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COMETS
Author: Sebastjan Zamuda
Adviser: Tomaž Zwitter
January 2002
Abstract
Comets have inspired people for centuries. Even today the apparition of a bright comet is still as
spectacular as it was centuries ago. But now we better understand their physics. In 1950 Fred
Whipple proposed the ’dirty-snowball’ model. Later observations and measurements confirmed
that the basic idea of this model was correct. When the ’snowball’ approaches the Sun it gets
warmer and the ices start to sublimate and form coma. Two tails usually form behind the coma;
a dust and a plasma tail. The shape and development of the former is governed mainly by Sun’s
gravitation and radiation pressure. The interaction between coma and solar wind (and magnetic
field it carries along) define the latter.
While our knowledge about comets is advancing rapidly there are still many mysteries. What
exactly are nuclei made of? How different are comets? Another important topic in studying comets
are their orbits. Basically they can be divided in two groups; short- and long-period comets. Ideas
that lie behind this classification are presented. Short-period comets have periods less than 200
years, small inclinations, average eccentricity about 0.5, many have aphelia close to the orbit of
Jupiter and the argument of perihelion near 0◦ or 180◦ . They are thought to originate from Kuiper
belt that extends from 30 to 100 astronomical units (AU) from the Sun.
Long-period comets have periods in excess of 200 years, many of them from 100,000 to 1 million
years. Their inclinations and arguments of perihelion are randomly distributed. They are thought
to have formed in the realm of the giant planets that perturbed comets’ orbits and sent some of
them to the Oort cloud that extends from 3,000 to 100,000 AU from the Sun.
In the last decade technology enabled many new discoveries. Among them is investigation of
comets by space probes, as armada of probes did in 1986 when comet Halley returned to the Sun.
Comets change with every approach to the Sun and also have different fates. Some of them will
collide with planets as Shoemaker-Levy 9 did in 1994, the orbits of others may be perturbed in
such a way that they either impact the Sun or are catapulted out of the Solar System.
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Introduction
People have observed the sky for millennia. Soon they discovered periodicity in motion of stars.
Daily and especially yearly changes played an important role in everyday life. Observing the Moon,
the stars and five planets (beside the Earth) became regular activity of court astronomers and
astrologers. There was also a number of phenomena that shook the established astronomical views
of the Universe but few were as spectacular as bright comets. Explanations of comet apparition
were different, depending on time and place, usually strongly associated with mystery. Sometimes
people explained it as coming of evil while at other times they were messengers of good news. In
18th century it became clear that some comets return to vicinity of the Sun. Later it turned out
there were many such comets. Beside the study of orbits, knowing what comets are made of and
explaining their features became the next task of astronomers. In this seminar we will try to unveil
some basic features of comets and processes that govern them. Another task will be to understand
the basic ideas about cometary orbits and their origin.
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Features of Comets
The range of features and processes we have been able to observe are heavily biased toward bright
comets. Many assumptions are influenced by studying them, especially Halley’s Comet.
2.1
Nucleus
Nucleus is a ’heart’ of a comet. While the comet is far from the Sun it is rather unspectacular. It is
only later, when it comes close to the Sun, that comet reveals its composition – by coma and tails.
Nucleus of a comet has a typical dimension of roughly 1 to 10 km. On the large end, ground based
observations are picking up icy objects with diameters of roughly 100 to 400 km that are from 30 to
50 AU from the Sun. 1 AU (astronomical unit) is the distance from the Sun to the Earth. Objects
with diameters less than 2 km are faint and hard to detect at these distances. A few have been
discovered simply because they came very close to the Earth. Several more have been discovered
near the Sun by the coronagraphs on orbiting spacecraft. Finally the Hubble Space Telescope is
starting to identify small nuclei. If a major population of small comets exists, they should continue
to be discovered over the next few years.
