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methane

methane A flammable, explosive, colorless, odorless, tasteless gas, CH4. Concentration in the air approximately 1.8 ppm. A greenhouse gas with 25 times the effect of CO2. Its current contribution to the greenhouse effect is estimated at 13%. The chief constituent of natural gas. Produced in all sorts of biological decay. Boiling point 161.6C, freezing point 182.5C. Probably also present in clathrates in abyssmal ocean floors.

Metis Moon of Jupiter, also designated JXVI. Discovered by S. Synnott in 1979, its orbit lies very close to that of Adrastea, with an eccentricity and inclination that are very nearly 0, and

a semimajor axis of 1.28 × 105 km. Its radius is 20 km, its mass 9.49 × 1016 kg, and its den-

sity 2.8 g cm3. It has a geometric albedo of 0.05, and orbits Jupiter once every 0.295 Earth days. Also, an asteroid, ninth asteroid to be discovered, in 1848. Orbit: semimajor axis 2.3865 AU, eccentricity 0.1217, inclination to the ecliptic 5.579, period 3.69 years.

metric The array of coefficients (components) which, in principle, depend on position and are needed to calculate the length of a curve segment when the coordinates of the ends of the segment are given, or the abstract operation (tensor) which is computed in a particular reference frame using these components. The notion can be applied in a space with an arbitrary number of dimensions and with an arbitrary curvature. The metric is the tensor that acts on vectors to return their length; it can also produce the scalar product of two vectors. The simplest example is that of a Euclidean space in rectangular Cartesian coordinates. Suppose the space is four-dimensional, and the end-points of

the straight segment (vector) have coordinates

(x1, x2, x3, x4) and (x1 +'x1, x2 +'x2, x3 +

'x3, x4 + 'x4). The length of the segment, 's, is then given by the Pythagorean theorem:

('s)2 = 'x1

2 + 'x2 2 + 'x3 2 + 'x4 2

,

and components of the metric form the array

 

g

 

 

0

1

0

0

.

 

 

=

1

0

0

0

 

 

 

0

0

0

1

 

 

 

 

0

0

1

0

 

 

 

 

 

 

 

 

 

 

 

The form of the metric expressed in components depends on the reference frame, and the zeros here stand for the absent terms 'x1'x2, 'x1'x3, etc. that would be present in nonrectangular coordinates.

In 3-dimensional Euclidean space, in rectangular coordinates (x, y, z) the metric is diag(1, 1, 1) similar to the above, but if the distance is expressed spherical coordinates (r, θ, ϕ) where

x = r sin ϑ cos ϕ,

y = r sin ϑ sin ϕ,

z= r cos ϑ ,

then the components of the metric are

g

 

0

r2

0

.

 

=

1

0

0

 

 

0

0

(r sin ϑ)2

 

From here, the metric of the surface of a sphere r = a = const can be read out:

g =

a2

0

.

0

(a sin ϑ)2

This metric on the 2-d surface of a sphere has nonconstant components no matter what reference frame is used for the 2-d surface, showing that the metric contains implicit information about the curvature, in fact, all geometrical properties of the space. In general relativity, the metric describes the geometry of the spacetime. Components of the metric are the unknown functions in Einstein’s equations. If the curvature implied by a given metric is nonzero, then the corresponding spacetime is a model of a system with a gravitational field (e.g., the interior of a star, the neighborhood of a star, the whole universe). In this case, the components of the metric are not globally constant in any coordinate system. If the curvature is zero, then the gravitational field is absent, and the metric describes the flat space that is the background of the special relativity theory. In rectangular Cartesian coordinates, it has the components diag(1, 1, 1, 1). The coordinate that is distinguished from the others by this “1” is the time.

metricity of covariant derivative The requirement that the covariant derivative have no effect on the metric:

g = 0 ,

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where Cβγ µ

Michelson–Morley experiment

or in components,

gαβ;γ = 0 ,

where ; denotes the covariant derivative. This form can be used to define the affine connection coefficients in terms of derivatives of the metric, the torsion, and the structure coefficients associated with the basis as Eβγρ = gρµEµβγ , where

Eµβγ = 21 gµβ,γ + gµγ,β gβγ,µ

+Cµβγ + Cµγβ Cβγ µ

Tµβσ + Tβµσ + Tσµβ ,

= gλµCβγ λ where Cβ µγ are the structure coefficients and T µγβ = gµρTργβ is the torsion tensor. See affine connection, struc- ture coefficients, torsion.

metric radio burst Solar radio emission in the metric range that is at frequencies between some MHz and about 500 MHz. Metric radio bursts are characterized by a frequency drift from high to low frequencies. The radio emission is caused by streams of energetic electrons that excite Langmuir oscillations as they travel through the solar corona. The frequency of such Langmuir oscillations depends on the electron density ne according to

ωpe = 4πnee2 . me

Thus with a density model of the corona, the height of the radio source at a certain time and thus also its propagation speed can be inferred from the frequency drift. Metric radio bursts are classified into five different types: the continuous radio noise from the sun (see type I radio burst), the slow (see type II radio burst) and fast (see type III radio burst) drifting bursts giving evidence for shocks and streams of energetic electrons, and the continuum emission following these bursts (see type IV radio burst, type V radio burst).

