An Etymological Dictionary of Astronomy and Astrophysics

La Niña. A condition in which a significant decrease (more than 0.5 °C from average water temperatures) occurs in sea surface temperature (cold event) in the central and eastern equatorial Pacific. La Niña has a natural 3-6 year cycle and can persist for 1-3 years. It is the counterpart to the → El Nino (warm event), and its spatial and temporal evolution in the equatorial Pacific is, to a considerable extent, the mirror image of El Niño, although La Niña events tend to be somewhat less regular in their behavior and duration.

See also: American Sp. La Niña “the girl,” to distinguish it from
→ El Nino.

The site of the → European Southern Observatory’s first observatory in Chile, inaugurated in 1969. It is located 160 km north of the town of La Serena and 600 km north of Santiago at an altitude of 2,400 m bordering the southern extremity of the Atacama Desert. La Silla is equipped with several optical telescopes with mirror diameters of up to 3.6 m. The 3.5 m New Technology Telescope was the first in the world to have a computer-controlled main mirror, a technology developed at ESO. The ESO 3.6 m telescope is now home to the world’s largest extrasolar planet hunter: HARPS (High Accuracy Radial velocity Planet Searcher), a spectrograph with unrivalled precision.

See also: From Sp. la silla “the saddle,” after the apparent shape of the mountain on which the observatory is situated. Originally known as Cinchado.

A building or place equipped for carrying out scientific research,
experimentation, investigation, observation, etc.

Etymology (EN): M.L. laboratorium “a place for labor or work,” from L. laboratus, p.p. of laborare “to work.”

Etymology (PE): Âzmâyešgâh, from âzmâyeš, → experiment,

• -gâh “place, time,” → university.

The Lizard. A small constellation in the northern hemisphere, at about 22h right ascension, 45° north declination. Its brightest star is only of magnitude +3.8, and the constellation contains no other star above fourth magnitude. Its most famous object is BL Lacerta, the prototype → BL Lac objects. Abbreviation: Lac; genitive: Lacertae.

Etymology (EN): From L. lacertus (fem. lacerta) “lizard,” of unknown origin.

Etymology (PE): Calpâsé “lizard,” variants karpâsa, karisa, kelpasa; cf. Skt. krakacapad- “saw-footed, a lizard, chameleon,” from krakaca- “saw” + pad “foot” (Pers. pâ).

1a) Deficiency or absence of something needed, desirable, or customary.

1b) Something missing or needed. See also → default, → deficiency, → shortage.

2a) (v.tr.) To be without or deficient in; to fall short in respect of.

2b) (v.intr.) to be absent or missing, as something needed or desirable (Dictionary.com).

Etymology (EN): M.E. lak; cognate with M.L.G. lak, M.Du. lac “deficiency;” akin to O.Norse lakr “deficient.”

Etymology (PE): Nast, from negation prefix na- “in-, non,” → not, + ast, hast “is,” from astan, hastan “to be,” → exist.

Absent; wanting; deficient.

See also: → lack; → -ing.

1. A piece of equipment consisting of a series of bars or steps between two upright lengths of wood, metal, or rope, used for climbing up or down something.
   

2. A series of ascending stages by which someone or something may progress (OxfordDictionaries.com).

Etymology (EN): M.E. laddre, O.E. hlæder “ladder, steps” (cognates: M.Du. ledere, O.H.G. leitara, Ger. Leiter), from PIE root *klei- “to lean,” → incline.

Etymology (PE): Nardebân “ladder.”

1a) A lagging or falling behind; retardation.

1b) Mechanics: The amount of retardation of some motion.

1c) Electricity: The retardation of one alternating quantity, as current, with respect to another related alternating quantity, as voltage.

2. To fail to maintain a desired pace or to keep up; fall or stay behind (Dictionary.com).

Etymology (EN): Possibly from Scandinavian; cf. Norwegian lagga “to go slowly.”

Etymology (PE): Lek, from lek lek kardan “to walk slowly, to lag behind.”

1. A body of seawater that is almost completely cut off from the ocean by a barrier beach.
   
2. The body of seawater that is enclosed by an atoll.

Etymology (EN): Lagoon, from Fr. lagune, from It. laguna “pond, lake,” from L. lacuna “pond, hole,” from lacus “pond;” → nebula.

