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.
Read more and visit our
model page
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)