absolute magnitude (H):
Measure of the intrinsic brightness of the object. The fainter is the body, the higher is H. Once the albedo is known, H is related to the size of the object.

albedo:
Measure of the reflectivity of the object. It is defined as the fraction of the received light that is reflected into space. Bodies made of carbon-rich material are dark, and thus have small albedos (~6%), while stony bodies and metallic bodies, have moderate (~20%) and large (~40%) albedos, respectively.

Amors: NEO sub-population with perihelion distance larger than 1 AU and smaller than 1.3 AU

aphelion distance (Q): Maximal distance from the Sun that the object reaches along its elliptic orbit.

Apollos: NEO sub-population with perihelion distance smaller than 1 AU and semi major axis larger than 1 AU.

apparent magnitude (V):
Measure of the brightness of the body seen by the observer. The fainter appears the body, the higher is V. Given the absolute magnitude of the object, the apparent magnitude depends on the position of the object relative to the Sun and the observer.

asteroids: Small bodies of rocky composition. Unlike comets, they do not liberate  gasses and dust due to the solar heat

Atens: NEO sub-population with semi major axis smaller than 1 AU and aphelion distance larger than 0.983 AU.

Astronomical Unit (AU):
Average distance of the Earth from the Sun. Approximately equal to 150 million kilometres.

bias:
Correction factor that relates the real population to the observed population. It is typically a function of the body's orbital elements a,e,i and absolute magnitude H. Once the bias B is known, in principle the real number of objects N can be estimated as N(a,e,i,H)=n(a,e,i,H)/B(a,e,i,H), where n is the number of objects detected by the survey.  The problem, however, is resolution; even a coarse binning in the 4-dimensional orbital-magnitude space of the bias function and of the observed distribution requires the use of about 10,000 cells.  The total number of NEOs detected by the most efficient surveys is a few hundreds. Thus, n is zero in the vast majority of the cells, and it is equal to 1 in most other cells; cells with n>1 are very rare. The de-biasing of the NEO population is therefore severely affected by small number statistics. This is the reason that motivated our innovative methodology.

bulk density:
Ratio between the mass of a body and its volume.

celestial mechanics:
Science that studies the motion of bodies in space.

close encounter:
The passage of a body in the vicinity of a planet, that causes the deflection of  the body's trajectory.

comets: Small bodies of icy compositions. When heated by the Sun in the inner solar system they liberate gasses and dust, which give them the typical cometary appearance. Nevertheless, it is believed that old comets, which have lost most or all of their volatiles, may become dormant, and assume an asteroidal appearance.

detection efficiency:
The fraction between the number of objects detected by the survey and that of the objects in the survey's field of view. The detection efficiency is never 100%, because the objects can overlap with stars or galaxies or, if they are faint, be confused within the noise of the image background.

eccentricity (e): Measure of the ellipticity of the orbit. A circular orbit has e=0 while a segment has e=1.

ecliptic:
The curve defined by the apparent motion of the Sun in the sky.

ecliptic latitude & longitude:
System of coordinates that define the position of an object in the sky. The latitude measures the distance of the object from the ecliptic while the longitude measures the position of the projection of the object on the ecliptic.

inclination (i): Angle between the plane that contains the orbit of the body and the  orbital plane of the Earth.

Inner Earth Objects (IEO): Objects with aphelion distance smaller than the perihelion distance of the Earth. Consequently, these objects are always inside the Earth's orbit. This makes them particularly difficult to be discovered from the ground, and in fact no object of this category has yet been found.

Intermediate Mars-Crossing (IMC) population:
Asteroid population with perihelion distance larger than  1.3 AU, semi major axis between 2.06 and  2.8 AU, inclination  below the location of the nu6 resonance, and crossing the orbit of Mars during a secular oscillation cycle of their eccentricity. Many asteroids in the IMC population become NEOs on a timescale of several tens of million years. Nevertheless the IMC population does not shrink in number, because it is directly replenished by an extensive network of resonances that continuously transport asteroids from the main belt into the IMC region.

Jupiter Family Comets (JFC):
Population of short periodic comets with low inclination, on Jupiter-crossing  or quasi-crossing orbits. They are believed to come from the populations situated beyond the orbit of Neptune: the Kuiper belt and the Scattered disk.

limiting magnitude:
The apparent magnitude at which the detection efficiency drops to 50% of the detector's peak efficiency.

longitude of perihelion:
Orientation of the perihelion of the orbit.

main belt:
Region between Mars and Jupiter inhabited by a large number of asteroids.

megaton TNT (MT):
Unit of measure for the energy of an explosion. The Hiroshima atomic bomb liberated an energy of 0.015 MT.

Minimal Orbital Intersection Distance (MOID);
The MOID is the minimal distance between the orbits of two objects.

nu6 resonance:
Resonance that occurs when the precession frequency of the asteroid's longitude of perihelion is equal to the sixth secular frequency of the planetary system. The latter is related to the mean precession frequency of Saturn's longitude of perihelion, but it is also relevant in the secular oscillation of the eccentricity of Jupiter.

Near Earth Objects (NEO):
Asteroids and comets on orbits with perihelion distance q<1.3 AU and aphelion distance Q>0.983 AU. They are subdivided in the Apollo, Amor and Aten subclasses. For simplicity in the text, under the name NEO we also include the population of Inner Earth Objects.

opposition:
Point in the sky that is opposite to the apparent position of the Sun.

Outer Belt (OB) population:
Asteroids with semi major axis larger than 2.8 AU and perihelion distance smaller than 2.4 AU. Like the asteroids in the IMC population, also bodies in the OB population become NEOs  on a timescale of several tens of million years.

perihelion distance (q): Minimal distance from the Sun that the object reaches along its elliptic orbit.

Potentially Hazardous Objects (PHOs):
NEOs with MOID<0.05 AU and H<22. These bodies pass sufficiently close to the Earth orbit and are big enough to constitute a potential danger. In fact, planetary perturbations can decrease in about a century the MOID from 0.05 AU to less than the Earth's radius, at which point a collision with our planet can occur.

precession:
Slow rotation of an angle that defines the orientation of the orbit in space.

semi major axis (a): Measure of the size of the orbit (mean between perihelion and aphelion distance). It is related to the orbital period by the third law of Kepler (the cube of the semi major axis is proportional to the square of the period).

Spaceguard goal:
The discovery and orbital determination of 90% of the H<18 NEOs within 2008.

steady state:
State reached when the number of  new elements entering the population equals the number of elements eliminated from the population in the same timespan.Hence, though individuals evolve, the population as a whole remains the same. An example of steady state is that of a society with zero growth, where the number of children born in the year is equal to the number of individuals that have passed away. For the NEO population, the existence of a steady state is suggested by the observation that the cratering rate of the Moon has been roughly constant over the last 3.5 billion years.

taxonomic class:
Group of asteroids with similar spectral properties of the reflected light. It is generally accepted that asteroids of the same taxonomic class share a similar chemical composition. The asteroids of the C taxonomic class should be similar to carbonaceous chondritic meteorites, while the asteroids of the S taxonomic class should be similar to ordinary chondritic meteorites.

terrestrial planet:
A planet of rocky composition, like Mercury, Venus, the Earth or Mars

Trojans:  Small bodies  having, on average, the same orbital period of a planet. They are located around the so-called L4 and L5 Lagrange equilibrium points. The latter form, with the Sun and the planet, two equilateral triangles.

3:1 resonance:
Resonance that occurs at 2.5 AU, where the orbital period of the asteroid is one third of that of Jupiter.