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lunar libration

mainly in their concentrations of the metal oxides, which are richer in calcium (Ca) and aluminum (Al) than are the lowlands.

Highlands geology consists of craters 1 m to more than 1000 km across, and overlapping layers of material ejected from craters. Rocks brought back from the highlands vary in age (the time since it last solidified from molten liquid) between 3.84 and 4.48 billion years old. The highlands are the oldest parts of the moon, not having been resurfaced by mare lava flows.

lunar libration The apparent rocking of the orientation of the moon due to geometrical and orbital relations between the Earth and the moon. These arise from (a) the ellipticity of the moon’s orbit (e = 0.055), (b) the slight nonalignments of the lunar orbit: the lunar equator is tilted from the ecliptic by 132 from the ecliptic and the lunar orbital plane is tilted 59 from ecliptic; thus the lunar equator is tilted from its orbital plane by 641 , (c) parallax from the Earth (different viewpoints between moonrise and moonset). This leads to longitudinal librations of about 7.7due to the ellipticity, latitudinal librations of about 6.7due to the tilt of the lunar equator from the ecliptic, and about 2total due to parallax from the Earth. As a result, about 15additional surface of the moon is visible at various times from the Earth.

Lunar Maria Darker low lying areas on the moon which are large basaltic lava flows. The maria (latin plural of mare, “sea”) are younger (they have fewer impact craters), and are richer in magnesium (Mg) and iron (Fe) than are the highlands. The maria were apparently formed by very large impacts and clearly represent flow into low lying regions. They solidified near or after the end of the cratering epoch because little subsequent cratering occurred. Although the impacts forming the maria may have occurred about 4 billion years ago, the maria were apparently kept molten by heating from heavier radioactive elements which flowed up to the surface following the impacts that formed them. Mare rocks have been measured to be between 3.15 and 3.77 years old, which provides an estimate of the time of the solidification of the mare. The maria occur essentially only on the side of

the moon facing the Earth; the far side is essentially all highlands.

lunar mascons The Lunar Maria are generally associated with strong positive gravity anomalies. Because the maria are low-lying, the gravity anomalies are attributed to buried positive density anomalies or loads. These loads are known as mascons.

lunar meteorites Currently there are 13 meteorites believed to be from the moon. After the discovery of young meteorites believed to be from Mars (see martian meteorites), scientists began searching for lunar meteorites. Since Martian meteorites are believed to be ejected from Mars by meteorite impact, it was argued that the lower escape velocity from the moon should allow lunar meteorites to be common as well. The first meteorite recognized to be from the moon was discovered in 1981–1982. The lunar meteorites are similar to lunar rocks returned by the Apollo and Luna missions, reflecting both basaltic (from the Lunar Maria) and anorthositic (from the lunar highlands) compositions. However, none of the lunar meteorites is exactly identical to the chemical composition of the returned lunar samples, which indicates the lunar meteorites are from locations on the moon not visited by the human and robotic explorers.

Lunar Prospector A NASA Discovery Mission launched to the moon on January 6, 1998, that marked the first NASA Moon mission in 25 years. It uses a complement of five instruments that address questions concerning the moon’s resources, its structure, and its origins. During its primary 1 year polar orbiting mission, data returned suggesting that the craters at the north and south poles contain up to 300 million metric tons of frozen water, as implied by the detection of hydrogen. The ice is probably in the form of frost mixed with lunar soil. The general consensus is that the water was supplied over billions of years via cometary bombardment. Because the sun makes a shallow angle at the moon’s poles, the bottoms of the polar craters never see sunlight and so trap the frozen water. The amount of ice may indicate the frequency of cometary hits and how long the poles have been in their present orientation.

© 2001 by CRC Press LLC

Lyman limit

Prospector then dropped to an altitude of 30 km above the surface and took additional data at significantly higher resolutions that pertain to hydrogen concentrations at the north and south poles, and the moon’s magnetic and gravity fields. Global maps of the moon’s elements will also benefit from these high-resolution data.

