What are NEOs?
What danger do NEOs represent?
How the asteroids and comets are named?
The orbital elements.
Orbit determination and improvement.
Absolute magnitude.
The correlation between absolute magnitude H and diameter D of asteroid.
The form of asteroids.
What are Atens, Apollos, Amors?
What are PHAs?
How many NEAs have been discovered until now?
What is the source of NEAs?
About resonances in the Solar system.
Known close approaches of asteroids to the Earth.
How correct a prediction of dangerous approaches can be?
The Torino and Palermo scales.
The goal of NASA in NEA discovery program.
About the observations of NEOs.
Who and how do study NEOs?
NEO discovery programs.
NEO follow-up activity.
Pulkovo works.

What are NEOs?
Near Earth objects (NEOs) are asteroids (NEAs) and comets that can approach to the Earth in a motion along their orbits. These close approaches may be very dangerous to the world civilization, because the possibility of collision is not zero. The investigation of these objects is a great and difficult task for specialists in many disciplines. One can notice in recent years a growth of interest to the study of asteroids and comets that could explain many problems of the origin and evolution of the Solar system. But there is a peculiarity about which no one can forget: small as it be a possibility of collision with a large object, the consequences of such phenomenon are catastrophic. So besides the scientific aspect this study has an important applied value. The international service is required for NEO discovery and follow-up in order to predict all dangerous approaches.

What danger do NEOs represent?
Each day many tons of space matter bombard the Earth in the form of meteoroids - small stone or metallic particles that mainly burn in the Earth's atmosphere. Such phenomenon is known as a meteor. If some fragments reach the Earth's surface they are called meteorites. The collections of meteorites exist all over the world. Their physical and chemical behavior can give some clues to the nature of greater Solar system bodies. The asteroids with sizes of a few meters are capable for the local destruction. The asteroids tens or hundreds meters in diameter can produce a devastation of a regional scale. The kilometer-sized asteroids have an energy that can destroy the most part of biosphere including a whole mankind. The global catastrophe is conditioned by the supplemental factors, such as earthquakes and tsunamis, fires, acid rains, the sunshine blockage and others. It is current hypothesis that the dinosaurs die out of such collision 65 million years ago. It is admitted also that phenomena of this sort happen one time in a few hundreds thousand years. But all these estimations are quite uncertain. Only one item is doubtless here - the global catastrophic consequences of such collision.

How the asteroids and comets are named?
The observations are sent to the Minor Planet Center (MPC, http://www.harvard.edu/, director Dr. B.Marsden) that works much on the collection, control, processing and dissemination of the data. When a new object is discovered it receives a provisional designation that consists of the year and alphanumeric combination that includes two letters and one to three numbers. The first letter identifies the half-month of discovery in natural order (except for reserved "I" and "Z"). The second letter points to the order of discovery in this time interval, the letter "Z" being used. If more than 25 new objects are discovered for a half-month the second letter repeats the same positions accompanied by the index 1. For the orders from 51 to 75 the index 2 is used and so on. For example: 2002 MN - the second half of June, 1996 JA1 - the first half of May, 1994 WR12 - the second half of November, 2000 SG344 - the second half of September. The ordinary numbers, not indexes, are used more frequently, especially in the data files. Sometimes the chains of various designations of the same object are fixed. If to take into account that the number of discovered asteroids is more than 400 thousand it is clear how important is the correct naming of these objects. The reduced seven symbol notation is used frequently where the first two digits of the year are changed to the letter (19 - J, 20 - K) and the first two symbols of three digits number are transformed into the letter according to the rule: 10 - A, 11 - B, ..., 35 - Z. This number is placed between two letters. The designations cited above are as follows in this notation: K02M00N, J96J01A, J94W12R, K00SY4G. Some non-standard designations point out the objects that were discovered within the special search programs, for example: 6344 P-L (Palomar-Leiden), 5036 T-3 (Troyan search). If the asteroid's orbit becomes known quite correctly, this object receives constant number. There are more than 300 thousand numbered asteroids now. At last each numbered asteroid in accordance with definite rules can receive the name that usually stands with the number in brackets or without them. For example: (1) Ceres or 1 Ceres, 4581 Asclepius, 27002 1998 DV9.

The comets are named in other manner. The designation of periodic comets contains the symbols "P/". If these symbols are preceded by a number it means that this comet has been observed in several apparitions. There are more than 200 such numbered comets with the names of discoverers included in designation, for example: 2P/Encke, 124P/Mrkos. The discoverer's name in designations of other comets is preceded by the year of discovery, the letter corresponding to the half month of discovery and the current number, for example: P/1986 A1 (Shoemaker 3). Two symbols are used additionally before a slash: "D" - for the dead comets (25D/Neujmin 2) and "C" - for long period comets observed only in one apparition (C/2001 RX14 (LINEAR)).

