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 Atiras, 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.
About the observations of NEOs.
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 can 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 Atiras, 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 163693 Atira, 2062 Aten, 1862 Apollo and 1221 Amor.

For Atiras: Q < 0.983à.å.
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 totally lie within the Earth's orbit, are the most difficult objects for the ground based optical observations, because they are always situated near the Sun on the celestial sphere. So they are to be paid special attention in space observations.

What are PHAs?
These are potentially hazard asteroids, i.e. the objects having the minimum orbit intersection distance (MOID) with the Earth less than 0.05 AU and absolute magnitude not more than 22.0 (the suitable size is about 150-200 meters). It does not mean that each PHA will impact the Earth. It means simply that there is a possibility of such collision. So these objects demand the special attention. A monitoring of such objects and a permanent improvement of their orbits should let us better predict their motion and possible risk. It is to be noted that due to the planetary perturbations the osculating orbit of any asteroid does not stay constant. The elements evolve with time, so the MOID value can vary. It means that the current list of PHAs is also variable even if the new discoveries being excluded. Some known asteroids cease to be PHA while the other ones become the members of this community. One can find on this page a current list of PHAs including their elements. Two dozens of them are potentially hazardous for all four inner planets simultaneously.

How many NEAs have been discovered until now?
For April 18, 2024 34759 NEAs have been discovered. 2413 of these NEAs are classified as PHA - Potentially Hazardous Asteroids. 7% of PHAs have a diameter of more than 1 kilometer.

What is the source of NEAs?
It is known that we can predict quite exactly the motion of the major planets for long time intervals. The same is valid for the majority of asteroids but for somewhat smaller intervals. This motion is called stable. Nevertheless the orbits of some asteroids can undergo the abrupt changes. As a result these objects migrate along the Solar system temporally delaying at some regions. There are various scenarios for these objects, for example: the ejection from the Solar system, the collision with a major planet or another asteroid or fall to the Sun. Such motion is called chaotic, and it can not be predicted precisely for long time intervals. The majority of NEAs shows the signes of a chaotic motion. The mean life time of these objects is small as compared to the stable ones. The mean density of NEAs seems to be non decreasing value so this group of asteroids must be replenished from the outer regions of the Solar system. The behavior of chaotic objects may originate from several reasons. Among them it is to be noted mutual collisions, close approaches of asteroids to major planets that briefly gravitationally dominate, and resonances. The first two reasons are able to change momentary or in a short time the orbit of rather stable object. The possible result of a collision may be generation of the whole family of fragments. The third reason acts much more slowly but inevitably as well. Sometimes it is to take into account the influence of other, more intricate factors that nevertheless could produce noticable effect over long time spans. These are the relativistic and magnetic effects, light pressure, reactive forces from the comet nuclear jets, the Yarkowsky effect, etc.

About resonances in the Solar system.

If an asteroid makes m revolutions arounf the Sun, and Jupiter makes n revolutions during the same time, one can say that this object is in m:n mean motion resonance with Jupiter. There are some other resonances connected to the motion of perihelion and nodes. Of course, each major planet has its resonance zones but Jupiter's resonances are the most noticeable in the Solar system. Some resonances lead to ejection of the asteroids from distinct zones. This produces the so called Kirkwood gaps in the Main Belt of asteroids. The other resonances, on the contrary, are favourable for existence of some stable groups of asteroids, for example: 1:1 - Trojans, 3:2 - Hildas. Here one can look at the motion of Trojans and Hildas. The histogram on the figure shows the number of asteroids as a function of the semimajor axis. All principal mean motion resonances with Jupiter are also noted. For resonance 1:1 the rotating coordinate system is more convenient. Here the Sun is in the center and the x-axis passes through a planet. There are four types of motion in this system: circular objects, troyans, the objects on the horse-shoe orbits, quasi-satellites (QS). The circular object moves either ahead of a planet or behind it in longitude depending on the ratio of their mean motions. The motion of the troyans in the vicinity of L4 è L5 Lagrangian libration points of a planet can be stable over long time spans. On the horse-shoe orbit asteroid can approach a planet from one side, then move in the opposite direction in order to approach a planet from the other side after some time. After several such "swings" an object can move to a circular orbit. Quasi-satellite (QS) - is an asteroid moving along a heliocentric orbit with values of mean motion and mean longitude close to the planet's ones. In projection onto ecliptic it describes retrograde loops around a planet. These loops can be shaped like an ellipse, banana, figure eight or some kind of chain. Quasi-satellites can move near a planet during numerous periods of its revolving around the Sun librating in longitude. Over time they leave the vicinity of a planet, moving to the horse-shoe or circular orbit. But in future they can become a quasi-satellites again. In some cases when exiting QS-mode such asteroids can critically approach to a planet and become potentially hazardous objects for it.

