Ångström (Å)

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	anomalistic month
Ångström (Å) A unit of length used in spec-	anisotropic turbulence See isotropic turbu-
troscopy, crystallography, and molecular struc-	lence.
ture, equal to 10−10 m.

angular diameter distance Distance of a galaxy or any extended astronomical object estimated by comparing its physical size to the angle subtended in the sky: if D is the diameter of the galaxy and δ the angle measured in the sky, then dA = D/ tan δ D/δ. For a Friedmann model with density Io in units of the critical density, and zero cosmological constant, the angular diameter dA of an object at redshift z can be given in closed form:

dA =		2cHo−1
		Io2(1 + z)2
	Ioz + (Io − 2) (Ioz + 1)1/2 − 1

Other operational deﬁnitions of distance can be made (see luminosity distance) depending on the intrinsic (assumed to be known) and the observed properties to be compared.

angular momentum L = r × p, where × indicates the vector cross product, r is the radius vector from an origin to the particle, and p is the momentum of the particle. L is a pseudovector whose direction is given by r, p via the righthand rule, and whose magnitude is

|L| = |r||p| sin θ ,

where θ is the angle between r and p. For a body or system of particles, the total angular momentum is the vectorial sum of all its particles. In this case the position is generally measured from the center of mass of the given body. See pseu- dovector, right-hand rule, vector cross product.

angular velocity (ω) The angle through which a body rotates per unit time; a pseudovector with direction along the axis given by the right-hand rule from the rotation.

anisotropic A material whose properties (such as intrinsic permeability) vary according to the direction of ﬂow.

anisotropic universe A universe that expands at different rates in different directions. The simplest example is Kasner’s model (1921) which describes a space that has an ellipsoidal rate of expansion at any moment in time. Moreover, the degree of ellipticity changes with time. The generic Kasner universe expands only along two perpendicular axes and contracts along the third axis.

anisotropy The opposite of isotropy (invariance under rotation), i.e., variation of properties under rotation. For example, if a rock has a fabric such as layering with a particular orientation,

.then phases of seismic waves may travel at different speeds in different directions through the rock, according to their alignment with the fabric. The wave speed along an axis varies when the axis is rotated through the rock with respect to the fabric, i.e., it is anisotropic. In terms of the material properties of the rock, this would be associated with an elasticity tensor that varies under rotation. This occurs in the real Earth: for example, wave speeds are observed to be faster in the upper mantle under the ocean in the direction perpendicular to the mid-ocean ridges. The Earth’s inner core has been determined to be anisotropic, with (to a ﬁrst approximation) faster wave speeds parallel to the Earth’s rotation axis than in directions perpendicular to it. Many other physical properties may also be anisotropic, such as magnetic susceptibility, diffusivity, and turbulence.

annual ﬂood The maximum discharge peak ﬂow during a given water year (October 1 through September 30) or annual year.

annular eclipse A solar eclipse in which the angular size of the moon is slightly too small to obscure the entire solar photosphere. As a result, a ring (“annulus”) of visible photosphere surrounds the dark central shadow of the moon. Annular eclipse occurs when the moon is near apogee, giving it a smaller angular size.

anisotropic scattering	Scattering that is not
spherically symmetric.	anomalistic month	See month.

anomalistic year

anomalistic year See year.

anomalous resistivity For a fully ionized collision-dominated plasma, such as the solar corona, the extremely low value of the classical resistivity ensures that the rate of energy release is negligible since the ﬁeld lines are prevented from diffusing through the plasma. In a turbulent plasma, the resistivity can be enhanced via the correlation of particles over length scales much larger than the usual plasma length scale, the Debye length. This increases the collision frequency and, consequently, the resistivity. This turbulently enhanced resistivity is known as anomalous resistivity.

anomaly See mean anomaly, true anomaly.

anomaly, South Atlantic The region above the southern Atlantic Ocean, in which the radiation belt descends to heights lower than elsewhere, so that near-earth satellites, nominally below the radiation belt, are likely to encounter peak radiation levels there.

The “anomaly” is caused by the non-dipole components of the main magnetic ﬁeld of the earth, which create a region of abnormally weak magnetic ﬁeld there (in the eccentric dipole model of the Earth’s ﬁeld, the dipole is furthest away from that region).

