Molecular vibration

From Wikipedia, the free encyclopedia

A molecular vibration occurs when atoms in a molecule are in periodic motion while the molecule as a whole has constant translational and rotational motion. The frequency of the periodic motion is known as a vibration frequency, and the typical frequencies of molecular vibrations range from less than 10¹³ to approximately 10¹⁴ Hz, corresponding to wavenumbers of approximately 300 to 3000 cm⁻¹.

In general, a molecule with N atoms has 3N – 6 normal modes of vibration, but a linear molecule has 3N – 5 such modes, because rotation about its molecular axis cannot be observed.^[1] A diatomic molecule has one normal mode of vibration. The normal modes of vibration of polyatomic molecules are independent of each other but each normal mode will involve simultaneous vibrations of different parts of the molecule such as different chemical bonds.

A molecular vibration is excited when the molecule absorbs a quantum of energy, E, corresponding to the vibration's frequency, ν, according to the relation E = hν (where h is Planck's constant). A fundamental vibration is excited when one such quantum of energy is absorbed by the molecule in its ground state. When two quanta are absorbed the first overtone is excited, and so on to higher overtones.

To a first approximation, the motion in a normal vibration can be described as a kind of simple harmonic motion. In this approximation, the vibrational energy is a quadratic function (parabola) with respect to the atomic displacements and the first overtone has twice the frequency of the fundamental. In reality, vibrations are anharmonic and the first overtone has a frequency that is slightly lower than twice that of the fundamental. Excitation of the higher overtones involves progressively less and less additional energy and eventually leads to dissociation of the molecule, because the potential energy of the molecule is more like a Morse potential.

The vibrational states of a molecule can be probed in a variety of ways. The most direct way is through infrared spectroscopy, as vibrational transitions typically require an amount of energy that corresponds to the infrared region of the spectrum. Raman spectroscopy, which typically uses visible light, can also be used to measure vibration frequencies directly. The two techniques are complementary and comparison between the two can provide useful structural information such as in the case of the rule of mutual exclusion for centrosymmetric molecules.

Vibrational excitation can occur in conjunction with electronic excitation in the ultraviolet-visible region. The combined excitation is known as a vibronic transition, giving vibrational fine structure to electronic transitions, particularly for molecules in the gas state.

Simultaneous excitation of a vibration and rotations gives rise to vibration-rotation spectra

Vibrational coordinates

The coordinate of a normal vibration is a combination of changes in the positions of atoms in the molecule. When the vibration is excited the coordinate changes sinusoidally with a frequency ν, the frequency of the vibration.

Internal coordinates

Internal coordinates are of the following types, illustrated with reference to the planar molecule ethylene,

• Stretching: a change in the length of a bond, such as C-H or C-C
• Bending: a change in the angle between two bonds, such as the HCH angle in a methylene group
• Rocking: a change in angle between a group of atoms, such as a methylene group and the rest of the molecule.
• Wagging: a change in angle between the plane of a group of atoms, such as a methylene group and a plane through the rest of the molecule,
• Twisting: a change in the angle between the planes of two groups of atoms, such as a change in the angle between the two methylene groups.
• Out-of-plane: a change in the angle between any one of the C-H bonds and the plane defined by the remaining atoms of the ethylene molecule. Another example is in BF₃ when the boron atom moves in and out of the plane of the three fluorine atoms.

In a rocking, wagging or twisting coordinate the bond lengths within the groups involved do not change. The angles do. Rocking is distinguished from wagging by the fact that the atoms in the group stay in the same plane.

In ethene there are 12 internal coordinates: 4 C-H stretching, 1 C-C stretching, 2 H-C-H bending, 2 CH₂ rocking, 2 CH₂ wagging, 1 twisting. Note that the H-C-C angles cannot be used as internal coordinates as the angles at each carbon atom cannot all increase at the same time.

Vibrations of a methylene group (-CH₂-) in a molecule for illustration

The atoms in a CH₂ group, commonly found in organic compounds, can vibrate in six different ways: symmetric and asymmetric stretching, scissoring, rocking, wagging and twisting as shown here:

Symmetrical stretching	Asymmetrical stretching	Scissoring (Bending)
Rocking	Wagging	Twisting

(These figures do not represent the "recoil" of the C atoms, which, though necessarily present to balance the overall movements of the molecule, are much smaller than the movements of the lighter H atoms).

Symmetry-adapted coordinates

Symmetry-adapted coordinates may be created by applying a projection operator to a set of internal coordinates.^[2] The projection operator is constructed with the aid of the character table of the molecular point group. For example, the four(un-normalised) C-H stretching coordinates of the molecule ethene are given by

${\displaystyle Q_{s1}=q_{1}+q_{2}+q_{3}+q_{4}\!}$

${\displaystyle Q_{s2}=q_{1}+q_{2}-q_{3}-q_{4}\!}$

${\displaystyle Q_{s3}=q_{1}-q_{2}+q_{3}-q_{4}\!}$

${\displaystyle Q_{s4}=q_{1}-q_{2}-q_{3}+q_{4}\!}$

where ${\displaystyle q_{1}-q_{4}}$ are the internal coordinates for stretching of each of the four C-H bonds.

Illustrations of symmetry-adapted coordinates for most small molecules can be found in Nakamoto.^[3]

Normal coordinates

The normal coordinates, denoted as Q, refer to the positions of atoms away from their equilibrium positions, with respect to a normal mode of vibration. Each normal mode is assigned a single normal coordinate, and so the normal coordinate refers to the "progress" along that normal mode at any given time. Formally, normal modes are determined by solving a secular determinant, and then the normal coordinates (over the normal modes) can be expressed as a summation over the cartesian coordinates (over the atom positions). The advantage of working in normal modes is that they diagonalize the matrix governing the molecular vibrations, so each normal mode is an independent molecular vibration, associated with its own spectrum of quantum mechanical states. If the molecule possesses symmetries, it will belong to a point group, and the normal modes will "transform as" an irreducible representation under that group. The normal modes can then be qualitatively determined by applying group theory and projecting the irreducible representation onto the cartesian coordinates. For example, when this treatment is applied to CO₂, it is found that the C=O stretches are not independent, but rather there is an O=C=O symmetric stretch and an O=C=O asymmetric stretch.

• symmetric stretching: the sum of the two C-O stretching coordinates; the two C-O bond lengths change by the same amount and the carbon atom is stationary. Q = q₁ + q₂
• asymmetric stretching: the difference of the two C-O stretching coordinates; one C-O bond length increases while the other decreases. Q = q₁ - q₂

When two or more normal coordinates belong to the same irreducible representation of the molecular point group (colloquially, have the same symmetry) there is "mixing" and the coefficients of the combination cannot be determined a priori. For example, in the linear molecule hydrogen cyanide, HCN, The two stretching vibrations are

1. principally C-H stretching with a little C-N stretching; Q₁ = q₁ + a q₂ (a << 1)
2. principally C-N stretching with a little C-H stretching; Q₂ = b q₁ + q₂ (b << 1)

The coefficients a and b are found by performing a full normal coordinate analysis by means of the Wilson GF method.^[4]

Newtonian mechanics

The HCl molecule as an anharmonic oscillator vibrating at energy level E₃. D₀ is dissociation energy here, r₀ bond length, U potential energy. Energy is expressed in wavenumbers. The hydrogen chloride molecule is attached to the coordinate system to show bond length changes on the curve.

Perhaps surprisingly, molecular vibrations can be treated using Newtonian mechanics to calculate the correct vibration frequencies. The basic assumption is that each vibration can be treated as though it corresponds to a spring. In the harmonic approximation the spring obeys Hooke's law: the force required to extend the spring is proportional to the extension. The proportionality constant is known as a force constant, k. The anharmonic oscillator is considered elsewhere.^[5]

${\displaystyle \mathrm {Force} =-kQ\!}$

By Newton’s second law of motion this force is also equal to a reduced mass, μ, times acceleration.

