Solar system a beginners guide1

“falling stars” in Gilgamesh, Revelation and the Book of Enoch as references to comets,
or possibly bolides.

In the first book of his Meteorology, Aristotle propounded the view of comets that would
hold sway in Western thought for nearly two thousand years. He rejected the ideas of
several earlier philosophers that comets were planets, or at least a phenomenon related to
the planets, on the grounds that while the planets confined their motion to the circle of the
Zodiac, comets could appear in any part of the sky. Instead, he described comets as a
phenomenon of the upper atmosphere, where hot, dry exhalations gathered and
occasionally burst into flame. Aristotle held this mechanism responsible for not only
comets, but also meteors, the aurora borealis, and even the Milky Way.

A few later classical philosophers did dispute this view of comets. Seneca the Younger,
in his Natural Questions, observed that comets moved regularly through the sky and were
undisturbed by the wind, behavior more typical of celestial than atmospheric phenomena.
While he conceded that the other planets do not appear outside the Zodiac, he saw no
reason that a planet-like object could not move through any part of the sky, humanity’s
knowledge of celestial things being very limited. However, the Aristotelean viewpoint
proved more influential, and it was not until the 16th century that it was demonstrated that
comets must exist outside the earth’s atmosphere.

In 1577, a bright comet was visible for several months. The Danish astronomer Tycho
Brahe used measurements of the comet’s position taken by himself and other,
geographically separated, observers to determine that the comet had no measureable
parallax. Within the precision of the measurements, this implied the comet must be at
least four times more distant from the earth than the moon.

Orbital studies

The orbit of the comet of 1680, fit to a parabola, as shown in Isaac Newton’s Principia.

Although comets had now been demonstrated to be in the heavens, the question of how
they moved through the heavens would be debated for most of the next century. Even
after Johannes Kepler had determined in 1609 that the planets moved about the sun in
elliptical orbits, he was reluctant to believe that the laws that governed the motions of the
planets should also influence the motion of other bodies—he believed that comets travel

among the planets along straight lines. Galileo Galilei, although a staunch Copernicanist,
rejected Tycho’s parallax measurements and held to the Aristotelean notion of comets
moving on straight lines through the upper atmosphere.

The first suggestion that Kepler’s laws of planetary motion should also apply to the
comets was made by William Lower in 1610. In the following decades, other
astronomers, including Pierre Petit, Giovanni Borelli, Adrien Auzout, Robert Hooke,
Johann Baptist Cysat, and Giovanni Domenico Cassini, all argued for comets curving
about the sun on elliptical or parabolic paths, while others, such as Christian Huygens and
Johannes Hevelius, supported comets’ linear motion.

The matter was resolved by the bright comet that was discovered by Gottfried Kirch on
November 14, 1680. Astronomers throughout Europe tracked its position for several
months. In 1681, the Saxon pastor Georg Samuel Doerfel set forth his proofs that comets
are heavenly bodies moving in parabolas of which the sun is the focus. Then Isaac
Newton, in his Principia Mathematica of 1687, proved that an object moving under the
influence of his inverse square law of universal gravitation must trace out an orbit shaped
like one of the conic sections, and he demonstrated how to fit a comet’s path through the
sky to a parabolic orbit, using the comet of 1680 as an example.

In 1705, Edmond Halley applied Newton’s method to twenty-four cometary apparitions
that had occurred between 1337 and 1698. He noted that three of these, the comets of
1531, 1607, and 1682, had very similar orbital elements, and he was further able to
account for the slight differences in their orbits in terms of gravitational perturbation by
Jupiter and Saturn. Confident that these three apparitions had been three appearances of
the same comet, he predicted that it would appear again in 1758-9. (Earlier, Robert
Hooke had identified the comet of 1664 with that of 1618, while Jean-Dominique Cassini
had suspected the identity of the comets of 1577, 1665, and 1680. Both were incorrect.)
Halley’s predicted return date was later refined by a team of three French
mathematicians: Alexis Clairaut, Joseph Lalande, and Nicole-Reine Lepaute, who
predicted the date of the comet’s 1759 perihelion to within one month’s accuracy. When
the comet returned as predicted, it became known as Comet Halley or Halley’s Comet (its
official designation is 1P/Halley). Its next appearance is due in 2061.

Among the comets with short enough periods to have been observed several times in the
historical record, Comet Halley is unique in consistently being bright enough to be visible
to the naked eye. Since the confirmation of Comet Halley’s periodicity, many other
periodic comets have been discovered through the telescope. The second comet to be
discovered to have a periodic orbit was Comet Encke (official designation 2P/Encke).
Over the period 1819-1821 the German mathematician and physicist Johann Franz Encke
computed orbits for a series of cometary apparitions observed in 1786, 1795, 1805, and
1818, concluded they were same comet, and successfully predicted its return in 1822. By
1900, seventeen comets had been observed at more than one perihelion passage and
recognized as periodic comets. As of April 2006, 175 comets have achieved this
distinction, though several have since been destroyed or lost. In ephemerides, comets are
often denoted by the symbol I.

Studies of physical characteristics

Comets have highly elliptical orbits. Note the two distinct tails.

Isaac Newton described comets as compact, solid, fixed, and durable bodies: in other
words, a kind of planet, which move in very oblique orbits, every way, with the greatest
freedom, persevering in their motions even against the course and direction of the planets;
and their tail as a very thin, slender vapour, emitted by the head, or nucleus of the comet,
ignited or heated by the sun. Comets also seemed to Newton absolutely requisite for the
conservation of the water and moisture of the planets; from their condensed vapours
and exhalations all that moisture which is spent on vegetations and putrefactions, and
turned into dry earth, might be resupplied and recruited; for all vegetables were thought
to increase wholly from fluids, and turn by putrefaction into earth. Hence the
quantity of dry earth must continually increase, and the moisture of the globe decrease,
and at last be quite evaporated, if it have not a continual supply. Newton suspected that
the spirit which makes the finest, subtilest, and best part of our air, and which is
absolutely requisite for the life and being of all things, came principally from the comets.

Another use which he conjectured comets might be designed to serve, is that of recruiting
the sun with fresh fuel, and repairing the consumption of his light by the streams
continually sent forth in every direction from that luminary —

“From his huge vapouring train perhaps to shake

Reviving moisture on the numerous orbs,
Thro’ which his long ellipsis winds; perhaps
To lend new fuel to declining suns,
To light up worlds, and feed th’ ethereal fire.”

• James Thomson, “The Seasons” (1730; 1748).

As early as the 18th century, some scientists had made correct hypotheses as to comets’
physical composition. In 1755, Immanuel Kant hypothesized that comets are composed
of some volatile substance, whose vaporization gives rise to their brilliant displays near
perihelion. In 1836, the German mathematician Friedrich Wilhelm Bessel, after

observing streams of vapor in the 1835 apparition of Comet Halley, proposed that the jet
forces of evaporating material could be great enough to significantly alter a comet’s orbit
and argued that the non-gravitational movements of Comet Encke resulted from this
mechanism.

However, another comet-related discovery overshadowed these ideas for nearly a century.
Over the period 1864–1866 the Italian astronomer Giovanni Schiaparelli com
puted the orbit of the Perseid meteors, and based on orbital similarities, correctly
hypothesized that the Perseids were fragments of Comet Swift-Tuttle. The link between
comets and meteor showers was dramatically underscored when in 1872, a major meteor
shower occurred from the orbit of Comet Biela, which had been observed to split into two
pieces during its 1846 apparition, and never seen again after 1852. A “gravel bank”
model of comet structure arose, according to which comets consist of loose piles of small
rocky objects, coated with an icy layer.

By the middle of the twentieth century, this model suffered from a number of
shortcomings: in particular, it failed to explain how a body that contained only a little ice
could continue to put on a brilliant display of evaporating vapor after several perihelion
passages. In 1950, Fred Lawrence Whipple proposed that rather than being rocky objects
containing some ice, comets were icy objects containing some dust and rock. This “dirty
snowball” model soon became accepted. It was confirmed when an armada of spacecraft
(including the European Space Agency’s Giotto probe and the Soviet Union’s Vega 1 and
Vega 2) flew through the coma of Halley’s comet in 1986 to photograph the nucleus and
observed the jets of evaporating material. The American probe Deep Space 1 flew past
the nucleus of Comet Borrelly on September 21, 2001 and confirmed that the
characteristics of Comet Halley are common on other comets as well.

Comet Wild 2 exhibits jets on lit side and dark side, stark relief, and is dry.

The Stardust spacecraft, launched in February 1999, collected particles from the coma of
Comet Wild 2 in January 2004, and returned the samples to Earth in a capsule in January
2006. Claudia Alexander, a program scientist for Rosetta from NASA’s Jet Propulsion
Laboratory who has modeled comets for years, reported to space.com about her
astonishment at the number of jets, their appearance on the dark side of the comet as well

as on the light side, their ability to lift large chunks of rock from the surface of the comet
and the fact that comet Wild 2 is not a loosely-cemented rubble pile.
Forthcoming space missions will add greater detail to our understanding of what comets
are made of. In July 2005, the Deep Impact probe blasted a crater on Comet Tempel 1 to
study its interior. And in 2014, the European Rosetta probe will orbit comet Comet
Churyumov-Gerasimenko and place a small lander on its surface.
Rosetta observed the Deep Impact event, and with its set of very sensitive instruments for
cometary investigations, it used its capabilities to observe Tempel 1 before, during and
after the impact. At a distance of about 80 million kilometres from the comet, Rosetta
was the only spacecraft other then Deep Impact itself to view the comet.

Debate over comet composition

Comet Borrelly exhibits jets, yet is hot and dry.
As late as 2002, there is conflict on how much ice is in a comet. NASA’s Deep Space 1
team, working at NASA’s Jet Propulsion Lab, obtained high-resolution images of the
surface of comet Borrelly. They announced that comet Borrelly exhibits distinct jets, yet
has a hot, dry surface. The assumption that comets contain water and other ices led Dr.
Laurence Soderblom of the U.S. Geological Survey to say, “The spectrum suggests that
the surface is hot and dry. It is surprising that we saw no traces of water ice.” However,
he goes on to suggest that the ice is probably hidden below the crust as “either the surface
has been dried out by solar heating and maturation or perhaps the very dark soot-like
material that covers Borrelly’s surface masks any trace of surface ice”.

