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characteristics, method of

This discrepancy is thought to be due to the fact that the Earth is deformable rather than rigid and also due to core-mantle and mantle-ocean coupling. The damping and excitation of the wobble are not entirely understood.

Chandrasekhar limit (or Chandrasekhar mass) The maximum mass of cold matter that can be supported by degeneracy pressure, especially of electrons. This sets the maximum possible masses for white dwarfs and for the cores of massive stars before they collapse (see supernovae, type II). The ﬁrst correct calculations were done by Chandrasekhar in 1930–33, for which he eventually received a Nobel Prize. The maximum possible mass for a white dwarf is about 1.4 solar masses if it is made of helium, carbon, and oxygen, rather less if it is made of heavier elements. The corresponding limit for a neutron star is sometimes called the Oppenheimer–Volkoff limit.

chaos Property of system described by a set of nonlinear equations, such that for at least some initial data the deterministic solutions diverge exponentially from each other in time.

chaotic cosmology The suggestion by Charles Misner (1967) that the universe began in a highly chaotic state but smoothed out into the present ordered state in the course of time via dissipative processes.

chaotic system A complex system exhibiting chaos.

chaotic terrain Part of the highland-lowland boundary of Mars, located between longitudes 10◦ W and 50◦ W and latitudes 20◦ S and 10◦ N, in the old cratered terrain between Lunae Planum and Chryse Planitia. It regularly connects with the large outﬂow channels draining northwards and merges with Valles Marineris to the west. Crater counts indicate it formed between the early to late Hesperian.

By analogy with Earth, it has been proposed to be terrain in which the ground has collapsed, to produce jumbled arrays of blocks at lower elevations than the surroundings. The depth to which collapse occurred becomes less to the east, away from Valles Marineris. Thus, its for-

mation may in some way be related to the formation of Valles Marineris.

Chapman layer Simple formal description for an atmospheric layer such as ionospheric layers. Assumptions are the atmosphere consists of one atomic species only, and the incoming radiation is monochromatic. According to the barometric height formula, the atmospheric density decreases with increasing height. The intensity of the incoming ionizing electromagnic radiation increases with increasing height: it is maximal at the top of the atmosphere and then is absorbed according to Bougert–Lambert–Beer’s law. Both effects combined lead to a Chapman proﬁle: at a certain height, the ionization, and, therefore, also the charge density, is highest. Below, it decreases as the intensity of the ionizing radiation decreases. At higher altitudes, it decreases too because the number of particles available for ionization decreases.

zDensity

	Intensity of the
Ionization	ionizing radiation
Ionization

Chapman layer.

characteristic earthquake Major faults in active tectonic regions have large characteristic earthquakes. The 1906 San Francisco earthquake was the last characteristic earthquake on the northern section of the San Andreas fault. The southern section of the San Andreas fault had a characteristic earthquake in 1857.

characteristics, method of A mathematical technique, where a problem represented by a set of partial differential equations is converted to

charge exchange

an ordinary differential equation problem. The solution may be obtained graphically or by numerical techniques. Used in the study of open channel ﬂow and elsewhere.

charge exchange An atomic process that may occur when a fast ion collides with a neutral atom, in which an electron is transferred from the atom to the ion. As a result, the atom becomes a slow ion, while the ion becomes an energetic neutral atom (ENA). It strongly depends on energy (also on the type of ion) and is much more pronounced around 5 keV than at 50 keV.

Charge exchange is believed to be the major mechanism by which ions produced in a magnetic storm are lost, leading to the decay of the enhanced ring current associated with the storm. Ions of that ring current are magnetically trapped by the Earth, but if they change into ENAs, the magnetic ﬁeld no longer affects them, and they move in straight lines, making them a possible means of remotely sensing the ring current.

Charles’ Law At constant pressure, the volume of an ideal gas is directly proportional to the absolute temperature of that gas.