${\displaystyle \mathrm {Force} =\mu {\frac {d^{2}Q}{dt^{2}}}}$

Since this is one and the same force the ordinary differential equation follows.

${\displaystyle \mu {\frac {d^{2}Q}{dt^{2}}}+kQ=0}$

The solution to this equation of simple harmonic motion is

${\displaystyle Q(t)=A\cos(2\pi \nu t);\ \ \nu ={1 \over {2\pi }}{\sqrt {k \over \mu }}.\!}$

A is the maximum amplitude of the vibration coordinate Q. It remains to define the reduced mass, μ. In general, the reduced mass of a diatomic molecule, AB, is expressed in terms of the atomic masses, m_A and m_B, as

${\displaystyle {\frac {1}{\mu }}={\frac {1}{m_{A}}}+{\frac {1}{m_{B}}}.}$

The use of the reduced mass ensures that the centre of mass of the molecule is not affected by the vibration. In the harmonic approximation the potential energy of the molecule is a quadratic function of the normal coordinate. It follows that the force-constant is equal to the second derivative of the potential energy.

${\displaystyle k={\frac {\partial ^{2}V}{\partial Q^{2}}}}$

When two or more normal vibrations have the same symmetry a full normal coordinate analysis must be performed (see GF method). The vibration frequencies,ν_i are obtained from the eigenvalues,λ_i, of the matrix product GF. G is a matrix of numbers derived from the masses of the atoms and the geometry of the molecule.^[4] F is a matrix derived from force-constant values. Details concerning the determination of the eigenvalues can be found in.^[6]

Quantum mechanics

In the harmonic approximation the potential energy is a quadratic function of the normal coordinates. Solving the Schrödinger wave equation, the energy states for each normal coordinate are given by

${\displaystyle E_{n}=h\left(n+{1 \over 2}\right)\nu =h\left(n+{1 \over 2}\right){1 \over {2\pi }}{\sqrt {k \over m}}\!}$,

where n is a quantum number that can take values of 0, 1, 2 ... In molecular spectroscopy where several types of molecular energy are studied and several quantum numbers are used, this vibrational quantum number is often designated as v.^[7][8]

The difference in energy when n (or v) changes by 1 is therefore equal to ${\displaystyle h\nu }$, the product of the Planck constant and the vibration frequency derived using classical mechanics. For a transition from level n to level n+1 due to absorption of a photon, the frequency of the photon is equal to the classical vibration frequency ${\displaystyle \nu }$ (in the harmonic oscillator approximation).

See quantum harmonic oscillator for graphs of the first 5 wave functions, which allow certain selection rules to be formulated. For example, for a harmonic oscillator transitions are allowed only when the quantum number n changes by one,

${\displaystyle \Delta n=\pm 1}$

but this does not apply to an anharmonic oscillator; the observation of overtones is only possible because vibrations are anharmonic. Another consequence of anharmonicity is that transitions such as between states n=2 and n=1 have slightly less energy than transitions between the ground state and first excited state. Such a transition gives rise to a hot band.

Intensities

In an infrared spectrum the intensity of an absorption band is proportional to the derivative of the molecular dipole moment with respect to the normal coordinate.^[9] The intensity of Raman bands depends on polarizability

Schrödinger's cat

From Wikipedia, the free encyclopedia

Schrödinger's cat: a cat, a flask of poison, and a radioactive source are placed in a sealed box. If an internal monitor (e.g. Geiger counter) detects radioactivity (i.e. a single atom decaying), the flask is shattered, releasing the poison, which kills the cat. The Copenhagen interpretation of quantum mechanics implies that after a while, the cat is simultaneously alive and dead. Yet, when one looks in the box, one sees the cat either alive or dead not both alive and dead. This poses the question of when exactly quantum superposition ends and reality collapses into one possibility or the other.

Schrödinger's cat is a thought experiment, sometimes described as a paradox, devised by Austrian physicist Erwin Schrödinger in 1935.^[1] It illustrates what he saw as the problem of the Copenhagen interpretation of quantum mechanics applied to everyday objects. The scenario presents a cat that may be simultaneously both alive and dead,^{[2][3][4][5][6][7][8]} a state known as a quantum superposition, as a result of being linked to a random subatomic event that may or may not occur. The thought experiment is also often featured in theoretical discussions of the interpretations of quantum mechanics. Schrödinger coined the term Verschränkung (entanglement) in the course of developing the thought experiment.

Origin and motivation

Life-size cat figure in the garden of Huttenstrasse 9, Zurich, where Erwin Schrödinger lived 1921–1926. Depending on the light conditions, the cat appears either alive or dead.

Schrödinger intended his thought experiment as a discussion of the EPR article—named after its authors Einstein, Podolsky, and Rosen—in 1935.^[9] The EPR article highlighted the strange nature of quantum superpositions, in which a quantum system such as an atom or photon can exist as a combination of multiple states corresponding to different possible outcomes. The prevailing theory, called the Copenhagen interpretation, said that a quantum system remained in this superposition until it interacted with, or was observed by, the external world, at which time the superposition collapses into one or another of the possible definite states. The EPR experiment showed that a system with multiple particles separated by large distances could be in such a superposition. Schrödinger and Einstein exchanged letters about Einstein's EPR article, in the course of which Einstein pointed out that the state of an unstable keg of gunpowder will, after a while, contain a superposition of both exploded and unexploded states.

To further illustrate, Schrödinger described how one could, in principle, create a superposition in a large-scale system by making it dependent on a quantum particle that was in a superposition. He proposed a scenario with a cat in a locked steel chamber, wherein the cat's life or death depended on the state of a radioactive atom, whether it had decayed and emitted radiation or not. According to Schrödinger, the Copenhagen interpretation implies that the cat remains both alive and dead until the state is observed. Schrödinger did not wish to promote the idea of dead-and-alive cats as a serious possibility; on the contrary, he intended the example to illustrate the absurdity of the existing view of quantum mechanics.^[1] However, since Schrödinger's time, other interpretations of the mathematics of quantum mechanics have been advanced by physicists, some of which regard the "alive and dead" cat superposition as quite real.^[8][5] Intended as a critique of the Copenhagen interpretation (the prevailing orthodoxy in 1935), the Schrödinger's cat thought experiment remains a defining touchstone for modern interpretations of quantum mechanics. Physicists often use the way each interpretation deals with Schrödinger's cat as a way of illustrating and comparing the particular features, strengths, and weaknesses of each interpretation.

Thought experiment

Schrödinger wrote:^[1][10]

One can even set up quite ridiculous cases. A cat is penned up in a steel chamber, along with the following device (which must be secured against direct interference by the cat): in a Geiger counter, there is a tiny bit of radioactive substance, so small, that perhaps in the course of the hour one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discharges and through a relay releases a hammer that shatters a small flask of hydrocyanic acid. If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. The first atomic decay would have poisoned it. The psi-function of the entire system would express this by having in it the living and dead cat (pardon the expression) mixed or smeared out in equal parts.

It is typical of these cases that an indeterminacy originally restricted to the atomic domain becomes transformed into macroscopic indeterminacy, which can then be resolved by direct observation. That prevents us from so naively accepting as valid a "blurred model" for representing reality. In itself, it would not embody anything unclear or contradictory. There is a difference between a shaky or out-of-focus photograph and a snapshot of clouds and fog banks.