The recent Deep Impact probe has also yielded results suggesting that the majority of a
comet’s water ice is below the surface, and that these resevoirs feed the jets of vaporised
water that form the coma of Tempel 1.

Notable comets

Great comets

While hundreds of tiny comets pass through the inner solar system every year, only a
very few comets make any impact on the general public. About every decade or so, a
comet will become bright enough to be noticed by a casual observer — such comets are
often designated Great Comets. In times past, bright comets often inspired panic and
hysteria in the general population, being thought of as bad omens. More recently, during
the passage of Halley’s Comet in 1910, the Earth passed through the comet’s tail, and
erroneous newspaper reports inspired a fear that cyanogen in the tail might poison
millions, while the appearance of Comet Hale-Bopp in 1997 triggered the mass suicide of
the Heaven’s Gate cult. To most people, however, a great comet is simply a beautiful
spectacle. See images of Hale-Bopp at the Comet Hale-Bopp Images webpage.

Predicting whether a comet will become a great comet is notoriously difficult, as many
factors may cause a comet’s brightness to depart drastically from predictions. Broadly
speaking, if a comet has a large and active nucleus, will pass close to the Sun, and is not
obscured by the Sun as seen from the Earth when at its brightest, it will have a chance of
becoming a great comet. However, Comet Kohoutek in 1973 fulfilled all the criteria and
was expected to become spectacular, but failed to do so. Comet West, which appeared
three years later, had much lower expectations (perhaps because scientists were much
warier of glowing predictions after the Kohoutek fiasco), but became an extremely
impressive comet.

The late 20th century saw a lengthy gap without the appearance of any great comets,
followed by the arrival of two in quick succession — Comet Hyakutake in 1996,
followed by Hale-Bopp, which reached maximum brightness in 1997 having been
discovered two years earlier. As yet, the 21st century has not seen the arrival of any great
comets.

Unusual comets

Of the thousands of known comets, some are very unusual. Comet Encke orbits from
inside the orbit of Jupiter to inside the orbit of Mercury while Comet 29P/Schwassmann-
Wachmann orbits in a nearly circular orbit entirely between Jupiter and Saturn. 2060
Chiron, whose unstable orbit keeps it between Saturn and Uranus, was originally
classified as an asteroid until a faint coma was noticed. Similarly, Comet Shoemaker-
Levy 2 was originally designated asteroid 1990 UL3. Some near-earth asteroids are
thought to be extinct nuclei of comets which no longer experience outgassing.

Some comets have been observed to break up. Comet Biela was one significant example,
breaking into two during its 1846 perihelion passage. The two comets were seen
separately in 1852, but never again after that. Instead, spectacular meteor showers were
seen in 1872 and 1885 when the comet should have been visible. A lesser meteor shower,

the Andromedids, occurs annually in November, and is caused by the Earth crossing
Biela’s orbit.

Several other comets have been seen to break up during their perihelion passage,
including great comets West and Comet Ikeya-Seki. Some comets, such as the Kreutz
Sungrazers, orbit in groups and are thought to be pieces of a single object that has
previously broken apart.

Another very significant cometary disruption was that of Comet Shoemaker-Levy 9,
which was discovered in 1993. At the time of its discovery, the comet was in orbit around
Jupiter, having been captured by the planet during a very close approach in 1992. This
close approach had already broken the comet into hundreds of pieces, and over a period
of 6 days in July 1994, these pieces slammed into Jupiter’s atmosphere — the first time
astronomers had observed a collision between two objects in the solar system. However,
it has been suggested that the likely object responsible for the Tunguska event in 1908
was a fragment of Comet Encke. Less likely is the attribution to an Encke fragment of
having caused the formation of the Giordano Bruno (crater) on the Moon in 1178.

Currently visible comets

Comet SWAN, also designated C/2006M4, discovered by SWAN/SOHO on June 20,
2006, as of October 6 is visible with binoculars in the predawn sky in the constellation
Canes Venatici. Perihelion was September 28.

The comet is moving rapidly into Bootes and will become an easy binocular target in the
early evening sky throughout the month of October.

Interplanetary dust cloud

The interplanetary dust cloud has been studied for many years in order to understand its
nature, origin, and relationship to planetary systems (our own, as well as extrasolar
systems).

The interplanetary dust particles (IDPs) not only scatter solar light (called the “zodiacal
light”, which is confined to the ecliptic plane), the IDPs also produce thermal emission,
which is the most prominent feature of the night-sky light in the 5-50 micrometer
wavelength domain (Levasseur-Regourd, A.C. 1996). The grains characterizing the
infrared emission near the earth’s orbit have typical sizes of 10-100 micrometers
(Backman, D., 1997). The total mass of the interplanetary dust cloud is about the mass of
an asteroid of radius 15 km (with density of about 2.5 g/cm3).

The sources of IDPs include at least: asteroid collisions, cometary activity and collisions
in the inner solar system, Kuiper Belt collisions, and interstellar medium (ISM) grains
(Backman, D., 1997). Indeed, one of the longest-standing controversies debated in the

interplanetary dust community revolves around the relative contributions to the
interplanetary dust cloud from asteroid collisions and cometary activity.

The main physical processes “affecting” (destruction or expulsion mechanims) IDPs are:
expulsion by radiation pressure, inward Poynting-Robertson (PR) radiation drag, solar
wind pressure (with significant electromagnetic effects), sublimation, mutual collisions,
and the dynamical effects of planets (Backman, D., 1997).

The lifetimes of these dust particles are very short compared to the lifetime of the Solar
System. If one finds grains around a star that is older than about 10^8 years, then the
grains must have been from recently released fragments of larger objects, i.e. they cannot
be leftover grains from the protoplanetary nebula (Backman, private communication).
Therefore, the grains would be “later-generation” dust. The zodiacal dust in the solar
system is 99.9% later-generation dust and 0.1% intruding ISM dust. All primordial grains
from the Solar System’s formation have been removed long ago.

The interplanetary dust cloud has a complex structure (Reach, W., 1997). Apart from a
background density, this includes:

• At least 8 dust trails—their source is thought to be short-period comets.
• A number of Dust bands, the sources of which are thought to be asteroid families

in the main asteroid belt. The three strongest bands arise from the Themis family,
the Koronis family, and the Eos family. Other source families include the Maria,
Eunomia, and possibly the Vesta and/or Hygiea families (Reach et al 1996).
• at least 2 resonant dust rings are known (for example, the Earth-resonant dust
ring, although every planet in the solar system is thought to have a resonant ring
with a “wake”) (Dermott, S.F. et al., 1994, 1997)

Orbit (celestial mechanics)

Two bodies with a slight difference in mass orbiting around a common barycenter. The
sizes, and this particular type of orbit are similar to the Pluto-Charon system.

In physics, an orbit is the path that an object makes around another object while under
the influence of a source of centripetal force, such as gravity.

History

Orbits were first analyzed mathematically by Johannes Kepler who formulated his results
in his three laws of planetary motion. First, he found that the orbits of the planets in our
solar system are elliptical, not circular (or epicyclic), as had previously been believed, and
that the sun is not located at the center of the orbits, but rather at one focus. Second,
he found that the orbital speed of each planet is not constant, as had previously been
thought, but rather that the speed of the planet depends on the planet’s distance from the
sun. And third, Kepler found a universal relationship between the orbital properties of all
the planets orbiting the sun. For each planet, the cube of the planet’s distance from the
sun, measured in astronomical units (AU), is equal to the square of the planet’s orbital
period, measured in Earth years. Jupiter, for example, is approximately 5.2 AU from the
sun and its orbital period is 11.86 Earth years. So 5.2 cubed equals 11.86 squared, as
predicted.

Isaac Newton demonstrated that Kepler’s laws were derivable from his theory of
gravitation and that, in general, the orbits of bodies responding to the force of gravity
were conic sections. Newton showed that a pair of bodies follow orbits of dimensions
that are in inverse proportion to their masses about their common center of mass. Where
one body is much more massive than the other, it is a convenient approximation to take
the center of mass as coinciding with the center of the more massive body.

Planetary orbits

Within a planetary system, planets, dwarf planets, asteroids (a.k.a. minor planets), comets
and space debris orbit the central star in elliptical orbits. Any comet in a parabolic or
hyperbolic orbit about the central star is not gravitationally bound to the star and therefore
is not considered part of the star’s planetary system. To date, no comet has been observed
in our solar system with a distinctly hyperbolic orbit. Bodies which are gravitationally
bound to one of the planets in a planetary system, either natural or
artificial satellites, follow orbits about that planet.

Due to mutual gravitational perturbations, the eccentricities of the orbits of the planets in
our solar system vary over time. Mercury, the smallest planet in the Solar System, has the
most eccentric orbit. At the present epoch, Mars has the next largest eccentricity while
the smallest eccentricities are those of the orbits of Venus and Neptune.

As two objects orbit each other, the periapsis is that point at which the two objects are
closest to each other and the apoapsis is that point at which they are the farthest from
each other.

In the elliptical orbit, the center of mass of the orbiting-orbited system will sit at one
focus of both orbits, with nothing present at the other focus. As a planet approaches
periapsis, the planet will increase in velocity. As a planet approaches apoapsis, the planet
will decrease in velocity.

• Kepler’s laws of planetary motion
• Variations séculaires des orbites planétaires

Understanding orbits

There are a few common ways of understanding orbits.

• As the object moves sideways, it falls toward the orbited object. However it
moves so quickly that the curvature of the orbited object will fall away beneath it.

• A force, such as gravity, pulls the object into a curved path as it attempts to fly off
in a straight line.

• As the object falls, it moves sideways fast enough (has enough tangential velocity)
to miss the orbited object. This understanding is particularly useful for
mathematical analysis, because the object’s motion can be described as the sum of
the three one-dimensional coordinates oscillating around a gravitational center.

As an illustration of the orbit around a planet (eg Earth), the much-used cannon model
may prove useful (see image below). Imagine a cannon sitting on top of a (very) tall
mountain, which fires a cannonball horizontally. The mountain needs to be very tall, so
that the cannon will be above the Earth’s atmosphere and we can ignore the effects of air
friction on the cannon ball.

