Probability of a single impact
The probability that a NEO of a certain
dimension will collide with Earth is fundamental to calculate the
frequency of impacts. This probability can be calculated in
several ways, from experimental observations or from theoretical
considerations (both on the observation of the Moon's craters
distribution and on the simulation of impact's frequency obtained
from computers). Here is presented a very simple estimation based
on the concept of dynamical classes of objects. From this
probability we will be able to calculate the number of impacts per years for a NEO of a
Determination of the probability of an impact
A very intuitive theoretical estimation of this probability, based on the concept of dynamical classes, has been made by the astronomer Ernst Opik in the 50s'.
The orbit of a NEO can only be determined in a statistical way, as a region of uncertainty (click here to know more about how orbits are studied statistically). So it is impossible to calculate for a single NEO the exact evolution of its orbit. Anyway, the characteristics of this orbit (such as eccentricity, and semimajor axis) are almost constant and vary only over long periods of time. In this way, all the asteroids with very similar orbital elements belong to a same dynamical class of asteroids and represent a real statistical sample. Determining a mean evolution of these orbits, it is possible to calculate a probability of impact over long periods of time.
There are two conditions the orbit of an asteroid has to respect to make an impact with a planet possible (click here to see the representation of the orbit of an asteroid, and the definitions of mutual nodes, nodal distance, etc) :
The probability that the last two hypothesis are verified at the same time, has been estimated for a single asteroid with mean values of orbital elements, obtaining :
This value has been determined in very simple, approximate conditions. A first correction of this calculus must be made considering that the real cross section of the Earth is not the geometrical one but it is bigger, making chances of collision higher, due to the phenomena of gravitational focusing. (Click here to know more about gravitational focusing). Considering this phenomenon the probability can be estimated as:
From probability to number of impacts
Once this probability of
a single impact has been estimated, it is possible to determine
the mean number of impacts per year multiplying this single
probability by the number
of NEOs of a certain dimension that
surround Earth .
We can therefore obtain an estimation of the frequency of impacts with bodies of a certain diameter:
|Diameter d||Frequency of the impact|
|d>10 Km||every 50 millions years|
|1Km<d<10Km||every 500.000 years|
|100m<d>1Km||every 5.000 years|
|30m<d<100m||every 500 years|
This table can be easily converted to the more notorious representation of the frequency versus the energy of the impact, since there is a direct correspondence between the dimension of the impactor and the energy freed in the impact event.