Schrödinger's famous thought experiment poses the question, "when does a quantum system stop existing as a superposition of states and become one or the other?" (More technically, when does the actual quantum state stop being a linear combination of states, each of which resembles different classical states, and instead begin to have a unique classical description?) If the cat survives, it remembers only being alive. But explanations of the EPR experiments that are consistent with standard microscopic quantum mechanics require that macroscopic objects, such as cats and notebooks, do not always have unique classical descriptions. The thought experiment illustrates this apparent paradox. Our intuition says that no observer can be in a mixture of states—yet the cat, it seems from the thought experiment, can be such a mixture. Is the cat required to be an observer, or does its existence in a single well-defined classical state require another external observer? Each alternative seemed absurd to Einstein, who was impressed by the ability of the thought experiment to highlight these issues. In a letter to Schrödinger dated 1950, he wrote:

You are the only contemporary physicist, besides Laue, who sees that one cannot get around the assumption of reality, if only one is honest. Most of them simply do not see what sort of risky game they are playing with reality—reality as something independent of what is experimentally established. Their interpretation is, however, refuted most elegantly by your system of radioactive atom + amplifier + charge of gunpowder + cat in a box, in which the psi-function of the system contains both the cat alive and blown to bits. Nobody really doubts that the presence or absence of the cat is something independent of the act of observation.^[11]

Note that the charge of gunpowder is not mentioned in Schrödinger's setup, which uses a Geiger counter as an amplifier and hydrocyanic poison instead of gunpowder. The gunpowder had been mentioned in Einstein's original suggestion to Schrödinger 15 years before, and Einstein carried it forward to the present discussion.

Interpretations of the experiment

Since Schrödinger's time, other interpretations of quantum mechanics have been proposed that give different answers to the questions posed by Schrödinger's cat of how long superpositions last and when (or whether) they collapse.

Copenhagen interpretation

The most commonly held interpretation of quantum mechanics is the Copenhagen interpretation.^[12] In the Copenhagen interpretation, a system stops being a superposition of states and becomes either one or the other when an observation takes place. This thought experiment makes apparent the fact that the nature of measurement, or observation, is not well-defined in this interpretation. The experiment can be interpreted to mean that while the box is closed, the system simultaneously exists in a superposition of the states "decayed nucleus/dead cat" and "undecayed nucleus/living cat", and that only when the box is opened and an observation performed does the wave function collapse into one of the two states.
However, one of the main scientists associated with the Copenhagen interpretation, Niels Bohr, never had in mind the observer-induced collapse of the wave function, so that Schrödinger's cat did not pose any riddle to him. The cat would be either dead or alive long before the box is opened by a conscious observer.^[13] Analysis of an actual experiment found that measurement alone (for example by a Geiger counter) is sufficient to collapse a quantum wave function before there is any conscious observation of the measurement,^[14] although the validity of their design is disputed.^[15] The view that the "observation" is taken when a particle from the nucleus hits the detector can be developed into objective collapse theories. The thought experiment requires an "unconscious observation" by the detector in order for waveform collapse to occur. In contrast, the many worlds approach denies that collapse ever occurs.

Many-worlds interpretation and consistent histories

The quantum-mechanical "Schrödinger's cat" paradox according to the many-worlds interpretation. In this interpretation, every event is a branch point. The cat is both alive and dead—regardless of whether the box is opened—but the "alive" and "dead" cats are in different branches of the universe that are equally real but cannot interact with each other.

In 1957, Hugh Everett formulated the many-worlds interpretation of quantum mechanics, which does not single out observation as a special process. In the many-worlds interpretation, both alive and dead states of the cat persist after the box is opened, but are decoherent from each other. In other words, when the box is opened, the observer and the possibly-dead cat split into an observer looking at a box with a dead cat, and an observer looking at a box with a live cat. But since the dead and alive states are decoherent, there is no effective communication or interaction between them.

When opening the box, the observer becomes entangled with the cat, so "observer states" corresponding to the cat's being alive and dead are formed; each observer state is entangled or linked with the cat so that the "observation of the cat's state" and the "cat's state" correspond with each other. Quantum decoherence ensures that the different outcomes have no interaction with each other. The same mechanism of quantum decoherence is also important for the interpretation in terms of consistent histories. Only the "dead cat" or the "alive cat" can be a part of a consistent history in this interpretation.

Roger Penrose criticises this:

I wish to make it clear that, as it stands, this is far from a resolution of the cat paradox. For there is nothing in the formalism of quantum mechanics that demands that a state of consciousness cannot involve the simultaneous perception of a live and a dead cat.^[16]

However, the mainstream view (without necessarily endorsing many-worlds) is that decoherence is the mechanism that forbids such simultaneous perception.^[17][18]

A variant of the Schrödinger's cat experiment, known as the quantum suicide machine, has been proposed by cosmologist Max Tegmark. It examines the Schrödinger's cat experiment from the point of view of the cat, and argues that by using this approach, one may be able to distinguish between the Copenhagen interpretation and many-worlds.

Ensemble interpretation

The ensemble interpretation states that superpositions are nothing but subensembles of a larger statistical ensemble. The state vector would not apply to individual cat experiments, but only to the statistics of many similarly prepared cat experiments. Proponents of this interpretation state that this makes the Schrödinger's cat paradox a trivial matter, or a non-issue.

This interpretation serves to discard the idea that a single physical system in quantum mechanics has a mathematical description that corresponds to it in any way.

Relational interpretation

The relational interpretation makes no fundamental distinction between the human experimenter, the cat, or the apparatus, or between animate and inanimate systems; all are quantum systems governed by the same rules of wavefunction evolution, and all may be considered "observers". But the relational interpretation allows that different observers can give different accounts of the same series of events, depending on the information they have about the system.^[19] The cat can be considered an observer of the apparatus; meanwhile, the experimenter can be considered another observer of the system in the box (the cat plus the apparatus). Before the box is opened, the cat, by nature of its being alive or dead, has information about the state of the apparatus (the atom has either decayed or not decayed); but the experimenter does not have information about the state of the box contents. In this way, the two observers simultaneously have different accounts of the situation: To the cat, the wavefunction of the apparatus has appeared to "collapse"; to the experimenter, the contents of the box appear to be in superposition. Not until the box is opened, and both observers have the same information about what happened, do both system states appear to "collapse" into the same definite result, a cat that is either alive or dead.

Objective collapse theories

According to objective collapse theories, superpositions are destroyed spontaneously (irrespective of external observation) when some objective physical threshold (of time, mass, temperature, irreversibility, etc.) is reached. Thus, the cat would be expected to have settled into a definite state long before the box is opened. This could loosely be phrased as "the cat observes itself", or "the environment observes the cat".

Objective collapse theories require a modification of standard quantum mechanics to allow superpositions to be destroyed by the process of time evolution.

Applications and tests

Play media

Schrödinger's cat quantum superposition of states and effect of the environment through decoherence

The experiment as described is a purely theoretical one, and the machine proposed is not known to have been constructed. However, successful experiments involving similar principles, e.g. superpositions of relatively large (by the standards of quantum physics) objects have been performed.^[20] These experiments do not show that a cat-sized object can be superposed, but the known upper limit on "cat states" has been pushed upwards by them. In many cases the state is short-lived, even when cooled to near absolute zero.