Each ion or electron trapped along a ﬁeld line in the Earth’s ﬁeld has a mirroring ﬁeld intensity Bm at which its motion along the line is turned around. Such particles also drift, moving from one ﬁeld line to the next, all the way around the Earth. If in this drift motion the mirror point where the particle is turned back (and where the ﬁeld intensity equals Bm) passes above the South Atlantic anomaly, it probably reaches an altitude lower there than anywhere else. The radiation belt thus extends lower in this region than elsewhere, and the loss of belt particles by collisions with atmospheric molecules is likely to occur there.

anorthosite Maﬁc igneous rock type that consists predominantly of the mineral plagioclase (silicates of feldspar group) that seems to have differentiated at high temperature at the crust-mantle boundary, where plagioclase crystallized before separating from the main magma

body and rose through the crust in a semi-molten state. Anorthosites are rare on Earth, but appear to be more common on the moon. See igneous.

anoxia The condition arising from insufﬁcient ambient oxygen to support biological respiration, or the effect of such lack.

Antarctic circle The latitude 66◦32 S. South of this line the sun does not rise on the southern winter solstice and does not set on the day of the southern summer solstice.

antarctic circumpolar current South Ocean current circling the Antarctic continent eastward. The largest oceanic current in terms of volume. Also called the West Wind Drift. Spans 40◦ to 60◦ South. Very close to the Antarctic continent is the East Wind Drift, driven by prevailing easterly winds near the continent.

Antarctic ozone depletion A rapid and accelerating decrease in the ozone over Antarctica each September and October, as the socalled “ozone hole”, which is due to the chemical activity of the chlorine atoms contained in the chloroﬂuorocarbons (CFCs or “Freons”). It was ﬁrst reported on May 16, 1985, by J.C. Farman et al. from the British Antarctic Survey published in the British journal Nature. Field campaigns incorporating remote sensing, in situ and satellite observations, have now clearly demonstrated that man-made CFCs and some other halogenated industrial compounds are responsible for this dramatic loss of ozone. These chemicals are released into the atmosphere where their long lifetimes (50 to 100 years) allow them to be transported to the middle and upper stratosphere, where they can be decomposed by shortwave solar radiation to release their chlorine and bromine atoms. These free radicals are extremely reactive and can destroy ozone readily, but in most parts of the atmosphere they react to form harmless “reservoir” compounds. In the Antarctic, however, very low temperatures in the late winter and early spring stratosphere permit the formation of natural Polar Stratospheric Cloud (PSC) particles, which provide sites for surface reactions in which the reservoir halogens revert to ozone-destroying radicals with the help of sunlight. The severity of the ozone loss is

anticyclone

also due, in part, to the special meteorology of the Antarctic winter stratosphere, which isolates the ozone hole, preventing the replenishment of ozone and the dilution of ozone destroying compounds. Thus, the ozone hole results from the combination of a range of special local and seasonal conditions with man-made pollution; its appearance in recent years simply corresponds to the build-up of anthropogenic halogenated gases in the atmosphere.

The production of CFCs and some other compounds potentially damaging to ozone is now limited by the Montreal Protocol and its amendments. However, the lifetimes of these gases are long, and although it is thought that stratospheric chlorine levels will peak in the next few years, recovery of the ozone hole may not be detectable for a number of years, and full recovery, to pre-ozone hole conditions, may not occur until the middle of the twenty-ﬁrst century.

Antarctic ozone hole A large annual decrease in the ozone content of the ozone layer over the Antarctic region during the southern hemisphere spring. Discovered in 1985, the ozone hole presumably appeared in the early 1980s and continued to increase in severity, size, and duration through the 1990s. In recent years, up to two-thirds of the total amount of ozone has been lost by mid-October, largely as a result of losses of over 90% in the layer between 14 and 22 km where a large fraction of the ozone is normally found. The onset of the ozone losses occurs in September, and the ozone hole usually recovers by the end of November.

Antarctic Zone In oceanography, the region in the Southern Ocean northward of the Continental Zone (which lies near the continent). It is separated from the Continental Zone by a distinct oceanographic front called the Southern Antarctic Circumpolar Current front.

Antares 0.96 magnitude star, of spectral type M1, at RA 16h 29m 24.3, dec −26◦25 55 .

anthropic principle The observation that humankind (or other sentient beings) can observe the universe only if certain conditions hold to allow human (or other sentient) existence. Whenever one wishes to draw general conclusions

from observations restricted to a small sample, it is essential to know whether the sample should be considered to be biased and, if so, how. The anthropic principle provides guidelines for taking account of the kind of bias that arises from the observer’s own particular situation in the world. For instance, the Weak Anthropic Principle states that as we exist, we occupy a special place of the universe. Since life as we know it requires the existence of heavy elements such as C and O, which are synthesized by stars, we could not have evolved in a time less than or of the order of the main sequence lifetime of a star. This principle can be invoked to explain why the age of astronomical objects is similar to the Hubble time. This time scale would represent the lapse of time necessary for life to have evolved since the Big Bang. On the other hand, in the Steady State Cosmology, where the universe has no origin in time, the coincidence mentioned above has no “natural” explanation.

