Orateur
Description
The modern asteroid surveys are producing very large databases of optical observations. Linking very short arcs (VSAs) of such observations we can compute the asteroid orbits. Searching for
efficient linkage algorithms is an interesting mathematical problem.
We show how this problem can be faced using the first integrals of Kepler's problem.
Using all these integrals we find an overdetermined polynomial system of 9 equations in 6 variables, that is generically inconsistent, i.e. it does not have solutions, not even in the complex field, also when the two VSAs belong to the same observed body. We show how we can select two polynomial subsystems $\mathcal{S}_1, \mathcal{S}_2$ that are still overdetermined, but consistent, and define two algebraic varieties with the lowest number of points (9 and 18 respectively). Moreover, we search for compromise solutions of both $\mathcal{S}_1$ and $\mathcal{S}_2$ using the concept of approximated gcd.
This is a joint work with Clara Grassi.