Etymology (PE): Mordâb “lagoon,” literally “dead water,” from mord, mordé “dead”

• âb “water.”
  The first element
  from mordan, mir- “to die,” marg “death,” mard “man;” Mid.Pers. murdan “to die;” O.Pers. marta- “dead,” martiya- “man;” Av. mərəta- “died, dead,” amərətāt- “immortality;” cf. Skt. mar- “to die,” mriyáe “dies;” Gk. emorten “to die,” ambrotos “immortal;” L. morior “to die” (Fr. mourir), mors, mortis “death” (Fr. mort), immortalis “immortal;” Lith. mirtis “mortal;” O.C.S. mrutvu “dead;” O.Ir. marb; Welsh marw “died;” O.E. morþ “murder;” PIE base *mor-/*mr- “to die.”
  The second element âb “water,” from
  Mid.Pers. âb “water;” O. Pers. ap- “water;” Av. ap- “water;” cf. Skt. áp- “water;”
  Hitt. happa- “water;” PIE āp-, ab- “water, river;”
  cf. Gk. Apidanos, proper noun, a river in Thessalia; L. amnis “stream, river” (from *abnis); O.Ir. ab “river,” O.Prus. ape “stream,” Lith. upé “stream;” Latv. upe “brook.”

A giant → H II region lying in the direction of
→ Sagittarius about 5,000 → light-years away. It represents a giant cloud of interstellar matter which is currently undergoing star formation, and has already formed a considerable cluster of young stars (NGC 6530).

See also: → lagoon; → nebula.

A set of second order → differential equations for a system of particles which relate the kinetic energy of the system to the → generalized coordinates, the generalized forces, and the time. If the motion of a → holonomic system is described by the generalized coordinates q₁, q₂, …, q_n and the → generalized velocities 

q^.₁, q^.₂, …, q^._n, the equations of the motion are of the form:

d/dt (∂T/∂q^._i) - ∂T/∂q^._i = Q_i (i = 1, 2, …, n), where T is the kinetic energy of the system and Q_i the generalized force.

See also: → Lagrangian; → equation.

1. Of or relating to Joseph-Louis Lagrange (1736-1813), see below.
   

2. Same as → Lagrangian function. The Lagrangian of a → dynamical system describes its → dynamics and when subjected to an → action gives rise to → field equations and a → conservation law for the theory. Lagrangians are the keys for the mathematical formulation of field theories ( → field theory).
   

See also:
→ inner Lagrangian point, → Lagrangian density, → Lagrangian dynamics, → Lagrangian formalism, → Lagrangian function, → Lagrangian method, → Lagrangian multiplier, → Lagrangian particle, → Lagrangian point.

See also: After the French/Italian mathematician Joseph-Louis Lagrange (1736-1813), who was the creator of the → calculus of variations (at the age of nineteen). He made also great advances in the treatment of → differential equations and applied his mathematical techniques to problems of → mechanics, especially those arising in astronomy.

A quantity, denoted L_d, describing a continuous system in the → Lagrangian formalism, and defined as the → Lagrangian per unit volume. It is related to the Lagrangian L by:
L = ∫∫∫L_d d³V.

Lagrangian density is often called Lagrangian when there is no ambiguity.

See also: → Lagrangian; → density.

A reformulation of → Newtonian mechanics in which dynamical properties of the system are described in terms of generalized variables.
In this approach the → generalized coordinates and → generalized velocities are treated as independent variables. Indeed applying Newton’s laws to complicated problems can become a difficult task, especially if a description of the motion is needed for systems that either move in a complicated manner, or other
coordinates than → Cartesian coordinates are used, or even for systems that involve several objects. Lagrangian dynamics encompasses Newton dynamics, and moreover leads to the concept of the → Hamiltonian of the system
and a process by means of which it can be calculated. The Hamiltonian is a cornerstone in the field of → quantum mechanics.

See also: → Lagrangian; → dynamics.

A reformulation of classical mechanics that describes the evolution of a physical system using → variational principle The formalism does not require the concept of force, which is replaced by the → Lagrangian function. The formalism makes the description of systems more simpler. Moreover, the passage from classical description to quantum description becomes natural.
Same as → Lagrangian dynamics.

See also: → Lagrangian; → formalism.