If the cannon fires its ball with a low initial velocity, the trajectory of the ball will curve
downwards and hit the ground (A). As the firing velocity is increased, the cannonball will
hit the ground farther (B) and farther (C) away from the cannon, because while the ball is
still falling towards the ground, the ground is curving away from it (see first point,
above). If the cannonball is fired with sufficient velocity, the ground will curve away
from the ball at the same rate as the ball falls — it is now in orbit (D). The orbit may be
circular like (D) or if the firing velocity is increased even more, the orbit may become
more (E) and more (F) elliptical. At a certain even faster velocity (called the escape
velocity) the motion changes from an elliptical orbit to a parabola, and will go off
indefinitely and never return. At faster velocities, the orbit shape will become a hyperbola.

Newton’s laws of motion

For a system of only two bodies that are only influenced by their mutual gravity, their
orbits can be exactly calculated by Newton’s laws of motion and gravity. Briefly, the sum
of the forces will equal the mass times its acceleration. Gravity is proportional to mass,
and falls off proportionally to the square of distance.

To calculate, it is convenient to describe the motion in a coordinate system that is
centered on the heavier body, and we can say that the lighter body is in orbit around the
heavier body.

An unmoving body that’s far from a large object has more gravitational potential energy
than one that’s close, because it can fall farther.

With two bodies, an orbit is a conic section. The orbit can be open (so the object never
returns) or closed (returning), depending on the total kinetic + potential energy of the

system. In the case of an open orbit, the speed at any position of the orbit is at least the
escape velocity for that position, in the case of a closed orbit, always less.

An open orbit has the shape of a hyperbola (when the velocity is greater than the escape
velocity), or a parabola (when the velocity is exactly the escape velocity). The bodies
approach each other for a while, curve around each other around the time of their closest
approach, and then separate again forever. This may be the case with some comets if they
come from outside the solar system.

A closed orbit has the shape of an ellipse. In the special case that the orbiting body is
always the same distance from the center, it is also the shape of a circle. Otherwise, the
point where the orbiting body is closest to Earth is the perigee, called periapsis (less
properly, “perifocus” or “pericentron”) when the orbit is around a body other than Earth.
The point where the satellite is farthest from Earth is called apogee, apoapsis, or
sometimes apifocus or apocentron. A line drawn from periapsis to apoapsis is the line-of-
apsides. This is the major axis of the ellipse, the line through its longest part.

Orbiting bodies in closed orbits repeat their path after a constant period of time. This
motion is described by the empirical laws of Kepler, which can be mathematically
derived from Newton’s laws. These can be formulated as follows:

1. The orbit of a planet around the Sun is an ellipse, with the Sun in one of the focal
points of the ellipse. Therefore the orbit lies in a plane, called the orbital plane.
The point on the orbit closest to the attracting body is the periapsis. The point
farthest from the attracting body is called the apoapsis. There are also specific
terms for orbits around particular bodies; things orbiting the Sun have a perihelion
and aphelion, things orbiting the Earth have a perigee and apogee, and things
orbiting the Moon have a perilune and apolune (or, synonymously, periselene and
aposelene). An orbit around any star, not just the Sun, has a periastron and an
apastron

2. As the planet moves around its orbit during a fixed amount of time, the line from
Sun to planet sweeps a constant area of the orbital plane, regardless of which part
of its orbit the planet traces during that period of time. This means that the planet
moves faster near its perihelion than near its aphelion, because at the smaller
distance it needs to trace a greater arc to cover the same area. This law is usually
stated as “equal areas in equal time.”

3. For each planet, the ratio of the 3rd power of its semi-major axis to the 2nd power
of its period is the same constant value for all planets.

Except for special cases like Lagrangian points, no method is known to solve the
equations of motion for a system with four or more bodies. The 2-body solutions were
published by Newton in Principia in 1687. In 1912, Karl Fritiof Sundman developed a
converging infinite series that solves the 3-body problem, however it converges too
slowly to be of much use.

Instead, orbits can be approximated with arbitrarily high accuracy. These approximations
take two forms.

One form takes the pure elliptic motion as a basis, and adds perturbation terms to account
for the gravitational influence of multiple bodies. This is convenient for calculating the
positions of astronomical bodies. The equations of motion of the moon, planets and other
bodies are known with great accuracy, and are used to generate tables for celestial
navigation. Still there are secular phenomena that have to be dealt with by post-
newtonian methods.

The differential equation form is used for scientific or mission-planning purposes.
According to Newton’s laws, the sum of all the forces will equal the mass times its
acceleration (F = ma). Therefore accelerations can be expressed in terms of positions.
The perturbation terms are much easier to describe in this form. Predicting subsequent
positions and velocities from initial ones corresponds to solving an initial value problem.
Numerical methods calculate the positions and velocities of the objects a tiny time in the
future, then repeat this. However, tiny arithmetic errors from the limited accuracy of a
computer’s math accumulate, limiting the accuracy of this approach.

Differential simulations with large numbers of objects perform the calculations in a
hierarchical pairwise fashion between centers of mass. Using this scheme, galaxies, star
clusters and other large objects have been simulated.

Analysis of orbital motion

To analyze the motion of a body moving under the influence of a force which is always
directed towards a fixed point, it is convenient to use polar coordinates with the origin
coinciding with the center of force. In such coordinates the radial and transverse
components of the acceleration are, respectively:

and

.

Since the force is entirely radial, and since acceleration is proportional to force, it follows
that the transverse acceleration is zero. As a result,

.

After integrating, we have

The constant of integration l is the angular momentum per unit mass. It then follows that

where we have introduced the auxiliary variable

.
The radial force is f® per unit is ar, then the elimination of the time variable from the
radial component of the equation of motion yields:

.
In the case of gravity, Newton’s law of universal gravitation states that the force is
proportional to the inverse square of the distance:

where G is the constant of universal gravitation, m is the mass of the orbiting body
(planet), and M is the mass of the central body (the Sun). Substituting into the prior
equation, we have

.
So for the gravitational force – or, more generally, for any inverse square force law – the
right hand side of the equation becomes a constant and the equation is seen to be the
harmonic equation (up to a shift of origin of the dependent variable).
The equation of the orbit described by the particle is thus:

,

where p, e and θ0are constants of integration,

If parameter e is smaller than one, e is the eccentricity and a the semi-major axis of an
ellipse. In general, this can be recognized as the equation of a conic section in polar
coordinates (r,θ).

Orbital period

Orbital decay

If some part of a body’s orbit enters an atmosphere, its orbit can decay because of drag.
At each periapsis, the object scrapes the air, losing energy. Each time, the orbit grows
less eccentric (more circular) because the object loses kinetic energy precisely when that
energy is at its maximum. Eventually, the orbit circularises and then the object spirals
into the atmosphere.

The bounds of an atmosphere vary wildly. During solar maxima, the Earth’s atmosphere
causes drag up to a hundred kilometres higher than during solar minimums.

Some satellites with long conductive tethers can also decay because of electromagnetic
drag from the Earth’s magnetic field. Basically, the wire cuts the magnetic field, and acts
as a generator. The wire moves electrons from the near vacuum on one end to the near-
vacuum on the other end. The orbital energy is converted to heat in the wire.

Another method of artificially influencing an orbit is through the use of solar sails or
magnetic sails. These forms of propulsion require no propellant or energy input, and so
can be used indefinitely. See statite for one such proposed use.

Orbital decay can also occur due to tidal forces for objects below the synchronous orbit
for the body they’re orbiting. The gravity of the orbiting object raises tidal bulges in the
primary, and since below the synchronous orbit the orbiting object is moving faster than
the body’s surface the bulges lag a short angle behind it. The gravity of the bulges is
slightly off of the primary-satellite axis and thus has a component along the satellite’s
motion. The near bulge slows the object more than the far bulge speeds it up, and as a
result the orbit decays. Conversely, the gravity of the satellite on the bulges applies torque
on the primary and speeds up its rotation. Artificial satellites are too small to have an
appreciable tidal effect on the planets they orbit, but several moons in the solar system are
undergoing orbital decay by this mechanism. Mars’ innermost moon Phobos is a prime
example, and is expected to either impact Mars’ surface or break up into a ring within
50 million years.

Finally, orbits can decay via the emission of gravitational waves. This mechanism is
extremely weak for most stellar objects, only becoming significant in cases where there is
a combination of extreme mass and extreme acceleration, such as with black holes or
neutron stars that are orbiting each other closely.

Earth orbits

• Low Earth orbit
• High Earth orbit
• Intermediate circular orbit
• Geostationary orbit
• Geosynchronous orbit
• Geostationary transfer orbit
• Molniya orbit
• Near equatorial orbit
• Polar orbit
• Polar sun synchronous orbit

Scaling in gravity

The gravitational constant G is measured to be:

• (6.6742 ± 0.001) × 10−11 N·m2/kg2
• (6.6742 ± 0.001) × 10−11 m3/(kg·s2)
• (6.6742 ± 0.001) × 10−11 (kg/m3)-1s-2.

Thus the constant has dimension density-1 time-2. This corresponds to the following
properties.

Scaling of distances (including sizes of bodies, while keeping the densities the same)
gives similar orbits without scaling the time: if for example distances are halved, masses
are divided by 8, gravitational forces by 16 and gravitational accelerations by 2. Hence
orbital periods remain the same. Similarly, when an object is dropped from a tower, the
time it takes to fall to the ground remains the same with a scale model of the tower on a
scale model of the earth.

When all densities are multiplied by four, orbits are the same, but with orbital velocities
doubled.

When all densities are multiplied by four, and all sizes are halved, orbits are similar, with
the same orbital velocities.

These properties are illustrated in the formula

for an elliptical orbit with semi-major axis a, of a small body around a spherical body
with radius r and average density σ, where T is the orbital period.

Role in the evolution of atomic theory

When atomic structure was first probed experimentally early in the twentieth century, an
early picture of the atom portrayed it as a miniature solar system bound by the coulomb
force rather than by gravity. This was inconsistent with electrodynamics and the model
was progressively refined as quantum theory evolved, but there is a legacy of the picture
in the term orbital for the wave function of an energetically bound electron state.

