seminar: An application of Groebner bases theory to a problem of Celestial Mechanics
speaker: Giovanni Gronchi (Università di Pisa)abstract: We consider the orbit computation problem for a Solar system body observed from a point on the surface of the Earth. In our case the available data are two elements of the tangent bundle of the celestial sphere at two different epochs, and the unknowns are the radial distances and velocities $\rho1$, $\rho2$, $\dot{\rho}1$, $\dot{\rho}2$ of the observed body at these epochs. Using the first integrals of Kepler's motion we can write algebraic equations for this problem, which can be put in polynomial form. From these we obtain a univariate polynomial equation of degree 9 in one of the radial distances.
Using Groebner bases theory we show that this equation has the minimum degree among the univariate polynomial equations in $\rho1$ or $\rho2$ that are consequence of the conservation laws of Kepler's problem, provided that we drop the dependence between the inverse of the heliocentric distance $1
r
$ of the observed body and the unknown radial distance.
timetable:
Wed 24 Jan, 15:00 - 16:00, Sala Conferenze Centro De Giorgi
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