Studying comet nucleus is not easy. When it is far from the Sun (and from the Earth) it is
difficult to resolve but when it comes close to the Sun it is hidden in coma. In contrast to centuries
of observing comets (positions and some structure) the direct study of nuclei began with space
missions. Before this very few comets were studied far enough from the Sun for observers to be
confident that no coma is present. Scientists have long questioned themselves what comets are
made of. In 1950 Fred L. Whipple proposed a model of nucleus that is best described as a ’dirty
snowball’ (or ’icy conglomerate’) model. Later this model has been extended by Armand Delsemme
but the basic idea remained the same till today.Any comprehensive and acceptable physical model
of comets must explain their features as well as how they change with heliocentric distance.
Historically, the masses of comets could be estimated only by assuming a size and a density
(usually 1 g/cm3 ). Some data from observations of Halley’s comet suggest that an overall density
is around 0.25 g/cm3 . This suggests that Halley’s nucleus is a porous and perhaps fragile structure
despite its size. We already witnessed some comets that break apart (like West in 1976 and
Shoemaker-Levy 9 in 1992) but most comets do not break.
From the fact that comae appear when comets are near 3 AU from the Sun scientists deduced
that water ice is the principal constituent of the nucleus, at least in its outer layers. Spectroscopic
observations and direct measurements have confirmed the predominance of ’water’, meaning both
H2 O and its derivatives OH, OH+ , H2 O+ and H3 0+ . Emissions from molecules such as CN and C2
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are often the first emissions observed as a comet approaches the Sun.This makes sense if the ice
occurs as a clathrate hydrate, in which minor constituents are trapped in cavities within waterice crystal lattice. Thus, the sublimation of water ice may control the release and escape of all
substances from the nucleus. The CO+ found in plasma tails may derive from CO in the clathrate
lattice or from the breakdown of a more complex molecule. Polymerized formaldehyde may explain
why the surface of Halley’s comet is so dark (albedo is about 0.04).
If this overall view is correct, then the outer crust of a comet near the orbit of Earth should have
a temperature of about 300 K, as was observed for Halley, and its sublimating ice about 215 K.
The dominance of water may not apply to comets approaching the inner solar system for the first
time or throughout a nucleus’ interior. During their first passage near the Sun comets often appear
abnormally bright at 3 AU from the Sun. Its water lattice can store no more than 17 percent of
the number of molecules forming the lattice itself. If other substances, like carbon dioxide, exceed
this value, they control their own thermodynamic destinies. Since CO2 and most other plausible
constituents sublimate at lower temperatures than water does, their presence could make comet
active quite far from the Sun.
Data suggest that 80 percent of Halley’s comet is water. However this is probably not true
for all the comets. Comets that pass close to the Sun show much lower H2 O : CO2 ratios than
Halley did. The composition derived for Halley, a comet that has passes through the inner solar
system many times, may not be representative of the pristine ices in comets. Such compositions
are not determined by measuring the nucleus directly but are gained with extrapolation on what
we discover in coma. For example, we cannot be sure that the wide range of molecules detected
in the coma indeed exist in the nucleus; they might be created from some parent molecules. The
expanding gaseous coma carries with it dust from the nucleus liberated by the sublimation of the
ices. Measurements of comet Halley made by probe Giotto revealed many small dusty particles not
previously suspected. This complicates our notion of what cometary dust really is. Most likely it
begins with grains of matter in interstellar clouds. Once inside the protosolar nebula, they acquired
a coating of ice. These stuck together to form the fluffy grains observed in the coma. The comet
dust collected in the Earth’s upper atmosphere comprises only the larger aggregates because the
smallest particles are blown out of the solar system by the Sun’s radiation pressure.
As a comet approaches the inner solar system, all the sunlight it absorbs goes into heating of
the nucleus. Closer in, the surface layers become warm enough to trigger the sublimation of ices.