• A "cat state" has been achieved with photons.^[21]
• A beryllium ion has been trapped in a superposed state.^[22]
• An experiment involving a superconducting quantum interference device ("SQUID") has been linked to the theme of the thought experiment: "The superposition state does not correspond to a billion electrons flowing one way and a billion others flowing the other way. Superconducting electrons move en masse. All the superconducting electrons in the SQUID flow both ways around the loop at once when they are in the Schrödinger's cat state."^[23]
• A piezoelectric "tuning fork" has been constructed, which can be placed into a superposition of vibrating and non vibrating states. The resonator comprises about 10 trillion atoms.^[24]
• An experiment involving a flu virus has been proposed.^[25]
• An experiment involving a bacterium and an electromechanical oscillator has been proposed.^[26]

In quantum computing the phrase "cat state" often refers to the special entanglement of qubits wherein the qubits are in an equal superposition of all being 0 and all being 1; e.g.,

${\displaystyle |\psi \rangle ={\frac {1}{\sqrt {2}}}{\bigg (}|00\ldots 0\rangle +|11\ldots 1\rangle {\bigg )}.}$

• Researchers at the Stanford PULSE Institute and the Department of Energy’s SLAC National Accelerator Laboratory have exploited this Schrödinger's cat behavior to create X-ray movies of atomic motion with much more detail than ever before.^[27][28]

Extensions

Wigner's friend is a variant on the experiment with two human observers: the first makes an observation on whether a flash of light is seen and then communicates his observation to a second observer. The issue here is, does the wave function "collapse" when the first observer looks at the experiment, or only when the second observer is informed of the first observer's observations?

In another extension, prominent physicists have gone so far as to suggest that astronomers observing dark energy in the universe in 1998 may have "reduced its life expectancy" through a pseudo-Schrödinger's cat scenario, although this is a controversial viewpoint.^[29][30]

Asteroid

From Wikipedia, the free encyclopedia

253 Mathilde, a C-type asteroid measuring about 50 kilometres (30 mi) across, covered in craters half that size. Photograph taken in 1997 by the NEAR Shoemaker probe.

Asteroids are minor planets, especially those of the inner Solar System. The larger ones have also been called planetoids. These terms have historically been applied to any astronomical object orbiting the Sun that did not show the disc of a planet and was not observed to have the characteristics of an active comet. As minor planets in the outer Solar System were discovered and found to have volatile-based surfaces that resemble those of comets, they were often distinguished from asteroids of the asteroid belt.^[1] In this article, the term "asteroid" refers to the minor planets of the inner Solar System including those co-orbital with Jupiter.

There are millions of asteroids, many thought to be the shattered remnants of planetesimals, bodies within the young Sun's solar nebula that never grew large enough to become planets.^[2] The large majority of known asteroids orbit in the asteroid belt between the orbits of Mars and Jupiter, or are co-orbital with Jupiter (the Jupiter trojans). However, other orbital families exist with significant populations, including the near-Earth objects. Individual asteroids are classified by their characteristic spectra, with the majority falling into three main groups: C-type, M-type, and S-type. These were named after and are generally identified with carbon-rich, metallic, and silicate (stony) compositions, respectively. The size of asteroids varies greatly, some reaching as much as 1000 km across.

Asteroids are differentiated from comets and meteoroids. In the case of comets, the difference is one of composition: while asteroids are mainly composed of mineral and rock, comets are composed of dust and ice. In addition, asteroids formed closer to the sun, preventing the development of the aforementioned cometary ice.^[3] The difference between asteroids and meteoroids is mainly one of size: meteoroids have a diameter of less than one meter, whereas asteroids have a diameter of greater than one meter.^[4] Finally, meteoroids can be composed of either cometary or asteroidal materials.^[5]

Only one asteroid, 4 Vesta, which has a relatively reflective surface, is normally visible to the naked eye, and this only in very dark skies when it is favorably positioned. Rarely, small asteroids passing close to Earth may be visible to the naked eye for a short time.^[6] As of March 2016, the Minor Planet Center had data on more than 1.3 million objects in the inner and outer Solar System, of which 750,000 had enough information to be given numbered designations.^[7]

The United Nations declared June 30 as International Asteroid Day to educate the public about asteroids. The date of International Asteroid Day commemorates the anniversary of the Tunguska asteroid impact over Siberia, Russian Federation, on 30 June 1908.^[8][9]

Discovery

243 Ida and its moon Dactyl. Dactyl is the first satellite of an asteroid to be discovered.

The first asteroid to be discovered, Ceres, was found in 1801 by Giuseppe Piazzi, and was originally considered to be a new planet.^{[note 1]} This was followed by the discovery of other similar bodies, which, with the equipment of the time, appeared to be points of light, like stars, showing little or no planetary disc, though readily distinguishable from stars due to their apparent motions. This prompted the astronomer Sir William Herschel to propose the term "asteroid",^[10] coined in Greek as ἀστεροειδής, or asteroeidēs, meaning 'star-like, star-shaped', and derived from the Ancient Greek ἀστήρ astēr 'star, planet'. In the early second half of the nineteenth century, the terms "asteroid" and "planet" (not always qualified as "minor") were still used interchangeably. ^{[note 2]}

Historical methods

Asteroid discovery methods have dramatically improved over the past two centuries.
In the last years of the 18th century, Baron Franz Xaver von Zach organized a group of 24 astronomers to search the sky for the missing planet predicted at about 2.8 AU from the Sun by the Titius-Bode law, partly because of the discovery, by Sir William Herschel in 1781, of the planet Uranus at the distance predicted by the law. This task required that hand-drawn sky charts be prepared for all stars in the zodiacal band down to an agreed-upon limit of faintness. On subsequent nights, the sky would be charted again and any moving object would, hopefully, be spotted. The expected motion of the missing planet was about 30 seconds of arc per hour, readily discernible by observers.

First asteroid image (Ceres and Vesta) from Mars – viewed by Curiosity (20 April 2014).

The first object, Ceres, was not discovered by a member of the group, but rather by accident in 1801 by Giuseppe Piazzi, director of the observatory of Palermo in Sicily. He discovered a new star-like object in Taurus and followed the displacement of this object during several nights. Later that year, Carl Friedrich Gauss used these observations to calculate the orbit of this unknown object, which was found to be between the planets Mars and Jupiter. Piazzi named it after Ceres, the Roman goddess of agriculture.

Three other asteroids (2 Pallas, 3 Juno, and 4 Vesta) were discovered over the next few years, with Vesta found in 1807. After eight more years of fruitless searches, most astronomers assumed that there were no more and abandoned any further searches.

However, Karl Ludwig Hencke persisted, and began searching for more asteroids in 1830. Fifteen years later, he found 5 Astraea, the first new asteroid in 38 years. He also found 6 Hebe less than two years later. After this, other astronomers joined in the search and at least one new asteroid was discovered every year after that (except the wartime year 1945). Notable asteroid hunters of this early era were J. R. Hind, Annibale de Gasparis, Robert Luther, H. M. S. Goldschmidt, Jean Chacornac, James Ferguson, Norman Robert Pogson, E. W. Tempel, J. C. Watson, C. H. F. Peters, A. Borrelly, J. Palisa, the Henry brothers and Auguste Charlois.

In 1891, Max Wolf pioneered the use of astrophotography to detect asteroids, which appeared as short streaks on long-exposure photographic plates. This dramatically increased the rate of detection compared with earlier visual methods: Wolf alone discovered 248 asteroids, beginning with 323 Brucia, whereas only slightly more than 300 had been discovered up to that point. It was known that there were many more, but most astronomers did not bother with them, calling them "vermin of the skies",^[11] a phrase variously attributed to Eduard Suess^[12] and Edmund Weiss.^[13] Even a century later, only a few thousand asteroids were identified, numbered and named.

Manual methods of the 1900s and modern reporting

Until 1998, asteroids were discovered by a four-step process. First, a region of the sky was photographed by a wide-field telescope, or astrograph. Pairs of photographs were taken, typically one hour apart. Multiple pairs could be taken over a series of days. Second, the two films or plates of the same region were viewed under a stereoscope. Any body in orbit around the Sun would move slightly between the pair of films. Under the stereoscope, the image of the body would seem to float slightly above the background of stars. Third, once a moving body was identified, its location would be measured precisely using a digitizing microscope. The location would be measured relative to known star locations.^[14]

These first three steps do not constitute asteroid discovery: the observer has only found an apparition, which gets a provisional designation, made up of the year of discovery, a letter representing the half-month of discovery, and finally a letter and a number indicating the discovery's sequential number (example: 1998 FJ₇₄).

