The word asteroid means "star-like", 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 Near-Earth 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 nucleus is the relatively solid and stable centrally located part, mostly formed of ice and gas with a small amount of dust and other solids like hydrocarbons. The sizes of cometary nuclei are mostly unknown since measuring them is a difficult task, but the few reliable measurements that have been done, show diameters that range from a few to 20 km.
    The composition of the nucleus is believed to be made by two parts: an interior structure embedded in a mantle.
    About the interior structure not much is known: the dominant volatile is water, followed by CO and CO2. Other minor species are believed to be present in low percentage ( <1% ). The relative abundance of the species, however varies among comets. For example, the CO/H2O ratio, which is an indication of the composition, reached 0.2 to 0.3 in Hale-Bopp but is typically 4 or 5 times smaller in other comets.
    The upper layers of the nucleus (the mantle) contain non-volatile dust, consisting of some silicate minerals and carbon rich grains. The ratio of volatile mass to refractory mass is probably near 1.
  • The coma is a dense atmosphere surrounding the nucleus, made of a cloud of water, carbon dioxide and other neutral gases as well as dust grains. It is formed when the nucleus is heated by the sun, making the gases sublimate, and is later swept into the elongated tails and a huge but very sparse hydrogen cloud (that can measure up to millions of km in diameter)
  • The dust tail is the most prominent part of a comet: it can be up to 10 million km long, composed of smoke-sized dust particles driven off the nucleus by escaping gases;
  • the ion tail is composed of plasma and laced with rays and streamers caused by interactions with the solar wind, which can be as much as several hundred million km long.

Lyapounov Time

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.



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).

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