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date: 25 February 2021


  • Leonid V. KsanfomalityLeonid V. KsanfomalityAstro Space Center, Russian Academy of Sciences


Cometary nuclei are small, despite the cosmic scale of the comet tails that they produce. The nuclei have the ability to create rarefied atmospheres, extending as a tail to giant distances comparable to the orbital distances of the planets. Giant tails of comets are sometimes observed for several years and cover a significant part of the sky. The cometary nucleus is capable of continuously renewing tails and supporting the material that is constantly dissipating in space. Large comets do not appear so often that they have become trivial celestial phenomena, but they appear often enough to allow astronomers to complete detailed studies. Many remarkable discoveries, such as the discovery of solar wind, were made during the study of comets. Comets are characterized by great diversity, and their appearance often becomes an ornament of the night sky. Comets have become remote laboratories, where experiments are performed in physical conditions that are not achievable on Earth.


Comets are classified among the small bodies of the solar system. Their physical and chemical properties are heterogeneous, as are the masses, sizes, and geometries of their nuclei. Forms identified as the “head” and “tail” of a comet are also extremely diverse, but their common property is the time of their appearance—the era of the formation of the solar system, which left its material traces in their composition, on the surface of their nuclei, and in the streams of dust and gas emitted into surrounding space as they approach the sun. Compared to planets, comet nuclei are very small, but the effects they create cover distances comparable to the scale of planetary orbits.

In historical documents, the appearance of comets has always been attributed to major events. Halley’s comet was mentioned for the first time in ancient Greek chronicles in 468−466 bc and at the same time was noted in Chinese records. Only in 1531 and 1607 did the appearance of Halley’s comet start to be recorded in the Julian and Gregorian calendars, respectively. However, before Edmond Halley (1656−1742), comets were not regarded as objects related to the solar system. According to Aristotle (384−322 bc), comets were not astronomical phenomena, but atmospheric events. Unlike the planets, their appearance was unpredictable, as was their movement, which was not related to the zodiacal constellations, where all the planets move. Comets appeared from “nowhere” and disappeared to “nowhere.” All this led Aristotle to assert that comets were vapors rising from Earth and accumulating in the upper “flamey” part of the atmosphere, where they slowly burnt out.

Centuries passed before Lucius Seneca (4 bc−65 ad) became the first to claim that the movement of comets outside the zodiacal belt is not a reason to exclude them from being astronomical objects and that the comet is an eternal product of nature.

Then another time arrived. For example, in 1578, Andreas Celichius criticized Aristotle’s ideas and viewed a comet as “the thick smoke of human sins, rising every day, every hour, every moment, full of stench and horror before the face of God, and becoming gradually so thick as to form a comet, with curled and plated tresses, which at last is kindled by the hot and fiery anger of the Supreme Heavenly Judge” (cited from a review by Hughes, 1986).

Around 1740, Halley’s comet became one of the dominant catalysts in the development of astronomy, and it is still the subject of intense research. The appearance of Halley’s comet in 1758−1759 was predicted by the calculations of Edmond Halley and the subsequent work of Newton. Besides its scientific interest, there are two additional reasons for public interest in the comet. First, Halley’s comet returns about every 76 years. The interval between returns is not so long that interest in the event is lost, and it is not so short that the appearance of a large comet becomes a trivial phenomenon. Second, although most comets are not bright enough to attract the attention of ordinary people, they are bright enough to be seen by the naked eye of an inquisitive amateur astronomer. Halley’s comet belongs to the brightest short-period comets (those with orbital periods less than 200 years). In the 17th century, it was called the Comet de Lacaille, in honor of the French Abbé Nicolas-Louis de Lacaille. However, by the time of its return in 1835, the name Halley’s comet had become generally accepted.

Halley’s comet (1P/Halley), one of the largest short-period comets, was destined twice to play a major role in comet research. First was the work of Edmond Halley, who observed a comet in 1682 in London and subsequently devoted all his life to comets. Halley was the first to establish the periodicity of the appearance of 1P/Halley and other comets and to create analytic tools for cometary research. He succeeded in attracting Newton to this work. The history of the problem is described in detail by Hughes (1986). It is interesting to note Newton’s conclusion, written in his Principia: “The bodies of comets are solid, compact, fixed, and durable, like the bodies of the planets.” Newton probably came to this conclusion mainly because the comet 1680/1 was preserved after passing its perihelion, which was very close to the sun. At the same time, Newton also wrote that, in approaching the sun, the comet’s head starts evaporating into the aether medium,

and those reflecting particles heated by this action, heat the matter of the aether which is involved with them. That matter is rarefied by the heat which it acquires, and because, by this rarefaction, the specific gravity with which it tended towards the Sun before is diminished, it will ascend therefrom, and carry along with it the reflecting particles of which the tail of the comet is composed.

The second time Halley’s comet appeared on the front pages of scientific publications was 300 years later, in 1986, when it became the first comet whose nucleus was explored by a spacecraft. Historical studies of 1P/Halley (1986) by the Vega, Giotto, and Suisei missions were a breakthrough in cometary physics. Since then, spacecraft have explored eight other comets. One of the most significant conclusions is the complicated physics of comets, indicating the great diversity of these objects. Differences in the physical properties of comets suggest the extreme complexity of the physicochemical properties of the environment where they originated.

Finally, another obvious problem that cannot be solved without the use of a spacecraft is the exploration of the relief, morphology, and detailed composition of different parts of the nuclei themselves. In this regard, the results of studies of the comet 67P/Churyumov-Gerasimenko (67P/CG) by the Rosetta mission exceeded all expectations. It was also expected that such studies could be conducted directly on the surface of the nucleus, but the unsuccessful landing of the Philae spacecraft in 2014 was a disappointing failure. Further development of this type of research is necessary.

The masses of cometary nuclei are millions of times smaller than the masses of the planets. Figuratively, cometary nuclei studies can be thought of as investigations of small-mass cosmic bodies with huge scientific baggage. In preparing for the Vega mission, one of the French participants compared the interest in comets to the effects of perfume: “Small amounts of substance that give rise to strong emotions.”

Spacecraft studies of the cometary nuclei are remarkable due to the heterogeneity of the obtained results. It is well known that cometary tails contain plasma and dust, and invariably water vapor, carbon monoxide, and carbon dioxide, as well as many varying ions, atoms, and molecules, in the coma and tail. However, most frequently, each comet has a unique composition. The relative abundance of deuterium (the D/H ratio) is commonly believed to characterize not only the physical conditions at the time the body formed but also the role of comets in the partial creation of the terrestrial hydrosphere, and the D/H ratio appears to be heterogeneous among comets. A comparison of the morphological properties of the surface of cometary nuclei—for example, the surfaces of the nuclei of 67P/CG, 1P/Halley, 19P/Borrelly, and 103P/Hartley-2—suggests the complexity and extreme heterogeneity of their formation processes, and a comet’s nucleus can be studied only from a closely located space laboratory or a probe descending to the surface of the nucleus.

An important role is played by long-term observations of the comet and its emissions conducted from landing or low-orbit spacecraft. Sometimes the results obtained are outstanding, as, for example, was the case with local oxygen emissions by the 67P/CG nucleus (presumably relic origin oxygen) or the presence of different components differently enriched with various sulfur isotopes. Although cometary nuclei are usually divided into types by the ejected material (mainly gas or dust components), a detailed classification of cometary nuclei is far from complete to date.

The meteor hazard associated with comets is widely known. It was considered, in particular, by Emelianenko and Shustov (2013). The probability of such events is not high, although the 2013 event in the Chelyabinsk region (near Lake Chebarkul) was a loud reminder of the possibility.

Figure 1 shows a detailed ground-based snapshot of Halley’s comet (1P/Halley) obtained when the Vega-1 and Vega-2 spacecraft were approaching the comet with a speed of up to 79 km/s (March 6−9, 1986). The image clearly shows the numerous strips, jets, and “rays” formed by gas and dust flows associated with separate sources on the surface of the nucleus. The relatively slow rotation of the nucleus causes the appearance of recurring material clusters (outside the image frame).

Figure 1. Ground-based image of comet 1P/Halley, one of the largest short-period comets, obtained during the operation of the Vega missions near the comet, 1986.

Source: IKI RAS archive.

Movement of Comets

Comets mainly are byproducts of the formation of the solar system. They were subjected to the gravitational action of much more massive bodies that threw them out to the periphery of the nascent solar system. Studies indicate that comets come from two main areas: the Kuiper Belt and the Scattered Disk, two connected, flattened systems extending from 38 AU (near the orbit of Pluto) and up to 100 AU. The orbits in the Kuiper Belt are relatively stable, and in the Scattered Disk, on the contrary, the stability of the orbits is limited. Hence the majority of comets, including low-mass comets, move gradually from the Scattered Disk to the zone of orbits of the outer planets. They are called centaurs. After moving to lower orbits (closer to the sun), they appear on the firmament as short-period comets (e.g., 103P/Hartley-2).