Constellation

Photo of the familar constellation Orion.

Orion is a remarkable constellation, visible from most places on the globe at one time or
another during the year. The constellation of Orion is the area outlined in the dashed
yellow line. Orion contains a striking and well-known star pattern that has the form of a
hunter.

A constellation is any one of the 88 areas into which the sky - or the celestial sphere - is
divided. The term is also often used less formally to denote a group of stars visibly
related to each other in a particular configuration or pattern.

Some well-known constellations contain striking and familiar patterns of bright stars.
Examples are Ursa Major (containing the Big Dipper), Orion (containing a figure of a
hunter), Leo (containing bright stars outlining the form of a lion) and Scorpius (a
scorpion). Other constellations do not encompass any discernible star patterns, and
contain only faint stars.

Explanation

The International Astronomical Union (IAU) divides the sky into 88 official
constellations with precise boundaries, so that every direction or place in the sky belongs
within one constellation. In the northern celestial hemisphere, these are mostly based
upon the constellations of the ancient Greek tradition, passed down through the Middle
Ages, and contains the signs of the zodiac.

The constellation boundaries were drawn up by Eugène Delporte in 1930, and he drew
them along vertical and horizontal lines of right ascension and declination. However, he
did so for the epoch B1875.0, the era when Benjamin A. Gould made the proposal on
which Delporte based his work. The consequence of the early date is that due to
precession of the equinoxes, the borders on a modern star map (eg, for epoch J2000) are
already somewhat skewed and no longer perfectly vertical or horizontal. This skew will
increase over the years and centuries to come.

In three-dimensional space, most of the stars we see have little or no relation to one
another, but can appear to be grouped on the celestial sphere of the night sky. Humans
excel at finding patterns and throughout history have grouped together stars that appear
close to one another.

A star pattern may be widely known but may not be recognized by the International
Astronomical Union; such a pattern of stars is called an asterism. An example is the
grouping called the Big Dipper (North America) or the Plough (UK).

The stars in a constellation or asterism rarely have any astrophysical relationship to each
other; they just happen to appear close together in the sky as viewed from Earth and
typically lie many light years apart in space. However, one exception to this is the Ursa
Major moving group.

The grouping of stars into constellations is essentially arbitrary, and different cultures
have had different constellations, although a few of the more obvious ones tend to recur
frequently, e.g., Orion and Scorpius.

History of the constellations

Our current list is based on those listed by Claudius Ptolemy, Greek-speaking
mathematician, geographer, astronomer, and astrologer who lived in the Hellenistic
culture of Roman Egypt. He may have been a Hellenized Egyptian, but he was probably
of Greek ancestry, although no description of his family background or physical
appearance exists, though it is likely he was born in Egypt, probably in or near
Alexandria.

In more recent times this list has been added to in order to fill gaps between Ptolemy's
patterns. The Greeks considered the sky as including both constellations and dim spaces
between. But Renaissance star catalogs by Johann Bayer and John Flamsteed required
every star to be in a constellation, and the number of visible stars in a constellation to be
manageably small.

The constellations around the South Pole were not observable by the Greeks. Twelve
were created by Dutch navigators Pieter Dirkszoon Keyser and Frederick de Houtman in
the sixteenth century and first cataloged by Johann Bayer. Several more were created by
Nicolas Louis de Lacaille in his posthumous Coelum Australe Stelliferum, published in
1763.

Other proposed constellations didn't make the cut, most notably Quadrans Muralis (now
part of Boötes) for which the Quadrantid meteors are named. Also the ancient
constellation Argo Navis was so big that it was broken up into several different
constellations, for the convenience of stellar cartographers.

Greek constellation myths

The first ancient Greek works which dealt with the constellations were books of star
myths. The oldest of these was a poem composed by Hesiod in the C8th BC, of which
only fragments survive.

The most complete extant works dealing with the mythic origins of the constellations are
by the Hellenstic writer termed pseudo-Eratosthenes and an early Roman writer styled
pseudo-Hyginus. Each of these drew extensively from the writings of older sources
(Hesiod and his successors), providing a clear overview of the stories which lay behind
the star groups we are so familiar with today.

Chinese constellations

Chinese constellations are different from the western constellations, due to the
independent development of ancient Chinese astronomy. Ancient Chinese skywatchers
divided their night sky in a different way, but there are also similarities. The Chinese
counterpart of the 12 western zodiac constellations are the 28 "Xiu" ( ) or "mansions" (a
literal translation).

Star names

All modern constellation names are Latin proper names or words, and some stars are
named using the genitive of the constellation in which they are found. The genitive is
formed using the usual rules of Latin grammar, and for those unfamiliar with that
language the form of the genitive is sometimes unpredictable and must be memorized.
Some examples include: Aries → Arietis; Taurus → Tauri; Gemini → Geminorum;
Virgo → Virginis; Libra → Librae; Pisces → Piscium; Lepus → Leporis.

These names include Bayer designations such as Alpha Centauri, Flamsteed designations
such as 61 Cygni, and variable star designations such as RR Lyrae. However, many
fainter stars will just be given a catalog number designation (in each of various star
catalogs) that does not incorporate the constellation name.

For more information about star names, see Star designations and the list of stars by
constellation.

Alpha Centauri

Alpha Centauri A/B/C

Constellation The position of Alpha Centauri.
Right ascension
Observation data

Epoch J2000

Centaurus

14h 39m 36.5/35.1s

Declination -60° 50' 02/13"
Apparent magnitude (V) -0.01/+1.34/+11.05
Characteristics
Spectral type G2 V/K1 V/M5.5 Ve
B-V color index 0.65/0.85/1.97
U-B color index 0.24/0.64/1.54
Variable type None
Astrometry
Radial velocity (Rv) -21.6 km/s
Proper motion (µ) RA: -3678.19 mas/yr
Parallax (π) Dec.: 481.84 mas/yr
Distance 747.23 ± 1.17 mas
Absolute magnitude (MV) 4.365 ± 0.007 ly
(1.338 ± 0.002 pc)
Mass 4.38/5.71/12.9
Radius Details
Luminosity 1.100/0.907/0.1 M
Temperature 1.227/0.865/0.2 R
1.519/0.500/0.00006 L
5,800/5,300/2700 K

Metallicity 130-230% Sun

Rotation ?

Age 5-6 × 109 years

Visual binary orbit

Companion Alpha Centauri B

Period (P) 79.24 years

Semimajor axis (a) 17.59"

Eccentricity (e) 0.516

Inclination (i) 79.24°

Node (Ω) 204.87°

Periastron epoch (T) 1955.56

Other designations

Rigil Kentaurus, Rigil Kent, Toliman, Bungula, FK5 538, CP(D)−60°5483, GC 19728,
CCDM J14396-6050
α Cen A
Gl 559 A, HR 5459, HD 128620, GCTP 3309.00, LHS 50, SAO 252838, HIP 71683
α Cen B
Gl 559 B, HR 5460, HD 128621, LHS 51, HIP 71681

Proxima Cen
LHS 49, HIP 70890

Alpha Centauri (α Cen / α Centauri) is the brightest star in the southern constellation of
Centaurus. Although it appears as a single point to the naked eye, Alpha Centauri is
actually a system of three stars, one of which is the fourth brightest star in the night sky.
Alpha Centauri is famous in the Southern Hemisphere as the outermost “pointer” to the
Southern Cross, but it is too far south to be visible in most of the northern hemisphere.
The two brightest components of the system are too close to be resolved as separate stars
by the naked eye and so are perceived as a single source of light with a total visual
magnitude of about −0.27 (brighter than the third brightest star in the night sky,
Arcturus).

Alpha Centauri is the closest star system beyond our own solar system, being 4.39 light-
years distant (about 25.8 trillion miles or 277,600 AU) (Proxima Centauri, often regarded
as part of the system, is 4.26 light-years distant). This makes it a logical choice as "first
port of call" for speculative fiction about space travel, which often assumes eventual
human exploration of the system or even colonization of possible planets within it. Such
themes are found in said speculative works of fiction such as novels and video games.

Names

It bears the proper name Rigil Kentaurus (often shortened to Rigil Kent), derived from
the Arabic phrase Al Rijl al Kentaurus, meaning "foot of the centaur," but is nonetheless
usually referred to by its Bayer designation Alpha Centauri. Another alternative name is
Toliman. It is also sometimes known as Bungula, possibly from the Latin word ungula
meaning "hoof". It and Beta Centauri (which is close to Alpha Centauri in angular
distance as seen from the Earth, but is actually many light-years away) are the "Pointers"
to the Southern Cross. Alpha and Beta Centauri are the second closest pair of first
magnitude stars as seen from the Earth, and due to the effects of proper motion, they will
become the closest pair in around 2166, overtaking Acrux and Becrux.

Alpha Centauri A is also known as HD 128620, HR 5459, CP-60°5483, GCTP 3309.00A,
and LHS 50. Alpha Centauri B is also known as HD 128621, HR 5460, GCTP 3309.00B,
and LHS 51.

It is known as (Nánmén'èr, the Second Star in the Southern Gate) in Chinese.

System components

Size and color of the Sun compared to the stars in the Alpha Centauri system

Alpha Centauri is a triple star system. It consists of two main stars, Alpha Centauri A and
Alpha Centauri B (which form a binary system together) at a distance of 4.36 ly, and a
dimmer red dwarf named Proxima Centauri at a distance of 4.22 ly (Hipparcos distances).
Both of the two main stars are rather similar to the Sun. The larger member of the binary
star, Alpha Centauri A, is the most similar to the Sun, but a little larger and brighter. Like
the Sun, its spectral type is G2 V, and, like the sun, shines in a yellowish-white light. The
smaller of the two, Alpha Centauri B, is dimmer, with a spectral type of K1 V, somewhat
smaller and dimmer than the sun, but astronomically similar enough, shining with more
of an orangish-yellow-white light. The two orbit one another elliptically (e=0.52),
approaching as close as 11.2 astronomical units (2×10−4 ly) and receding to 35.6 AU
(6×10−4 ly), with a period of just under 80 years.[citation needed] Hence the sum of the two
masses is 23.43 / 802 = 2.0 times that of the Sun (see formula).

