Dictionary
The word asteroid means
"starlike", even if these minor bodies of the
Solar System don't emit light on their own, but are
visible only because they reflect sunlight. The size of
asteroids range from dust particles to significant bodies
hundreds of miles in diameter (Ceres, the largest
observed is 913 km of diameter). Globally, the total mass
of all the asteroids is less than that of the Moon. Asteroids are found in different places in the solar system: most of them orbit around the Sun, grouped in the main belt, while others are farther objects, with highly unpredictable orbits, such as the Trojans, which lie on the orbit of Jupiter, or such as the Centaurs, in the very outer solar system. Asteroids that, for some dynamical mechanism, closely approach the Earth are named NearEarth Asteroids (NEAs) and form a class of particular interest. 
Comets are made of several distinct
parts: first of all, there is a solid
snowball, called nucleus, made of dust and ice. When the
comet comes near the Sun, the nucleus heats up and
becomes active, causing volatile gas to sublime. The released gas
and dust form a cloud, or coma, and the dust element of
the tail.
Let's see in detail the different
parts of a comet :


The Lyapounov time (L) is a parameter that measures the speed rate at which orbits diverge (or, in other words, it measures how much chaotic an orbit is). L is the period of time for the distance between two near possible orbits to increase of a factor e. The bigger this value is, the more stable is the orbit (L has typical values of a few years for chaotic asteroids, upt to 5 million years for the inner planets and hundred million years for the external planets).
For a non chaotic orbit (above picture) the distance
between two near orbits that have similar initial
conditions, is a linear function of time. The two orbits
diverge slowly, and their distance can be expressed as a
linear function of time:
For chaotic orbits, the distance between two near orbits can be expressed as an exponential function of time with the formula: This formula means that after a period of 2 L, the 2 orbits will be at a distance of , meaning that this distance varies exponentially with time. 
MT
The energy freed during an impact is
usually measured by Megatons (MT). 1 MT is the energy of almost
100 Hiroshima bombs. To have an idea of the scale of energies: if
a 2 meters compact body with a speed of 20 Km/s impacts the
Earth, about 1 MT is released.
The word NEO stands for Near Earth Object, meaning a minor
body of the solar system (or in other words a comet or an
asteroid) which comes into the Earth neighborhood.
A first classification of NEOs divides NEC (Near earth comets)
from NEAs, Near Earth Asteroids.
NEAs constitute the vast majority of NEOs
and are further divided into three main families, depending on
the features of their orbits. In particular they are classified
in three groups (Amor, Apollo and Atens) according to their
perihelion and aphelion distances and their semi major axes.
In this image you can see the Earth's orbit (in blue ) and the classical shape of the obits of the three main classes of NEAs. 
Region of uncertainty  virtual asteroid
Let's consider an asteroid: making a first unique observation, its real position can only be determined with some errors. This means we can associate to the asteroid a region of uncertainty. Every point inside this region is a possible position of the object, and is therefore called virtual asteroid. For every virtual asteroid a trajectory can be calculated using computers. This can be done over periods of 50 years maximum. Doing this determination for every virtual asteroid inside the region, it is possible to know how this region evolves in time, moving and changing shape (since every virtual asteroid can follow a different orbit).