CCD (charged couple devices) are electronic light detectors made of finely array arrays of semiconductor picture elements called pixels. The CCD is placed on the focal plane of the telescope, replacing the old photographic plate. When light hits one pixel, its energy causes positive and negative charges to separate, leaving free electrons in the pixel. These electrons are counted all over the picture and provide an image of the light pattern seen by the telescope.


Conics are plane sections of a right-circular cone. These sections give birth to four different curves: circle, ellipse, parabola and hyperbola. These curves represent the orbits solution of the 2-body problem. They were found by Newton, who invented the infinitesimal calculus to solve this precise problem.

Escape velocity

The Escape velocity is the initial speed required for a projectile to escape from a massive body to a point at infinity.
If we consider the projectile having mass m, and the central body having mass M, this velocity can be obtained imposing that the initial kinetic energy must be equal to the potential energy of the mass M at a distance r:

Solving for v we obtain the escape velocity:



Magnitude (absolute and relative)

The brightness of any celestial body (stars, asteroids, planets, etc) is measured by a quantity called magnitude.
The classification of stars of different magnitudes is made first of all, on an historically basis: the stars cataloged by Ptolemy (2d cent. A.D.), all visible with the unaided eye, were ranked on a brightness scale such that the brightest stars were of 1st magnitude and the dimmest stars were of 6th magnitude.
The modern magnitude scale was placed on a precise basis by N. R. Pogson (1856). It was found by photometric measurements that stars of the 1st magnitude were about 100 times as bright as stars of the 6th magnitude, 5 magnitudes lower. For this reason, Pogson defined a mathematical, exponential law to formalize the magnitude's scale. This modern scale allows a precise expression of a star's relative brightness and extends to both extremely bright and very dim objects.
The measurable brightness of any celestial object depends on many parameters such as
the object's size and the distance from the observer (a candle very near you is much brighter than a very far -and very bright- star!). For this reason, the brightness of any celestial body, measured directly as you can see it, is also called relative magnitude. Since all the objects in the solar system are moving (and changing), the relative magnitude of an object changes in time.
It is therefore necessary to define an absolute magnitude for every class of objects (which can be asteroid, stars etc). An absolute magnitude is a quantity which measures a brightness independent of the distance. Normally, it indicates the magnitude the object would have if it were 1 AU from the Earth. Absolute magnitude is a measure of the intrinsic luminosity of the star, i.e., its true brightness.


Momentum and Angular momentum

Ordinary momentum is a measure of an object's tendency to move at constant speed along a straight path. Momentum depends on speed and mass. A train moving at 20 mph has more momentum than a bicyclist moving at the same speed. A car colliding at 5 mph does not cause as much damage as that same car colliding at 60 mph. For things moving in straight lines:

momentum= mass speed

When things move in curved paths, the idea of momentum can be generalized as angular momentum. Angular momentum measures an object's tendency to continue to spin or, in other words, the angular momentum is the physical quantity which describes the dynamics of objects that are spinning or revolving round an axis. An ``object'' can be either a single body or two or more bodies acting together as a single group. The angular momentum is normally defined as:

angular momentum = mass velocity distance (from the point object is spinning or orbiting around)

Let's suppose the object (or group of objects) has no outside forces acting on it (in a way to produce torques that would disturb the angular motion of the object). In these cases, we have conservation of angular momentum.

This means that the total amount of angular momentum does not change with time no matter how the objects interact with one another.

A simple example:
the angular momentum L of a dumbbell (two masses m, connected by a massless bar of length d) freely spinning on a plane with angular velocity w around the axis perpendicular to this plane and passing through the center of the bar, is computed as:

Since the dumbbell is a free spinning body, L is conserved. If, for a particular reason, the distance d changes, the angular velocity must change according to equation:

Hence, if d becomes smaller, the dumbbell must spin faster. This is, for example, the reason why an ice-skater spins faster when she keeps her arms closer to her body!!


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.


TNO (transneptunian objects)

There are at least 70,000 small bodies with diameters larger than 100 km orbiting the sun beyond Neptune, in a zone going from the orbit of Neptune (at 30 AU) to 50 AU. These objects are called TNOs and mostly occupy a thick band around the ecliptic, which is generally referred to as the Kuiper Belt. This belt is the source of the short-period comets, acting as a reservoir for these bodies in the same way the Oort Cloud acts as a reservoir for long-period comets.
The Kuiper Belt also deserves some very special attention since the objects that inhabit it are believed to be extremely primitive remnants from the early accretional phases of the solar system.
Astronomers have become aware of TNOs starting from 1992, when D. Jewitt (University of Hawaii) and J. Luu (University of California at Berkeley) reported the discovery of 1992 QB1 a very faint object which is the first TNO ever detected (in the animation: the first images of 1992 QB1).


Confidence region or 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).


Virtual impactor

Once the region of uncertainty of a NEO has been determined and its shape and position have been calculated over a long enough period of time, it is possible to evaluate the probability of impact with a planet -for example Earth-. If one of the virtual asteroids belonging to the region of uncertainty has a chance to hit Earth, it will be called virtual impactor.
To evaluate the probability of impact, we first have to define the concept of "target plane" which is the plane where the asteroid comes closer to the planet . If we consider the intersection of the region of uncertainty with this plane, we will have a plane figure (par example an ellipse). In this case, if the planet lies inside this figure, the impact is possible and its probability can be estimated as the ratio of the areas of the ellipse and the planet.
What normally happens when a virtual impactor is found, is a "follow-up" meaning that the position of the asteroid is measured again after some time has passed. In this way, the position is better determined and the region of uncertainty associated to the asteroid becomes smaller. After a second observation, the ellipse on the target plane is surely smaller. For this reason if the impact is still possible (the planet is inside the ellipse) the probability of the event will have grown up. If after a third observation the planet falls out of the region, the probability will fall to 0.

The Torino Scale

The Torino scale is a classification (similar to the Ritcher scale for earthquakes) to quantify the impact hazard of a certain NEO. This classification has been introduced, for the first time, at an International Conference on Near-Earth objects held in June 1999 in the city of Torino, as a revised version of the "Near-Earth Object Hazard Index" created by Professor P.Binzel of the MIT.
The Torino scale is a two parameters scale: it utilizes numbers form 0 to 10 to indicate the chance of a collision, while the color is used as a second parameter to give an information about the danger of the event (going from white, non dangerous bodies, to red, catastrophic events) .
The parameters that lead to the classification of an object, aside to its position and its dimension, are its kinetic energy and its collision probability. This means that, an object that will make several different close approaches of Earth, will have a different Torino scale value for each approach. Normally, only the highest of these values is considered to identify an object.
Another important thing about the Torino scale value, is that it will change in time. This change will be the result of better measurements of the object's orbit
(see probability of impact).


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