A physical quantity (denoted L), defined as the difference between the → kinetic energy (T) and the → potential energy (V) of a system: L = T - V. It is a function of → generalized coordinates, → generalized velocities, and time. Same as
→ Lagrangian, → kinetic potential.

See also: → Lagrangian; → function.

Fluid mechanics: An approach in which a single fluid particle (→ Lagrangian particle) is followed during its motion. The physical properties of the particle, such as velocity, acceleration, and density are described at each point and at each instant. Compare with → Eulerian method.

See also: → Lagrangian; → method.

Math.: A constant that appears in the process for obtaining extrema of functions of several variables. Suppose that the function f(x,y) has to be maximized by choice of x and y subject to the constraint that g(x,y)≤ k. The solution can be found by constructing the → Lagrangian function  L(x,y,λ) = f(x,y) + λ[k - g(x,y)], where λ is the Lagrangian multiplier.

See also: → Lagrangian point; → multiplier.

Fluid mechanics: In the → Lagrangian method, a particle that moves as though it is an element of fluid. The particle concept is an approach to solving complicated fluid dynamics problems by tracking a large number of particles representing the fluid. The particle may be thought of as the location of the center of mass of the fluid element with one or more property values.

See also: → Lagrangian; → particle.

On of the five locations in space where the → centrifugal force and the → gravitational force of two bodies (m orbiting M) neutralize each other. A third, less massive body,
located at any one of these points, will be held in equilibrium with respect to the other two. Three of the points, L1, L2, and L3, lie on a line joining the centers of M and m. L1 lies between M and m, near to m, L2 lies beyond m, and L3 on the other side of M beyond the orbit. The other two points, L4 and L5, which are the most stable, lie on either side of this line, in the orbit of m around M, each of them making an equilateral triangle with M and m. L4 lies in the m’s orbit approximately 60° ahead of it,
while L5 lies in the m’s orbit approximately 60° behind m. See also → Trojan asteroid; → Roche lobe; → equipotential surface; → horseshoe orbit.

See also: → Lagrangian; → point.

A body of fresh or salt water entirely surrounded by land.

Etymology (EN): From O.Fr. lack, from L. lacus “pond, lake,” related to lacuna “hole, pit,” from PIE *lak- (cf. Gk. lakkos “pit, tank, pond,” O.C.S. loky “pool, cistern,” O.Ir. loch “lake, pond”).

Etymology (PE): Daryâcé, from daryâ “sea” Mid.Pers. daryâp variant zrah; O.Pers. drayah-; Av. zrayah- “sea;” cf. Skt. jráyas- “expanse, space, flat surface”

• -cé diminutive suffix, from Mid.Pers. -cak, variants -êžak (as in kanicak “little girl,” sangcak “small stone,” xôkcak “small pig”), also Mod.Pers. -ak.

A young sheep; the meat of a young sheep.

Etymology (EN): M.E., O.E.; cognate with Du. lam, Ger. Lamm, Goth. lamb; akin to Gk. elaphos “deer.”

Etymology (PE): Mid.Pers. warrag “lamb; sheep;” warân “ram;” Av. varən-; cf. Skt. uaran-; L. vervex (Fr. brebis); Arm. garn; Baluci garând “ram;” Lori, Laki veran “ram;” PIE *wrhen- “lamb.”

A tiny change in the → energy levels of the → hydrogen atom between the states 2S_1/2 and 2P_1/2, which creates a shift in the corresponding → spectral lines. The 2P_1/2 state is slightly lower than the 2S_1/2 state, contrarily to the Schrodinger’s solution. The difference is explained by the interaction between → vacuum energy fluctuations and the hydrogen electron in different orbitals.

See also: Named after Willis Eugene Lamb, Jr. (1913-2008), an American physicist who discovered this effect in 1951, and won the Nobel Prize in physics in 1955 “for his discoveries concerning the fine structure of the hydrogen spectrum;” → shift.

The eleventh letter of the Greek alphabet. In lower case, λ, it denotes → wavelength. It is also used in the → Bayer designation system to identify a specific star in a → constellation. See also → lambda point.

In upper case, Λ, it represents the → cosmological constant or → dark energy.

See also: From Phoenician lamedh.