These two stars are about 5 to 6 billion years old. The red dwarf Proxima Centauri is
about 13,000 astronomical units away from Alpha Centauri (1 ly = 63,241 AU, hence this
is 0.21 ly, about 1/20 of the distance between Alpha Centauri and the Sun) and may be in
orbit about it, with a period on the order of 500,000 years or more.[citation needed] For this
reason, Proxima is sometimes referred to as Alpha Centauri C. However, it is not clear if
it really is in orbit, although the association is unlikely to be entirely accidental as it
shares approximately the same motion through space as the larger star system.

Seen from Earth, Proxima is separated by 2 degrees from Alpha Centauri A and B (about
4 times the angular diameter of the full Moon), and the latter are at an angular distance of
up to 40" from each other.

Apparent and real trajectory of B component relative to A component

The closest neighbours to the Alpha Centauri system are the Sun and Barnard's star (1.98
pc or 6.47 ly), which is also the next nearest star from Earth, at a distance of 5.96 ly.

Possibility of planet formation

Computer models of planetary formation suggest that terrestrial planets would be able to
form close to both Alpha Centauri A and B, but that gas giant planets similar to our
Jupiter and Saturn would not be able to form because of the binary stars' gravitational
effects. Given the similarities in star type, age and stability of the orbits it has been
suggested that this solar system may hold one of the best possibilities for extraterrestrial
life. However, some astronomers have speculated that any terrestrial planets in the Alpha
Centauri system may be dry because it is believed that Jupiter and Saturn were crucial at
directing comets into the inner solar system and providing the inner planets with a source
of water. This would not be a problem, however, if Alpha Centauri B happened to play a
similar role for Alpha Centauri A that the gas giants do for the Sun, and vice versa. Both
stars are of the right spectral type to harbor life on a potential planet.

A planet around Alpha Centauri A would be about 1.25 AU away from the star if it were
to have Earthlike temperatures, or about halfway between the distances of Earth's orbit
and Mars' orbit in our own solar system. For dimmer, cooler Alpha Centauri B, the
distance would be about 0.7 AU, or about the distance of Venus from the Sun.

Sky appearance from the Alpha Centauri system

Viewed from near the Alpha Centauri system, the sky (other than the Alpha Centauri
stars) would appear very much as it does to observers on Earth, with most of the
constellations such as Ursa Major and Orion being almost unchanged. However,
Centaurus would be missing its brightest star and our Sun would appear as a 0.5-
magnitude star in Cassiopeia. Roughly speaking, the \/\/ of Cassiopeia would become a
/\/\/, with the Sun at the leftmost end, closest to ε Cassiopeiae. The position can easily be
plotted as RA 02h39m35s, dec +60°50', or antipodal to Alpha Centauri's position as seen
from Earth.

Looking back towards Sol from Alpha Centauri.

Nearby very bright stars such as Sirius and Procyon would appear to be in very different
positions, as would Altair to a lesser extent. Sirius would become part of the constellation
of Orion, appearing 2 degrees to the west of Betelgeuse, slightly dimmer than from here

(-1.2). The stars Fomalhaut and Vega, although further away, would appear somewhat
displaced as well. Proxima Centauri would be an inconspicuous 4.5 magnitude star,
which considering it would only be a quarter of a light-year away shows just how dim
Proxima really is.

A hypothetical planet around either α Centauri A or B would see the other star as a very
bright secondary. For example, an Earth-like planet at 1.25 Astronomical Units from α
Cen A (with an orbital period of 1.34 a) would get Sun-like illumination from its primary,
and α Cen B would appear 5.7 to 8.6 magnitudes dimmer (−21.0 to −18.2), 190 to 2700
times dimmer than α Cen A but still 170 to 2300 times brighter than the full Moon.
Conversely, an Earth-like planet at 0.71 AUs from α Cen B (with a revolution period of
0.63 a) would get Sun-like illumination from its primary, and α Cen A would appear 4.6
to 7.3 magnitudes dimmer (−22.1 to −19.4), 70 to 840 times dimmer than α Cen B but
still 520 to 6300 times brighter than the full Moon. In both cases the secondary sun
would, in the course of the planet's year, appear to circle the sky. It would start off right
beside the primary and end up, half a period later, opposite it in the sky (a "midnight
sun"). After another half period, it would complete the cycle. For a hypothetical Earthlike
planet around either star, the secondary sun would not be bright enough to adversely
affect climate or plant photosynthesis (being as far away as Saturn is from our Sun), but
would mean that for about half the year, the night sky, instead of a pitch black would
appear a dark blue, and one could walk around and even read rather easily without
artificial light. The surface of the planet would be illuminated as well as a city street by
street lamps.

The discovery of planets in binary star systems such as Gamma Cephei, the high
metallicity of the Alpha Centauri system, and the mere existence of the extensive satellite
systems around all the giant planets in our own Solar System suggest that the existence of
rocky Earthlike planets around the two stars in the system is not unlikely. Radial velocity
methods by various planet-hunting teams have failed to find any giant planets or brown
dwarfs in the system, which (if they existed) could disrupt the orbits of any potential
terrestrial planets orbiting in or near the stars' habitable zones. Certainly, if technology
advances enough for humans to start sending interstellar robotic probes, Alpha Centauri
will be near the top of the list for exploration.

Apparent movement

Apparent motion of Alpha Centauri relative to Beta Centauri.

In about 4000 years, the proper motion of Alpha Centauri will mean that from the point
of view of Earth it will appear close enough to Beta Centauri to form an optical double
star. Beta Centauri is in reality far more distant than Alpha Centauri.

Alpha Centauri in fiction

Because of its status as our star's nearest galactic neighbor, Alpha Centauri has frequently
been referred to in science fiction stories involving interstellar travel.

Globular cluster

The Globular Cluster M80 in the constellation Scorpius is located about 28,000 light
years from the Sun and contains hundreds of thousands of stars.
A globular cluster is a spherical collection of stars that orbits a galactic core as a
satellite. Globular clusters are very tightly bound by gravity, which gives them their
spherical shapes and relatively high stellar densities toward their centers. Globular
clusters, which are found in the halo of a galaxy, contain considerably more stars and are
much older than the less dense galactic, or open clusters, which are found in the disk.
A globular cluster is sometimes known more simply as a globular; the word is derived
from the Latin globulus (a small sphere).
Globular clusters are fairly common; there are about 150 currently known globular
clusters in the Milky Way, with perhaps 10–20 more undiscovered. Large galaxies can
have more: Andromeda, for instance, may have as many as 500. Some giant elliptical
galaxies, such as M87, may have as many as 10,000 globular clusters. These globular
clusters orbit the galaxy out to large radii, 40 kiloparsecs (approximately 131 thousand
light years) or more.
Every galaxy of sufficient mass in the Local Group has an associated group of globular
clusters, and almost every large galaxy surveyed has been found to possess a system of

globular clusters. The Sagittarius Dwarf and Canis Major Dwarf galaxies appear to be in
the process of donating their associated globular clusters (such as Palomar 12) to the
Milky Way. This demonstrates how many of this galaxy’s globular clusters were
acquired in the past.

Although it appears that globular clusters were some of the first stars to be produced in the
galaxy, their origins and their role in galactic evolution are still unclear. It does
appear clear that globular clusters are significantly different from dwarf elliptical galaxies
and were formed as part of the star formation of the parent galaxy rather than as a
separate galaxy.

Observation history

The first globular cluster discovered Early Globular Cluster Discoveries

was M22 in 1665 by Abraham Ihle, a Discovered by Year
German amateur astronomer. However, Cluster name

due to the small aperture of early M22 Abraham Ihle 1665

telescopes, individual stars within a ω Cen Edmond Halley 1677
globular cluster were not resolved until

Charles Messier observed M4. The first M5 Gottfried Kirch 1702

eight globular clusters discovered are M13 Edmond Halley 1714
shown in the table. Subsequently, Abbé
Lacaille would list NGC 104, NGC M71 Philippe Loys de Chéseaux 1745

4833, M55, M69, and NGC 6397 in his M4 Philippe Loys de Chéseaux 1746

1751–52 catalogue. The M before a M15 Jean-Dominique Maraldi 1746
number refers to the catalogue of

Charles Messier, while NGC is from M2 Jean-Dominique Maraldi 1746

the New General Catalogue by John

Dreyer.

William Herschel began a survey program in 1782 using larger telescopes and was able
to resolve the stars in all 33 of the known globular clusters. In addition he found 37
additional clusters. In Herschel’s 1789 catalog of deep sky objects, his second such, he
became the first to use the name globular cluster as their description.

The number of globular clusters discovered continued to increase, reaching 83 in 1915,
93 in 1930 and 97 by 1947. A total of 151 globular clusters have now been discovered in
the Milky Way galaxy, out of an estimated total of 180 ± 20. These additional,
undiscovered globular clusters are believed to be hidden behind the gas and dust of the
Milky Way.

Beginning in 1914, Harlow Shapley began a series of studies of globular clusters,
published in about 40 scientific papers. He examined the cepheid variables in the clusters
and would use their period–luminosity relationship for distance estimates.

M75 is a highly-concentrated, Class I globular cluster.

Of the globular clusters within our Milky Way, the majority are found in the vicinity of
the galactic core, and the large majority lie on the side of the celestial sky centered on the
core. In 1918 this strongly asymmetrical distribution was used by Harlow Shapley to
make a determination of the overall dimensions of the galaxy. By assuming a roughly
spherical distribution of globular clusters around the galaxy’s center, he used the
positions of the clusters to estimate the position of the sun relative to the galactic center.
While his distance estimate was significantly in error, it did demonstrate that the
dimensions of the galaxy were much greater than had been previously thought. Shapley’s
estimate was, however, within the same order of magnitude of the currently accepted
value.

Shapley’s measurements also indicated that the Sun was relatively far from the center of
the galaxy, contrary to what had previously been inferred from the apparently nearly even
distribution of ordinary stars. In reality, ordinary stars lie within the galaxy’s disk and are
thus often obscured by gas and dust, whereas globular clusters lie outside the disk and can
be seen at much further distances.