Besides the Kuiper Belt and the Scattered Disk, there is another source of comets. Gravitational interactions in the emerging solar system led to the formation of a giant peripheral sphere of celestial bodies, the Oort Cloud, which includes several trillion cometary nuclei of different masses. Their total mass is estimated to be about five times the mass of the Earth, about 3 ∙ 1025 kg. It is believed that the inner boundary of the Oort Cloud lies at a distance of 2,000 to 5,000 AU, while the outer boundary of the Oort Cloud is at 50,000 AU (that is, about 0.8 light years). Tremendous swarms of cometlike bodies are thought to orbit the sun in these distant regions, each in a roughly circular orbit. The average distance between them is several tens of millions of kilometers, which is comparable to the semimajor axis of the orbit of Mercury. Gravitational effects of stars and galaxies here are similar to the weak influence of the sun and are able to change the orbit of the body and direct it toward the sun. Through millions of years of movement, such a body appears on the firmament as a new long-period comet. The name of a comet of this type includes the letter C: for example, comet C/1999 F. Its destiny depends not only on how close the comet approaches the sun at perihelion but also on accidental interaction with massive planets, which affects their moment of motion. As a result, in the distant future, the comet becomes a short-period comet (e.g., 67P/CG), or it may be permanently thrown out of the solar system, or it may even collide with the sun or another body. Because of the exchange of angular momentum, orbits of short-period comets are also unstable.

The orbits of comets are usually very elongated ellipses, with a very long semimajor axis a, a significant eccentricity of the orbit ε‎ reaching unity (ε‎ = 1 in the case of a parabolic orbit when a = ∞), and inclination i to the ecliptic plane. If ε‎ > 1, the orbit becomes hyperbolic, and the comet will go away forever. Although the comet McNaught (2007) had ε‎ = 1.000019, due to small changes in its orbit, it remained a long-period comet, with a period of 92,600 years. The long-period West comet has its aphelion located at 70,000 AU, and its period is 6 million years. The orbits of the planets are only slightly inclined toward the ecliptic (the plane of the Earth’s orbit), but the orbits of comets that came from the Oort Cloud are distinguished by the fact that they can have any inclination i.

Away from the sun, a comet moves along an ideally elliptical orbit, which can be determined if there are at least three exact consecutive observations. The orbit thus obtained is called an osculating ellipse and is represented by sections of a cone. However, in the zone of the planets, the orbit inevitably changes so much that it is impossible to reproduce it with conic sections, and the osculating orbit becomes a conditional idealization. Due to the orbital motion of the Earth, the visible path of the comet is represented by a sequence of loops. Figure 2 shows the path of Halley’s comet, from October 1974 until the approach of the Vega and Giotto spacecraft in 1986. The dynamics of comets has been considered by many authors (Eicher, 2013; Levy, 1998; and Meierhenrich, 2014, among others).

Figure 2. Apparent path of Halley’s comet during the period 1974−1986 before the Vega-1, Vega-2, Giotto, and Suisei spacecraft approached its nucleus.

The orbital motion of the comets follows the three laws of Kepler:


The orbit is a conical section (ellipse, parabola, hyperbola), with one of the focal points being the sun (more precisely, the barycenter of the system).


In orbital motion, the radius-vector (the line connecting the body with the sun) covers equal areas in an equal time.


The squares of the periods P of revolution of celestial bodies around the sun are proportional to the cubes of the large semi-axes a of their orbits (i.e., the ratio P2/a3 is the same for all bodies in the given system).

If a comet’s orbit with the semimajor axis a and the current radius r is almost circular, in other words ra and ε‎ ≈ 0, then the velocity of the body is vc = (GM/r)½, where G is the gravitational constant and M is the mass of the sun. In an elliptical orbit (ε‎ > 0 and in the general case ra), the velocity of the body ve = [GM/(2/r − 1/a)]½ at a distance r. The calculations use the minimum distance q at perihelion, where vq=vc2. At a distance q, the speed of a comet is practically independent of its mass, no matter how elongated its orbit is, even if the orbit is parabolic—that is, the comet has come from “infinity” (infinity practically begins at more than 1 light year). But one can imagine an interstellar body that already has a random velocity and that is directed to the sun. Such a comet will pass perihelion with a velocity v > vq. The sun cannot capture it, and at a distance of the Earth’s orbit, its speed will exceed 42 km/s—the 3d space speed, and the body will leave the solar system forever. Such comets are called hyperbolic. For a long time, experts doubted their existence, but a few hyperbolic comets were discovered.

If the period P is known, the semimajor axis a and the eccentricity ε‎ are determined by simple expressions, a = P(2/3) and ε‎ = 1 − q/a. So, in the case of Halley’s comet, for which P = 75.5 years, a = 17.86 AU, and ε‎ = 0.968. Kepler’s second law indicates there is a slowing down of the comet in aphelion—for example, the movement of Halley’s comet in aphelion is 7.8 times slower than at perihelion (velocities of 7.1 and 55.2 km/s, respectively).

The aphelions of many cometary orbits are concentrated at massive planets and, accordingly, such comets are called the “Jupiter family” or the “Neptune family.” However, the term family indicates not the relationship between the origin of the comet and the planet, but its capture by the gravitational field of the planet. As a result of its interaction with the planet, the orbit of the comet can be changed beyond recognition, and the comet may even go to another family. For example, the evolution of the orbit of comet 67P/Churyumov-Gerasimenko (67P/CG) has undergone numerous changes, which were established by calculations. In 1660, it moved along an almost circular orbit, with ε‎ = 0.1, it had perihelion q of more than 4 AU, and the orbit’s inclination was about 29°. During the period 1660−1960, it approached Jupiter 10 times. A close passage to Jupiter in 1840 abruptly reduced its q to 2.8 AU and increased the eccentricity to 0.36. Another approach to Jupiter, in 1959, increased eccentricity to 0.63, and perihelion was halved, to q = 1.3 AU, with the inclination of the orbit reduced to 7°. As a result, the orbit became typical for the Jupiter family; in perihelion, it has q = 1.2432 AU, and the period of revolution of the comet is 6.45 years. In the same way, other long-period comets also gradually transform into short-period comets (having P < 200 years).

Along with the perturbing influence of the bodies of the solar system, the comets are subject to nongravitational effects—the reactive action of the jets and streams of gas and dust that they emit, which the nucleus never does symmetrically. In addition, jets vary considerably in intensity on the day and night sides of the nucleus. For a massive nucleus, the effects that change the comet’s orbit are small, but over a long time they become significant, even for a massive body. The effects are almost impossible to predict, since the active regions on the nucleus are randomly distributed. Nongravitational effects are especially significant in comets with a low perihelion (and with a small mass), because such comets lose a lot of material in perihelion.

Tails, Comas, and Nuclei of Comets

Periodic convergence of comets with the sun causes their gradual “aging,” which manifests as a decrease in the intensity of gas-dust emissions after each end of the cycle. A typical massive comet of middle age is shown in Figure 1: comet Halley, with a revolution period of 75.5 years. In the picture, a well-defined, dense, orange tail extends beyond the comet for an entire astronomical unit. The appearance of the tail and head of Halley’s comet and their development vary little in successive appearances of the comet, which has passed perihelion several thousand times. As for “older” comets, the period of their revolution is short, and the orbits are becoming circular, because with numerous encounters with the bodies of the solar system, the eccentricity and inclination of cometary orbits are constantly decreasing due to tidal energy scattering. Sometimes the nucleus breaks down, forming meteor streams and smaller, daughter nuclei. In the process of orbital motion of comets, condensed volatiles gradually evaporate, and dust and stones form a dark crust—a protective layer that slows the evaporation of volatiles. The crust is dark, so its surface heats up, and as the temperature rises, the pressure of the sublimated gas breaks the crust, and its pieces are captured by gas streams and are carried away to the tail.

After many thousands of passages through perihelion, the resources of even a massive nucleus are exhausted, the comet’s orbit becomes similar to the orbits of asteroids, and the nucleus becomes one of the “extinct comets” that make up a small part of the asteroid belt. Usually, they are revealed by a very small, loose, and unstable spherical coma.

Figure 3. “Great Comet 2007”─McNaught C/2006 P1─in the sky over the Pacific Ocean. SOHO satellite image.

The appearance of new comets is quite different. In “young” comets, the surface of the core is formed by open deposits of condensed volatiles with impurities of dust. At the first appearance of a new comet, it is sometimes possible to observe a celestial extravaganza (Figure 3). The remarkable “Great Comet 2007,” comet McNaught 2007, passed perihelion on January 12, 2007—the distance q at perihelion was only 26 million kilometers, much less than the orbit of Mercury. The emission of gas and dust was very intense, the coma was dense, and the reflected light of the sun prevailed in the comet’s spectrum (which usually also leads to the comet’s being considered “young”). Conditions of observation were very favorable. Cameras on the spacecraft SOHO managed to get great pictures (Figure 3), almost immediately after the comet’s passage of perihelion. The steep bend of the tail (at the bottom of Figure 3) covered a significant part of the sky. The curved tail was accompanied by blue rays radially directed from the sun. The comet was visible even during the day. Of course, such conditions for observation of a long-period comet were unique. The activity of the comet lasted a long time. A picture taken in Australia 10 days later is shown in Figure 4.

Figure 4. Comet McNaught C/2006 P1 in the sky of Australia (10 days after the picture in Figure 3). The West comet in 1975 had a very similar tail.

The tail of a comet often stretches for many tens of millions of kilometers and is a spectacular sight, but in the physics of comets, tails are a secondary product. The main part of the comet—the nucleus—is veiled by its surrounding foggy atmosphere, which is created by the nucleus and continuously flows into space. The very foggy atmosphere around the core is called a coma. It is impossible to see the nucleus of a comet by telescopic means. Before the Space Age, the study of the structure, physics, and chemistry (and photochemistry) of the nucleus relied on theoretical considerations and observations of the evolution of the head and tail of the comet. The head is called the brightest front of the comet, which includes the coma (with a shell of a parabolic shape) surrounding the nucleus and passing into the tail. Far from the sun, the head looks symmetrical, often spherical. Then, as the comet approaches the sun, the head lengthens and a tail appears. On average, its length reaches 0.1 to 1 AU. With the approach to the sun, the diameter of the head increases to 50,000 to 80,000 km. Experiments in space have discovered giant cometary hydrogen clouds surrounding comets.