The orbital elements.
An asteroid moves along the orbit close to an ellipse with the Sun in one of the focal points. The difference between the real and ideal elliptic motion is caused mainly by the gravitational influence of major planets, and it is taken into account in numerical integration of differential equations of perturbed motion. But at once the form, size and orientation of this ellipse are to be determined. Usually the rectangular coordinate system is used with ecliptic as fundamental plane and x-axis oriented to the point of vernal equinox, these plane and direction being referred to the fixed epoch. The plane of orbital ellipse passes through the coordinate origin and is defined by two angles: the longitude of ascending node (that is the angle between the x-axis and the point where z-coordinate changes the sign from minus to plus) and the inclination of orbital plane to ecliptic. The inclination varies from 0 to 180 degrees. If it is less than 90 degrees we have the prograde motion (i.e. counterclockwise motion, if one looks from the north pole of ecliptic), otherwise the motion is retrograde, clockwise. The semi-major axis determines the size of ellipse, or its largest radius. It is usually expressed in astronomical units (1AU=149597870.691 km). The eccentricity determines the form of ellipse, or its degree of oblongness. This value for an ellipse varies from 0 to 1. If the eccentricity is equal to zero an ellipse transforms to a circle, if it is equal to unity an ellipse becomes a parabola. The values of eccentricity greater than unity correspond to a hyperbola. The orbits of many comets have great values of eccentricity. The point of orbit nearest to the Sun is called perihelion, and the most distant point is called aphelion. The line linking these points (the apsidal line) forms with the nodal line the angle called the longitude of perihelion. This fifth element determines the orientation of orbit in its plane. If to define a moment of perihelion passage then the object's motion is defined uniquely. It is possible to specify some other elements. For example, a mean motion or perihelion distance instead of a semi-major axis, or a mean anomaly instead of a moment of perihelion passage.

Orbit determination and improvement.
After a few observations near the moment of discovery the values of right ascension and declination can be derived. Then the most appropriate ellipse is determined that could represent the observed motion of object. This is the initial orbit determination. It helps not to lose a new object in a nearest future. But the short observational arc does not permit to determine the orbit with sufficient accuracy. So the new observations from time to time are used to obtain the corrections to adopted values of elements. This process is called the orbit improvement.

Absolute magnitude.
Absolute magnitude H is the apparent stellar magnitude of an object placed to the point remote from the Sun and observer at 1 AU, the phase angle (the angle the Sun - object - observer) being equal to zero. It is the abstract value (this configuration is never possible) but it is widely used in practice. For asteroids apparent stellar magnitude m is calculated so

where D is geocentric distance, r - heliocentric distance of object in AU, f - phase angle, G - so called slope parameter, that is always placed with the H value. The second classic item is due to the fact that the intensity of radiation is inversely proportional to the square of distance from the Sun to asteroid and from asteroid to observer. The third item takes into account the peculiarities of the asteroidal brightness for low values of the phase angle according to E.Bowell et al. (Asteroids II, 1989). For estimation of the total brightness of comets the formula is as follows

where the value is specified with the value H in the catalog of elements.

The correlation between absolute magnitude H and diameter D of asteroid.
The following formula is used for asteroid's diameter

where D is diameter in km, H is the absolute magnitude, and A is so called geometric albedo, that evaluates the ratio of reflected radiant energy to the total one received from the Sun. Usually the albedo value is unknown. But for majority of asteroids this value is thought to be between 0.05 and 0.25. Of course, it might be noticeably greater for metal-containing objects, or slightly lesser for the dark objects of the Edgeworth-Kuiper belt. The following table gives the diameter values, corresponding to the range of albedo values from 0.25 to 0.05, for objects with given value of H.

But such evaluation is valid for some model of thermal equilibrium of slowly rotating spherical asteroid. It is clear that this model is far from reality in many cases, and these data should be controlled by the right methods of determination of size and form of asteroids from observations.

The form of asteroids.
The greatest asteroids are known to have the form of sphere or ellipsoid of rotation, i.e. really are like the minor planets. On the other hand the images from space probes showed extremely irregular form of small asteroids (Ida, Gaspra, Toutatis, Castalia, Mathilde, Eros). It is considered that near some critical diameter, approximately 200 km, the pressure of upper layers ceases to smooth heterogeneities of internal structure, and the form of asteroid transforms from spherical to irregular one. So one can use the term "diameter" concerning a few objects only. For most of them it is more correct to use the word "size". Generally the description of the form can be done by several methods. Two of them are most popular. At first, one can specify the value of radius for some step in longitude and latitude. The inconvenience of this method is densification of a pattern near the poles. Secondly, it is possible to specify a set of vertexes in some rectangular coordinate system and then build the triangular facets. The form of asteroid or comet's nuclei is an important characteristic of object because it is closely linked to its gravitational field and rotation.

What are Atens, Apollos, Amors? 

In general NEAs are asteroids with perihelion distance q less than 1.3 AU. But there is additional division with respect to a combination of semi-major axis a, perihelion distance q and aphelion distance Q: the subgroups of NEAs, called in honor of their typical representatives - asteroids 2062 Aten, 1862 Apollo and 1221 Amor.

For Atens: a < 1 AU and Q > 0.983 AU.
For Apollos: a > 1 AU, q < 1.017 AU.
For Amors: a > 1 AU and 1.017 AU < q < 1.3 AU.

The orbits of above asteroids are shown on the picture, and their positions with positions of inner planets for the moment January 1, 2003 are marked by the shaded circles. It is to be noted that the Atens, whose orbits nearly tot