In the more controversial strong version, the relevant anthropic probability distribution is supposed to be extended over an ensemble of cosmological models that are set up with a range of different values of what, in a particular model, are usually postulated to be fundamental constants (such as the well-known example of the ﬁne structure constant). The observed values of such constants might be thereby explicable if it could be shown that other values were unfavorable to the existence of anthropic observers.

Thus the Strong Anthropic Principle states that the physical properties of the universe are as they are because they permit the emergence of life. This teleological argument tries to explain why some physical properties of matter seem so ﬁne tuned as to permit the existence of life. Slight variations in nuclear cross-sections could have inhibited the formation of heavy elements in stars. A different ﬁne-structure constant would lead to a different chemistry and presumably life would not exist.

anticyclone A wind that blows around a high pressure area, in the opposite sense as the Earth’s rotation. This results in a clockwise rotation in the Northern Hemisphere and counterclockwise in the Southern Hemisphere.

anticyclonic

anticyclonic Any rotation that is opposite the sense of the locally measured Earth rotation: clockwise in the Northern Hemisphere, counterclockwise in the Southern Hemisphere.

antidune Dunes that form in rivers or canals at relative high ﬂow speeds. Dunes and antidunes are similar in shape, but the water surface above a dune is out of phase with the bed, whereas the water surface above antidunes is in phase with the bed. Antidunes and the corresponding surface waves often march gradually upstream.

antinode A point on a standing wave where the ﬁeld has maximum amplitude. For a standing water wave, this corresponds to a point with maximum vertical motion. For a standing wave transverse on a string, the antinode corresponds to a point which has maximum motion in a direction normal to that axis deﬁned by the string.

antiparticle A particle having the same mass as a given elementary particle and a charge equal in magnitude but opposite in sign.

apastron In planetary motion, the farthest distance achieved from the gravitating central star. Generically one says apapse. Speciﬁc applications are aphelion, when referring to the motion of planets in our solar system; apogee, when referring to orbits around the Earth. Similar constructions are sometimes invented for orbits about the moon or other planets.

aperture correction The difference between the photometric magnitude of an object as measured with two different-sized apertures.

When making photometric measurements of stars on an image, the resulting magnitudes are often referenced to the light measured in a ﬁxedsize aperture (perhaps a few arcseconds in diameter). However, this aperture is usually smaller than the full proﬁle of the star (which can be as large as an arcminute or more for light that is still detectable above the background). The aperture correction is the difference between the small, measurement aperture and a larger, reference aperture that is large enough to include any frame-to-frame variations that may be due to seeing or other variable effects. The aper-

ture correction is calculated for each frame and added to the magnitude of the objects in the frame to get a total magnitude. The aperture correction can be calculated by modeling the stellar proﬁle, then integrating it out to inﬁnity (or some large radius), or it may be calculated by simply measuring a number of isolated bright stars in an image using the small and large apertures and taking the average difference.

aperture synthesis Method whereby the information-gathering capability of a large aperture is achieved by two or more smaller apertures operating together as interferometers.

aphelion The point in an elliptical orbit around the sun that is farthest from the sun. (The perihelion is the point closest to the sun.) The time of aphelion passage for the Earth is around July 4.

aphotic zone That portion of the ocean where light is insufﬁcient for plants to carry on photosynthesis.

Ap index The planetary index for measuring the strength of a disturbance in the Earth’s magnetic ﬁeld deﬁned over a period of one day from a set of standard stations around the world. See geomagnetic activity.

apoapsis The point in an elliptical orbit where the orbiting body is the farthest distance from the body being orbited. (The periapsis is the point of the shortest distance.) When the sun is the central body, the point of apoapsis is called the aphelion.

Apollo asteroid One of a family of minor planets with Earth-crossing orbits. The majority of asteroids orbit between Jupiter and Mars, but the Apollos cross Earth’s orbit and thus pose at least the potential for collision with Earth. It is estimated that there are at least 2000 Earthcrossing Apollo asteroids with diameters of 1 km or larger, and at least 106 larger than 50 meters.

Impact with an asteroid 1 km in size would deposit about 1021 J of energy if it impacted the Earth. This is about 105 Mtons of equivalent nuclear weapons, equivalent to exploding a good fraction of all the nuclear weapons on Earth at