The model of the structure of the nucleus of the comet, confirmed in experiments and observations, was proposed by F. Whipple in the 1950s. The model was called a “dirty snowball,” because it proposed a conglomerate of ices, H2O, CH4, CO, CO2, and other volatile and refractory rocky particles, and the model later was confirmed. Thus, the dust of Halley’s comet is a mixture of carbon-hydrogen-oxygen-nitrogen refractory organic compounds, the so-called CHON, and rocky matter of chondrite composition. The model made it possible to explain the occurrence of gas-dust tailings and meteorite swarms formed in the orbit of a comet as a result of detaching core fragments, and the destruction of nuclei into large parts. Subsequently, space experiments have shown that a typical core is a loose formation, with high porosity, but that it also includes sufficiently solid rocks.

The masses of the cometary nuclei are very different, from small bodies like the Chebarkul event, which was 107 kg (Emelianenko & Shustov, 2013), to the giants like 1P/Halley (2.2 ∙ 1014 kg) and C/1995 O1 (Hale-Bopp). In the case of comet Hale-Bopp, the mass is unknown, but from comparison of the dimensions of the two giants (15 × 7 × 7 km and 40−70 km, respectively), it can be assumed that the mass of C/1995 O1 was about 1015 kg. For a comet, 1015 kg is a very large mass, but it is 60 million times smaller than the Earth. The comets 103P/Hartley-2 (3 ∙ 1011 kg) and 67P/CG (1013 kg) are referred to as average. Determining the mass of a comet is difficult. The number of comets with known masses is small, despite the fact that the number with known orbits at the end of 2017 exceeded 5,000. With decreasing mass, the number of discovered comets first increases and then falls, which is explained by the selection effect—the smaller the comets, the greater their number, but the more difficult it is to detect them.

The parabolic shape of the comet’s head, as in Figure 1, is explained by the “fountain” mechanism. The gas-dust flows emitted by the nucleus are similar to the fountain jets on Earth, but they are not deflected by gravity, but by the pressure p of sunlight on the particle. The radial pressure depends on the radiation power E per particle area divided by the speed of light c, as p = E/c. On the Earth’s orbit, Ee = 1.37 kW/m2 and pressure is 4.5 Pa. The same particle (with mass m) is affected by the gravitation of the sun, with the force GMm/a2. Equating the radial pressure to the gravitation of the sun, one obtains the size of the particle whose radiant repulsion force exceeds its gravitation. If the density of dust particles is 1.9 ∙ 103 kg/m3, as in the case of 67P/CG, equilibrium is achieved at a very small radius of spherical particles, only 0.3 μ‎m. At the same time, the molecules and atoms of some gases in the tail of the comet experience a much stronger light pressure, depending on the absorption coefficient. This creates the gas-dust tail of the comet, which seems curved due to the movement of the comet, which throws out all new portions of the material that forms the tail, as shown in Figures 1, 3, 4, and 5.

Figure 5. Gas-dust tail of comet Hale-Bopp (C/1995 O1), May 14, 1997.

The tail of the long-period comet Hale-Bopp (1997, Figure 3), where many regular stripes were visible, developed very actively. The process is continuous, but uneven. Numerous bands are noticeable in the picture of the comet Mrkos, too, whose tail had an unusual appearance (Figure 6). Generally, the tail is increasing or decreasing on the descending or ascending branches of the orbit, as emissions from separate sources are imposed, which occurs with a delay, due to the gradual heating of the core surface and its rotation. But even in the most productive nuclei, the sources of emissions cover far from the entire surface and are distributed unevenly, sometimes forming chaotic jets in the coma and tail (Figure 6). Gas jets pick up dust and pieces of the broken crust and carry them to the tail of the comet. The velocity of the outflow of gas and evaporating material is on average close to 400 to 450 m/s.

Figure 6. Mrkos comet, 1957.

The blue radial rays in Figure 1 and Figure 3 have a different, plasma nature. The motion of ionized atoms and molecules in the rays occurs with accelerations exceeding the gravitation of the sun by several thousand times, and which cannot be explained by light pressure. There is no dust in the plasma tail. A straight blue strip of the plasma tail of comet Hale-Bopp separated from the curved tail of dust with neutral gas (Figure 7). A similar ray is visible at the top of the head of the comet Mrkos (Figure 6). The density of both dust and plasma tails does not remain constant: after 2 months, the plasma tail of the same comet was almost invisible (Figure 5), but then it appeared again.

Figure 7. Blue plasma and orange gas-dust tail of comet Hale-Bopp C/1995 O1, March 20, 1997.

For the first time, indications of the special nature of the direct blue tail were obtained by analyzing a photo of comet Morehouse (1908; Figure 8). The comet threw out a little dust, but a lot of ionized gas, and with great speed, which for a long time remained unexplained. But in the 1950s, a source of the huge acceleration of plasma tails was established. It turned out to be solar wind, corpuscular streams emitted by the sun with magnetic “frozen-in” fields attached to them.

Figure 8. Morehouse comet, 1908.

The speed of the solar wind at the level of the Earth’s orbit is about 400 km/s. The influence of the solar wind on the cometary ions causes the formation and colossal acceleration of the flow of charged particles ejected by the comet to the velocities of the solar wind.

The density and directions of the solar wind fields do not remain strictly constant. Along with its ordered structure, as in Figure 1, numerous bends and curved rays could be seen in Halley’s comet (Figure 9A). In space, the solar magnetic field has a sectorial structure, and at the boundary of the sectors, the field changes its direction. When it crossed the intersectorial boundary, the tail of Halley’s comet was broken, as shown in Figure 9B.

Figure 9. Irregularities in the structure of the solar wind cause curvature and bending of the tail rays (A) and even a rupture of the tail (B). Halley’s comet, photos from 1986.

There are various classifications of comet tails, but the huge variety of their forms requires detailed generalization of all their features. Not all types of tails have an exhaustive physical explanation. A few comets have narrow anomalous peaks (“anomalous tails”) emerging from the head but directed strait to the sun. A well-known example is the long-period (possibly even hyperbolic) Arend-Roland comet C/1956 R1 (1957). Among the other unusual properties of the comet Arend-Roland was the detected decameter radio emission, and its source was in the tail, ten million kilometers from the comet’s head. The radio emission power was so great that even radio amateurs on Earth registered it. They were the first to report a source of unusual radio emission, which led to the subsequent discovery of the comet. On April 22, 1957, in addition to the usual tail on the Arend-Roland comet directed away from the sun, a narrow, anomalous spear tail appeared directed toward the sun. As the plane of the cometary orbit rotated relative to the terrestrial observer, the tail took the form of a contoured divergent ray. The anomalous tail appeared suddenly and just as suddenly disappeared in early May. Its direction was slightly different from the direction of the main tail (Figure 10). Abnormal tails are found on two dozen comets, including one appearing on comet Hale-Bopp. One of the explanations for them is the hypothesis that, along with the broken lumps from the nucleus directed randomly, the comet is surrounded by numerous fairly large particles that form a flat structure, like a disk. When the Earth is in the plane of such a structure, the observer sees it “from the rib” as a line, just as the rings of Saturn become a line when the Earth passes through their plane. But why and how such a structure arises, remains unclear.

Figure 10. Comet Arend-Roland with an anomalous spear-shaped tail pointing toward the sun (1957). It can be seen that the directions of the main and spearlike tails are slightly different.

At great distances from the sun, the plasma tail of comets that emit a lot of ionized gas, but little dust, forms a narrow tail that stretches from the spherical coma. This phenomenon was observed in another comet of McNaught, 2010 (Figure 11). The search for, and discovery of, such comets is complicated because of their low visibility. However, in recent decades, automated search methods have been developed that cover a large field and that use computer analysis of the results of observations. Initially, the method was designed to detect celestial bodies that are potentially dangerous to the Earth. It allows detection objects after very little movement (Geherels & Ksanfomality, 2000).

Figure 11. Comet McNaught C/2009 R1 (2010). At great distances from the sun, the plasma tail forms a narrow tail that stretches from the spherical coma.

Many cometary nuclei retain traces of processes that occurred during the first stages of the solar system’s formation. At present, improvement in the spectroscopic equipment of ground-based and space observatories makes it possible to investigate cometary emissions with a very high resolution. It might seem that the chemical composition of cometary nuclei should be known with sufficient accuracy, but this is not the case. The spectrum of the so-called photometric “nucleus” can simply be the reflected solar continuum or the molecular emission spectrum, which does not carry any information about the nature of the reflecting area. The emission gas spectrum itself provides information about the chemical composition of the atmosphere surrounding the nucleus, but not about its surface. The molecules in the investigated range (C2, CN, CH, NH, and others) are secondary, subsidiary molecules of more complex molecules or molecular complexes of which the nucleus consists. These complex parental molecules are sublimated into a supranuclear gas-dust envelope and are immediately destroyed under the action of solar radiation and due to interaction with the environment. They decay or dissociate into simpler molecules whose emission spectra are “seen” by spectrometers, and the parent molecules themselves mainly produce a continuous spectrum.

