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
2body problem, where the dynamics of two isolated bodies is examined,
and the much more complicated nbody problem. On the
basis of these examples, a first approximated study of the dynamics of the solar
system can be faced.

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. 