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Newtonian invariance

where ρ is the mass density of the object at the point r and dV is the volume element at that position. From this latter expression one also has the partial differential equation

2φ = 4πρ

where 2 is the Laplacian. See density, gradient.

Newtonian invariance

See Galilean invari-

ance.

 

Newtonian relativity See Galilean relativity.

Newtonian simultaneity In Newtonian Mechanics, since time is absolute, the simultaneity of two events is independent of the reference system. That is if one observer finds that two given events are simultaneous, then all other observers regardless of their respective reference systems will also observe that the two events are simultaneous. This does not in general hold in Relativistic Mechanics.

Newton (N) Unit of force equal to 1 m kg s−2.

Newton’s laws of motion 1. A body at rest remains at rest, and a body in uniform motion remains in uniform motion, unless acted on by an external force.

2. The acceleration of a body is equal to the net applied force, divided by the mass of the body:

a= F/m .

3.For every force there is an equal and opposite reaction force.

The third law is exemplified by a person attracted by gravity toward a planet. There is simultaneously an equal opposite force attracting the planet toward the person.

NGC 5195 Irregular Galaxy, Canes Venatici at RA 13h30m.0, dec +47◦16 , mV = 9.6. Companion of M51, lying about 4 35 North of M101.

Nielsen–Olesen vortex (1973) In condensed matter physics, and in cosmology, a defect (a string) that arises from a breaking of a high temperature symmetry, in a model with a complex

(i.e., 2-component) scalar (Higgs) field φ, and a massless gauge vector field Aµ. The phase transition requires a potential for φ which has a minimum at a nonzero value σ of |φ| and which is indifferent to the complex phase of φ. One finds a physical “magnetic” flux proportional to

the circulation of the gauge field · (

A d2 Aµ is the gauge field associated with the local U(1)

symmetry). Here, is taken along an arbi- d2

trary closed loop encircling the defect in physical space. Moreover, this flux is quantized, since solutions of the Higgs field φ can have a complex phase that increases by multiples of 2π as one moves around the vortex.

Kinetic terms of the Higgs field contribute to the overall energy of the configuration in the form of a logarithmically divergent energy per unit length. The presence of the gauge field Aµ cancels this divergence and hence the energy of the configuration is confined to a cylindrical core of radius roughly given by the Compton wavelengths of the Higgs and gauge bosons. Such vortices exist in superconductors, and represent the typical model for the description of cosmic strings. See Abelian Higgs model, cosmic string, local topological defect, winding num- ber.

nimbus See cloud classification.

nitrogen Colorless, odorless gas, N, atomic number 7. Natural atomic weight 14.0067. Melting point 63.05 K, boiling point 77.36 K. Naturally occurring isotopes 14N (99.6%) and 15N (0.4%). Relatively inert at low temperatures, but its compounds are vital for biological processes. Nitrogen constitutes about 78% (volume) of the Earth’s atmosphere.

Noachian Geophysical epoch on the planet Mars, more than 3.5 Gy BP, exemplified by the oldest and heavily cratered regions lying in the southern hemisphere of Mars.

nocturnal Pertaining to occurrences during the night, as opposed to diurnal occurrences.

nodal month See month.

© 2001 by CRC Press LLC

non-thermal spectral energy distribution

node A point of zero displacement. Standing waves in a water basin have nodes and antinodes.

no-hair theorems (Also known as uniqueness theorems.) A set of propositions proved in classical general relativity which restricts possible black hole geometries. All black hole metrics (including dilatonic black holes arising in some string theories) belong to a small number of families. Each family is identified by the set of Killing vectors on the event horizon (see Killing horizon) or, equivalently, by the isometry of the asymptotically flat space-time outside the event horizon.

For instance, if the black hole is spherically symmetric then it is described by the Schwarzschild metric if electrically neutral (see Birkhoff’s theorem) and by the Reissner– Nordström metric if the net electric charge is not zero. Rotating cases are given by the (electrically neutral) Kerr metric and the (charged) Kerr–Newman metric. Thus, general relativistic black holes have no properties that make them individually distinguishable when their mass, charge, and angular momentum are identical. A few other quantities can contribute to define classes of black holes, such as Yang–Mills charges. See black hole, dilatonic black hole, domain of outer communication, future/past event horizon, isometry, Kerr–Newman metric, Reissner–Nordström metric, Schwarzschild metric.

non-Abelian string In condensed matter or in cosmology, a string defect in which the symmetry describing the string has non-commuting components: the order of applying different symmetry actions leads to different results. For instance, the isotropic-nematic transitions in liquid crystals, where molecules have the form of rods, and are end-to-end symmetric. In the high temperature phase, the rods can point in any direction, but at low temperatures they line up and are symmetric under rotations around the reflections reversing their direction. Since a left-handed rotation turns into a right-handed one under reflection, the rotation symmetry does not commute with the reflection. Non-Abelian strings are principally characterized by their different behavior under collision; in particular, in-

tercommutation is not then mandatory in string collisions.

nonderivative absorption

See ionospheric

absorption.