Known close approaches of asteroids to the Earth.
For the last century there have been fixed in observations or reconstructed nearly thirty close approaches of asteroids to the Earth, up to two mean distances to the Moon. Among these objects there were 3 asteroids with the size more than 1 km, 9 asteroids 100-300 meters in diameter, the rest of them were the objects less than 50 meters. The third part of objects has been observed for the time interval less than 5 days, five of them - less than 1 day. So their determined orbits are not quite correct. But worst of all is the fact that part of the small objects has been discovered after approaches. This confirms the difficulty of discovery of dangerous objects.

On October 7, 2008 the asteroid 2008 TC3 few meters of size burned in atmosphere above the Northern Sudan. It was the unic case of real collisional prediction. This object was discovered a day before at nearly Lunar distance from the Earth, and its determined orbit forecasted a collision. Some fragments of this object achieved the Earth surface and were found later during the several special expeditions for study of this meteor matter. Six more small asteroids are currently (2023) known to have collided with the Earth.

How correct a prediction of dangerous approaches can be?
The long observational history is needed for certain prognosis of object's motion. It is impossible for newly discovered asteroid. Each new observation, or the archive revealed one, can essentially change the orbital parameters. Close approaches to major or minor planets (about which one could not know in advance) also represent the additional source of uncertainty. Therefore at this moment the prediction of dangerous approach after a time interval of many years is incorrect. It is inadmissible to give way to panic and to declare the future catastrophe, what already took place. The solely right way is to make note of it and follow it carefully. At the same time the list of dangerous objects with current and clear estimation of their threat must be opened for public. The power structures (surely continuously informed) start to take measures when the threat becomes real. Hence it is necessary to improve the links of astronomical community with the public, power authorities and mass media. This can help to adequate perception of possible danger.

The Torino and Palermo scales.
The Torino scale is a result of International NEO workshop held in Torino (Italy) in 1999. It was suggested for communicating the problem of NEO risk to the public. The risk of predicted impacts is expressed as an integer value from zero (no hazard) to ten (global catastrophe) depending on a probability and kinetic energy of the event. The energy is proportional to the mass of an object and the square of its velocity and is expressed in megatons (MT) of TNT explosive. The following values are used: for probability - from 10-8 to 1, for energy - from 1 to 108 MT. In this way a few meters object that certainly would collide with the Earth, burning in the atmosphere, has zero value in Torino scale, as well as a kilometer-sized asteroid capable to destroy the whole civilization but having extremely little chance of encounter with the Earth. Since impacts with large asteroids have a very small probability the absolute majority of predicted events receive a zero value in Torino scale. The meeting in Palermo (Italy, 2001) generated more quantitative Palermo scale that is designed for astronomical community rather than for the public. This scale naturally describes the impacts with respect to their energy, probability and date. In general it is more sensitive and gives to the specialists more clear way of planning the observational and computational efforts.