Thus, at distances greater than 3 to 4 AU from the sun, the spectrum of the comet is continuous, as a result of the reflection of sunlight from dust particles or its scattering by polyatomic molecules. Closer than 3 AU, a bright violet emission band of cyan CN (3,883 Å) appears in the typical spectrum of the comet’s head. Closer than 2 AU, the cyanogen band is amplified and the emission of triatomic molecules C3 and NH2 is excited. The Swan bands (carbon emission) appear closer to 1.8 AU, and from a distance of 1.5 AU, the emission of radicals—OH, NH, CH, and others—occurs in the spectrum of the comet’s head, and the bands of the emerging ions CO+, N2+, CO2+, CH+, OH+, H2O+, and others appear in the tail. Finally, at about the distance of the Venus orbit, a doublet of sodium (5,890−5,896 Å) appears that is a resonant re-radiation of the sunlight photons being filled in. For different comets, the intensities of the bands differ, and “forbidden” oxygen lines, atomic hydrogen, and others are also observed. In general, the spectra of comets reveal a great number of organic and inorganic molecules and atoms (among the organic molecules, besides the named ones, are C3CH, CS, HCN, CH3CN) and the metals Na, Ca, Co, Cr, Mn, Fe, Ni, Cu, and V. There is silicon (Si), mainly in the dust. According to direct measurements in the Rosetta mission, the gas composition of the coma 67P/CG included water, carbon monoxide, carbon dioxide, ammonia, methane, methanol, formaldehyde, hydrogen sulfide, hydrogen cyanide, and sulfur. The dust composition included sulfur dioxide, carbon disulfide, sulfur, carbonyl sulfide, sodium, and magnesium.

As regards the dust, most often it represents a mix of carbon-hydrogen-oxygen-nitrogen infusible organic compounds (CHON) and a rocky substance composed of chondrite. To investigate its components, impact mass spectrometers are needed, and they operate only in the immediate vicinity of the object.

The results of studies of cometary nuclei obtained over the last decades are impressive. Among the findings is detailed information about the nuclei of comets 67P/CG and 1P/Halley, which is given in the next section.

Direct Investigation of Comets 1P/Halley and 67P/Churyumov-Gerasimenko

On March 6 and 9, 1986, the Russian Vega-1 and Vega-2 spacecraft (Sagdeev, Elyasberg, & Moroz, 1988), and after them, on March 14, 1986, the Giotto space probe (Reinhard, 1986) of the European Space Agency (ESA) initiated historic research on cometary nuclei using space missions. At the same time, on March 8, 1986, the Suisei (“Planet”) spacecraft of the Japanese Space Agency (JAXA) passed by Halley’s comet (Hirao & Itoh, 1986).

Comet 67P was discovered on October 23, 1969, by astronomers K. I. Churyumov and S. I. Gerasimenko of the Astronomical Observatory of Kiev State University during an analysis of photographic plates that had been obtained in September, 1969, during their comet patrol expedition at the Almaty Observatory. The comet was named the 67P/Churyumov-Gerasimenko comet (67P/CG). Between its discovery in 1969 and 2018, 67P/CG has passed perihelion seven times: in 1976, 1982, 1989, 1996, 2002, 2009, and 2015. In 2014−2016, the comet was the focus of the Rosetta mission of the European Space Agency. The Rosetta mission entered into quasi-satellite orbit around the 67P/CG nucleus on October 31, 2014.

The circumstances of the experiments with Vega-1, Vega-2, and Rosetta were different. The dust component emitted by the comet fell on the Rosetta devices at low speeds, which did not pose a serious threat to the Rosetta spacecraft, although near the perihelion (in August 2015) it was kept at a distance of at least 350 km from the nucleus, for safety. In contrast, the Vega-1, Vega-2, and Giotto spacecraft approached the cometary nucleus in collision courses, with a tremendous relative velocity, up to 79 km s−1. The transmission of images of nuclei and detailed study of the composition of the dust and gas emitted by the nucleus, of the magnetic field, and of the plasma in the tail and surrounding the comet were performed under unprecedented conditions of an enormous meteor hazard. For the first time, at a distance of about 1 million km, the spacecrafts crossed a shock wave (Figure 12), and at a distance of about 160,000 km, they crossed the theoretically predicted “cometopause,” where a sharp change in the proton distribution function occurred.

Figure 12. Trajectories of Vega-1 and Vega-2, Giotto, and Suisei spacecraft approaching the nucleus of Halley’s comet. The arrows on the Suisei trajectory show the changes in the magnetic field.

The energy carried by dust grains and small fragments of the cometary nucleus crust exceeds the energy of an artillery projectile (per unit mass) 7,000-fold. Therefore, the Vega-1 and Vega-2 spacecraft, designed and built at the Lavochkin Science and Production Association (NPOL), were equipped with unprecedented means of protection, which to a large extent ensured the missions’ success (Sagdeev et al., 1986).

The spacecraft Vega, Giotto, and Suisei are shown in Figure 13 and the Rosetta spacecraft in preflight preparation is shown in Figure 14.

Figure 13. (a) Vega,

Figure 13. (b) Giotto,

Figure 13. (c) Suisei spacecraft.

Note: The scales of the images are different. The spacecraft are shown without their heat-insulating covers.

Source: IKI RAS archive.

Figure 14. Rosetta spacecraft assembled for tests. The gray protruding block is the Philae probe. (ESA, 140109134929-rosetta-spacecraft-horizontal-large-gallery.)

67P/CG and 1P/Halley Missions: Morphological Properties of the Surface, Limited Possibilities for Comparison, and Landing of the Philae Probe

Starting with Halley’s comet, eight cometary nuclei had been explored by spacecraft by 2017, and taking photographs of the nuclei was one of the main and most important mission tasks. Along with the narrow-angle camera(NAC) and wide-field cameras (Auger et al., 2015) of the Rosetta spacecraft, images in different bands were also taken by other devices ( A significant number of detailed images have been obtained. However, comparing the morphology of the surface of 67P/CG and 1P/Halley is the most difficult. For 67P/CG, there are numerous detailed images with a resolution of up to a few dozen centimeters, but the resolution of the images of the surface of the nucleus of Halley’s comet is about 1 km. In addition, all the spacecraft that participated in the studies of Halley’s comet imaged reliably only about 25% of its surface, and the Rosetta mission obtained images of almost the entire surface of the nucleus of 67P/CG with high resolution. The nucleus of Halley’s comet was observed through a rather dense layer of gas and dust, which are intensively ejected by the nucleus.

After initial processing, the images of the nucleus of Halley’s comet (Avanesov et al., 1989) taken by the CCD camera of the Vega spacecraft yielded an improved image of the nucleus (Zelenyi & Ksanfomality, 2017a) and refinement of its shape (Figure 15A). Figure 15B shows the nucleus of comet 67P/CG. The scale of the images is shown in the figure. The sizes of the respective bodies are 15.3 × 7.2 × 7.2 km and about 4.1 × 3.1 × 2.2 km. The scale in the figure allows estimation of the size of individual elements of the nucleus. The nuclei of both comets have a topographically diverse surfaces, with hills, mountains, ridges, dips, and craters. In the lower part of the orbit, near the perihelion, when the temperature on the surface of the nucleus increased, active processes destroyed some forms and created other ones. At the perihelion of Halley’s comet, at 0.5712 AU, the registered temperature of the dark crust of the nucleus was about 300 K, and at the hottest points it reached 400 K (Combes et al., 1986).

Figure 15. First images of 1P/Halley and 67P/CG comets. (A) The nucleus of Halley’s comet after initial image processing (Zelenyi & Ksanfomality, 2017a). (B) One of the first images of the nucleus of comet 67P/CG taken by the Rosetta mission in 2014.

Near the perihelion, heated pieces of crust were destroyed, separated, and carried away by dust and gas. Nevertheless, the temperature deep inside the nucleus was found to remain very low (which was also noted in the case of comet 67P/CG). Thus, according to the data of the VIRTIS experiment, together with the daytime surface temperature of about 200 K, at a depth of 5 to 6 cm of the investigated areas, the temperature remained constant at about 130 K (De Sanctis et al., 2015). An analysis of the formation conditions of some of the emitted gas components suggests a temperature of 35 K deep inside the nucleus.

More detailed images of Halley’s comet (Figure 16) were obtained by a camera aboard the Giotto spacecraft (Keller et al., 1986; Reinhard, 1986), which operated on a closer trajectory near the nucleus, but was damaged at a distance of 1,200 km. The side of the nucleus observed was opposite that in the upper image in Figure 15 that was taken by Vega. Due to the favorable location of the spacecraft, gas emissions obscured the nucleus less.

Figure 16. Image of Halley’s comet taken by the Giotto spacecraft camera on March 14, 1986.

Source: IKI RAS archive.

The image of the nucleus of Halley’s comet reconstructed from the Giotto observations is shown in Figure 17 (frame 1) in comparison to the nucleus of 67P/CG (frame 2). New processing methods (Ksanfomality, 2014) allowed obtaining the more detailed image shown in Figure 17(frame 1). In comparing the nuclei, first of all, the general similarity of the shapes of the two bodies is clearly seen, despite a fourfold difference in their sizes. The surfaces of both comets are similar in large details. The head (larger part) of the 67P/CG core ends in the Imhotep area and has a flatter shape than the head of the nucleus of Halley’s comet. Landing the Philae probe was planned for near the Imhotep area, in the Agilkia region. The spectrophotometric properties of these areas were considered by Fornasier et al. (2015). The average geometric albedo of the surface is very low: for Halley’s comet it is close to 0.04, while for comet 67P/CG it is about 0.065 at a wavelength of 649 nm.