 

nonminimal coupling

The expression of

the behavior of some field in a second field, which includes additional interaction terms beyond those of minimal coupling. See minimal coupling.

nonsimultaneous Big Bang The Big Bang in inhomogeneous models that occurs at different times in different places. In the Robertson– Walker cosmological models, the Big Bang is a single event in spacetime (i.e., all matter explodes out of a single point in the same instant). In generic inhomogeneous models, it is a process extended in time, which could in principle be determined by observing that different regions of the universe are of different ages.

non-thermal line broadening Excess width seen in solar soft X-ray emission lines. The width of these lines often exceeds that of the width expected from a thermal (Maxwell– Boltzmann) velocity distribution and is thought to be due to a combination of effects including small-scale flows, turbulent motions, and waveparticle interactions.

non-thermal particles A distribution of particles which does not conform to that of the Maxwell–Boltzmann distribution characteristic of particles subject to purely thermal motions. See Maxwell–Boltzmann distribution.

non-thermal radiation Radiation emitted by the interaction of charged particles where the distribution of the incident particles is non-thermal (e.g., bremsstrahlung from flareaccelerated particles).

non-thermal spectral energy distribution

A spectral energy distribution of light produced if electrons bound to atoms are not distributed among atomic levels according to the Maxwell– Boltzmann law, or if the velocity distribution of free, radiating particles is not a velocity distribution that follows Maxwell’s law. A non-thermal

© 2001 by CRC Press LLC

non-topological soliton

spectrum differs substantially from black-body (following Planck’s law) or thermal free-free emission, in the case when the source is optically thick or optically thin, respectively. Stars are regarded as thermal sources par excellence; hence, non-thermal spectrum is often a synonym for non-stellar spectrum. A typical non-thermal spectrum is the spectrum of synchrotron radiation. In this case, radiating electrons are accelerated to relativistic speed, and do not follow a Maxwellian distribution.

non-topological soliton Solitons are nontrivial solutions of a nonlinear field theory, usually associated with some topological conservation law, i.e., for fields having particular boundary conditions imposed, leading to a conserved number. In some cases, however, these boundary conditions yield no conserved quantity, even though the solution is still non-trivial. These configurations, usually unstable, are called nontopological solitons. See Derrick theorem, soliton.

nonuniqueness When models are compared with (or “inverted” from) measurements by examining the error between the measurements and those predicted by the models, it may sometimes be found that the best possible fit to the data can be achieved by more than one model. This means that the data cannot uniquely determine a best-fit model. It may be due to the sparse or restricted nature of the observations, but may also be related to fundamental physical difficulties. For example, the gravitational potential φ outside of source regions (i.e., where the density ρ is non-zero) obeys Laplace’s equation, 2φ = 0, and hence a uniqueness theorem tells us that if the gravitational acceleration on a surface external to the Earth is known then the gravitational field is known down to the Earth’s surface. However, sources of gravitational anomalies lying within the Earth cannot be uniquely determined using this knowledge alone because many different distributions of ρ within the Earth will allow the gravitational Poisson’s equation 2φ = 4πGρ to match the field at the Earth’s surface, and therefore external to the Earth. Nevertheless, the range of possibilities is restricted by the available measurements. Nonuniqueness may be alleviated either

through adding other data or by making other assumptions that help to pick between the models

— for example, by penalizing some measure of model complexity in order to find the simplest of the best fit models. See inverse theory.

norite A granular crystalline igneous mafic rock found in the lunar highlands composed of plagioclase and pyroxene; an orthopyroxene gabbro.

normal fault In geophysics, a type of dipslip fault, where displacement occurs up or down the dip (i.e., the angle that the stratum makes with the horizontal) of the fault plane. A normal fault is a dip-slip fault upon which the deformation is extensional. The direction of slip motion in a normal fault is opposite that of a reverse fault. Parallel normal faults can give rise to downdropped valleys called graben or elevated ridges called horsts.

normal incidence frame Frame of reference in which the shock is at rest. The upstream plasma flow is normal to the shock but oblique to the magnetic field, the downstream flow is oblique to both the shock normal and the magnetic field. See de Hoffman–Teller frame.