The prototype of a small class of stars (A-F types) which have weak metallic lines (indicating that they are depleted in metals heavier than Si, but with solar abundances of C, N, O, and S). Moreover, they have moderately large rotational velocities and small space velocities. Lambda Boo stars may be pre-main-sequence objects, or they may be main sequence stars that formed from gas whose metal atoms had been absorbed by interstellar dust.

See also: Named after the prototype, the star → Lambda (λ) of constellation → Bootes; → star.

The → standard model of → Big Bang that incorporates both → dark matter and → dark energy. See also → cold dark matter (CDM).

See also: → lambda, → cosmological constant; → cold; → dark; → matter; → model.

Same as → Meissa.

See also: Lambda (λ), a Greek letter used in the → Bayer designation of star names.

The temperature (roughly 2.17 K) at which → liquid helium (→ helium I) becomes → superfluid (→ helium II).

See also: The name was given by the Dutch physicist Willem Hendrik Keesom (1876-1956), who discovered the behavior of helium near this transition point and successfully solidified helium in 1926 (under an external pressure of 25 atmospheres). The name was originally suggested by Paul Ehrenfest (1880-1933), who
was inspired by the shape of the → specific heat curve, which
resembles the Gk. letter → lambda; → point.

A centimeter-gram-second (cgs) unit of luminance (or brightness) equal to 1/π candle per square centimeter. Physically, the lambert is the luminance of a perfectly diffusing white surface receiving an illuminance of 1 lumen per square centimeter.

See also: Johann Heinrich Lambert (1728-1777), German scientist and mathematician; → law.

The intensity of the light emanating in any given direction from a perfectly diffusing surface is proportional to the cosine of the angle between the direction and the normal to the surface. Also called → Lambert’s law.

See also: → lambert; → cosine; → law.

Same as → Lambert’s cosine law.

See also: → lambert; → law.

A → planetary or → satellite disk with → Lambertian surface. Such a disk has the same → surface brightness at all angles.

See also: → lambert; → disk.

A surface whose → luminous intensity obeys → Lambert’s cosine law. Such a source has a → reflectance that is uniform across its surface and uniformly emits in all directions from all its points. It appears equally bright from all viewing directions. Lambertian surface is a very useful concept for the approximation of radiant power transfer.

See also: → lambert; → surface.

1a) A real or imagined cause for → complaint, especially unfair treatment.

1b) A feeling of resentment over something believed to be wrong or unfair.

2. To feel or express sorrow or regret for; to mourn for or over (OxfordDictionaries.com).

Etymology (EN): M.E., from M.Fr. lament and directly from L. lamentum “a wailing, moaning, weeping” from lamentum “a wailing,” from PIE root *la- “to shout, cry.”

Etymology (PE): Šekvé, Pers. construction from Ar. šakvâ “complaint.”

A thin plate, layer, or flake.

Etymology (EN): From L. lamina “thin plate or layer, leaf.”

Etymology (PE): Varaqé “sheet, plate,” from varaq “a leaf of tree or of paper,” from Ar. waraq, from Pers. barg “leaf” (Tabari, Gilaki valg, balg; Kurd. belg, balk, Semnâni valg); Mid.Pers. warg “leaf;” Av. varəka- “leaf;” cf. Skt. valká- “bark, bast, rind;” Russ. volokno “fibre, fine combed flax.”

Composed of, or arranged in, laminae, sheets.

See also: → lamina + → -ar.

In a fluid flow, layer next to a fixed boundary. The fluid velocity is zero at the boundary but the molecular viscous stress is large because the velocity gradient normal to the wall is large. → turbulent boundary layer.

See also: → laminar; → boundary; → layer.

A flow in which the particles of fluid are moving orderly, and in which adjacent layers or laminas glide smoothly over another
with little mixing between them. A laminar flow may rapidly transform into a → turbulent flow for large → Reynolds numbers.

See also: → laminar; → flow.

A layer in which the fluid undergoes smooth, nonturbulent flow. It is found between any surface and a turbulent layer above.

See also: → laminar; sublayer, from → sub- + → layer.

Any of various devices producing artificial light, as by electricity, gas, or oil.

Etymology (EN): From O.Fr. lampe, from L. lampas, from Gk. lampas “torch, lamp, beacon, meteor, light,” from lampein “to shine,” from PIE base *lap- “to shine” (cf. Lith. lope “light,” O.Ir. lassar “flame”).