Then almost all solar radiation goes into maintaining that conversion process. As the ices vaporize,
a dusty crust forms that insulates the deeper layers and regulates the sublimation process (now
occurring a few centimeters below the surface). Irregularities in the materials cause sublimation
to occur faster in some areas, a situation that can produce jets and ultimately the irregular shape
and surface of the nucleus.
It is worth noting why in the case of comets sublimation is much more important process than
phase transitions we usually observe on Earth - melting and vaporization. Remember the phase
diagram which is, of course, different for each substance. For example let us consider the one for
water in Figure 1.
When comets are not active the pressure is very small. As soon as the sublimation starts
the pressures increases and the equilibrium temperature is higher. When the comet warms up
sublimation increases. The important thing is that it is all happening well below the pressure of 6
mbar which corresponds to the pressure of the triple-point for water. If the pressure was higher we
would also get liquid water and not just ice and vapor.
2.2
Coma
Coma is an envelope of gas and dust. This gas flows away at an average speed of 0.5 to 1.0 km
per second and extends 100,000 to 1,000,000 km out from the nucleus. It is the outflow of coma
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Figure 1: Phase diagram for water
and gas that drags dust particles off into space. Comae usually appear at around 3 AU from the
Sun when water ice begins to sublimate vigorously. A bright comet must be losing 1029 hydrogen
atoms per second. Hale-Bopp, a very large comet, was losing 1,000 metric tons of dust and 130
metric tons of water per second in late March. By April these values dropped to 900 and 80 metric
tons, respectively. The density of Hale-Bopp’s coma was roughly one small dust particle per cubic
centimeter. For most comets, stars can be seen through the tails and their light is dimmed in the
coma only if seen very close to the nucleus. Remarkably, a comet usually sheds only 0.1 to 1 percent
of its mass per passage through the inner solar system.
Gases within the coma are determined by Earth-based spectroscopy and mass spectrometers
aboard spacecrafts. Dozens of different atoms and molecules have been detected, many of which
are chemically related. However, astronomers suspect that variety of constituents that lie frozen
or trapped in the nucleus is smaller. Once warmed by sunlight and released into the coma, these
’parent molecules’ either break or react to form other species. Relatively complex compounds can
give rise to a host of byproducts. Emissions from heavier metals like iron and aluminum, present
in dust, begin to appear in the coma as a comet nears the Sun.
2.3
Tails
To the eye tails are comets’ most distinguished features. Tails can stretch across 1 AU or more.
Photographs of comets usually show two distinct kinds of tails: dust and ion (or plasma) tail. Each
of them is governed by different processes.
2.3.1
Dust tail
The dust tail appears pearly yellow because its light is reflected sunlight. Usually observed as
sweeping arcs, dust tails typically have a homogeneous appearance and lengths ranging from 1
to 10 million km. The vast majority of dust grains are smaller than 1 micron, the size of smoke
particles. Once released from the nucleus, this dust moves away from the nucleus in ways controlled
by its ejection velocity, the Sun’s gravitation, the outward push of solar radiation pressure, and the
masses of individual particles.
First consider the effect of radiation pressure on grains of dust. For an idealized spherical dust
grain of radius R that is located a distance r from the Sun and that absorbs all of the incident light
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that strikes it we calculate the force caused by radiation pressure. Using σ = πR2 and j =
get
L
4πr2
we
jσ
L πR2
=
,
c
4πr2 c
where σ is particle’s cross section, L is Sun’s luminosity and j is flux i.e. magnitude of timeaveraged Poynting vector. The other force acting on the grain is the Sun’s gravitational force
Frad =
Fg =
GM mgrain
4πGM ρR3
=
,
r2
3r2
where we used mgrain = 34 πR3 ρ. Compare both effects by writing
Fg
16πGM Rρc
=
.
Frad
3L
Setting this ratio to 1, we get critical radius
Rcrit =
3L
.
