Where do NEOs move?

The orbits of 7 NEAs. Orbits and image courtesy of Scott Hudson

 After having discovered a NEO, a new difficulty is posed to scientists: how can its path be predicted to verify if that precise object is due to impact the Earth?
The theoretical concept of orbit is necessary to be able to answer to this question. To illustrate this concept, two physical cases are very useful: the very simple 2-body problem, where the dynamics of two isolated bodies is examined, and the much more complicated n-body problem. On the  basis of these examples, a first approximated study of the dynamics of the solar system can be faced.


The orbits of 8 asteroids
Image courtesy of Andrea Carusi

In the case of NEOs' orbits, however, the above applications are not enough, since NEOs have highly unpredictable or chaotic orbits. In fact, even for asteroids which normally seem to have precise orbits (as the asteroids of the pictures of this page) there are several physical mechanisms that act on the dynamics of the object, modifying its theoretical, initial path.
If in the past some methods have been developed to predict orbits, such as Gauss method of determination, today, the prediction of an orbit is usually made on statistical bases, using numerical simulations with computers.