Etymology (PE): Lâmp, loanword from Fr., as above.
Cerâq “lamp” (variants Kurd. cira, cerâh, Laki cerâx, Zâzâ cərâ, cərâx “lamp, candle,” Shughni cirow, cirâw, cərêγ “candle, lamp”); Mid.Pers. cirâq “lamp,” related to foruq “light,”
afruxtan “to light, kindle,” rowšan “bright, clear,” rowzan “window, aperture;” ruz “day;”
Mid.Pers. rôšn “light; bright, luminous,” rôc “day;” O.Pers. raucah-rocânak “window;” O.Pers. raocah- “light, luminous; daylight;”
Av. raocana- “bright, shining, radiant;”
akin to Skt. rocaná- “bright, shining,” roka- “brightness, light;” Gk. leukos “white, clear;” L. lux “light” (also lumen, luna); Fr. lumière; E. light; O.E. leoht, leht, from W.Gmc. *leukhtam (cf. O.Fris. liacht, M.Du. lucht, Ger. Licht), from PIE *leuk- “light, brightness.”

Any part of the earth’s surface not covered by a body of water.

Etymology (EN): M.E., from O.E. land, lond, “ground, soil, territory;” PIE base *lendh- “land, heath” (cf. O.N., O.Fris. Du., Ger., Goth. land; O.Ir. land; Welsh llan “enclosure, church,” Breton lann “heath,” source of Fr. lande; O.C.S. ledina “waste land, heath,” Czech lada “fallow land”).

Etymology (PE): Xoški, from xošk, → dry, + noun suffix -i; zamin “land, → earth.”

A coastal breeze blowing from land to sea after sunset, caused by the temperature difference when the sea surface is warmer than the adjacent land. The warmer air above the water continues to rise, and cooler air from over the land replaces it, creating a breeze.

Etymology (EN): Land, → lander; → breeze.

Etymology (PE): Xoški “land,” from xošk “dry;” Mid.Pers. xušk “dry;” O.Pers. uška- “mainland;” Av. huška- “dry;” cf. Skt. śuska- “dry, dried out;” Gk. auos “dry, dried up;” O.E. sēar “dried up, withered;” Lith. sausas “dry, barren.”

The process wherein a → plasma gains energy at the expense of the → Langmuir wave. In the presence of the → Landau resonance, the particles in resonance moving slightly faster than the wave lose energy, while those moving slightly slower will gain energy. Since the Maxwellian distribution is decreasing with velocity, in a Maxwellian plasma, near the Landau resonance, there are more particles at lower velocities than at higher velocities. Also called collisionless damping.

See also: Lev Landau (1908-1968), a prominent Soviet physicist, 1962 Nobel Prize in Physics for his development of a mathematical theory of → superfluidity; → damping.

The → energy level which can be occupied by
a → free electron in a → magnetic field.

See also: → Landau damping; → level.

For parallel propagating → electrostatic waves in a → plasma, the → resonance which occurs when the particle velocity equals the parallel phase velocity of the wave.

See also: → Landau damping; → damping.

The constant of proportionality relating the separations of lines of successive pairs of adjacent components of the levels of a spectral multiplet to the larger of the two J-values for the respective pairs. The interval between two successive components J and J + 1 is proportional to J + 1.

See also: After Alfred Landé (1888-1976), a German-American physicist, known for his contributions to quantum theory; → facteur.

A → space probe designed to land on a → planet or other solid → celestial body.

See also: → land; → -er.

A second-order nonlinear → differential equation that gives the structure of a → polytrope of index n.

See also: Named after the American astrophysicist Jonathan Homer Lane (1819-1880) and the Swiss astrophysicist Robert Emden (1862-1940); → equation

Equation of motion for a weakly ionized cold plasma.

See also: Paul Langevin (1872-1946), French physicist, who developed the theory of magnetic susceptibility of a paramagnetic gas; → equation.