The last step of discovery is to send the locations and time of observations to the Minor Planet Center, where computer programs determine whether an apparition ties together earlier apparitions into a single orbit. If so, the object receives a catalogue number and the observer of the first apparition with a calculated orbit is declared the discoverer, and granted the honor of naming the object subject to the approval of the International Astronomical Union.

Computerized methods

2004 FH is the center dot being followed by the sequence; the object that flashes by during the clip is an artificial satellite.

There is increasing interest in identifying asteroids whose orbits cross Earth's, and that could, given enough time, collide with Earth (see Earth-crosser asteroids). The three most important groups of near-Earth asteroids are the Apollos, Amors, and Atens. Various asteroid deflection strategies have been proposed, as early as the 1960s.

The near-Earth asteroid 433 Eros had been discovered as long ago as 1898, and the 1930s brought a flurry of similar objects. In order of discovery, these were: 1221 Amor, 1862 Apollo, 2101 Adonis, and finally 69230 Hermes, which approached within 0.005 AU of Earth in 1937. Astronomers began to realize the possibilities of Earth impact.

Two events in later decades increased the alarm: the increasing acceptance of the Alvarez hypothesis that an impact event resulted in the Cretaceous–Paleogene extinction, and the 1994 observation of Comet Shoemaker-Levy 9 crashing into Jupiter. The U.S. military also declassified the information that its military satellites, built to detect nuclear explosions, had detected hundreds of upper-atmosphere impacts by objects ranging from one to 10 metres across.

All these considerations helped spur the launch of highly efficient surveys that consist of Charge-Coupled Device (CCD) cameras and computers directly connected to telescopes. As of spring 2011, it was estimated that 89% to 96% of near-Earth asteroids one kilometer or larger in diameter had been discovered.^[15] A list of teams using such systems includes:^[16]

• Lincoln Near-Earth Asteroid Research (LINEAR)
• Near-Earth Asteroid Tracking (NEAT)
• Spacewatch
• Lowell Observatory Near-Earth-Object Search (LONEOS)
• Catalina Sky Survey (CSS)
• Campo Imperatore Near-Earth Object Survey (CINEOS)
• Japanese Spaceguard Association
• Asiago-DLR Asteroid Survey (ADAS)
• Pan-STARRS

The LINEAR system alone has discovered 138,393 asteroids, as of 20 September 2013.^[17] Among all the surveys, 4711 near-Earth asteroids have been discovered^[18] including over 600 more than 1 km (0.6 mi) in diameter.

Terminology

Euler diagram showing the types of bodies in the Solar System.

A composite image, to scale, of the asteroids that have been imaged at high resolution except Ceres. As of 2011 they are, from largest to smallest: 4 Vesta, 21 Lutetia, 253 Mathilde, 243 Ida and its moon Dactyl, 433 Eros, 951 Gaspra, 2867 Šteins, 25143 Itokawa.

The largest asteroid in the previous image, Vesta (left), with Ceres (center) and the Moon (right) shown to scale.

Traditionally, small bodies orbiting the Sun were classified as comets, asteroids, or meteoroids, with anything smaller than 10 meters across being called a meteoroid (such as in Beech and Steel's 1995 paper).^[19][20] The term "asteroid", from the Greek word for "star-like", never had a formal definition, with the broader term minor planet being preferred by the International Astronomical Union.

However, following the discovery of asteroids below 10 meters in size, Rubin and Grossman in a 2010 paper revised the previous definition of meteoroid to objects between 10 µm and 1 meter in size in order to maintain the distinction between asteroids and meteoroids.^[4] The smallest asteroids discovered (based on absolute magnitude H) are 2008 TS₂₆ with H = 33.2 and 2011 CQ1 with H = 32.1 both with an estimated size of about 1 meter.^[21]

In 2006, the term "small Solar System body" was also introduced to cover both most minor planets and comets.^[22][23] Other languages prefer "planetoid" (Greek for "planet-like"), and this term is occasionally used in English especially for larger minor planets such as the dwarf planets as well as an alternative for asteroids since they are not star-like.^[24] The word "planetesimal" has a similar meaning, but refers specifically to the small building blocks of the planets that existed when the Solar System was forming. The term "planetule" was coined by the geologist William Daniel Conybeare to describe minor planets,^[25] but is not in common use. The three largest objects in the asteroid belt, Ceres, Pallas, and Vesta, grew to the stage of protoplanets. Ceres is a dwarf planet, the only one in the inner Solar System.

When found, asteroids were seen as a class of objects distinct from comets, and there was no unified term for the two until "small Solar System body" was coined in 2006. The main difference between an asteroid and a comet is that a comet shows a coma due to sublimation of near surface ices by solar radiation. A few objects have ended up being dual-listed because they were first classified as minor planets but later showed evidence of cometary activity. Conversely, some (perhaps all) comets are eventually depleted of their surface volatile ices and become asteroid-like. A further distinction is that comets typically have more eccentric orbits than most asteroids; most "asteroids" with notably eccentric orbits are probably dormant or extinct comets.^[26]

For almost two centuries, from the discovery of Ceres in 1801 until the discovery of the first centaur, Chiron, in 1977, all known asteroids spent most of their time at or within the orbit of Jupiter, though a few such as Hidalgo ventured far beyond Jupiter for part of their orbit. When astronomers started finding more small bodies that permanently resided further out than Jupiter, now called centaurs, they numbered them among the traditional asteroids, though there was debate over whether they should be considered asteroids or as a new type of object. Then, when the first trans-Neptunian object (other than Pluto), 1992 QB₁, was discovered in 1992, and especially when large numbers of similar objects started turning up, new terms were invented to sidestep the issue: Kuiper-belt object, trans-Neptunian object, scattered-disc object, and so on. These inhabit the cold outer reaches of the Solar System where ices remain solid and comet-like bodies are not expected to exhibit much cometary activity; if centaurs or trans-Neptunian objects were to venture close to the Sun, their volatile ices would sublimate, and traditional approaches would classify them as comets and not asteroids.

The innermost of these are the Kuiper-belt objects, called "objects" partly to avoid the need to classify them as asteroids or comets.^[27] They are thought to be predominantly comet-like in composition, though some may be more akin to asteroids.^[28] Furthermore, most do not have the highly eccentric orbits associated with comets, and the ones so far discovered are larger than traditional comet nuclei. (The much more distant Oort cloud is hypothesized to be the main reservoir of dormant comets.) Other recent observations, such as the analysis of the cometary dust collected by the Stardust probe, are increasingly blurring the distinction between comets and asteroids,^[29] suggesting "a continuum between asteroids and comets" rather than a sharp dividing line.^[30]

The minor planets beyond Jupiter's orbit are sometimes also called "asteroids", especially in popular presentations.^[31] However, it is becoming increasingly common for the term "asteroid" to be restricted to minor planets of the inner Solar System.^[27] Therefore, this article will restrict itself for the most part to the classical asteroids: objects of the asteroid belt, Jupiter trojans, and near-Earth objects.

When the IAU introduced the class small Solar System bodies in 2006 to include most objects previously classified as minor planets and comets, they created the class of dwarf planets for the largest minor planets—those that have enough mass to have become ellipsoidal under their own gravity. According to the IAU, "the term 'minor planet' may still be used, but generally the term 'Small Solar System Body' will be preferred."^[32] Currently only the largest object in the asteroid belt, Ceres, at about 950 km (590 mi) across, has been placed in the dwarf planet category.