Charon Moon of Pluto, although it is close enough in size to Pluto to be considered a double planet. It was discovered by Christy in 1978. Its orbit has an eccentricity of 0.0001, an inclination of 98.3◦, and a semimajor axis of 1.96×104 km. Both Pluto and Charon rotate in such a way as to always keep the same face towards each other. Its radius is not well determined, with measurements giving between 590 and 630 km. Its mass and density are not well known. Its geometric albedo is 0.36, and it orbits every 6.387 Earth days.

chemically peculiar star A star whose surface composition deviates from the standard set by the sun (3/4 hydrogen, 1/4 helium, a few percent of everything else in standard proportions: See cosmic abundance). This happens for one of three reasons: (1) products of nuclear reactions in the star itself have been mixed to the surface (as in carbon stars or R Coronae Borealis stars),

(2) products of nuclear reactions in a companion star have been transferred to the observed, or (3) a combination of radiation pressure and

a very steady atmosphere has separated out unusual atoms, often in regions of strong magnetic ﬁelds. Europium and strontium are among the elements sometimes greatly overabundant in the third sort of star, called an Ap star (A for its spectral type, p for peculiar).

chenier Beach ridge.

Chezy coefﬁcient, Chezy equation The

Chezy equation is used to relate ﬂow speed to ﬂow geometry and other parameters. The equation is V = C RSf , where V is ﬂow speed, C is the Chezy coefﬁcient, R = A/P = hydraulic radius, and Sf is friction slope (head loss per unit length). The Chezy coefﬁcient is determined primarily by channel roughness but decreases with increasing roughness. An alternative to the Manning equation.

chlorinity The concentration of chloride ions by mass in seawater (g/kg). Typical ocean chlorinity is of order 19 g/kg of seawater. There is an observed constant ratio of chlorinity to salinity: Salinity in parts per thousand = (1.80655) (chlorinity in parts per thousand). See salinity.

chlorophyll Chemical compounds occurring in plants that enable radiant energy to be converted to chemical energy in the process of photosynthesis; there are several types (e.g., denoted as chl a, b, etc.) with chl a typically the most abundant.

chondrite A relatively abundant stony meteorite characterized by the presence of small ( 1 mm) glassy spherical inclusions called chondrules. Chondrites are further subdivided into ordinary, carbonaceous, and enstatite chondrites, depending on details of composition and thermal processing.

chondrite, carbonaceous A form of chondrite with high abundances of water, organic, and other volatile materials. This, and the fact that the heavier elements are present in roughly solar proportions, indicates that these bodies have been little processed. These meteorites are further classiﬁed by their volatile content into CI (or C1), which are most nearly solar in composition, CII (CM) and CIII (CO or CV),

cigar distribution

which are successively poorer in volatile content. C1 chondrites do not contain chondrules but are chemically very similar to other chondrites.

chondrite, ordinary The most common form of meteorite. Composed mostly of olivine with signiﬁcant amounts of other metallic silicates. Ordinary chondrites are further classiﬁed according to their iron content into H (high iron), L (low iron), and LL (very low iron) chondrites. An additional subdivision, E (enstatite), is characterized by lower Mg/Si ratios, which give rise to a composition richer in enstatite and containing little olivine.

chondrule Small spheroidal ( 1 mm) glassy bead of silicates (olivine or enstatite) found within stony meteorites, called chondrites. Chondrules generally have a composition very similar to the matrix material of the chondrite in which they are embedded, but this material has undergone an episode of melting and rapid quenching early in the history of solar system formation. The actual process causing the melting is poorly understood.

Christoffel symbol	See afﬁne connection,
metricity of covariant derivative.
chromatic aberration	A situation arising in

lens-based (refracting) optical instruments, in which light of different colors cannot be brought into focus at the same point, arising because glass or other lens material is dispersive and so produces different deviation of the path of light of different colors.

chromosphere The layer in the sun or a cool star between the photosphere and corona. The layer is relatively thin and at a temperature of about 10,000 K in the sun. During a total solar eclipse, it is seen as a red ring (hence the name) around the moon’s shadow. Outside eclipse, it contributes emission lines to the spectrum of the sun (or star). The intensity of the chromosphere varies through the solar cycle.

chromospheric evaporation The upward

ﬂow of hot plasma in a solar ﬂare resulting from the fast deposition of energy in the chro-

mosphere. In the chromospheric evaporation process, the energy released during a solar ﬂare rapidly dissipates in the chromosphere (typically assumed to involve non-thermal electron beams or a thermal conduction front). The chromosphere is suddenly heated to coronal temperatures and subsequently expands upward. Evidence for these ﬂows generally comes from blueshifts measured in spectral lines, such as those observed by a Bragg Crystal Spectrometer.

chromospheric heating The process behind the enhanced temperature of the sun’s chromosphere above that of the sun’s surface (photosphere). Radiation is the bulk energy loss mechanism in the chromosphere, conductive losses being negligible, and both the photosphere and corona contribute to its heating. The amount of heating required to balance radiative losses in the chromosphere is about 4 × 103 Wm−2 for quiet sun and coronal hole regions. This rises to 2 × 104 Wm−2 for the chromosphere in active regions. The exact nature of the heating mechanism is uncertain.

chronological future/past The chronological future/past I±(S) of a set S is deﬁned as the union of all points that can be reached from S by a future/past-directed time-like curve. (A time-like curve must be of non-zero extent, thus isolated points are excluded.)