Figure 17. (1) Image of Halley’s comet taken by the Giotto spacecraft and processed additionally by the author; scale 1:4. (2) One of the first images of the nucleus of comet 67P/CG; scale 1:1. On the right panel, the objects are shown on the same scale.

The nuclei of both comets also have a similar narrow region, a “neck,” seen as light in 67P/CG and dark in 1P/Halley (Figure 17). The neck of the nucleus of Halley’s comet is less prominent and relates to the darkest areas of the surface.

Note that the physical conditions (for example, the radiation conditions) at the neck are somewhat different from those at the peripheral parts. The solid angle at which a platform on a flat surface near the neck “sees” free space is 2π‎, and a pad at the neck sees less than 2π‎. As shown below, the density of the neck material can be significantly different from that of the adjacent parts. The dark cavity at the neck of the nucleus of Halley’s comet has a complex form and can be a process developing in the destruction of the body. At the same time, the origin of the neck of 67P/CG can be a consequence of other processes (Massironi et al., 2015). Ksanfomality (2012) calculated the stress on the comet neck using the example of 103P/Hartley-2, which is close to destruction. Extended dumbbell cometary nuclei (as in comet 103P/Hartley) are most convenient for analysis of the physical state and possible evolution of the comet nucleus. A detailed calculation has not been carried out for Halley’s comet. The comet is much larger in size and mass M, but its rotation velocity ω‎ is three times lower (the spin period of the nucleus of Halley’s comet is 52 hours, and that of the comet 67P/CG is 12.4 hours). Stresses F caused by centrifugal forces in their equilibrium cross-section turn out to be close to destructive, but smaller than in the case of 103P/Hartley-2. However, such calculations require that the shape of the 1P/Halley comet nucleus be known with a higher precision. As seen in Figure 17, on the surface of most of the nucleus of Halley’s comet (at the center and on the right), there are three large annular formations (apparently craters) and a more complex structure on the left side of the nucleus, where two closely related objects with a bright boundary are visible. In both parts, they are joined by long plains. The contours of the annular formations are fuzzy; perhaps they are dilapidated craters. Hills, mountains, and hollows are also noticeable. It should also be noted that some of the smallest details in Figure 17 may be artifacts of the processing codes.

The mechanical model for 67P/CG is much more complicated and includes protruding parts and a complex diagram of the distribution of mechanical stresses. The estimated stresses are approximately the same, but the results need improvement.

The surface of the 67P/CG nucleus, which was studied in much more detail, turned out to be very heterogeneous in comparison with Halley’s comet. Detailed pictures given below show the peculiar properties of this nucleus, which sharply distinguish it from the already familiar 1P/Halley or 103P/Hartley-2. Typical 67P/CG and 103P/Hartley nuclei surface images are presented in Figure 18. On the left in Figure 18 is a deep saddle between the larger and smaller parts of the nucleus. Apparently, their surfaces are so different that their properties are difficult to compare. Unlike the relatively smooth dust cover of 103P/Hartley-2, the nucleus of 67P/CG is covered with coarse faults, dips, and lumps.

Figure 18. Variety of forms and relief of cometary nuclei. (A) The surface of the 67P/CG nucleus (image ESA/Rosetta/Navcam.CC BY-SA IGO 3.0, obtained on January 31, 2015). (B) The surface of the 103P/Hartley-2 nucleus (image by JASA, 2005). The 67P/CG nucleus is twice as large (4.1 and 2.2 km, respectively).

Images taken at different positions of the nucleus of 67P/CG are demonstrative of the nature of the nucleus and its surface. One of the most detailed pictures is shown in Figure 19. Both halves and the neck are visible. Large blocks are scattered over the smooth (as if powdered) part of the neck of Hapi. The spatial resolution of the image is about 30 cm. On the adjacent Hathor slope (smaller half of the nucleus), there is a distinct layered structure with a sharp boundary on a smoother surface at the top. Apparently, the nature of the latter surface is a more recent destruction and is identical to the nature of the lower half of the comet facing the observer. In both parts, there are numerous traces of impact craters of different depths and different degradations. There are coarse fractures of the surface. The lighter shades in the figure are deceptive: the surface is very dark—the albedo here is about 3% (darker than soot). It can be considered light only in comparison to the adjacent dark cosmic background. Deep shadows do not necessarily indicate troughs: the surface is illuminated by direct sunlight, and weak diffuse light is reflected by other areas of the relief. This is the surface of a body that has hardly changed over 4.5 billion years, since the origin of the solar system.

Figure 19. One of the most detailed images showing both halves and the neck of the nucleus of 67P/CG. The image was taken by a narrow-angle camera of the Rosetta mission on August 7, 2015, from a distance of 104 km. (Image: MPS/MPD/LAM/IAA/SSO/INTA/UPM/DASP/IDA.)

The steep, layered slope of Hathor in Figure 19 has a height of about 1 km. The barycenter of the body is located at the Hapi saddle near the greater half of the body. The fragmentary sand-dust deposits are apparently formed by screes from the slopes of Hathor. However, as became clear after the Philae landing, a thin dust layer covering the surface can conceal very hard rocks, which cannot be drilled. Presumably, the composition is a low-temperature ice environment with inclusions of dust and debris of silicate rocks. The shedding itself occurs very slowly, and the free-fall acceleration gc = GM/r2 is not the same at the top and bottom of the wall. With the body mass M = 1013 kg and the gravity constant G, the acceleration gc is 0.167 ∙ 10−3 m/s2 at the peak (r = 2 km to the gravity center) and 0.667 ∙ 10−3 m/s2 on the surface of the saddle (r =1 km). In these conditions, it would take more than an hour for debris to fall from the top.

On the basis of morphological and structural features, El-Maarry et al. (2015) identified 19 characteristic surface types, each given a name borrowed from ancient Egyptian mythology. The nucleus rotates (more accurately) with a period of 12.4043 h about the axis passing through the mass center. Rotation leads to the appearance of centrifugal forces. It can be assumed that, under their action, a slow but continuous elongation of the neck occurs, which should result in separation of the nucleus fragments. This is impeded by the strength of the neck material, the attraction between the parts of the nucleus, and the gradual deceleration of its rotation due to friction losses in the neck material and the gradual elongation of the body.

The diversity of relief of the 67P/CG nucleus is also illustrated in Figure 20, where the processed image of the complex Atum-Anubis region is shown. The length of the site is 1.6 km. Among the types of surface, the most common is what El-Maarry et al. called “consolidated and destroyed surface.” In some cases, regions with a smooth surface (formed by fine-grained dust material with block inclusions) adjoin it. Such areas are also numerous. El-Maarry et al. (2015) noted that their formation is probably related to the ongoing sublimation of the volatiles that make up the comet nucleus. The inhomogeneity of the propagation of subliming inclusions is evident, which results in the formation of huge gaps. In many places, a layered surface structure is observed. The structure of the wide (up to 1 km), steep slope of the nucleus head (Figure 20), with screes of collapsing material and signs of stratification, is interesting, in sharp contrast to the adjacent neck region. The variety of areas includes small hills, annular formations (some of which can be destroyed craters), plains, and deep faults. The surface is extremely heterogeneous: the left part of the region is composed of elements resembling layered structures, and the Anubis area (on the right) is covered with smoother sediments. On the bottom right, a part of the “shaded” neck can be seen. Partial sublimation of the nucleus material leaves fragile formations with a bizarre shape. The origin of some objects, the features, the heterogeneity, and the “variegation” of the surface structure of 67P/CG were considered in detail by Auger et al. (2015), El-Maarry et al. (2015), Sierks et al. (2015), Oklay et al. (2016), Pätzold et al. (2016), and Vincent et al. (2015). It was expected that important data would be obtained by the Philae probe.

Figure 20. Heterogeneous region Atum-Anubis; the length of the site is 1.6 km, the resolution is 1.6 m/pixel. The image was taken on January 5, 2016, from a distance of 18.8 km. (Image ESA/Rosetta/NAVCAMiCC BY-SA IGO 3.0.)

The Rosetta mission was equipped with a landing module to explore the surface of the comet’s nucleus. Philae was the first probe designed for a soft landing on the nucleus of a comet. It was equipped with different instruments for scientific research. The mass of Philae was 100 kg. Prior to the Rosetta mission, two spacecraft, NEAR Shoemaker (2000) and Hayabusa (“Peregrine”; 2005), had made experimental (unplanned beforehand) soft landings on the Eros and Itokawa asteroids, respectively, and then the Hayabusa probe took off and returned to Earth.