Formation

Artist’s impression shows how an asteroid is torn apart by the strong gravity of a white dwarf.^[33]

It is thought that planetesimals in the asteroid belt evolved much like the rest of the solar nebula until Jupiter neared its current mass, at which point excitation from orbital resonances with Jupiter ejected over 99% of planetesimals in the belt. Simulations and a discontinuity in spin rate and spectral properties suggest that asteroids larger than approximately 120 km (75 mi) in diameter accreted during that early era, whereas smaller bodies are fragments from collisions between asteroids during or after the Jovian disruption.^[34] Ceres and Vesta grew large enough to melt and differentiate, with heavy metallic elements sinking to the core, leaving rocky minerals in the crust.^[35]

In the Nice model, many Kuiper-belt objects are captured in the outer asteroid belt, at distances greater than 2.6 AU. Most were later ejected by Jupiter, but those that remained may be the D-type asteroids, and possibly include Ceres.^[36]

Distribution within the Solar System

The asteroid belt (white) and Jupiter's trojan asteroids (green)

Various dynamical groups of asteroids have been discovered orbiting in the inner Solar System. Their orbits are perturbed by the gravity of other bodies in the Solar System and by the Yarkovsky effect. Significant populations include:

Asteroid belt

The majority of known asteroids orbit within the asteroid belt between the orbits of Mars and Jupiter, generally in relatively low-eccentricity (i.e. not very elongated) orbits. This belt is now estimated to contain between 1.1 and 1.9 million asteroids larger than 1 km (0.6 mi) in diameter,^[37] and millions of smaller ones. These asteroids may be remnants of the protoplanetary disk, and in this region the accretion of planetesimals into planets during the formative period of the Solar System was prevented by large gravitational perturbations by Jupiter.

Trojans

Trojans are populations that share an orbit with a larger planet or moon, but do not collide with it because they orbit in one of the two Lagrangian points of stability, L4 and L5, which lie 60° ahead of and behind the larger body.
The most significant population of trojans are the Jupiter trojans. Although fewer Jupiter trojans have been discovered as of 2010, it is thought that they are as numerous as the asteroids in the asteroid belt.

A couple of trojans have also been found orbiting with Mars.^{[note 3]}

Near-Earth asteroids

Near-Earth asteroids, or NEAs, are asteroids that have orbits that pass close to that of Earth. Asteroids that actually cross Earth's orbital path are known as Earth-crossers. As of June 2016, 14,464 near-Earth asteroids are known^[15] and the number over one kilometre in diameter is estimated to be 900–1,000.

Frequency of bolides, small asteroids roughly 1 to 20 meters in diameter impacting Earth's atmosphere.

Characteristics

Size distribution

Sizes of the first ten asteroids to be discovered, compared to the Moon

Ceres as imaged by Dawn on 4 February 2015

Asteroids vary greatly in size, from almost 1000 km for the largest down to rocks just 1 meter across.^{[note 4]} The three largest are very much like miniature planets: they are roughly spherical, have at least partly differentiated interiors,^[38] and are thought to be surviving protoplanets. The vast majority, however, are much smaller and are irregularly shaped; they are thought to be either surviving planetesimals or fragments of larger bodies.

The dwarf planet Ceres is by far the largest asteroid, with a diameter of 975 km (610 mi). The next largest are 4 Vesta and 2 Pallas, both with diameters of just over 500 km (300 mi). Vesta is the only main-belt asteroid that can, on occasion, be visible to the naked eye. On some rare occasions, a near-Earth asteroid may briefly become visible without technical aid; see 99942 Apophis.

The mass of all the objects of the asteroid belt, lying between the orbits of Mars and Jupiter, is estimated to be about 2.8–3.2×10²¹ kg, or about 4% of the mass of the Moon. Of this, Ceres comprises 0.95×10²¹ kg, a third of the total.^[39] Adding in the next three most massive objects, Vesta (9%), Pallas (7%), and Hygiea (3%), brings this figure up to 51%; whereas the three after that, 511 Davida (1.2%), 704 Interamnia (1.0%), and 52 Europa (0.9%), only add another 3% to the total mass. The number of asteroids then increases rapidly as their individual masses decrease.

The number of asteroids decreases markedly with size. Although this generally follows a power law, there are 'bumps' at 5 km and 100 km, where more asteroids than expected from a logarithmic distribution are found.^[40]

The asteroids of the Solar System, categorized by size and number

Approximate number of asteroids (N) larger than a certain diameter (D)

D	100 m	300 m	500 m	1 km	3 km	5 km	10 km	30 km	50 km	100 km	200 km	300 km	500 km	900 km
N	~25000000	4000000	2000000	750000	200000	90000	10000	1100	600	200	30	5	3	1

Largest asteroids

The relative masses of the twelve largest asteroids known,^[41] compared to the remaining mass of the asteroid belt.^[42]
 

1 Ceres   4 Vesta   2 Pallas   10 Hygiea   31 Euphrosyne

704 Interamnia   511 Davida   532 Herculina   15 Eunomia   3 Juno

16 Psyche   52 Europa   all others

Although their location in the asteroid belt excludes them from planet status, the three largest objects, Ceres, Vesta, and Pallas, are intact protoplanets that share many characteristics common to planets, and are atypical compared to the majority of "potato"-shaped asteroids.

Ceres is the only asteroid with a fully ellipsoidal shape and hence the only one that is a dwarf planet.^[43] It has a much higher absolute magnitude than the other asteroids, of around 3.32,^[44] and may possess a surface layer of ice.^[45] Like the planets, Ceres is differentiated: it has a crust, a mantle and a core.^[45] No meteorites from Ceres have been found on Earth.

Vesta, too, has a differentiated interior, though it formed inside the Solar System's frost line, and so is devoid of water;^[46] its composition is mainly of basaltic rock such as olivine.^[47] Aside from the large crater at its southern pole, Rheasilvia, Vesta also has an ellipsoidal shape. Vesta is the parent body of the Vestian family and other V-type asteroids, and is the source of the HED meteorites, which constitute 5% of all meteorites on Earth.

Pallas is unusual in that, like Uranus, it rotates on its side, with its axis of rotation tilted at high angles to its orbital plane.^[48] Its composition is similar to that of Ceres: high in carbon and silicon, and perhaps partially differentiated.^[49] Pallas is the parent body of the Palladian family of asteroids.

The fourth-most-massive asteroid, Hygiea, is the largest carbonaceous asteroid and, unlike the other largest asteroids, lies relatively close to the plane of the ecliptic.^[50] It is the largest member and presumed parent body of the Hygiean family of asteroids. Between them, the four largest asteroids constitute half the mass of the asteroid belt.

Attributes of largest asteroids
Name	Orbital radius (AU)	Orbital period (years)	Inclination to ecliptic	Orbital eccentricity	Diameter (km)	Diameter (% of Moon)	Mass (×1018 kg)	Mass (% of Ceres)	Density[51] g/cm3	Rotation period (hr)	Axial tilt	Surface temperature
Vesta	2.36	3.63	7.1°	0.089	573×557×446 (mean 525)	15%	260	28%	3.44 ± 0.12	5.34	29°	85–270 K
Ceres	2.77	4.60	10.6°	0.079	975×975×909 (mean 952)	28%	940	100%	2.12 ± 0.04	9.07	≈ 3°	167 K
Pallas	2.77	4.62	34.8°	0.231	580×555×500 (mean 545)	16%	210	22%	2.71 ± 0.11	7.81	≈ 80°	164 K
Hygiea	3.14	5.56	3.8°	0.117	530×407×370 (mean 430)	12%	87	9%	2.76 ± 1.2	27.6	≈ 60°	164 K

Rotation

Measurements of the rotation rates of large asteroids in the asteroid belt show that there is an upper limit. No asteroid with a diameter larger than 100 meters has a rotation period smaller than 2.2 hours. For asteroids rotating faster than approximately this rate, the inertial force at the surface is greater than the gravitational force, so any loose surface material would be flung out. However, a solid object should be able to rotate much more rapidly. This suggests that most asteroids with a diameter over 100 meters are rubble piles formed through accumulation of debris after collisions between asteroids.^[52]

Composition

Cratered terrain on 4 Vesta

The physical composition of asteroids is varied and in most cases poorly understood. Ceres appears to be composed of a rocky core covered by an icy mantle, where Vesta is thought to have a nickel-iron core, olivine mantle, and basaltic crust.^[53] 10 Hygiea, however, which appears to have a uniformly primitive composition of carbonaceous chondrite, is thought to be the largest undifferentiated asteroid. Most of the smaller asteroids are thought to be piles of rubble held together loosely by gravity, though the largest are probably solid. Some asteroids have moons or are co-orbiting binaries: Rubble piles, moons, binaries, and scattered asteroid families are thought to be the results of collisions that disrupted a parent asteroid.