MHD See magnetohydrodynamics.

MHD condition The mathematical condition E = −v × B, obeyed to a good approximation in highly conducting fluids or plasmas and in collision-free plasmas. The MHD condition

prescribes the components of the electric field E which are perpendicular to the local magnetic field B, in a fluid obeying it which is moving with bulk velocity v. It signifies the vanishing of the perpendicular (non-relativistic) electric field in a frame of reference moving with the fluid velocity v. In many situations, the component parallel to B can be assumed to vanish as well.

The MHD condition also assures the freez- ing-in of magnetic flux, into the fluid or plasma moving with bulk velocity v.

MHD simulation The numerical simulation of the behavior and motion of a plasma assumed to obey the MHD equations, using a fast computer. MHD simulations of the global magnetosphere, its tail region, shocks and reconnection in plasmas, comet behavior, the expansion of the solar wind and other phenomena in space plasma physics are widely used to study situations that cannot be duplicated in the lab and are not easy to observe in nature with sufficient resolution.

Some results of MHD simulations, e.g., for collision-free shocks, are very encouraging. However, MHD equations do not cover all details of plasma behavior, some of the boundary conditions (e.g., in the atmosphere) must be approximated, and results may be hard to check against observations. Still, the use of this method is growing.

Michelson Doppler Imager/Solar Oscillations Investigation (MDI/SOI) Helioseismology instrument aboard SOHO spacecraft which analyzes the vibrational modes of the sun and also measures the sun’s magnetic field in the photosphere.

Michelson–Morley experiment In 1887, in Cleveland, Ohio, Albert A. Michelson and Edward Morley attempted to detect a difference in the speed of light in two different directions: parallel to and perpendicular to the motion of the Earth around the sun. Such an effect would be expected if there was a fixed ether through which the Earth moves. The experiment, which was a repeat of one done in 1881 by Michelson, used an interferometer with right angle arms of 11.0 m optical path length. If light travels with constant speed c with regard to a fixed ether (the name given to this hypothetical substance), and

© 2001 by CRC Press LLC

Miche–Rundgren theory

the Earth moves through this ether with speed v, then the travel time for light along the arms should be aligned along and across the motion should differ by .5(v/c)2; the “cross stream” time is shorter. Note that this difference is second order in the ratio of the velocity to the speed of light. In the interferometer, this path difference will lead to a phase difference and an interference between the two beams of light in the interferometer. Furthermore, the interferometer can be turned (Michelson and Morley mounted theirs on granite and floated it in mercury to facilitate this) and the interference pattern should shift as the device is turned. To their amazement, Michelson and Morley found no such effect, with an experimental accuracy of about 2 to 3%. Multiple repeat experiments arrived at the same result. This result was debated for a very long time. It is now regarded as one of the fundamental experiments supporting special relativity.

Miche–Rundgren theory A theory for description of wave-induced forces on a wall (nonbreaking waves).

micrometeorite A meteorite less than 1 mm in diameter. Micrometeorite strikes are a major source of erosion on the moon, and of the production of the lunar surface (the regolith).

microstructure Fluctuations on scales at which entropy is generated by the smoothing effect of molecular viscosity and diffusivity are referred to as microstructure. This scale lies typically below 1 m in the ocean and lakes; often structures in CTD profiles (< some dm) resolving the Kolmogorov or Batchelor scale are generally called microstructure; see Kolmogorov scale, Batchelor scale.

microwave background radiation In observational cosmology, the radiation field at microwave frequencies with a black body spectrum corresponding to heat radiation at about 3 K; the radiation left over from the early period when the universe was dense and hot, 105 years (1013 sec.) after the Big Bang. Initially the temperature was so high that ordinary elementary particles could not exist. Matter emerged from the Big Bang in the form of a mixture of its sim-