16πGM ρc
If the force due to the radiation pressure Frad is negligible compared to Sun’s gravitational force
the particle will stay in the same orbit as the comet. As Frad gets bigger the particle will orbit the
Sun in ellipse of higher eccentricity than original. When both forces are equal the net force on the
particle is zero and it moves in a straight line. If Frad is bigger than Fg particle will move away
from the Sun. Because both forces obey an inverse square law, the ratio between them, and critical
radius, do not depend on distance r from the Sun.
While radiation pressure pushes particles away from the Sun there is another competing process,
caused by Poynting-Robertson effect, that makes particles spiral toward the Sun. It is the net force
that determines the future orbit of the particle.
Antitails seem to be pointing Sunward but are not directed at the Sun at all. They merely
result from our seeing a dust tail projected ahead of the Earth-comet line.
Figure 2: Formation of dust tail
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2.3.2
Ion (plasma, Type I) tail
Once the gas flowing away from the nucleus is ionized it ultimately interacts with the solar wind.
Some of the ions in the coma become trapped on the magnetic field lines that are being carried away
from the Sun by the solar wind. This causes the field, now burdened with more mass, to decelerate
in the vicinity of the comet and wrap around the nucleus like a folding umbrella, forming the plasma
tail. In this scenario, the plasma tail is normally connected to the region near the nucleus by this
’captured’ magnetic field.
These phenomena can be photographed because trapped molecular ions serve as visual tracers
of the field lines. The most obvious is CO+ , which becomes evident in the plasma tail when carbon
monoxide becomes abundant in the coma, about 1.5 AU from the Sun. Direct measurements by
spacecraft confirmed that a reversal of magnetic polarity occurs as predicted in the central denser
tail. Shock fronts were detected because comets are ionized obstacles in the solar wind. A shock
front lowers the wind’s speed and allows it to flow smoothly around the comet. The ion tail
looks blue because ions of carbon monoxide (CO+ ) within it fluoresce in the presence of sunlight.
This emission peaks at about 420 nm. Ion tails are usually straight, contain a great deal of fine
structure, and reach lengths roughly 10 times that of dust tails - up to 100 million km or more.
The plasma races outward almost directly away from the Sun, lagging the true antisolar direction
by a few degrees in the sense opposite to that of the comet’s motion. Locally the plasma becomes
concentrated into thin bundles called rays or streamers. Such ubiquitous details provide convincing
evidence that a magnetic field threads the tail’s entire length. Consisting of a dense, cold mixture
of electrons and molecular ions, the ion-tail streamers seem to be rooted in a limited zone on
the Sun-facing side of the nucleus. Their turning and lengthening provide a good hint as to the
characteristics of the magnetic field that entrains them.
Plasma tails routinely become detached from the comet’s head during disconnection events.
During a disconnection event, part or all of the old plasma tail drifts away and a new one forms.
Such events are relatively common. 19 such events were observed during Comet Halley’s most
recent appearance and a dramatic one occurred in the tail of Comet Hyakutake. We now realize that
disconnection events occur when the polarity of solar-wind magnetic field changes. In this situation,
adjacent field lines within the tail cross and reconnect, severing the connection to the near-nuclear
region on the Sunward side. Direct measurements by the Ulysses spacecraft have established that
comets are exposed to different solar-wind environments, depending on the heliocentric latitude.
The solar wind’s interaction with comets is the likely explanation for the X-rays observed in Comet
Hyakutake by the Roentgen X-ray Satellite in March 1996. Browsing through images in archives
revealed similar X-ray emissions in other comets. Thus X-ray emission may be a common feature
of comets. Some theorists suspect that the X-rays arise due to charge exchanges among ions in the
coma and the solar wind. However, no proposed mechanism has yet accounted for the combination
of steady emission and impulsive events observed.
2.3.3
Na tail
A third tail, dominated by the element sodium, was discovered unexpectedly in Comet Hale-Bopp.