Asteroids contain traces of amino acids and other organic compounds, and some speculate that asteroid impacts may have seeded the early Earth with the chemicals necessary to initiate life, or may have even brought life itself to Earth (also see panspermia).^[54] In August 2011, a report, based on NASA studies with meteorites found on Earth, was published suggesting DNA and RNA components (adenine, guanine and related organic molecules) may have been formed on asteroids and comets in outer space.^[55][56][57]

Asteroid collision – building planets (artist concept).

Composition is calculated from three primary sources: albedo, surface spectrum, and density. The last can only be determined accurately by observing the orbits of moons the asteroid might have. So far, every asteroid with moons has turned out to be a rubble pile, a loose conglomeration of rock and metal that may be half empty space by volume. The investigated asteroids are as large as 280 km in diameter, and include 121 Hermione (268×186×183 km), and 87 Sylvia (384×262×232 km). Only half a dozen asteroids are larger than 87 Sylvia, though none of them have moons; however, some smaller asteroids are thought to be more massive, suggesting they may not have been disrupted, and indeed 511 Davida, the same size as Sylvia to within measurement error, is estimated to be two and a half times as massive, though this is highly uncertain. The fact that such large asteroids as Sylvia can be rubble piles, presumably due to disruptive impacts, has important consequences for the formation of the Solar System: Computer simulations of collisions involving solid bodies show them destroying each other as often as merging, but colliding rubble piles are more likely to merge. This means that the cores of the planets could have formed relatively quickly.^[58]

On 7 October 2009, the presence of water ice was confirmed on the surface of 24 Themis using NASA’s Infrared Telescope Facility. The surface of the asteroid appears completely covered in ice. As this ice layer is sublimated, it may be getting replenished by a reservoir of ice under the surface. Organic compounds were also detected on the surface.^{[59][60][61][62]} Scientists hypothesize that some of the first water brought to Earth was delivered by asteroid impacts after the collision that produced the Moon. The presence of ice on 24 Themis supports this theory.^[61]

In October 2013, water was detected on an extrasolar body for the first time, on an asteroid orbiting the white dwarf GD 61.^[63] On 22 January 2014, European Space Agency (ESA) scientists reported the detection, for the first definitive time, of water vapor on Ceres, the largest object in the asteroid belt.^[64] The detection was made by using the far-infrared abilities of the Herschel Space Observatory.^[65] The finding is unexpected because comets, not asteroids, are typically considered to "sprout jets and plumes". According to one of the scientists, "The lines are becoming more and more blurred between comets and asteroids."^[65] In May 2016, significant asteroid data arising from the Wide-field Infrared Survey Explorer and NEOWISE missions have been questioned,^[66][67][68] but the criticism has yet to undergo peer review.^[69]

Surface features

Most asteroids outside the "big four" (Ceres, Pallas, Vesta, and Hygiea) are likely to be broadly similar in appearance, if irregular in shape. 50-km (31-mi) 253 Mathilde is a rubble pile saturated with craters with diameters the size of the asteroid's radius, and Earth-based observations of 300-km (186-mi) 511 Davida, one of the largest asteroids after the big four, reveal a similarly angular profile, suggesting it is also saturated with radius-size craters.^[70] Medium-sized asteroids such as Mathilde and 243 Ida that have been observed up close also reveal a deep regolith covering the surface. Of the big four, Pallas and Hygiea are practically unknown. Vesta has compression fractures encircling a radius-size crater at its south pole but is otherwise a spheroid. Ceres seems quite different in the glimpses Hubble has provided, with surface features that are unlikely to be due to simple craters and impact basins, but details will be expanded with the Dawn spacecraft, which entered Ceres orbit on 6 March 2015.^[71]

Color

Asteroids become darker and redder with age due to space weathering.^[72] However evidence suggests most of the color change occurs rapidly, in the first hundred thousands years, limiting the usefulness of spectral measurement for determining the age of asteroids.^[73]

Classification

Asteroids are commonly classified according to two criteria: the characteristics of their orbits, and features of their reflectance spectrum.

Orbital classification

Many asteroids have been placed in groups and families based on their orbital characteristics. Apart from the broadest divisions, it is customary to name a group of asteroids after the first member of that group to be discovered. Groups are relatively loose dynamical associations, whereas families are tighter and result from the catastrophic break-up of a large parent asteroid sometime in the past.^[74] Families have only been recognized within the asteroid belt. They were first recognized by Kiyotsugu Hirayama in 1918 and are often called Hirayama families in his honor.

About 30–35% of the bodies in the asteroid belt belong to dynamical families each thought to have a common origin in a past collision between asteroids. A family has also been associated with the plutoid dwarf planet Haumea.

Quasi-satellites and horseshoe objects

Some asteroids have unusual horseshoe orbits that are co-orbital with Earth or some other planet. Examples are 3753 Cruithne and 2002 AA29. The first instance of this type of orbital arrangement was discovered between Saturn's moons Epimetheus and Janus.

Sometimes these horseshoe objects temporarily become quasi-satellites for a few decades or a few hundred years, before returning to their earlier status. Both Earth and Venus are known to have quasi-satellites.

Such objects, if associated with Earth or Venus or even hypothetically Mercury, are a special class of Aten asteroids. However, such objects could be associated with outer planets as well.

Spectral classification

This picture of 433 Eros shows the view looking from one end of the asteroid across the gouge on its underside and toward the opposite end. Features as small as 35 m (115 ft) across can be seen.

In 1975, an asteroid taxonomic system based on color, albedo, and spectral shape was developed by Clark R. Chapman, David Morrison, and Ben Zellner.^[75] These properties are thought to correspond to the composition of the asteroid's surface material. The original classification system had three categories: C-types for dark carbonaceous objects (75% of known asteroids), S-types for stony (silicaceous) objects (17% of known asteroids) and U for those that did not fit into either C or S. This classification has since been expanded to include many other asteroid types. The number of types continues to grow as more asteroids are studied.

The two most widely used taxonomies now used are the Tholen classification and SMASS classification. The former was proposed in 1984 by David J. Tholen, and was based on data collected from an eight-color asteroid survey performed in the 1980s. This resulted in 14 asteroid categories.^[76] In 2002, the Small Main-Belt Asteroid Spectroscopic Survey resulted in a modified version of the Tholen taxonomy with 24 different types. Both systems have three broad categories of C, S, and X asteroids, where X consists of mostly metallic asteroids, such as the M-type. There are also several smaller classes.^[77]

The proportion of known asteroids falling into the various spectral types does not necessarily reflect the proportion of all asteroids that are of that type; some types are easier to detect than others, biasing the totals.

Problems

Originally, spectral designations were based on inferences of an asteroid's composition.^[78] However, the correspondence between spectral class and composition is not always very good, and a variety of classifications are in use. This has led to significant confusion. Although asteroids of different spectral classifications are likely to be composed of different materials, there are no assurances that asteroids within the same taxonomic class are composed of similar materials.