plest components: protons, neutrons, electrons, photons, and neutrinos. (Cosmology also considers still earlier epochs, e.g., inflation; and the epoch when even protons and neutrons had not existed because the cosmic matter was a mixture of quarks.) At first, matter was so hot that no stable atoms could form and the particles remained in thermodynamical equilibrium with photons. However, the universe was cooled because of expansion, and later, 105 years after the Big Bang and at the temperature 3000 K, the atomic nuclei that had come into existence in the meantime (these were hydrogen [protons], deuterium, tritium, helium, lithium, beryllium, and boron, formed in reactions of the protons and neutrons that were there from the beginning) could capture the electrons. At this moment, the radiation was emitted for the last time (this moment is called last scattering) and it has evolved without significant contact with matter until now. It has kept the spectrum of a black body radiation, but its temperature is constantly decreasing. Exactly this kind of radiation was detected in 1965, with the temperature at 2.73 K. Its black-body spectrum has been verified with a very high precision, and it comes to us from all directions in space, with the relative fluctuations of temperature ('T /T ) not exceeding 105 (this result is obtained after the anisotropies in T caused by the motion of the Earth on its orbit, of the sun in the galaxy and of the whole galaxy in the local group have been subtracted). This discovery eliminated the steady-state models and is still the strongest confirmation that the idea of a Big Bang is correct. The radiation was in fact detected in 1935 by A. McKellar, through excitations in the CN-molecules in interstellar space, but the results were not understood at that time. The existence of the background radiation was predicted by George Gamow and co-workers in 1946–1948 on the basis of theoretical speculations. Robert Henry Dicke and James Peebles with co-workers were preparing an experiment to detect the radiation in 1965, when it was actually (and accidentally) discovered by Arno Penzias and Robert W. Wilson in the course of a quite different experiment, as an irremovable noise in a microwave antenna.

microwave burst A transient enhancement of solar radio emission in the mm–cm wave-

© 2001 by CRC Press LLC

Milankovich cycle

length range, normally associated with optical and/or X-ray flares. Microwave bursts provide a powerful diagnostic of energetic electrons in the solar atmosphere.

mid-ocean ridge A location of seafloor spreading (divergence zone). The more or less continuous line centered in the oceans where new material reaches the surface of the Earth, driven by convection in the Earth’s mantle. The Mid-Atlantic ridge begins in the North polar region, wanders south between W15and W45, essentially staying in the middle of the Atlantic Ocean. It connects to the Southwest Indian Ridge at about latitude S50, longitude 0. The Southwest Indian Ridge connects with the Indian Ridge at about S30, E70. From this junction, the Indian Ridge extends north as the Central Indian Ridge through the Red Sea; it extends South and East as the Southeast Indian Ridge along about S45, becoming the Pacific Antarctic Ridge at S60, E150. This becomes the East Pacific Rise at about S60, W120. The East Pacific Rise runs north along approximately W100, up the west coast of North America, ending around N50as the Juan de Fuca ridge.

Mie scattering Scattering of light by a spherical particle. Given the complex index of refraction of the particle, and the ratio of its radius to the wavelength of the light, it is possible to exactly solve Maxwell’s equations to find the fraction of light absorbed, and the fraction scattered, as well as the phase function of the scattered light and its polarization. The detailed solution of this problem is called Mie scattering.

Mie size parameter For scattering by spheres, the ratio of a sphere’s circumference to the wavelength.

migration (seismic) This is a technique which, when implemented on data from seismic reflection surveys, can help to elucidate the structure of the underlying rock. In a reflection survey, seismic waves are generated at one point on the Earth’s surface and recorded at geophones (i.e., seismic wave detectors) distributed nearby (for example, in a linear fashion behind a ship). Each time the seismic signal encounters a “reflector”, i.e., a rock layer that causes part

of the seismic energy to be reflected back to the surface, a seismic pulse is returned to the geophones. The time delay between the generation of the seismic signal and its detection at a geophone depends on the speed of seismic waves in the rock, the depth of the reflector, and the horizontal distance between seismic source and geophone, but also on the geometry of the reflector. For example, if the reflector is inclined upwards toward the geophone from the direction of the source, then the part of the reflection that is recorded at the geophone will have been reflected closer to the geophone, rather than midway between the geophone and the source if the reflector had been horizontal. Migration corrects this effect, and also removes other geometrical artifacts such as diffractions associated with scattering centers in the rock.

Milankovich cycle Cyclic variations in climate driven by periodic changes in orbital and Earth orientation parameters. Climate in a particular area depends on the solar flux, and therefore on both the distance from the Earth to the sun and the angle between the surface of the area in question and the sun’s rays over the course of a day (overhead sunlight leading to a greater flux than tangential sunlight). These both cause the seasonal variations in weather. The importance of the former depends on the eccentricity of the Earth’s orbit, which varies on a 96,000year cycle, while the importance of the latter depends on the obliquity, i.e., the angle between the planes defined by the Earth’s equator and by the Earth’s orbit around the sun (the ecliptic plane), which varies between 21and 24(it is currently at 23.5) and which varies on a 41,000-year cycle. The effect of the eccentricity may be either to augment the seasonal variations in either the northern or southern hemisphere while reducing the variations in the other hemisphere (if the closest approach of the Earth to the sun occurs near a solstice, i.e., northern or southern winter), or to have a relatively neutral effect (if it occurs near an equinox, i.e., northern or southern spring). The orientation of the orbit is also cyclic, so that these effects vary on a 22,000-year timescale. As long, hard winters are thought to be important for growing ice sheets, these cycles may therefore have significant impact on global climate, although they

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