Shapley was subsequently assisted in his studies of clusters by Henrietta Swope and
Helen Battles Sawyer (later Hogg). In 1927–29, Harlow Shapley and Helen Sawyer
began categorizing clusters according to the degree of concentration the system has
toward the core. The most concentrated clusters were identified as Class I, with
successively diminishing concentrations ranging to Class XII. This became known as the
Shapley–Sawyer Concentration Class. (It is sometimes given with numbers [Class 1–12]
rather than Roman numerals.)

Composition

Globular clusters are generally composed of hundreds of thousands of low-metal, old
stars. The type of stars found in a globular cluster are similar to those in the bulge of a
spiral galaxy but confined to a volume of only a few cubic parsecs. They are free of gas
and dust and it is presumed that all of the gas and dust was long ago turned into stars.

While globular clusters can contain a high density of stars, they are not thought to be
favorable locations for the survival of planetary systems. Planetary orbits are dynamically
unstable within the cores of dense clusters due to the perturbations of passing stars. A
planet orbiting at 1 astronomical unit around a star that is within the core of a dense
cluster such as 47 Tucanae would only survive on the order of 108 years. However, there
has been at least one planetary system found orbiting a pulsar (PSR B1620−26) that
belongs to the globular cluster M4.

With a few notable exceptions, each globular cluster appears to have a definite age. That
is, most of the stars in a cluster are at approximately the same stage in stellar evolution,
suggesting that they formed at about the same time. All known globular clusters appear to
have no active star formation, which is consistent with the view that globular clusters are
typically the oldest objects in the Galaxy, and were among the first collections of stars to
form.

Some globular clusters, like Omega Centauri in our Milky Way and G1 in M31, are
extraordinarily massive (several million solar masses) containing multiple stellar
populations. Both can be regarded as evidence that supermassive globular clusters are in
fact the cores of dwarf galaxies that are consumed by the larger galaxies. Several globular
clusters (like M15) have extremely massive cores which are expected to harbor black
holes.

Metallic content

Globular clusters normally consist of Population II stars, which have a low metallic
content compared to Population I stars such as the Sun. (To astronomers, metals includes
all elements heavier than helium, such as lithium and carbon.)

The Dutch astronomer Pieter Oosterhoff noticed that there appear to be two populations
of globular clusters, which became known as Oosterhoff groups. The second group has a
slightly longer period of RR Lyrae variable stars. Both groups have weak lines of
metallic elements. But the lines in the stars of Oosterhoff type I (OoI) cluster are not quite
as weak as those in type II (OoII). Hence type I are referred to as “metal-rich” while type
II are “metal-poor”.

These two populations have been observed in many galaxies (especially massive
elliptical galaxies). Both groups are of similar ages (nearly as old as the universe itself)
but differ in their metal abundances. Many scenarios have been suggested to explain
these subpopulations, including violent gas-rich galaxy mergers, the accretion of dwarf
galaxies, and multiple phases of star formation in a single galaxy. In our Milky Way, the

metal-poor clusters are associated with the halo and the metal-rich clusters with the
Bulge.
In the Milky Way it has been discovered that the large majority of the low metallicity
clusters are aligned along a plane in the outer part of the galaxy’s halo. This result argues
in favor of the view that type II clusters in the galaxy were captured from a satellite
galaxy, rather than being the oldest members of the Milky Way’s globular cluster system
as had been previously thought. The difference between the two cluster types would then
be explained by a time delay between when the two galaxies formed their cluster
systems.

Exotic components

Globular clusters have a very high star density, and therefore close interactions and near-
collisions of stars occur relatively often. Due to these chance encounters, some exotic
classes of stars, such as blue stragglers, millisecond pulsars and low-mass X-ray binaries,
are much more common in globular clusters. A blue straggler is formed from the merger
of two stars, possibly as a result of an encounter with a binary system. The resulting star
has a higher temperature than comparable stars in the cluster with the same luminosity,
and thus differs from the main sequence stars.

Globular cluster M15 has a 4,000-solar mass black hole at its core. NASA image.

Astronomers have searched for black holes within globular clusters since the 1970s. The
resolution requirements for this task, however, are exacting, and it is only with the
Hubble space telescope that the first confirmed discoveries have been made. In
independent programs, a 4,000 solar mass intermediate-mass black hole has been
discovered in the globular cluster M15 and a 20,000 solar mass black hole in the Mayall
II cluster in the Andromeda Galaxy.

These are of particular interest because they are the first black holes discovered that were
intermediate in mass between the conventional stellar-mass black hole and the
supermassive black holes discovered at the cores of galaxies. The mass of these
intermediate mass black holes is proportional to the mass of the clusters, following a
pattern previously discovered between supermassive black holes and their surrounding
galaxies.

Claims of intermediate mass black holes have been met with some skepticism. The
densest objects in globular clusters are expected to migrate to the cluster center due to
mass segregation. These will be white dwarfs and neutron stars in an old stellar
population like a globular cluster. As pointed out in two papers by Holger Baumgardt and
collaborators, the mass-to-light ratio should rise sharply towards the center of the cluster,
even without a black hole, in both M15 and Mayall II.

Color-magnitude diagram

The Hertzsprung-Russell diagram (HR-diagram) is a graph of a large sample of stars that
plots their visual absolute magnitude against their color index. The color index, B−V, is
the difference between the magnitude of the star in blue light, or B, and the magnitude in
visual light (green-yellow), or V. Large positive values indicate a red star with a cool
surface temperature, while negative values imply a blue star with a hotter surface.

When the stars near the Sun are plotted on an HR diagram, it displays a distribution of
stars of various masses, ages, and compositions. Many of the stars lie relatively close to a
sloping curve with increasing absolute magnitude as the stars are hotter, known as main
sequence stars. However the diagram also typically includes stars that are in later stages
of their evolution and have wandered away from this main sequence curve.

As all the stars of a globular cluster are at approximately the same distance from us, their
absolute magnitudes differ from their visual magnitude by about the same amount. The
main sequence stars in the globular cluster will fall along a line that is believed to be
comparable to similar stars in the solar neighborhood. (The accuracy of this assumption is
confirmed by comparable results obtained by comparing the magnitudes of nearby short-
period variables, such as RR Lyrae stars and cepheid variables, with those in the cluster.)

By matching up these curves on the HR diagram, the absolute magnitude of main
sequence stars in the cluster can also be determined. This in turn provides a distance
estimate to the cluster, based on the visual magnitude of the stars. The difference between
the relative and absolute magnitude, the distance modulus, yields this estimate of the
distance.
When the stars of a particular globular cluster are plotted on an HR diagram, nearly all of
the stars fall upon a relatively well-defined curve. This differs from the HR diagram of
stars near the Sun, which lumps together stars of differing ages and origins. The shape of
the curve for a globular cluster is characteristic of a grouping of stars that were formed at
approximately the same time and from the same materials, differing only in their initial
mass. As the position of each star in the HR diagram varies with age, the shape of the
curve for a globular cluster can be used to measure the overall age of the collected stars.

Color-magnitude diagram for the globular cluster M3. Note the characteristic “knee” in
the curve at magnitude 19 where stars begin entering the giant stage of their evolutionary
path.
The most massive main sequence stars in a globular cluster will also have the highest
absolute magnitude, and these will be the first to evolve into the giant star stage. As the
cluster ages, stars of successively lower masses will also enter the giant star stage. Thus
the age of a cluster can be measured by looking for the stars that are just beginning to
enter the giant star stage. This forms a “knee” in the HR diagram, bending to the upper
right from the main sequence line. The absolute magnitude at this bend is directly a
function of the globular cluster, and the age range can be plotted on an axis parallel to the
magnitude.

In addition, globular clusters can be dated by looking at the temperatures of the coolest
white dwarfs. Typical results for globular clusters are that they may be as old as 12.7
billion years. This is in contrast to open clusters which are only tens of millions of years
old.

The age of globular clusters, place a bounds on the age limit of the entire universe. This
lower limit has been a significant constraint in cosmology. During the early 1990s,
astronomers were faced with age estimates of globular clusters that appeared older than
cosmological models would allow. However, better measurements of cosmological
parameters through deep sky surveys and satellites such as COBE have resolved this
issue as have computer models of stellar evolution that have different models of mixing.

Evolutionary studies of globular clusters can also be used to determine changes due to the
starting composition of the gas and dust that formed the cluster. That is, the change in the
evolutionary tracks due to the abundance of heavy elements. (Heavy elements in
astronomy are considered to be all elements more massive than helium.) The data
obtained from studies of globular clusters are then used to study the evolution of the
Milky Way as a whole.

In globular clusters a few stars known as blue stragglers are observed. The origins of
these stars is still unclear, but most models suggest that these stars are the result of mass
transfer in multiple star systems.

Morphology

In contrast to open clusters, most globular clusters remain gravitationally-bound for time
periods comparable to the life spans of the majority of their stars. (A possible exception is
when strong tidal interactions with other large masses result in the dispersal of the stars.)

At present the formation of globular clusters remains a poorly understood phenomenon.
However, observations of globular clusters shows that these stellar formations arise
primarily in regions of efficient star formation, and where the interstellar medium is at a
higher density than in normal star-forming regions. Globular cluster formation is
prevalent in starburst regions and in interacting galaxies.

After they are formed, the stars in the globular cluster begin to gravitationally interact
with each other. As a result the velocity vectors of the stars are steadily modified, and the
stars lose any history of their original velocity. The characteristic interval for this to occur
is the relaxation time. This is related to the characteristic length of time a star needs to
cross the cluster as well as the number of stellar masses in the system. The value of the
relaxation time varies by cluster, but the mean value is on the
order of 109 years.

Ellipticity of Globulars

LMGCalaxy 0E.1ll6ip±t0i.c0it5y
MSMilCky Way 00..1097±±00..0064

Although globular clusters generally appear spherical in form, M31 0.09±0.04
ellipticities can occur due to tidal interactions. Clusters within

the Milky Way and the Andromeda Galaxy are typically oblate

spheroids in shape, while those in the Large Magellanic Cloud are more elliptical.

Radii

Astronomers characterize the morphology of a globular cluster by means of standard
radii. These are the core radius (rc), the half-light radius (rh) and the tidal radius (rt). The
overall luminosity of the cluster steadily decreases with distance from the core, and the
core radius is the distance at which the apparent surface luminosity has dropped by half.
A comparable quantity is the half-light radius, or the distance from the core at which half
the total luminosity from the cluster is received. This is typically larger than the core
radius.