CHUMP (Charged Hypothetical Ultra Massive Particle) In the framework of grand uniﬁcation models, hypothetical CHUMPs are among the candidates to explain the missing mass problem in the universe (the fact that the observed luminous matter cannot account for the dynamical properties observed on large scales). As they carry an electric charge, they need to be very massive, otherwise they would already have been detected. An example of such a particle is the vorton, which would appear in theories having current-carrying cosmic strings. See dark matter, vorton.

cigar distribution In plasma physics, a pitch angle distribution in which the highest intensities are ﬁeld aligned, so that a contour of the ﬂux

circulation

density against polar angle θ resembles a cigar. See pancake distribution, conics.

circulation In ﬂuid ﬂow, the circulation of a closed loop (a circuit) C, which is the boundary of a topological disk S, is

v · dx

C=δS

that is ﬁxed in the ﬂuid, i.e., moves with the ﬂuid elements. According to Stokes’ theorem, this is equal to

× v · ndS ,

where × v is the curl of v, also called the circulation of v. Here n is the unit normal to the surface S. If the circulation vanishes, then v = φ for some scalar potential φ.

cirrus See cloud classiﬁcation.

CISK (Convective Instability of the Second Kind) An atmospheric instability responsible for hurricane and other intense “warm core” disturbances which form over the sea. In contrast to baroclinic instability, which feeds upon preexisting horizontal temperature gradients, these storms generate their own “warm core” by absorbing latent and sensible heat from the sea surface and converting latent heat into sensible heat in the rain areas near their centers.

civil time The time in use by a nation’s civilian population, as legislated by its government. It approximates the standard time in its time zone, aside from daylight savings adjustments.

civil twilight See twilight.

Clapeyron–Clausius equation An equation that gives the relation between the vapor pressure of a liquid and its temperature. It is

dP	=		L12
dT		T (v2 − v1)

where L12 is the latent heat absorbed for transferring from phase 1 to phase 2, v1 and v2 are the volumes of phase 1 and phase 2, respectively.

Applied to a water and water vapor system, it is

dEsw	=	Lv	≈	Lv
dT	=	T (vv − vw)	≈	T · vv

where Esw is saturated vapor pressure at the water surface, Lv is condensation latent heat, and vv and vw are the volumes of unit mass vapor and water. Thus

Esw = Es(T0) · exp	RvT0		− RvvT
		Lv		L

where Rv is the water vapor gas constant, and T0 is reference temperature. If T0 = 273.15 K, then Es(T0) = 6.11 hP a.

Applied to an ice and water vapor system, it

	dEsi	≈			Ls
	dT	≈		T · vv		− RvT
Esi = Es(T0) · exp			RvT0			− RvT
					Ls		Ls

where Esi is saturated vapor pressure at the ice surface, Ls is sublimation latent heat. In general 273.15 K is the reference temperature, then

Esw	=	6.11 · exp	Rw		273.15	− T
				Lv	1		1
Esi	=	6.11 · exp	Rw		273.15	− T		.
				Ls	1	1

The unit of Esw and Esi is hPa.

clapotis A term used in the study of water waves on a free surface, such as waves on the surface of the ocean. Denotes a complete standing wave — a wave which does not travel horizontally but instead has distinct nodes and antinodes. Results from complete reﬂection of waves from a structure; may also arise in other scenarios.

classical radius of electron	The quantity
e2/mc2 = 2.82 × 10−13 cm.

clathrate When water freezes, it can trap other, more volatile gases in “cages” formed by the crystal structure. As long as the water ice is solid, it will hold the trapped gas, even at temperatures where that gas would ordinarily sublimate. The ice-gas combination is called a clathrate, and the vapor pressure above such a clathrate generally has a value between that of the water and that of the gas.

clay A ﬁne-grained sediment, with particle sizes less than 4 µm (deﬁnitions vary). Inter-