It was long (almost 7◦ ) and narrow (10’ wide) feature that ran very close to the line from the
Sun through the comet. Apparently atoms of sodium were accelerated rapidly by the radiation
pressure of sunlight, a process involving the absorption and release of photons, which produced
the element’s characteristic yellow-line emission. Sodium had been detected in past comets but
never in such an extent. Scientists suspect that exceptional size and intrinsic brightness of comet
Hale-Bopp undoubtedly contributed to the detection.
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2.4
Hydrogen Cloud (Hydrogen Halo, Envelope)
Impressive as comet tails might be, they are not a comet’s largest feature. In 1970, observations
made above Earth’s atmosphere at Lyman-alpha wavelength of 121.6 nm indicated that comets
Tago-Sato-Kosaka and Bennett were surrounded by huge tenuous clouds of hydrogen atoms. Similar clouds have accompanied several other comets and span many million kilometers. Given the
strength of this ultraviolet emission, astronomers estimate that bright comets in the vicinity of
Earth’s orbit can produce more than 1029 hydrogen atoms per second. This gas cannot originate
directly from the icy nucleus because its observed outflow speed is roughly 8 km/s, about 10 times
faster than predicted for material simply sublimating from the nucleus’ surface. Most of this hydrogen probably comes from the dissociation by sunlight of hydroxyl radicals, OH, which themselves
are derived from molecules of water.
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Origin and Orbits of Comets
An important element of studying origin of comets is knowing their orbits. But even without this
information comets would seem to be a byproduct of the processes responsible for creation of the
solar system. Measurements show that key isotopic ratios, particularly 12 C : 13 C, 14 N : 15 N and 32 S :
34 S, of comets are consistent with solar system values. Therefore we can conclude that comets were
created with the planets and not in the interstellar medium. The real difficulty lies in determining
the initial formation zone.
We will try to roughly determine some properties of cometary orbits by studying orbital elements
of 315 observable comets. This data are freely accessible on internet[4]. The Catalogue of Cometary
Orbits that was issued in August 1999 (127 pages contains 1722 sets of orbital elements for 1688
cometary apparitions of 1036 different comets through July 1999) would certainly give even more
detailed results. But even with previously mentioned list it is possible to grasp some basic ideas
that come from studying the orbits. In Figure 3 we see peak that tells us that a large number of
comets lie close to the plane of ecliptic. Apart from this peak inclinations seem to be randomly
distributed. Inclinations larger than 90◦ mean retrograde motion.
Figure 3: Number of comets per interval of inclination
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Figure 4: Number of comets per interval of period
Figure 4 shows us that a great portion of comets have periods in small interval around 7 years.
Another Figure 5 leads us to the idea that comets fall in two distinct groups when their orbits are
considered; one on the left and other on the upper part of this figure.
Figure 5: Eccentricity versus inclination
A more detailed study would give us more precise characteristics of each group. An important
study of orbits by Oort[2] summarizes these findings. Comets can be classified by their orbits as
short-period and long-period comets. First have periods less than 200 years and the latter from
200 up to 10 million years. A large fraction of short-period comets have periods in narrow interval
around 6 years; 60 percent have periods between 5 and 6.5 years. The orbits of long-period comets
are oriented essentially at random, while short-period orbits are strongly concentrated to the ecliptic
with an average inclination of 13◦ (73 percent have inclinations less than 15◦ while only 3 percent
are inclined more than 45◦ ). Similarly, there is a difference for the argument of perihelion ω, an
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angle between perihelion and the ascending node (see Figure 6).
Figure 6: The number of comet orbits per interval of argument of perihelion
For short-period comets ω has two peaks near 0◦ and 180◦ , about 90◦ from that of Jupiter,
while there is no such anisotropy for the long-period comets. Oort also discussed 66 selected orbits
of long period comets. In order to avoid nongravitational forces (insolation and subsequent mass
ejections), comets coming close to the Sun have been excluded from the sample. It had been shown
that these forces can be quite appreciable in orbits with small perihelion distances, but they are
practically negligible if the perihelion distance q exceeds 1.8 AU. The reciprocal semimajor axes
G
1/a in Figure 7 is a measure of orbital energy per mass unit, M
a , where M is solar mass and G
is the universal gravitational constant. A heavy curve includes corrections for mean error.