Note that the half-light radius includes stars in the outer part of the cluster that happen to
lie along the line of sight, so theorists will also use the half-mass radius (rm)—the radius
from the core that contains half the total mass of the cluster. When the half-mass radius
of a cluster is small relative to the overall size, it has a dense core. An example of this is
the Globular Cluster M3, which has an overall visible dimension of about 18 arc seconds,
but a half-mass radius of only 1.12 arc seconds.

Finally the tidal radius is the distance from the center of the globular cluster at which the
external gravitation of the galaxy has more influence over the stars in the cluster than
does the cluster itself. This is the distance at which the individual stars belonging to a
cluster can be separated away by the galaxy. The tidal radius of M3 is about 38″.

Mass segregation and luminosity

In measuring the luminosity curve of a given globular cluster as a function of distance
from the core, most clusters in the Milky Way steadily increase in luminosity as this
distance decreases, up to a certain distance from the core, then the luminosity levels off.
Typically this distance is about 1–2 parsecs from the core. However about 20% of the
globular clusters have undergone a process termed “core collapse”. In this type of cluster,
the luminosity continues to steadily increase all the way to the core region. An example
of a core-collapsed globular is M15.

47 Tucanae - the second most luminous globular cluster in the Milky Way, after Omega
Centauri.

Core-collapse is thought to occur when the more massive stars in a globular encounter
their less massive companions. As a result of the encounters the larger stars tend to lose
kinetic energy and start to settle toward the core. Over a lengthy period of time this leads
to a concentration of massive stars near the core.

The Hubble Space Telescope has been used to provide convincing observational evidence
of this stellar mass-sorting process in globular clusters. Heavier stars slow down and
crowd at the cluster’s core, while lighter stars pick up speed and tend to spend more time
at the cluster’s periphery. The globular star cluster 47 Tucanae, which is made up of
about 1 million stars, is one of the densest globular clusters in the Southern Hemisphere.
This cluster was subjected to an intensive photographic survey, which allowed
astronomers to track the motion of its stars. Precise velocities were obtained for nearly
15,000 stars in this cluster.

The overall luminosities of the globular clusters within the Milky Way and M31 can be
modeled by means of a gaussian curve. This gaussian can be represented by means of an
average magnitude Mv and a variance σ2. This distribution of globular cluster
luminosities is called the Globular Cluster Luminosity Function (GCLF). (For the Milky
Way, Mv = −7.20±0.13, σ=1.1±0.1 magnitudes.) The GCLF has also been used as a
“standard candle” for measuring the distance to other galaxies, under the assumption that
the globular clusters in remote galaxies follow the same principles as they do in the
Milky Way.

N-body simulations

Computing the interactions between the stars within a globular cluster requires solving
what is termed the N-body problem. That is, each of the stars within the cluster
continually interacts with the other N−1 stars, where N is the total number of stars in the
cluster. The naive CPU computational “cost” for a dynamic simulation increases in
proportion to N3,so the potential computing requirements to accurately simulate such a
cluster can be enormous An efficient method of mathematically simulating the N-body
dynamics of a globular cluster is done by sub-dividing into small volumes and velocity
ranges, and using probabilities to describe the locations of the stars. The motions are then

described by means of a formula called the Fokker-Planck equation. This can be solved
by a simplified form of the equation, or by running Monte Carlo simulations and using
random values. However the simulation becomes more difficult when the effects of
binaries and the interaction with external gravitation forces (such as from the Milky Way
galaxy) must also be included.

The results of N-body simulations have shown that the stars can follow unusual paths
through the cluster, often forming loops and often falling more directly toward the core
than would a single star orbiting a central mass. In addition, due to interactions with other
stars that result in an increase in velocity, some of the stars gain sufficient energy to
escape the cluster. Over long periods of time this will result in a dissipation of the cluster,
a process termed evaporation.The typical time scale for the evaporation of a globular
cluster is 1010 years.

Binary stars form a significant portion of the total population of stellar systems, with up
to half of all stars occurring in binary systems. Numerical simulations of globular clusters
have demonstrated that binaries can hinder and even reverse the process of core collapse
in globular clusters. When a star in a cluster has a gravitational encounter with a binary
system, a possible result is that the binary becomes more tightly bound and kinetic energy
is added to the solitary star. When the massive stars in the cluster are sped up by this
process, it reduces the contraction at the core and limits core collapse.

Intermediate forms

The distinction between clusters types is not always clear-cut, and objects have been
found that blur the lines between the categories. For example, BH 176 in the southern
part of the Milky Way has properties of both an open and a globular cluster.[38]

In 2005, astronomers discovered a completely new type of star cluster in the Andromeda
Galaxy, which are, in several ways, very similar to globular clusters. The new-found
clusters contain hundreds of thousands of stars, a similar number of stars that can be
found in globular clusters. The clusters also share other characteristics with globular
clusters, e.g. the stellar populations and metallicity. What distinguishes them from the
globular clusters is that they are much larger – several hundred light years across – and
hundreds of times less dense. The distances between the stars are, therefore, much greater
within the newly discovered extended clusters. Parametrically, these clusters lie
somewhere between a (low dark-matter) globular cluster and a (dark matter-dominated)
dwarf spheroidal galaxy.[39]

How these clusters are formed is not yet known, but their formation might well be related
to that of globular clusters. Why M31 has such clusters, while the Milky Way has not, is
not yet known. It is also unknown if any other galaxy contains this kind of clusters, but it
would be very unlikely that M31 is the sole galaxy with extended clusters.[39]

Tidal encounters

When a globular cluster has a close encounter with a large mass, such as the core region
of a galaxy, it undergoes a tidal interaction. The difference in the pull of gravity between
the part of the cluster nearest the mass and the pull on the furthest part of the cluster
results in a tidal force. A “tidal shock” occurs whenever the orbit of a cluster takes it
through the plane of a galaxy.

As a result of a tidal shock, streams of stars can be pulled away from the cluster halo,
leaving only the core part of the cluster. These tidal interaction effects create tails of stars
that can extend up to several degrees of arc away from the cluster.[40] These tails typically
both precede and follow the cluster along its orbit. The tails can accumulate significant
portions of the original mass of the cluster, and can form clump-like features.[41]

The globular cluster Palomar 5, for example, is near the perigalactic point of its orbit
after passing through the Milky Way. Streams of stars extend outward toward the front
and rear of the orbital path of this cluster, stretching out to distances of 13,000 light
years.[42] Tidal interactions have stripped away much of the mass from Palomar 5, and
further interactions as it passes through the galactic core are expected to transform it into
a long stream of stars orbiting the Milky Way halo.

Tidal interactions add kinetic energy into a globular cluster, dramatically increasing the
evaporation rate and shrinking the size of the cluster. Not only does tidal shock strip off
the outer stars from a globular cluster, but the increased evaporation accelerates the
process of core collapse.

Ceres (dwarf planet)

Ceres

Discovery A

Discoverer Giuseppe Piazzi
January 1, 1801
Discovery date A899 OF; 1943 XB

Alternate
designations B

Category Main belt,Dwarf Planet

Orbital elements C

Epoch November 26, 2005 (JD 2453700.5)

Eccentricity (e) 0.080

Semi-major axis (a) 413.715 Gm (2.766 AU)

Perihelion (q) 380.612 Gm (2.544 AU)

Aphelion (Q) 446.818 Gm (2.987 AU)

Orbital period (P) 1679.819 d (4.599 a)

Mean orbital speed 17.882 km/s

Inclination (i) 10.587°

Longitude of the 80.410°
ascending node (Ω)

Argument of 73.271°
perihelion (ω)

Mean anomaly (M) 108.509°
Physical characteristics D

Dimensions 975×909 km
Mass 9.46 ± 0.04 × 1020 kg

Density 2.08 g/cm³

Surface gravity 0.27 m/s²

Escape velocity 0.51 km/s

Rotation period 0.3781 d

Spectral class G-type asteroid

Absolute magnitude 3.34

Albedo (geometric) 0.113

Mean surface ~167 K
temperature max: 239 K (-34 ° C)

Ceres (IPA / si riz/, Latin: Cerēs), also designated 1 Ceres or (1) Ceres (See Minor
Planet Names), is the smallest dwarf planet in the Solar System and the only one located
in the asteroid belt.. It was discovered on January 1, 1801, by Giuseppe Piazzi. With a
diameter of about 950 km, Ceres is by far the largest and most massive body in the
asteroid belt, and contains approximately a third of the belt’s total mass. Recent
observations have revealed that it is spherical, unlike the irregular shapes of smaller
asteroids with less gravity.

Name

Piazzi’s Book “Della scoperta del nuovo pianeta Cerere Ferdinandea” outlining the
discovery of Ceres

Ceres was originally named Ceres Ferdinandea (Cerere Ferdinandea) after both the
mythological figure Ceres (Roman goddess of plants and motherly love) and King
Ferdinand III of Sicily. “Ferdinandea” was not acceptable to other nations of the world
and was thus dropped. Ceres was also called Hera for a short time in Germany. In

Greece, it is called ∆ήµητρα (Demeter), after the goddess Ceres’ Greek equivalent; in
English usage, Demeter is the name of a different asteroid (1108 Demeter).

Due to the rarity of the usage, there is no consensus as to the proper adjectival form of the
name, although the nonce forms Cerian and Cerean have been used in fiction.

Symbol

Ceres’ astronomical symbol is a sickle ( ), similar to Venus’ symbol ( ) which is the
female gender symbol and Venus’ hand mirror. There have been several variants of the
sickle design, including , and .

Discovery

Piazzi was searching for a star listed by Francis Wollaston as Mayer 87 because it was
not in Mayer’s zodiacal catalogue in the position given. Instead, Piazzi found a moving
star-like object, which he thought at first was a comet.