Naming

2013 EC, shown here in radar images, has a provisional designation

A newly discovered asteroid is given a provisional designation (such as 2002 AT4) consisting of the year of discovery and an alphanumeric code indicating the half-month of discovery and the sequence within that half-month. Once an asteroid's orbit has been confirmed, it is given a number, and later may also be given a name (e.g. 433 Eros). The formal naming convention uses parentheses around the number (e.g. (433) Eros), but dropping the parentheses is quite common. Informally, it is common to drop the number altogether, or to drop it after the first mention when a name is repeated in running text.^[79] In addition, names can be proposed by the asteroid's discoverer, within guidelines established by the International Astronomical Union.^[80]

Symbols

The first asteroids to be discovered were assigned iconic symbols like the ones traditionally used to designate the planets. By 1855 there were two dozen asteroid symbols, which often occurred in multiple variants.^[81]

Asteroid	Symbol		Year
1 Ceres	⚳	Ceres' scythe, reversed to double as the letter C	1801
2 Pallas	⚴	Athena's (Pallas') spear	1801
3 Juno	⚵	A star mounted on a scepter, for Juno, the Queen of Heaven	1804
4 Vesta	⚶	The altar and sacred fire of Vesta	1807
5 Astraea		A scale, or an inverted anchor, symbols of justice	1845
6 Hebe		Hebe's cup	1847
7 Iris		A rainbow (iris) and a star	1847
8 Flora		A flower (flora), specifically the Rose of England	1847
9 Metis		The eye of wisdom and a star	1848
10 Hygiea		Hygiea's serpent and a star, or the Rod of Asclepius	1849
11 Parthenope		A harp, or a fish and a star; symbols of the sirens	1850
12 Victoria		The laurels of victory and a star	1850
13 Egeria		A shield, symbol of Egeria's protection, and a star	1850
14 Irene		A dove carrying an olive branch (symbol of irene 'peace') with a star on its head,[82] or an olive branch, a flag of truce, and a star	1851
15 Eunomia		A heart, symbol of good order (eunomia), and a star	1851
16 Psyche		A butterfly's wing, symbol of the soul (psyche), and a star	1852
17 Thetis		A dolphin, symbol of Thetis, and a star	1852
18 Melpomene		The dagger of Melpomene, and a star	1852
19 Fortuna		The wheel of fortune and a star	1852
26 Proserpina		Proserpina's pomegranate	1853
28 Bellona		Bellona's whip and lance[83]	1854
29 Amphitrite		The shell of Amphitrite and a star	1854
35 Leukothea		A lighthouse beacon, symbol of Leucothea[84]	1855
37 Fides		The cross of faith (fides)[85]	1855

In 1851,^[86] after the fifteenth asteroid (Eunomia) had been discovered, Johann Franz Encke made a major change in the upcoming 1854 edition of the Berliner Astronomisches Jahrbuch (BAJ, Berlin Astronomical Yearbook). He introduced a disk (circle), a traditional symbol for a star, as the generic symbol for an asteroid. The circle was then numbered in order of discovery to indicate a specific asteroid (although he assigned ① to the fifth, Astraea, while continuing to designate the first four only with their existing iconic symbols). The numbered-circle convention was quickly adopted by astronomers, and the next asteroid to be discovered (16 Psyche, in 1852) was the first to be designated in that way at the time of its discovery. However, Psyche was given an iconic symbol as well, as were a few other asteroids discovered over the next few years (see chart above). 20 Massalia was the first asteroid that was not assigned an iconic symbol, and no iconic symbols were created after the 1855 discovery of 37 Fides.^[87] That year Astraea's number was increased to ⑤, but the first four asteroids, Ceres to Vesta, were not listed by their numbers until the 1867 edition. The circle was soon abbreviated to a pair of parentheses, which were easier to typeset and sometimes omitted altogether over the next few decades, leading to the modern convention.^[82]

Exploration

951 Gaspra is the first asteroid to be imaged in close-up (enhanced color).

Vesta imaged by the Dawn spacecraft

Several views of 433 Eros in natural colour

Until the age of space travel, objects in the asteroid belt were merely pinpricks of light in even the largest telescopes and their shapes and terrain remained a mystery. The best modern ground-based telescopes and the Earth-orbiting Hubble Space Telescope can resolve a small amount of detail on the surfaces of the largest asteroids, but even these mostly remain little more than fuzzy blobs. Limited information about the shapes and compositions of asteroids can be inferred from their light curves (their variation in brightness as they rotate) and their spectral properties, and asteroid sizes can be estimated by timing the lengths of star occulations (when an asteroid passes directly in front of a star). Radar imaging can yield good information about asteroid shapes and orbital and rotational parameters, especially for near-Earth asteroids. In terms of delta-v and propellant requirements, NEOs are more easily accessible than the Moon.^[88]

The first close-up photographs of asteroid-like objects were taken in 1971, when the Mariner 9 probe imaged Phobos and Deimos, the two small moons of Mars, which are probably captured asteroids. These images revealed the irregular, potato-like shapes of most asteroids, as did later images from the Voyager probes of the small moons of the gas giants.

The first true asteroid to be photographed in close-up was 951 Gaspra in 1991, followed in 1993 by 243 Ida and its moon Dactyl, all of which were imaged by the Galileo probe en route to Jupiter.

The first dedicated asteroid probe was NEAR Shoemaker, which photographed 253 Mathilde in 1997, before entering into orbit around 433 Eros, finally landing on its surface in 2001.

Other asteroids briefly visited by spacecraft en route to other destinations include 9969 Braille (by Deep Space 1 in 1999), and 5535 Annefrank (by Stardust in 2002).

In September 2005, the Japanese Hayabusa probe started studying 25143 Itokawa in detail and was plagued with difficulties, but returned samples of its surface to Earth on 13 June 2010.

The European Rosetta probe (launched in 2004) flew by 2867 Šteins in 2008 and 21 Lutetia, the third-largest asteroid visited to date, in 2010.

In September 2007, NASA launched the Dawn spacecraft, which orbited 4 Vesta from July 2011 to September 2012, and has been orbiting the dwarf planet 1 Ceres since 2015. 4 Vesta is the second-largest asteroid visited to date.

On 13 December 2012, China's lunar orbiter Chang'e 2 flew within 2 miles (3.2 km) of the asteroid 4179 Toutatis on an extended mission.

Planned and future missions

The Japan Aerospace Exploration Agency (JAXA) launched the Hayabusa 2 probe in December 2014, and plans to return samples from 162173 Ryugu in December 2020.

In May 2011, NASA selected the OSIRIS-REx sample return mission to asteroid 101955 Bennu; it launched on September 8, 2016.

In early 2013, NASA announced the planning stages of a mission to capture a near-Earth asteroid and move it into lunar orbit where it could possibly be visited by astronauts and later impacted into the Moon.^[89] On 19 June 2014, NASA reported that asteroid 2011 MD was a prime candidate for capture by a robotic mission, perhaps in the early 2020s.^[90]

It has been suggested that asteroids might be used as a source of materials that may be rare or exhausted on Earth (asteroid mining), or materials for constructing space habitats (see Colonization of the asteroids). Materials that are heavy and expensive to launch from Earth may someday be mined from asteroids and used for space manufacturing and construction.

In the U.S. Discovery program the Psyche spacecraft proposal to 16 Psyche and Lucy spacecraft to Jupiter trojans made it to the semifinalist stage of mission selection.

Fiction

Asteroids and the asteroid belt are a staple of science fiction stories. Asteroids play several potential roles in science fiction: as places human beings might colonize, resources for extracting minerals, hazards encountered by spacecraft traveling between two other points, and as a threat to life on Earth or other inhabited planets, dwarf planets and natural satellites by potential impact.