Figure 7: The number of comet orbits per interval of orbital energy
The figure shows that reliable orbital major axes go up to 105 AU. Most important there is a
surprisingly narrow peak at 1/a = 3.2 × 10−5 AU−1 . A single passage through the inner planetary
system is expected to produce a much bigger dispersion. Therefore it seems that the comets in this
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part of the figure could not have previously passed through the planetary system. Their aphelia
populate a shell between about 0.2 and 0.7 × 105 AU from the Sun. Four of five comets with
appreciable negative values of 1/a are probably results of nongravitational forces and one remains
unexplained.
It is plausible to think that comets originated at the birth of the Solar System in the same
way and in the same regions where the planets formed. There are two classes of proto-comets that
survived from the time of birth of the Solar System.
The short-period comets formed in the trans-Neptunian protosolar disk. As was pointed out
by Kuiper in 1950, it is probable that there is a considerable swarm of comets with perihelia larger
than 30 AU. These will be almost free from perturbations and therefore long-lived. Short-period
comets are intimately related to Jupiter. From Figure 8 it is particularly evident that their aphelia
concentrate toward Jupiter’s orbit (Jupiter’s average distance from the Sun is 5.2 AU). Assuming
Jupiter’s capture of comets also explains the distribution of arguments of perihelion, ω, and its two
well defined maxima at 0◦ and 180◦ .
Figure 8: The number of comet orbits per interval of aphelion
The comets in the second group formed in the region of the giant planets. Many of them collided
with the planets but the ones in orbits, deviating from circles, managed to escape the collisions
and captures by planets. However, they must have been subjected to strong perturbations by the
planets and have consequently been diffused away. Most of them were thrown out of the Solar
System. But for about 10 percent of them this process stopped when their orbits grew 3 × 104
AU, corresponding to 1/a = 0.00006 AU−1 . At this size of the orbit a new type of perturbations
begins to take over. These are perturbations caused by other stars and tidal forces of the Galaxy.
In contrast to planetary perturbations, which influence the major axes only, the galactic forces can
also cause changes in perihelion distances and inclinations, and thereby withdraw the orbits from
the influence of Jupiter or Saturn. These proto-comets are trapped in a region extending from
1.7 × 104 to about 105 AU, where their orbits are virtually safe from further disturbances. This
shell is called the Oort cloud. It must be assumed that during transfer of comets to the Oort cloud
they were able to retain the frozen gases of which they largely consist. Numerical calculations
have shown that proto-comets require a few million years, a small fraction of the age of the Solar
System, to get from their bound initial orbits into comet cloud with 1/a = 0.00006 AU−1 . The
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stellar perturbations gave the cloud its spherical shape and randomized orbital inclinations. It
should be noted that the constituents of the cloud are dark bodies, which become visible when
perturbations bring them into orbits passing close enough to the Sun to become observable as
comets.
Although stars rarely come close to one another, on average about 10 to 12 must pass within
200,000 AU of the Sun every million years. A star is expected to pass within 10,000 AU of the Sun
every 35 million years and within 3,000 AU every 400 million years. The closest stellar approach
over the entire 4.5-billion-year history of the solar system has probably been about 900 AU, still
far beyond the planetary region.
To summarize: If we assume that comets were born in the same regions as the planets, a
large fraction will automatically evolve within a million years into the cloud that has the three
characteristic properties of the long period comets: orbits extending to roughly 105 AU, isotropy of
orbital orientations, and sharp inner edge at 1.7 × 104 AU. Those formed beyond the outer planets
will remain semipermanently as a thin swarm outside of Neptune’s orbit.