Piazzi observed Ceres a total of 24 times, the final time on February 11, when illness
interrupted. On January 24, 1801, Piazzi announced his discovery in letters to fellow
astronomers, among them his fellow countryman, Barnaba Oriani of Milan. He reported it
as a comet but “since its movement is so slow and rather uniform, it has occurred to me
several times that it might be something better than a comet”. By early February Ceres
was lost as it receded behind the Sun. In April, Piazzi sent his complete observations to
Oriani, Bode, and Lalande in Paris. They were shortly thereafter published in the
September, 1801 issue of the Monatliche Correspondenz.

To recover Ceres, Carl Friedrich Gauss, then only 24 years old, developed a method of
orbit determination from three observations. In only a few weeks, he predicted its path,
and sent his results to Franz Xaver, Baron von Zach, the editor of the Monatliche
Correspondenz. On December 31, 1801, von Zach and Heinrich W. M. Olbers
unambiguously confirmed the recovery of Ceres.

Status

Ceres (left) in comparison with the Moon (right).

Johann Elert Bode believed Ceres to be the “missing planet” that Johann Daniel Titius
had proposed to exist between Mars and Jupiter, at a distance of 419 million km (2.8 AU)
from the Sun. Ceres was assigned a planetary symbol, and remained listed as a planet in
astronomy books and tables (along with 2 Pallas, 3 Juno and 4 Vesta) for about half a
century until further asteroids were discovered. Due to Ceres’ small size, its relatively
high inclination, and its sharing an orbital region with 2 Pallas, Sir William Herschel
coined in 1802 the term asteroid (“star-like”) for such bodies, writing, “they resemble
small stars so much as hardly to be distinguished from them, even by very good
telescopes”.

The 2006 debate surrounding Pluto and what constitutes a ‘planet’ led to Ceres being
considered for reclassification as a planet. An unsuccessful proposal before the
International Astronomical Union for the definition of a planet would have defined a
planet as “a celestial body that (a) has sufficient mass for its self-gravity to overcome
rigid body forces so that it assumes a hydrostatic equilibrium (nearly round) shape, and
(b) is in orbit around a star, and is neither a star nor a satellite of a planet”. Had this
resolution been adopted, this would have made Ceres the fifth planet in order from the
Sun. Instead, the new definition of ‘planet’ is “a celestial body that is in orbit around the
sun, has sufficient mass for its self-gravity to overcome rigid body forces so that it
assumes a ... nearly round shape, and has cleared the neighborhood around its orbit.” By
this definition, Ceres (along with Pluto) cannot be classified as a planet, and both are now
classified as “dwarf planets”.

The classification of Ceres has changed more than once. At the time of its discovery it
was considered a planet, but upon the realization that it represented the first of a class of
many similar bodies, it was reclassified as an asteroid for over 150 years. As the first
such body to be discovered, it was given the designation 1 Ceres under the modern
system of asteroid numbering. After the discovery of the trans-Neptunian object Eris, the
International Astronomical Union put forward a proposal to once again define Ceres as a
planet, along with Eris and Pluto’s moon Charon. This draft definition was not accepted,
and in its place an alternate definition of “planet” came into effect as of August 24, 2006.
Under this definition, Ceres is a ‘dwarf planet’, although it remains unclear as to whether
or not it is also classified as an asteroid.

Orbit of Ceres

Orbit

Ceres follows an orbit between Mars and Jupiter, within the main asteroid belt, with a
period of 4.6 years. The orbit is moderately inclined (i=10.6° to be compared with 7° for
Mercury and 17° for Pluto) and moderately eccentric (e=0.08 to compare with 0.09 for
Mars).

The diagram illustrates the orbits of Ceres (blue) and several planets (white/grey). The
segments of orbits below the ecliptic are plotted in darker colours, and the orange plus
sign is the Sun’s location. The top left diagram is a polar view that shows the location of
Ceres in the gap between Mars and Jupiter. The top right is a close-up demonstrating the
locations of the perihelia (q) and aphelia (Q) of Ceres and Mars. Interestingly, the
perihelia of Ceres (as well as those of several other of the largest MBAs) and Mars are on
the opposite sides of the Sun. The bottom diagram is a perspective view showing the
inclination of the orbit of Ceres compared to the orbits of Mars and Jupiter.

Physical characteristics

Hubble Space Telescope images of Ceres, taken in 2003/4 with a resolution of about 30
km. The nature of the bright spot is uncertain. A movie was also made.

Hubble Space Telescope UV image of Ceres, taken in 1995 with a resolution of about 60
km. The “Piazzi” feature is the dark spot in the center.

Ceres is the largest object in the asteroid belt, which mostly lies between Mars and
Jupiter. However, it is not the largest object besides the Sun, planets and their satellites,
in the solar system: the Kuiper belt is known to contain larger objects, including Eris,
Pluto, 50000 Quaoar, 90482 Orcus, and 90377 Sedna.

At certain points in its orbit, Ceres can reach a magnitude of 7.0. This is generally
regarded as being just barely too dim to be seen with the naked eye, but under
exceptional viewing conditions a very sharp-sighted person may be able to see the
asteroid with the naked eye. The only other asteroid that can be seen with the naked eye
is 4 Vesta.

Ceres’ size and mass are sufficient to give it a nearly spherical shape. That is, it is close
to hydrostatic equilibrium. Other large asteroids such as 2 Pallas, 3 Juno, and 4 Vesta are
known to be quite irregular, while lightcurve analysis of 10 Hygiea indicates it is oblong
although it appears spheroidal in low-resolution images (presumably due to viewing
angle).
With a mass of 9.5×1020 kg, Ceres comprises about a third of the estimated total
3.0±0.2×1021 kg mass of all the asteroids in the solar system (note how all these amount
to only about 4% of the mass of the Moon).

There are some indications that the surface of Ceres is relatively warm and that it may
have a tenuous atmosphere and frost. The maximum temperature with the Sun overhead
was estimated from measurements to be 235 K (about -38 °C) on May 5, 1991. Taking
into account also the heliocentric distance at the time, this gives an estimated maximum
of ~239 K at perihelion.

Diagram showing differentiated layers of Ceres

A study led by Peter Thomas of Cornell University suggests that Ceres has a
differentiated interior: observations coupled with computer models suggest the presence
of a rocky core overlain with an icy mantle. This mantle of thickness from 120 to 60 km
could contain 200 million cubic kilometres of water, which is more than the amount of
fresh water on the Earth.

There has been some ambiguity regarding surface features on Ceres. Low resolution
ultraviolet Hubble Space Telescope images taken in 1995 showed a dark spot on its
surface which was nicknamed “Piazzi” in honour of the discoverer of Ceres. This was
thought to be a crater. Later images with a higher resolution taken over a whole rotation
with the Keck telescope using adaptive optics showed no sign of “Piazzi”. However, two
dark features were seen to move with the asteroid’s rotation, one with a bright central
region. These are presumably craters. More recent visible light Hubble Space Telescope
images of a full rotation taken in 2003 and 2004 show an enigmatic white spot, the nature
of which is currently unknown. The dark albedo features seen with Keck are, however,
not immediately recognizable in these images.

These last observations also determined that Ceres’ north pole points (give or take about
5°) in the direction of right ascension 19 h 24 min, declination +59°, in the constellation
Draco. This means that Ceres’ axial tilt is very small (about 4±5°).

Ceres was long thought to be the parent body of the “Ceres asteroid family”. However,
that grouping is now defunct because Ceres has been shown to be an interloper in its
“own” family, and physically unrelated. The bulk of that asteroid group is now called the
Gefion family.

Observations

Some notable observation milestones for Ceres include:

An occultation of a star by Ceres was observed in Mexico, Florida and across the
Caribbean on November 13, 1984.

Features on Ceres’ surface have been telescopically imaged several times in recent years.
These include:

• Ultraviolet Hubble Space Telescope images with 50 km resolution taken in 1995.
• Visible images with 60 km resolution taken with the Keck telescope in 2002 using

adaptive optics.
• Infrared images with 30 km resolution also taken with the Keck telescope in 2002

using adaptive optics.
• The best resolution to date (30 km) visible light images using Hubble again in

2003 and 2004.
Radio signals from spacecraft in orbit around Mars and on its surface have been used to
estimate the mass of Ceres from the perturbations induced by it onto the motion of Mars.

Exploration of Ceres

Artist’s conception of Dawn visiting Ceres and Vesta.
To date no space probes have visited Ceres. However, NASA is currently developing the
Dawn Mission, with a projected launch in 2007. According to the current mission profile,
Dawn is expected to explore the asteroid 4 Vesta in 2011 before arriving at Ceres in
2015.

Namesakes

• The chemical element cerium (atomic number 58) was discovered in 1803 by
Berzelius and Klaproth, working independently. Berzelius named the element
after Ceres.

• William Hyde Wollaston discovered palladium (atomic number 46) as early as
1802 and at first called it Ceresium. By the time he openly published his
discovery in 1805, the name was already taken (by Berzelius) and he switched it
to palladium in honour of 2 Pallas.

Aspects

Stationary, Opposition Distance Maximum Stationary, Conjunction
retrograde to brightness prograde to Sun

Earth (mag)
(AU)

March 21, May 8, 2005 1.68631 7.0 June 30, 2005 December 28,
2005 2005

June 26, 2006 August 12, 1.98278 7.6 November 27, March 22,
2006
2006 2007

September 20, November 9, 1.83690 7.2 January 1, June 28, 2008
2008
2007 2007

January 17, February 24, 1.58526 6.9 April 16, 2009 October 31,
2009 2009 2009

April 28, 2010 June 18, 2010 1.81988 7.0 August 9, January 30,
2010 2011

July 31, 2011 September 16, 1.99211 7.7 November 12, April 26, 2012
2011 2011

October 30, December 17, 1.68842 6.7 February 4, August 17,
2012 2012
2013 2013

March 1, 2014 April 15, 2014 1.63294 7.0 June 7, 2014 December 10,
2014

June 6, 2015 July 25, 2015 1.94252 7.5 September 16, March 3, 2016
2015

September 1, October 20, 1.90844 7.4 December 15, June 5, 2017
2016
2016 2016

December 21, January 31, 1.59531 8.8 March 20, October 7,
2018 2018
2017 2018

April 9, 2019 May 29, 2019 1.74756 7.0 July 20, 2019 January 14,
2020

July 13, 2020 August 28, 1.99916 7.7 October 23, April 7, 2021
2020 2020