The ballistic (uncontrolled) descent of the Philae probe took place on November 12, 2014. The choice of the landing site was very important. On the one hand, the possibility of easily observing the adjacent relief and studying the surface was assumed; on the other hand, the safety of the landing surface was important, and the lighting conditions had to ensure the operation of solar batteries. Due to low gravity, the descent time (in fact, falling on a comet from a height of 20 km) reached 7 hours. The probe descended along a ballistic (uncontrolled) trajectory aimed for the surface. A system of three pillars was equipped with mechanisms to weaken the impact of landing. Three devices, including a clamping rocket motor on the upper side of the Philae probe, ice screws on the supports, and harpoons to pierce the surface, were supposed to prevent a bounce. The ice screws were driven by the impact energy of landing and were supposed to crash into the surface. Then harpoons, fired by special pyrocartridges, were to be pushed into the surface at a speed of 70 m/s. The clamping motor was a kind of thruster, but it worked on a cold gas in order not to pollute the surface under investigation. This should have reduced the bounce of the spacecraft and reduced the impact of shooting the harpoons. Unfortunately, none of the three devices fulfilled its task. The only thing that could keep Philae from leaping was the insignificant weight of the spacecraft on the surface of the comet. Assuming that the surface is at a distance r = 1 km from the gravity center of the body, then the free-fall acceleration on the comet gc is only 6.8 ∙ 10−4 m/s2, and the weight of the spacecraft is only 0.068N for its mass of 100 kg. The supports sprang off and threw the lander upward at a speed of about 0.4 m/s. With the low gravity of the comet, the kinetic energy of the lander at the time of landing (about 50 J) was enough to bring Philae to a height of about 1 km and to re-descend almost 2 hours later. The lander then sprang off and ascended again, but not high, and finally stopped 2 hours after the first contact. While the Philae lander rose and fell, the comet continued spinning. Instead of a flat, open area, fully illuminated by the sun, the area under the probe became a surface made of rough stone slopes and dips. The lander finally stopped, but in extremely difficult conditions. The lander got into a hollow among high, jagged rocks, near a dead wall, and the probe itself was in a deep shadow, where the solar batteries were useless. Before the energy of the batteries was exhausted, the lander managed to transmit only the data accumulated during the landing. The failure with the Philae landing was very disappointing, but it was partially compensated for by subsequent approaches of the Rosetta spacecraft to the nucleus at a distance of several kilometers.

Mass Loss of Comets in the Perihelion

The activity of the nucleus of a comet increases when the comet approaches perihelion. Halley’s comet at perihelion (0.5712 AU) ejected intense gas-dust jets (Figure 21, frame 1) that propagated for millions of kilometers. The nucleus was observed from spacecrafts in a fly-by mode on March 6, 9, and 14, 1986. The perihelion of comet 67P/CG was located much more distant. The daily surface temperature on the 1P comet was in the range 140 to 200 K (Capaccioni et al., 2015; De Sanctis et al., 2015) and only at some points rose to 230 K. Mass loss from the nucleus of comet 67P/CG was found to be much smaller, because of both the higher perihelion (1.2432 AU) and the smaller size of the nucleus. The mass of the 67P/CG nucleus is 1/22 that of the nucleus of Halley’s comet. Observations of the gas/dust activity of the 67P/CG nucleus are presented in Figure 21, frames 2−5. The areas of the 67P/CG neck were markedly active (Figure 21, frames 2 and 3). In frame 4, emissions cover a significant part of the nucleus and are visible in the center of the lower, unilluminated part of it, where a gushing ejection is visible. As can be seen from Figure 21, unlike with Halley’s comet, the mass outflow from the 67P/CG nucleus was limited to few local sources. However, it should be recalled that the total area of the sources of the ejected gas-dust medium of Halley’s comet at perihelion was also estimated to be 10% (Cevolani & Bortolotti, 1987), although the ejecta were incomparably larger in mass and length than those from 67P/CG. A narrow jet (Figure 21, frame 5) appeared irregularly on July 29, 2015. Similar jets were observed in other regions.

Figure 21. (1) Activity of the nucleus of Halley’s comet (1986). Activity development for comet 67P/CG in February−June 2015.

Figure 21. (2) Emissions from the neck, February 6, 2015. (Image ESA/Rosetta/NAVCAM.CC BY-SA IGO 3.0.) (3) Development of gas-dust emissions from the neck (Hapi region), February 9, 2015. (Image ESA/Rosetta/NAVCAM.CC BY-SA IGO 3.0.) (4) High activity of gas-dust emissions, March 12, 2015. A gushing outflow from the lower, unilluminated part of the nucleus is seen. (Image: ESA/Rosetta/MPS/MPD/LAM/IAA/SSO/INTA/UPM/DASP/IDA.) (5) Irregular narrow jet, July 29, 2015. (Camera OSIRIS. Image ESA/rosetta/MPS for OSIRIS team.)

The dust particles of Halley’s comet comprise mostly a mix of CHON refractory organic compounds and rocky chondrite material. In the experiments GIADA and OSIRIS on the Rosetta spacecraft, a dust component was detected near the nucleus of the comet along the route of flight in the interval 3.6−3.4 AU (Rotundi et al., 2015). In total, 35 particles or fragments with masses from 10−7 to 10−4 g and 48 pieces with masses from 10−2 to 10 g were detected in the experiments. The mean dust:gas ratio over the daylight part of the nucleus was found to be 4 ± 2 when accounting for data obtained in the MIRO experiment (Gulkis et al., 2015).

The average dust:gas ratio turns out to be 3. Up to 100 ∙ 103 particles and debris up to one meter in size rotate around the nucleus, and the density of the particles themselves is close to (1.1−1.9) ∙ 103 kg/m3. The loss of water for 3 months in June−August 2014 increased from 0.3 to 1.2 liters per second. The total mass loss from the nucleus of 67P/CG per one perihelion passage was (3−5) ∙ 109 kg (Taylor et al., 2015), with variations by a factor of five (Gulkis et al., 2015). The activity of the nucleus near the perihelion increased significantly (Figure 22), but the absolute values of the losses remained small.

Figure 22. Comet 67P/CG passing the perihelion, August 22, 2015. Emission activity increased significantly. (Image ESA/Rosetta/NAVCAMiCC BY-SA IGO 3.0.)

The boundaries of the cross-section of the coma of Halley’s comet exceeded 105 km, which is typical for large comets. Due to photolysis, the main component, water vapor, dissociated, and the extent of the gas and ionic components (hydrogen and other volatiles) is estimated to reach 20 ∙ 106 km. The mass loss from Halley’s comet at perihelion has been considered in many papers (see review by Cevolani & Bortolotti, 1987).

According to the data obtained by Churyumov, the gas production of water, QH2O, in Halley’s comet after the perihelion passage, at a distance of 0.9 AU from the sun, was 4 ∙ 1029 molecules s−1, which makes 4 ∙ 1029 × 18 × 1.66 ∙ 10−27 = 1.20 ∙ 104 kg s−1. The 67P/CG atmosphere consists of about 80% water vapor. In August 2015, H2O gas production, according to Lee et al. (2015), ranged from 1024 to 3 ∙ 1025 (s sr)−1, so within a month, the maximum H2O productivity varied by a factor of 30. The maximum H2O production rate was 4π‎ × 3 · 1025 × 18 × 1.66 ∙ 10−27 = 112.6 kg s−1, and the minimum was about 3.75 kg s−1. The data on the dimensionality are somewhat inconsistent: Gulkis et al. (2015) indicated 2 · 1025 molecules s−1 (in June 2014), while Lee et al. (2015) estimated up to 3 · 1025 molecules (s sr)−1 in August 2014.

The atmosphere of comet 67P/CG includes 17% carbon monoxide and about 3% carbon dioxide. Small amounts of methane and ammonia were also found (Biver et al., 2015). Measurements of the dust component were more complicated. With the gas:dust short-term mass ratio of 7:1, the total losses reached 1.60 ∙ 104 kg s−1.

There are significant discrepancies in estimates of the mass loss of Halley’s comet near the perihelion. Estimates of mass losses per orbital period (75.5 years) range from 2.2 ∙ 1011 to 5 ∙ 1011 kg, i.e., from 10−3 to 2 ∙ 10−3 of the total mass of the nucleus. Three dust experiments, DUCMA (Dust Counter and Mass Analyzer), SP-1, and SP-2 were performed on board the Vega-1 spacecraft (Mazets et al., 1986; Simpson, Tuzzolino, Ksanfomality, & Sagdeev, 1990; Vaisberg et al., 1987). The data of the Vega-1 and Vega-2 DUCMA experiment on the registration of particles with masses from1.5 ∙ 10−13 to 10−10 g were reported by Simpson et al. (1990; Simpson, Rabinovitz, Tuzzolino, Perkins, & Ksanfomality, 1993; Simpson, Tuzzolino, Ksanfomality, Sagdeev, & Vaisberg, 1989). Figure 23 illustrates the increase in, and subsequent decrease in, the count rate in the DUCMA experiment (Simpson et al., 1993) when approaching the nucleus at a minimum distance of 8,045 km. The integration of data obtained by dust instruments (with the assumed mass distribution functions of particles) increased the maximum mass loss rate at the perihelion up to 2.9 ∙ 104 kg s−1.

Figure 23. Measurements of the dust-particle count rate in the DUCMA experiment on March 9, 1986 (Simpson et al., 1993) during the Vega-2 maximum approach to the nucleus (8,045 km).

The total mass of the nucleus of Halley’s comet (2.2 ∙ 1014 kg) is calculated using its estimated density (Sagdeev et al., 1986, 1988), estimated from 100 to 700 (and even up to 1500) kg m−3, and the poorly known density of dust particles. Usually, 600 kg m−3 is assumed, which indicates a highly porous nucleus formed by a large number of small, loosely bound elements.

Halley’s comet is assumed to have passed perihelion approximately 2,300 times (Cevolani & Bortolotti, 1987), which leads to a very large initial mass, by assuming mass losses (Δ‎m) each period from 10−3 to 2 ∙ 10−3 of the total mass of the nucleus. It yields the initial mass:


where n is the number of perihelion passages, MHalley = 2.2 ∙ 1014 kg, which yields M0 = 2.2 ∙ 1015 kg for Δ‎m = 10−3 and M0 = 2.2 ∙ 1016 kg for Δ‎m = 2 ∙ 10−3. Comets with such large masses are unknown. However, on large time scales, for example, beyond 40 to 50 orbits, calculations of the dynamics of a comet become unreliable. With a mass loss rate of 2.9 ∙ 104 kg s−1 at the perihelion and 1.20 ∙ 104 kg s−1 at a distance of 0.9 AU, the mass fraction 10−3 actually rapidly accumulates near the perihelion in less than 220 days. The speed V of the nucleus Halley at the perihelion is

VHalley=[ GMs(1+εHalley)/qHalley ]½=55.2km/s

where qHalley = 0.5712 AU is the perihelion distance, the eccentricity is εHalley= 0.9671, and the solar mass is Ms = 1:989 ∙ 1030 kg. The orbit is inclined to the ecliptic by 162° (retrograde rotation).

