# SEMINARI DI ANALISI MATEMATICA

## Evento

Titolo:
An application of Groebner bases theory to a problem of Celestial Mechanics
Quando:
07.04.2017 14.40 h
Dove:
Palazzo Campana - Torino
Aula:
Aula 5
Relatore:
Prof. Giovanni Gronchi
Afferenza:
Università di Pisa
Proponente:
W. Dambrosio
Locandina:

## Descrizione

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 $\rho_1$, $\rho_2$, $\dot{\rho}_1$,$\dot{\rho}_2$ 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 $\rho_1$or $\rho_2$ 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.

## Sede

Sede:
Palazzo Campana   -   Sito web
Via:
Via Carlo Alberto, 10
Cap:
10123
Città:
Torino
Provincia:
To
Paese:

## Descrizione

Dipartimento di Matematica, Università degli Studi di Torino