DICTIONARY OF GEOPHYSICS, ASTROPHYSICS, and ASTRONOMY

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 Vshaped.
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 x ′ 0 = x0 + δx0 generate totally
different trajectories after a long time. Let xn
evolve from x0 while x ′ n evolves from x′ 0
. For a
chaotic map an exponential increase of the difference
|xn − x ′ n |∼|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
© 2001 by CRC Press LLC
Lyman limit
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, L † is its hermitian
conjugate, and the infinitesimal variation
in the solution δx(t) satisfies a linearized equation
δx(t) = L(t)δx(0). IfL 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 s −1 ) 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
λ −1 = R∞ ,
called the Lyman limit (where R∞is 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
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