According to measurements in early 2015, the gas composition of the 67P/CG coma included water, carbon monoxide, carbon dioxide, ammonia, methane, methanol, formaldehyde, hydrogen sulfide, hydrogen cyanide, sulfur dioxide, carbon disulfide, sulfur, and carbonyl sulfide, as well as sodium and magnesium in the composition of dust grains (Biver et al., 2015; Capaccioni et al., 2015; Taylor et al., 2015). Earlier reports indicated that hydrogen sulfide contained the sulfur isotope 32S, and the 34S isotope could have a different origin. The ROSINA experiment discovered inert argon gas among other gas components in the nucleus of the comet (Figure 24; Balsiger et al., 2015), and the 36Ar:38Ar ratio of isotopes is 5.4 ± 1.4, which is close to the terrestrial value 5.3. Argon in comets had been reported earlier, when argon emissions were detected in comet Hale-Bopp (Stern et al., 2000), in which a synthesis of organic substances was also presumably found (Rodgers & Charnley, 2002).

Figure 24. Isotopes 36Ar and 38Ar and other gaseous components of comet 67P/CG, registered in the ROSINA (Rosetta Orbiter Spectrometer for Ion and Neutral Analysis) experiment (Balsiger et al., 2015).

An important discovery was molecular oxygen in the atmosphere of the 67P/CG comet by the ROSINA mass spectrometer aboard the Rosetta mission (Bieler et al., 2015), and oxygen was among the four most abundant constituents of the comet’s atmosphere (Figure 25). Its concentration (from 1% to 10% of water vapor, 3.8% on average) changed little during the six months when the measurements were carried out, which suggests that the nucleus is its steady source.

Figure 25. The abundance of oxygen and other gaseous constituents in the atmosphere of comet 67P/CG measured by the ROSINA mass spectrometer at different distances from the nucleus (Bieler et al., 2015). The peak to the right is methanol (CH3OH).

Oxygen diffuses from the interior of the nucleus and is not supposed to be a product of water dissociation, but it is preserved in the nucleus after its formation. However, it remains unclear which initial medium could be significantly enriched with relic oxygen and why oxygen, a highly reactive element, is not bound in reactions with nuclear materials. The connection between the abundance of the observed components and the original composition of the comet nucleus is among the topical problems of the physics of comets (Marboeuf & Schmit, 2014).

The main feature of the Rosetta mission, in contrast to Vega, is that due to the quasi-satellite position of the spacecraft relative to the nucleus of 67P/CG, systematic and long-term observations were possible, as in the case of the detection of oxygen. Nevertheless, the Vega and Giotto missions also yielded many surprises during the short-time approach of the spacecraft to the comet. Immediate direct measurements of the composition of cometary plasma indicated the presence of ions with the mass 56 (Figure 26), which were hypothetically identified as iron ions (Fe+) that had not previously been observed in the plasma of Halley’s comet.

Figure 26. Iron ions (Fe+) were first detected in the plasma of Halley’s comet in the Vega mission experiments. The curves were obtained during the spacecraft’s approach to the nucleus (Verigin, 2015).

Comet 67P/CG, in contrast to Halley’s comet, is classified as a dust/gas comet (with the dust:gas ratio close to 3:1). The peak dust productivity near the perihelion of 2002−2003 was 60 kg s−1, and in 1982−1983 it reached 220 kg s−1. Long-term H2O productivity would range from 3.75 kg s−1 to 112 kg s−1, according to Lee et al. (2015). The productivity of water vapor is about 10−4 of that in Halley’s comet. Therefore, the dust:gas ratios result in a minimum dust loss estimate of about 15 kg s−1. In general, the scatter in the estimates makes it difficult to determine the total losses, but they are negligibly small in comparison with the mass of the nucleus (1013 kg). Dynamic impacts of micrometeorites, gas, and plasma with the surface of the nucleus and coma depend partly on orbital motion of the body. They are, in general, much lower than for Halley’s comet. The orbital speed V67P at the perihelion (q67P = 1.2432 AU, ε67P = 0.6410) is:

V67P=[ GMs(1+ε67P)/q67P]½=34.2kms1.

An interesting phenomenon was discovered thanks to the rapid motion of the Vega spacecraft itself relative to the nucleus of Halley’s comet. The spatial distribution of the dust grains in the vicinity of the nucleus was inhomogeneous and indicated a certain periodicity in the dust medium structure. The phenomenon was interpreted by Vaisberg as a spatial spiral form of the most intense dust jets, which is due to the rotation of the nucleus (Vaisberg et al., 1986, 1987). Thanks to its rapid motion, the Vega spacecraft consecutively crossed the dust jets several times (Simpson et al., 1989).

Origin and Deuterium Abundance of Comets 1P/Halley and 67P/CG

Comparison of cometary atmosphere compositions suggests a significant difference between comets 1P and 67P that is due to differences in their origins. The Kuiper Belt is thought to be the solar system region where bodies similar to comet 67P are located (Altwegg et al., 2015). Features of the orbit of Halley’s comet suggest its ancient origin from a more distant region, the Oort Cloud, the bodies in which are unrelated to the ecliptic plane and have D/H ratios that can be different from other bodies of the solar system. Halley’s comet belongs to the short-period group (with the period less than 200 years), but its orbital features suggest that it originated in the Oort Cloud and, due to perturbations by the giant planets in the lower part of its orbit, turned out to be in a short-period orbit. At the same time, the available historical data show that 1P/Halley has been in this modern, relatively stable orbit for a long time (Cevolani & Bortolotti, 1987). As mentioned above, ancient Greek and Chinese records first documented it in 468−466 bc, and its description can be found in Chinese chronicles dated 240 bc. In the Middle Ages, the Julian and Gregorian calendars marked the dates of the appearance of 1P beginning in 1531 and 1607, respectively. The evolution of the 67P/CG orbit is not traced that far. Calculations of the evolution before the 19th century give unreliable results. Until 1840, its distance at the perihelion (as the backward integration of the orbit shows) was 4.0 AU, three times larger than the modern distance. Later, a series of approaches to Jupiter reduced the distance at the perihelion first to 3.0 AU, and then to 2.77 AU. More recently, in 1959, there was a further decrease in the perihelion of the comet to 1.29 AU. The orbital period of 67P/CG is now 6.45 years.

It is extremely important to know and compare the D/H (deuterium/protium) ratios in solar system bodies (Hallis, 2017). Analysis of the isotopic composition of the significant masses of water vapor emitted by the 67P/CG nucleus indicated an unusually high D/H ratio. The topic of the D/H ratio in connection with the origin of terrestrial oceans has been considered by many researchers, among them Tobias C. Owen and Akiva Bar-Nun, whose work covers the period starting in the 1980s (Owen, 1998; Owen & Bar-Nun, 1995). It was assumed that the volatiles fell on the inner planets in the form of planetesimals and ice nuclei of comets (Benz, 2015; Owen, 1998; Owen & Bar-Nun, 1995), and that comets brought up to 35% to 40% of the water in Earth’s oceans, with planetesimals and asteroids accounting for about 60% to 65% of the water. However, experimental findings about the D/H ratio, which have been gradually accumulated, shifted the evidence for origin of terrestrial water to favor of planetesimals and asteroids. It was noted by Owen and Bar-Nun (2001) that comets alone could not form oceans on Earth; other sources with a lower D/H ratio were needed for this. This problem was considered in detail by Drake (2005). The measured D/H ratio in Rosetta mission experiments was (5.3 ± 0.7) ∙ 10−4 (Auger et al., 2015). The authors note that the earlier cometary measurements and new results suggest that the broad limits of D/H in the water of the Jupiter family of comets rule out the possibility that this reservoir was the only source of water for terrestrial oceans. Although this conclusion is cautious, numerous comments have nevertheless suggested that the Rosetta results finally close the issue with comets, which is not the case. It cannot be ruled out that the terrestrial value of D/H itself could evolve (Genda & Ikoma, 2008). There is not much water in various phases on the surface of the cometary nucleus (De Sanctis et al., 2015), as daily diurnal cycles showing that are observed. However, water ice is among the main components of the cometary nuclei, which have brought a significant proportion of matter to Earth. There are 156 molecules of heavy water (HDO) for every 106 ordinary Earth water molecules (H2O), i.e., 156 ppm (parts per million). In contrast, the Rosetta measurements yield 530 ppm, i.e., 530 molecules of HDO for every 106 molecules of ordinary water.

Figure 27 is based on data from Altwegg et al. (2015) and other publications. In Halley’s comet, D/H was 310 ppm (Eberhardt et al., 1987), which is twice the terrestrial value (156 ppm). The ratio in the Hale-Bopp comet was almost the same (330 ppm; Meier et al., 1998). Thus, these celestial bodies are enriched, respectively, with deuterium 2 and 3.4 times as much as Earth, and more than 15 times more than the protostellar nebula. The thick horizontal line in Figure 27 shows terrestrial water (156 ppm), and the lower part of the figure shows the initial D/H ratio in the protostellar nebula (20−23 ppm; Geiss & Gloeckler, 1998). Recent measurements for 103P/Hartley-2 yielded D/H equal to (1.61 ± 0.24) ∙ 10−4 (Ceccarelli et al., 2014). Although both comets, 103P/Hartley-2 and 67P/CG, appear to have come from the Kuiper Belt (Marboeuf & Schmit, 2014), their D/H ratios differ by a factor of 3.