Lunar Rille Trenchlike or cracklike valley, up to several hundred kilometers long and up to a few kilometers wide, on the moon’s surface. Some rilles may be relatively straight. However, many rilles may be extremely irregular with meandering courses (“sinuous rilles”). They are lava channels and collapsed lava tubes which were probably active during the maria formation (many have a sinuous appearance resembling river meanders, so were once thought to be dry river beds). These sinuous rilles typically begin at craters, and end by fading into the mare surface. Channels are U-shaped or V- shaped. Scales are much larger than equivalent terrestrial lava tubes, presumably because of differences in physical conditions and/or outflow rates.

Lux An illuminance equal to one lumen per square meter.

Lyapunov exponent The time for the distance between two chaotic trajectories to increase by a factor e when the initial conditions are altered infinitesimally. It indicates how fast nearby trajectories diverge and how unpredictable such trajectories become. A dynamical system is said to be chaotic if it possesses sensitive dependence on the initial conditions. Consider a one-dimensional mapping xn+1 = f (xn). That the mapping is chaotic means that randomly chosen very close initial values x0 and x0 = x0 + δx0 generate totally different trajectories after a long time. Let xn evolve from x0 while xn evolves from x0. For a chaotic map an exponential increase of the difference |xn xn| |δx0| exp(λn) is observed for an infinitesimal |δx0|. The long-time average of the separation rate λ is called the Lyapunov exponent of the map. Chaotic trajectories correspond to a positive Lyapunov exponent while stable trajectories correspond to a negative exponent. In a continuous n-dimensional dynamical

system dx/dt = F (x) a more general definition of the Lyapunov exponent of this system is given by λ = limt→∞(1/2t) ln{Tr[L(t)L(t)]} where L is a square matrix of dimension n, Lis its hermitian conjugate, and the infinitesimal variation in the solution δx(t) satisfies a linearized equation δx(t) = L(t)δx(0). If L is independent of time, λ is the greatest real part of eigenvalues of

L.

Lyman α forest A large number of narrow (width 10 km s1) absorption lines observed in quasars shortward of the wavelength of the hydrogen line Lyman α. Spectra of many moderate and high redshift quasars show a characteristic “eroded” appearance due to the high number of absorptions per unit wavelength. It is very difficult to explain the Ly α forest as due to matter associated to the quasar; the current view is that the narrow lines are produced by relatively low density, cold hydrogen in shreds or clouds between the quasar and the observer. The absence of strong absorption lines of heavy elements suggests that the chemical composition is very different from the chemical composition of the sun, with heavy elements 10 to 100 times less abundant in the absorbing clouds than in solar gas.

Lyman alpha (Ly α) A strong ultraviolet emission line of hydrogen, at 1216 Å(121.6 nm). Ly α is a major component of the geocoronal glow, observed in space from the region around Earth.

Lyman limit In spectroscopy of hydrogen, the Lyman series (in the ultraviolet) corresponds to transitions between the ground state and higher states. The emitted or absorbed wavelength approaches from above the limit given

by

λ1 = R,

called the Lyman limit (where Ris the Rydberg constant). Because of the state structure of the hydrogen atom, there are an infinite number of consecutive lines of the Lyman series between the longest wavelength (4/(3R)) and the limit, and the distance between the lines decreases and approaches a continuum as the limit is approached. For wavelengths shorter than this limit (912 Å), photons are energetic enough to

© 2001 by CRC Press LLC

Lyman series

ionize hydrogen from the ground state. Thus, hydrogen is opaque to radiation of wavelength shorter than the Lyman limit. There are corresponding limits associated with transitions from the second, third, fourth, fifth . . . excited states, called the Balmer, Paschen, Brackett, Pfund . . .

limits.

Lyman series The set of spectral lines in the far ultraviolet region of the hydrogen spectrum with frequency obeying

ν = cR1/n2f 1/n2i ,

where c is the speed of light, Ris the Rydberg constant, and nf and ni are the final and initial quantum numbers of the electron orbits, with nf = 1 defining the frequencies of the

spectral lines in the Lyman series. This frequency is associated with the energy differences of states in the hydrogen atom with different quantum numbers via ν = @E/h, where h is Planck’s constant, and where the energy levels of the hydrogen atom are:

En = hcR/n2 .