Knowing accurate orbital elements is very important when discussing cometary orbits. Knowing
total energy of the body orbiting the Sun we can calculate semimajor axis and orbital period. What
measurements determine the accuracy of these data? Writing the total energy per unit mass for a
bound orbit we get
v 2 GM
GM
−
=−
,
2
r
2a
where v is velocity of orbiting body, G universal gravitational constant, M mass of the Sun,
r body’s distance from the Sun and a semimajor axis. We see that knowing the orbit means
knowing velocity and distance from the Sun at the same time. Both of them can be measured with
considerable accuracy when the comet is close to the Earth, hence even semi-major axis of 105 AU
and a period of millions of years can be accurately determined.
E=
4
Great Comets and space missions
Comet Halley Observations of Halley’s Comet go back to Chinese records of its appearance in
240 BC, and it has been observed at each perihelion passage for more than two millennia. But this
was not realized until Edmond Halley. He noted that orbits of comets observed in 1531, 1607, and
1682 were quite similar. He assumed that in fact this was the same comet at successive apparitions.
On this basis he predicted return of the comet in 1758 or 1759. Halley died in 1742 and could not
see the comet for himself. The comet appeared on Christmas Day of 1758 and it proved that
Halley’s calculations and Newton’s gravitational law Halley used were correct. Later the comet
was named after Halley and officially designated 1P, indicating it is the first known periodic comet.
Much of what we know about comets is based on studying Halley’s Comet. No other object of this
type has been studied in such detail.
Halley’s Comet has an average period of 76 years, with a perihelion 0.59 AU from the Sun
(inside Venus’s orbit) and an aphelion of 35 AU (beyond Neptune’s orbit). In March of 1986 it was
visited by a number of space probes. Among them were two Japanese (Suisei and Sakigake) and two
Russian (Vega 1 and Vega 2) probes. International Cometary Explorer (ICE) from USA flew past
comet Giacobini-Zinner six months earlier. The closest approach was made by ESA’s (European
Space Agency) probe Giotto. Giotto was named after 14th century Italian artist Giotto di Bondone.
Work on his famous painting began two years after the 1301 appearance of Comet Halley. Giotto
spacecraft was steered deep into the comet’s coma within 600 km of the cometary nucleus. Its 10
instruments recorded many images at various wavelengths, measured the composition of the coma
and the mass, distribution, and composition of the dust tail, and analyzed its interaction with the
solar wind.
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The probe continued its way to the next comet Grigg-Skjellerup in July 1992. It flew by at
a distance of 200 km and eventhough it was damaged it gathered valuable data. The appearance
of Halley’s Comet surprised most astronomers. It is a potato shaped objects with dimensions
15 km × 7.2 km × 7.2 km and albedo close to 0.04. This was very different from what researchers
expected (diameter of about 5 km and much larger albedo - more than 0.6). Infrared radiation
emanating from the surface indicates a temperature of approximately 330 K. A limited number
of bright jets was visible and were confined to the Sunward side. Despite the close inspection by
spacecraft, the rotation of Halley’s nucleus remains uncertain.
Comet Hyakutake Hyakutake (C/1996 B2) was a bright comet that passed within 15 million
km of the Earth in 1996, reaching a brightness of zero magnitude. Its bluish plasma tail was
stretching more than 55◦ across the northern sky.
Comet Hale-Bopp Hale-Bopp (1995 O1) is a large comet with a core 40 km across. It was
discovered by Alan Hale and Thomas Bopp in July 1995. It reached perihelion in 1997, its maximum
brightness was about magnitude -1. Its impressive visual display lasted for months despite the fact
that it never came closer than 1.3 AU to Earth.
Comet West West (1976 VI) was a brilliant comet that passed within 30 million km of the Sun
in February 1976. The comet nucleus broke into at least four fragments, accompanied by massive
outbursts of gas and dust.
