The orbit determination problem consists in determining the position and velocity of a solar system body at some epoch from observations of this body. In particular, the case of optical observations, i.e. right ascension and declination, is considered here. Carl F. Gauss proposed a method that uses only three topocentric observations. His work was motivated by the challenge of recovering Ceres, the first main belt asteroid, which had been discovered on 1st January 1801 by Giuseppe Piazzi. Another classical method due to Pierre-Simon Laplace uses three observations which are assumed to be geocentric.
While at the beginning of the XIX century telescopes were able to collect only a few observations per night, modern asteroid surveys can collect many more and a much higher number of asteroids can be observed. Therefore, new problems arise in orbit determination, like for example linking together short arcs of observations of the same object taken at different nights.
In this seminar, after describing Gauss's and Laplace's methods, I will present two linkage methods that have been recently proposed