Lysithea Moon of Jupiter, also designated JX. Discovered by S. Nicholson in 1938, its orbit has an eccentricity of 0.107, an inclination of 29.02, and a semimajor axis of 1.172×107 km. Its radius is approximately 18 km, its mass, 7.77 × 1016 kg, and its density 3.2 g cm3. Its geometric albedo has not been well determined, and it orbits Jupiter once every 259.2 Earth days.

© 2001 by CRC Press LLC

Mach number

M

M51 Object 51 in the Messier list, a bright Sc spiral galaxy notable for the grand design of its spiral arms (and sometimes referred to as the “Whirlpool” galaxy). M 51 is perturbed by a smaller companion galaxy which appears to be in touch with and distorts one of its spiral arms. Optical spectra of the M 51 nucleus show emission lines suggestive of non-thermal nuclear activity, and whose intensity ratios are intermediate between those of LINERs and Seyfert 2 nuclei.

M87 (NGC 4486) Giant elliptical galaxy, type E1, in Virgo at RA 12h30m.8, dec +1224 , mV = 8.6, angular diameter 7 . Distance 18 Mpc, giving a linear diameter of about 40 kpc at the center of the Virgo cluster. Also a radio source, Virgo A; also a strong source of X-rays. Total mass about 3×1012M . M87 has two very notable features. One is a strong jet ( 2 kpc in length), which is also a source in the radio and connects the central core of M87 with the more diffuse emission of its northwestern lobe. The other remarkable feature is the large number (up to 15,000) of globular clusters associated with M87.

M87 has also been identified as containing a probable supermassive black hole, of mass about 3 × 109M . See cD galaxies.

M101 (NGC 5457). The “Pinwheel” galaxy, type Sc, in Ursa Major at RA 14h03m.2, Dec +5421 , mV = 7.9, angular diameter 22 .0. Distance, by recent measurements using the period-magnitude relation of Cepheid variable stars detected by the Hubble Space Telescope, is 8.3 Mpc, giving a physical diameter of about 50 kpc.

Mach, Ernst (1838–1916) An outstanding experimental physicist whose seminal works (essentially, his criticisms of the Newtonian world picture) paved the way for the major revision of physics in the beginning of the 20th

century. He is sometimes considered more as a philosopher of science, though he persistently denied this title.

Born on February 18, 1838, in 1855 he enrolled in Vienna University, and received from it his Ph.D. degree in 1860. He continued as a Privat–Dozent delivering lectures on mathematics, psychophysics, and Helmholtz’s studies in the perception of sound. From 1864, he held the chair of mathematics in Graz, then (from 1867) for 28 years he taught at the experimental physics department of the Charles University (its German branch). In 1895, Mach moved to Vienna as the philosophy professor of the university (the theory and history of inductive sciences) where he worked up to his retirement in 1901. He died on February 19, 1916.

Mach’s scientific interests were primarily focused on acoustic phenomena and processes in continuous media (for example, the unit of velocity in terms of the velocity of sound in a medium, now generally used in aerospace techniques, bears his name — mach), but he was in general a deep thinker, and his achievements in experimental studies were intimately connected with his fundamental methodological quest as well as with his research in the organs of perception physiology and, finally, the epistemology (he influenced these areas profoundly). His sharp critical analysis of the basic concepts of Newtonian mechanics is widely known, and it influenced the development of both the relativities by Einstein. Especially popular among gravitational physicists is Mach’s principle (the term introduced by Einstein) which relates local inertial properties of matter with its global distribution (and, finally, motion). Mach was the first who clearly formulated the idea of Gedankenexperiment (thought experiment) and pointed out its great importance for physics.

Mach’s ideas were greatly appreciated by Einstein and L. Boltzmann, and disdained by Planck (who was shocked by Mach’s negative attitude toward religion) and Lenin (who accused Mach of fideism, i.e., a point-blank acceptance of religion).

Mach number Ratio of the speed of an object to the sound (or by extension, the light) speed in

© 2001 by CRC Press LLC

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