NEW MATHEMATICAL METHODS IN PLANETARY AND GALACTIC RESEARCH


Our project in applied mathematics studies inverse problems in the fields of planetary research and astrophysics. Data for the project are obtained from several observatories, both groundbased and satellite ones. Main sources in the near future will be large-scale sky surveys such as Pan-STARRS. The project is part of the research programme of the Finnish Centre of Excellence in Inverse Problems Research and is funded by the Academy of Finland.

In the field of space remote sensing and solar system studies, the first large group of detailed physical models of minor planets is constructed using modern mathematical methods of generalized projection operators to interpret photometric data that are also complemented by other data sources such as radar and space telescope observations as well as stellar occultations and adaptive optics. The models describe the rotational states, shapes, and surface properties of the targets. Inverse problems in general remote sensing are studied in this context as well.
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Galactic modelling and dynamical tomography aims at the construction of the first complete self-consistent dynamical model of our Galaxy (and its dark matter) using the data from large-scale sky surveys, i.e., an extensive library of measurements of stellar positions and velocities. The approach is based on the dynamical principle of viewing the Galaxy as a collection of orbits in phase space. This collection can be described self-consistently with the aid of the powerful methods of theoretical dynamics by finding phase-space distribution functions and gravitational potentials that match the data. Other related fields such as the dynamics of planetary systems also have many topics of interest such as the shield effect of giant planets.
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Modern mathematical methods as tools

The most conspicuous common property to all of the above projects is the relative simplicity of data as compared to the inferred detailed model. After all, the bulk of the observations are just simple observables such as brightnesses, positions, or velocities. Their large number facilitates the construction of unique rich models, and it is this mathematical detective job that is the common denominator in all these topics. Inverse problems are one of the most important fields of study of modern applied mathematics, and mathematically well constructed methods are the basis of our analysis.




Mikko Kaasalainen (DPhil, Oxon)
Professor of Mathematics
Department of Mathematics, Tampere University of Technology
PO Box 553, 33101 Tampere (Room: TD321)
Finland
Finnish Centre of Excellence in Inverse Problems Research
and adjunct professor at
Department of mathematics and statistics, University of Helsinki
E-mail:firstname.familyname (..) tut.fi




Links to some collaborating projects and institutes:

Astronomical Institute of the Charles University

Sodankylš Geophysical Observatory

Theoretical Astrophysics, Oxford University

Poznan Astronomical Observatory

Palmer Divide Observatory

Pan-STARRS

UC Berkeley