Shoemaker-Levy 9 Shoemaker-Levy 9 (D/1993 F2) was a comet discovered in March 1993 in a
two-year orbit around Jupiter by Caroline and Eugene Shoemaker and David Levy. It had broken
into about 20 fragments in July 1992, which crashed successively into Jupiter at 60 km/s over
a period of six days in July 1994. Succession of dramatic collisions created titanic fireballs and
marked Jupiter’s atmosphere with huge, dark clouds that stayed there for many months. The size
of the original comets and of the individual fragments remains uncertain. Some scientists say the
original comet was 10 km across while other data suggest it was between 1 and 2 km.
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Fates of Comets
Comets have very different fates. They can collide with the planets or the Sun or they can be
catapulted out of the Solar System and captured by a passing star. They may lose all their water
and other ’fuel’ to become asteroids leaving meteoroid streams behind. When the Earth passes
through a meteoroid stream meteor showers are active.
Consider a dust grain with cross section σgrain orbiting the Sun at distance r. It absorbs and
then reemits solar radiation. In the reference frame of a grain this radiation is isotropic. But in
the Sun’s reference frame the light is reemitted preferentially in the direction of motion and the
particle is decelerated, eventually falling into the Sun. It can be shown that the rate at which the
particle loses angular momentum is given by
dΓ
σgrain L
=−
Γ,
dt
4πr2 mc2
where L is Sun’s luminosity, m mass of the particle and c speed of light[3]. Consider, for example,
a particle that orbits the Sun in the same way the Earth does. After rearranging the equation we
can calculate the characteristic time of free fall of the particle to the Sun τ . We get
τ=
4Rρc2
,
3j0
12
where R is grain’s radius, ρ its density and j0 solar constant. After putting in characteristic
numbers, R = 1µm, ρ = 3 kg dm−3 and knowing j0 ≈ 1 kW m−2 , we get τ ≈ 104 years. This gives
us reasonable explanation for meteor showers when compared to the age of the Solar System (about
4.5 billion years). If τ was much larger, meaning it would take a particle much longer to fall to the
Sun, we would expect meteor showers to be much more abundant. If, on the other hand, τ was
much lower the particles would fall to the Sun in such short times that there would be virtually no
meteor showers.
6
Conclusion
Comets have remained amazing objects to people through the history. When we began to unveil
the secrets that lie behind the formation of comets’ features the topic became even more interesting.
There were two very important discoveries. Whipple’s dirty snow-ball model gave the basic idea
of constitution of comets while the studies of orbits showed there are two main sources of comets;
Kuiper belt and Oort cloud. With space probes a new era of comet exploration had begun. Already
the first probes that visited comets gave us valuable data. They also contributed to a large number
of questions that still wait to be answered. Some of them are: What exactly are comets made
of? How many objects are there in both reservoirs of comets? Why do some comets become very
bright when they are far from the Sun? What is the relation between comets and asteroids? In
this decade a lot of energy will be devoted to space and ground observations many new probes will
visit the comets. We hope this will help us solve the mysteries which still remain.
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References
[1] J. K. Beatty, C. C. Petersen, A. Chaikin, Andrew, The new solar system, Sky Publishing
Corporation, Cambridge : Cambridge University Press, 1999.
[2] W. F. Huebner, Physics and chemistry of comets, Springer, 1990.
[3] Carroll, Ostlie, An introduction to modern astrophysics, Addison-Wesley, 1996.
[4] MPC, http://cfa-www.harvard.edu/iau/Ephemerides/Comets/SoftwareComets.html
[5] J. S. Lewis, Physics and chemistry of the solar system, Academic Press, 1995, cop.1997.
[6] M. E. Bailey, S. V. M. Clube, W. M. Napier, The origin of comets, Pergamon Press, 1990.
[7] Yeomans, Donald K., Comets : a chronological history of observation, science, myth and
folklore, John Wiley, 1991.
[8] Črni Vrh Observatory, http://www.fiz.uni-lj.si/astro/comets
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