About the observations of NEOs.
Astrometric observations of NEOs aim at obtaining the spherical coordinates of an object by measuring positions of this object in a frame and positions of reference stars with well known catalog coordinates. The methods of photographic astrometry are used in this procedure. These observations make more exact our knowledge about the object's motion. Astrophysical observations (photometric, spectral, polarimetric, etc.) are oriented at derivation of information about physical properties of objects. This traditional division is quite conventional because a CCD camera is mainly used in observations. On the other hand photometric observations can give the information about the size and rotation of objects. Radiolocation of asteroids also combines the elements of these two types of observations. The space missions give still more wide range of research tools. Since the ninetieths of the 20th century the international activity in NEO research have started. There are two components of this work: observations and calculations. The first one is further divided to discovery of NEOs and their follow-up. From the start the most part of this activity, especially connected with discovery, was concentrated at USA. But gradually the investments of other countries increase, observational and theoretical. Usually the search of new objects is the subject of activity of the groups working at place with good climate and having sufficiently large full-time telescope with good CCD camera and automation facilities. Of course, the discovery of a new object can be accidental. But the work of above groups is not oriented at an occasion. The task is formulated rigorously: to make the whole search of accessible sky up to a limited visual magnitude as soon as possible. As usual the productivity and quality define a leader. Since the moment of discovery the follow-up process starts. These observations executed with the other telescopes are to obtain first of all the astrometric coordinates of an object in order not to lose it. At the same time the astrophysical observations are fulfilled. After some period of time an asteroid will return to the Earth, and there will be favorable conditions for its following detection - recovery. The more accurate were the orbital elements of object determined the more confidently it is detected. But there are also the losses. Sometimes the archive frames give the positions of object unidentified at that time. This can improve the orbit essentially. Usually the discovery centers cannot make follow-up observations, and they are executed at other places. Among the countries actively working in this field the following are to be noted: Italy, Czech Republic, Australia, Japan. The activity is developing in the other European countries, in China and Latin America. The number of follow-up centers is still insufficient, it is to be enlarged at least an order of magnitude. They are usually equipped a lesser degree and are not in time to make all necessary observations. But a tendency to growth of their capabilities and cooperation is evident.

Pulkovo works.
Despite the lack of large telescopes, unstable weather and extremely bounded financing astronomers of the Pulkovo Observatory make their contribution to the NEO study. For a long time the episodic observations of asteroids and comets were executed with 26" refractor, normal astrograph and later with smaller telescopes (N.M.Bronnikova, T.P.Kiseleva, I.S.Guseva et al.). Theoretical works were also developed. The method of apparent motion parameters of A.A.Kiselev was developed and applied by the author and by his colleagues and pupils (O.P.Bykov et al.) to the orbit determination of various objects - artificial satellites, double stars and, of course, asteroids. A.A.Kiselev and his colleagues worked out the method of observations of apparent close approaches of asteroids to the stars and their processing. The test observations of the main belt object and the Kuiper belt object in one frame simultaneously were fulfilled with the 6 m BTA telescope of the Special Astrophysical Observatory (Yu.N.Gnedin, K.L.Maslennikov). The works are executed on computer archiving of the Pulkovo glass library (E.V.Polyakov). But the most active work on NEO study became possible under the auspice of A.V.Devyatkin. The joined efforts of astronomers, engineers and programmers have led to a positive result.The stuff members of astronomical instrument elaboration department (I.I.Kanaev) made the renovation and full automation of the two telescopes ZA-320 (Pulkovo) and MTM-500 (Pulkovo Mountain Station, Northern Caucasus). The Pulkovo specialized software packages were developed such as APEX (V.V.Kouprianov et al) and IZMCCD (I.S.Izmailov) for astronomical image processing and EPOS (V.N.L'vov, S.D.Tsekmeister) for ephemeris support and control of observations. All these steps led to more comfortable conditions of work, to intensification of NEO observations and to improvement in their accuracy. Moreover, the additional observational programs became possible: photometry of asteroids, the observations of apparent close approaches of asteroids to the stars, and of occultations of stars by asteroids. So Pulkovo Observatory is becoming one of the world NEO follow-up centers.