normal incidence optics At normal incidence light strikes the surface more or less at right angles, as with an ordinary wall mirror; X-rays and extreme ultraviolet light (EUV) are mostly absorbed at these angles.

normal modes In seismology, the free oscillations of the Earth, i.e., the set of elastic standing waves that are natural to the Earth. There are different types of standing waves that the Earth can sustain, such as “spheroidal” modes that involve radial motions such as a simple, spherically symmetric compression and expansion of the Earth, or the oscillation of the Earth between oblate and prolate spheroidal shapes, and “torsional” modes that involve only toroidal motions (i.e., no radial component) and which involve twisting motions of the Earth. For each of these types of motion, there is a discrete spectrum of permitted frequencies and wavenumbers. Nevertheless, any elastic deformation of the Earth can be represented as a sum of these normal

© 2001 by CRC Press LLC

nuclear reactions

modes. Normal modes are excited by earthquakes, and there have also been claims of excitation by atmospheric processes. The frequency and spatial structure of each normal mode depends on Earth properties such as density, bulk modulus, and shear modulus, so since different normal modes involve differing amounts of motion in the various parts of the Earth, observations of normal modes can be used to constrain Earth structure.

North Atlantic current A warm ocean current, an extension of the Gulf Stream, flowing northeastward from south of Greenland at about 45◦N extending north of the British Isles and along the coast of Scandinavia.

The current then joins the North Equatorial Current in the eastern tropical Atlantic Ocean and turns west. The Northern Equatorial Current mixes with water from the South Equatorial Current and the Guyana Current and moves past the Windward Islands into the Caribbean Basin.

North Atlantic Oscillation (NAO) A sea level pressure (SLP) seesaw between the Icelandic low and Azores high pressure systems, most pronounced in winter months. A NAO index is often defined as the SLP difference between Azores and Iceland. At the positive phase of the NAO when the SLP rises on the Azores but falls on Iceland, western Greenland and eastern Canada tend to be anomalously cold, while northern Europe experiences warm and humid winters as the strengthened westerly winds enhance inland advection of the warm Atlantic air. Recent studies indicate that the NAO may be part of the Arctic Oscillation.

North Equatorial current A westward flowing ocean current fed on the East from the southern end of the Canary current, and extending westward into the Caribbean basin.

Northern Plains (Mars) The bulk of plains material on Mars is found in the northern lowlands. They cover an area equivalent to half the size of the U.S. and are flatter than the Sahara Desert. Crater studies show they formed over a protracted period of time from the early Hesperian until the Amazonian. Two alternative hypotheses exist for their formation. The first is

sedimentary and the second is volcanic. A sedimentary origin has been proposed on the basis that Mars may have had a significant climatic history. Examples cited of sedimentary deposits include alluvial fans and polygonal terrain. The general consensus, however, is that the Northern Plains are principally of volcanic origin as indicated by the combined presence of lobate flow fronts, wrinkle ridges, and lava rilles. Additionally, marginal locations of the plains show no erosion but are either lobate or thin gradually. Images taken by the Mars Global Surveyor spacecraft also support a volcanic origin having revealed huge plates of solidified volcanic lava.

nova The subset of cataclysmic variables in which hydrogen accreted onto a white dwarf has ignited while degenerate and so burned explosively. The system survives and the explosions repeat in periods from about 30 years (recurrent novae) up to 104−5 years (classical novae). Most or all of the accreted hydrogen and its burning products are expelled at speeds of about 1000 km/sec, leading to a visible nebula called a nova remnant. These remain detectable for decades until the gas (only about 10−5 solar masses) dissipates. A few novae are found in the Milky Way each year, and the total number is probably 20 to 50, many of which are hidden behind galactic dust. The ejecta make some contribution to the galactic inventory of carbon and of rare isotopes like nitrogen-15 and (probably) aluminum-26.

nuclear fusion The exothermic process by which nuclei combine to form heavier nuclei releasing vast amounts of energy. The process that generates the emitted energy of the sun via the “burning” of hydrogen into helium.

nuclear reactions Reactions that rearrange the protons and neutrons in the nuclei of atoms (in contrast to chemical reactions, which merely rearrange the outer electrons of the atoms). Typically, two particles come together, and two different ones go out. The nucleus of an atom is represented by its chemical symbol, with a superscript indicating the total number of neutrons + protons in the nucleus, for instance 12C or 16O (formerly written C12 or O16, and properly still spoken in the latter order). The incoming and

© 2001 by CRC Press LLC

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