TITLE:
Efficient Usage of Self Validated Integrators for Space Applications

AUTHORS:
Elisa M. Alessi, Ariadna Farres, Angel Jorba, Carles Simo, Arturo Vieiro
Departament de Matematica Aplicada i Analisi
Universitat de Barcelona
Gran Via 585
08007 Barcelona, Spain
E-mails: elim@maia.ub.es, ari@maia.ub.es, angel@maia.ub.es,
carles@maia.ub.es, vieiro@maia.ub.es

ABSTRACT:
The present report addresses the possibilities offered by validated
integrators to deal with some space problems. First, we survey
previous results on validated methods for ODEs and we discuss their
sharpness and efficiency, keeping in mind their suitability for
space-related computations.

We have considered two concrete situations. The first one is the
propagation of the orbit of a NEO asteroid, starting from data
affected by observational error for a moderate time span. We have
focused on the concrete case of 99942 Apophis, which is having close
approaches to the Earth on the years 2029 and 2037. The goal here is
to check if the use of validated methods can be useful to elucidate
possible collisions of these objects with the Earth. The second
problem considered is the transfer of a probe with low thrust
propulsion from parking orbit around the Earth to a much higher orbit,
including a capture by the Moon. The goal is to see how the
uncertainties in the initial condition and the thrust affect the
propagation of the orbit.