Figure 27. Generalized diagram of the D/H ratio in solar system bodies. The height of the rectangles shows differences in the values in the group or dispersion of the measurements. The thick horizontal line is the water on Earth. The upper value, 530 ppm, is for 67P. The initial D/H ratio in the protostellar nebula is about 20 ppm. Jupiter and Saturn have similar D/H values. Twofold (on average) terrestrial D/H values are typical for Oort Cloud comets, such as Halley’s comet. (Enceladus is a satellite of Saturn.) The horizontal position of rectangles has no physical meaning.

It is naive to believe that the issue of the origin of water in terrestrial oceans can be solved based on the results of the 67P/CG studies only. Figure 27 also indicates the complexity of the problem, and the concentration of D/H values near the terrestrial value supports the planetesimals and asteroids hypothesis, although there were other sources of water. Undoubtedly, comets also brought part of the oceanic water, and the water of the oceans is a mixture of different sources.

Organic Substances on the Surface of the 67P/CG Nucleus

About a year after the unsuccessful landing of the Philae probe, its solar illumination increased slightly and its automation tried to turn on the transmitter of the probe. However, the illumination was too low and, after a few indistinct messages, Philae fell silent again. Nevertheless, a huge amount of data from the Rosetta mission is at the disposal of scientists; the data include 80,000 images and the only communication session that was made during the landing of Philae.

Until the last days of the Rosetta’s work (Rosetta was deliberately dropped to the surface of the comet’s core on September 30, 2016, and remains there as a monument to the project), the search for Philae continued. The approximate area where the probe is located was known, but it was only at the very end of the mission, on September 5, 2016, that a reliable image of it was obtained. Philae is under a large block, in deep shade, and the sun sometimes illuminates its very edge.

At the first contact with the surface, the probe instruments (two mass spectrometers) captured a small amount of regolith and gas and had time to analyze them. The conclusion is that the surface is covered with a 20-cm layer of dust and granulated grains, in part, as expected, of basalt composition, as was awaited for (Zelenyi & Ksanfomality, 2017a). The grains range in size from 1 to 15 mm.

The detected gas components, in addition to H2O and CO2, include a complex mixture of organic components, among which is presumably polyoxymethylene (CH2O)n. A total of 16 organic compounds were found, of which at least four were first detected in comets (CH3CNOH2, CH3NCO, C2H5CNO, (CH3)2CO). They were formed in photochemical and other processes, and the initial materials were probably water, carbon monoxide, ammonia, and methane. In the coma 67P, formaldehyde and molecular hydrogen were found. Like the oxygen, the molecular hydrogen was incorporated in the nucleus in a low-temperature environment. It may be recalled that in discussions about the origin of life it is often mentioned that the necessary organic substances were brought to the Earth by comets.

Formation of Complex Cometary Nuclei in Low-Speed Collisions

A significant portion of cometary nuclei have the form of a dumbbell, with a narrow “neck” separating more massive parts. This is true of the nuclei of comets 67P/CG, 1P/Halley, 103P/Hartley-2, 19P/Borrelly, and others. As in the case of 67P/CG, the most intensive material outbursts are often observed from the narrow neck, which suggests that the gradual destruction of nuclei occurs precisely in the narrow section. The decrease in the neck is accompanied by an increase in the mechanical stresses arising under the action of centrifugal forces from the rotation of the body, and by a number of other physical factors. An attempt to analyze the mechanical stresses was given in Ksanfomality (2012) for comet 103P/Hartley-2, where the body was kept from disruption mainly by friction forces. Probably in a number of cases, rupture occurs if the regolith of the neck is sufficiently crumbly. The nucleus of Halley’s comet has an average density of about 600 kg/m3 and a porosity of about 50%. This indicates that it consists of a large number of weakly coupled small elements. There are only estimations for the mechanical stresses in the 1P nuclei.

The nucleus of comet 67P/CG also has a low density, 533 ± 6 kg/m3, according to improved data, and a high porosity, 72 ± 74% (Pätzold et al., 2016). Pätzold et al. noted that, in general, the dust composition and porosity of the 67P/CG body are similar to those of comet 9P/Tempel 1. Their probable dust:ice ratio is about 4 by mass and 2 by volume. Similar results of the Rosetta mission have been cited by Gulkis et al. (2015). The nucleus material is mainly sufficiently homogeneous, and the presence of voids is unlikely.

At the same time, experiments performed during the Philae probe landing showed that, although the mean porosity of the core is high, the material at the final landing point in the Abydos region had the rigidity of frozen ice mixed with dust grains. However, at the point of the first contact (Agilkia), the surface was weak, but hard enough to rebound the probe.

As a result of these observations, the assumption that the dumbbell shape of cometary nuclei results from a previous merger of independent bodies, rather than signaling their future destruction, is becoming more popular. It is the nucleus of comet 67P/CG that presents such evidence (Benz, 2015; Massironi et al., 2015; Vincent et al., 2015). Massironi et al. (2015) also discussed the hypothesis about deposition of material layers on the previously formed body. The shape of the nucleus and its properties raise the question of whether the body formed from contact between two (or more) large planetesimals 4.5 billion years ago or is a single, slowly destructing body (Sierks et al., 2015). The idea of the formation of a nucleus from colliding pieces is not new but meets with difficulty in that the energy released in collisions destroys the impactors, rather than uniting them.

Of course, in most cases, exactly such destructive collisions have occurred. However, there have been a lot of colliding bodies, including those whose collision speeds were small, 1 to 1.5 m/s, such that the impactors could collide without significant damage, and the neck material could be compressed. Such conditions could lead to the formation of dumbbell-shaped comets (67P/CG, 103P/Hartley-2, 1P/Halley, 19P/Borrelly), which, of course, does not contradict their continuing destruction in the narrow cross-section.

A convincing example of the heterogeneity of the 67P/CG nucleus is shown in Figure 28. The Hathor ledge shows signs of continuing destruction, and the exposed surface has a structure resembling layering. At the base of the ledge, crumbling material and detached blocks overlapping the neck Hapi can be seen. Apparently, the surface is heterogeneous and carries traces of fractures and cracks (Sierks et al., 2015). The structure of the opposite side, Seth, is completely different. Thus, the two parts of the 67P/CG nucleus have different characteristics (Massironi et al., 2015), which favors the hypothesis of fusion of proto-comet bodies (Zelenyi & Ksanfomality, 2017b). In that case, the regolith should have an increased density in the contact area of the colliding bodies. Perhaps such a heterogeneity of the regolith on the surface of the 67P/CG nucleus was what was found on the Philae probe landing site.

Figure 28. Slope of the smaller half of the 67P/CG nucleus (Hathor ledge), which has a height of about 1 km. The image shows a crumbling slope and regolith and clods falling on the neck Hapi. The opposite side, the Seth region, has a different nature. (Image OSIRIS, ESA/Rosetta/MPS for OSIRIS Team MPS/UPD/LAM/IAA/SSO/INTA/UPM/DASP/IDA, with changes.)

The hypothesis of cometary nuclei fusing in low-speed collisions is supported by many researchers. In collisions, the probability of destruction is much higher than the probability of merger, but during the solar system’s formation, low-speed collisions also occurred among the countless primary bodies. The coalescence of primary bodies should occur differently in bodies of small and large mass. In the latter case, even at low collision velocities, the energy dissipated was so great that the contact area must have been completely compressed. If we assume that the nucleus of Halley’s comet experienced a similar process, its image (Figure 17) may confirm this idea. However, the statistics are still too scarce. Thus, “necks” in cometary bodies (and asteroids) should be encountered more often for smaller masses, as in the nucleus of 67P/CG (Figure 29). Of course, the image in Figure 29 cannot be direct proof of a previous merger of independent nuclei, but the impression is that the unification occurred precisely along the plane of the narrow section in the figure. The analysis and development of the hypothesis of a merger of proto-comet bodies (Benz, 2015; Zelenyi & Ksanfomality, 2017b) are new steps in the study of comets.

Figure 29. During the solar system’s formation, the probability of collisional destruction of bodies was much higher than that of merger, but low-speed collisions of the countless primary bodies did occur. It cannot be ruled out that the core of 67P/CG was created in such a merger. (Image OSIRIS, ESA/Rosetta/MPS for OSIRIS Team MPS/UPD/LAM/IAA/SSO/INTA/UPM/DASP/IDA, August 12, 2015.)


The description of certain properties of cometary nuclei, comas, and tails is, of course, far from complete. Direct studies of cometary nuclei launched in 1986 by the Vega and Giotto missions suggest the diverse nature of cometary bodies, their atmospheres, and their formation regions. Comparisons of the most thoroughly studied comets, such as 1P/Halley and 67P/Churyumov-Gerasimenko, indicate significant differences in their physicochemical properties, origin, dynamics, and evolution. It can even be noted that the widespread assertion that the study of the physics and the evolution of comets will speed up the resolution of cardinal issues concerning the origin of our solar system is somewhat naive. On the contrary, new processes are being revealed, complicating existing hypotheses about the solar system’s formation.


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