."

The Lutetia fly-by also proved the accuracy of the generalised method for asteroid modelling, which is based only on ground-based analysis and was developed by Kaasalainen in collaboration with the international research network. "We were amazed to notice that the preliminary model made of Lutetia prior to the fly-by and used in the planning of the flight path of the spacecraft proved valid with the accuracy of a minor percentage for the entire area of which we got spacecraft images."

In autumn 2008, Rosetta made a similar fly-by past the notably smaller Steins asteroid. The asteroid was analysed using the same method as Lutetia, and the results were published in Science magazine in 2010. In terms of its structure, Steins is quite different from Lutetia. It more closely resembles a gravel heap, and its development has been shaped by the effect of sunlight on its spin state. The observations concerning this phenomenon, as made by Kaasalainen's team, were published in Nature magazine in 2007. The Rosetta spacecraft is currently heading toward its final destination, the comet Churyumov-Gerasimenko, which it is expected to reach in 2014.

Kaasalainen is involved in ESA's Rosetta research consortium, which has 58 members representing 11 countries and 33 different research institutes. It is this consortium that is responsible for the Lutetia publication. Kaasalainen is also vice director of the Finnish Centre of Excellence in Inverse Problems Research, which develops and applies mathematical methods for the interpretation of different observational data for many different fields, ranging from biology to cosmology.

Note: If no author is given, the source is cited instead.

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