A disturbance of a → plasma in the form of a
longitudinal, → electrostatic wave that propagates in the plasma due to variations in the plasma’s electron density. More specifically,
Langmuir waves are collective oscillations of inhomogeneous bunches of electrons displaced from their natural equilibrium, in which the inertia of the relatively massive ions serves to establish an electrostatic restoring force that tries to bring the electrons back to their equilibrium positions. → Landau damping causes dissipation of Langmuir waves as the electrons are either accelerated or decelerated so as to be in resonance with the phase velocity of the waves themselves.

See also: Irving Langmuir (1881-1957), American chemist and physicist, Nobel Prize in Chemistry 1932; → wave.

See also: Suggested by Irving Langmuir (1881-1957) in 1921, who was awarded the Nobel Prize in Chemistry in 1932 for his work in surface chemistry. And further developed by Cyril Hinshelwood (1897-1967) in 1926, who received the Nobel Prize in Chemistry in 1956 for his researches into the mechanism of chemical reactions.

Any means of conveying or communicating ideas; specifically, human speech.

Etymology (EN): M.E., from O.Fr. langage, from L. lingua “tongue; speech, language.”

Etymology (PE): Zabân “tongue; language,” from Mid.Pers. uzwân “tongue; language;” O.Pers. hzanm, hizânam “tongue,” Av. hizuua-, hizū- “tongue;” cf. Skt. jivhā- “tongue;” L. lingua “tongue, speech, language;” O.Ir. tenge; Welsh tafod; Lith. liezuvis; O.C.S. jezyku; M.Du. tonghe; Du. tong; O.H.G. zunga; Ger. Zunge; Goth. tuggo; PIE base *dnghwa-.

An approach in which terms reconstructed in the → proto-language are used to make inferences about its speakers’ culture and environment.

See also: → language;→ paleontology.

A → supercluster of galaxies that includes our → Local Group and about 300 to 500 known → galaxy clusters and groups. Also called → Local Supercluster. If approximated as round, it has a diameter of 12,000 km s^-1 in units of the → cosmic expansion or 160 megaparsecs, and encompasses about 10¹⁷ → solar masses.
Our Local Group lies toward the outer regions of Laniakea. Its main components are the four previously known superclusters:

→ Virgo supercluster (the part where the → Milky Way resides),
Hydra-Centaurus Supercluster (including the → Great Attractor, Antlia Wall, known as Hydra Supercluster, → Centaurus supercluster), Pavo-Indus Supercluster, and Southern Supercluster (including Fornax Cluster, Dorado and Eridanus clouds).

The most massive galaxy clusters of Laniakea are Virgo, Hydra, Centaurus, Abell 3565, Abell 3574, Abell 3521, Fornax, Eridanus, and Norma. The Laniakea supercluster was discovered by Tully et al. (2014, Nature 513, 71).

See also: From the Hawaiian words lani “heaven,” and akea “spacious, immeasurable;” → supercluster.

Any of the series of 15 consecutive → chemical elements in the → periodic table from → lanthanum to lutetium (→ atomic numbers 57 to 71 inclusive). The atoms of these metals have similar configurations and similar physical and chemical properties. They are grouped apart from the rest of the elements in the → Periodic Table because they all behave in a similar way in chemical reactions. Also called
→ rare-earth element. International Union of Pure and Applied Chemistry currently recommends the name lanthanoid rather than lanthanide.

See also: From the chemical element → lanthanum.

A soft, malleable, ductile, silver-white metallic → chemical element; symbol La. → atomic number 57; → atomic weight 138.9055; → melting point about 920°C; → boiling point about 3,460°C; → specific gravity 6.19 at 25°C; → valence +3. Lanthanum is a member of the → lanthanide group, also called → rare-earth elements. Two naturally occurring → isotopes of lanthanum are known,
¹³⁹La (more than 99%) and ¹³⁸La (less than 0.1%). The → half-life of ¹³⁸La is 1.1 x 10¹¹
years.

See also: From lanthan- + suffix -um, variant of → -ium.
The first component from Gk. lanthanein for “to lie hidden, to escape notice” because it hid in cerium ore and was difficult to separate from that rare-earth mineral. It was discovered in the form lanthanium oxide, called lanthana, by the Swedish surgeon and chemist Carl-Gustav Mosander (1797-1858) in 1839. Subsequently, in 1842, Mosander separated his lanthanium sample into two oxides; for one of these he retained the name lanthanum and for the other he gave the name didymium (or twin).

The French great mathematician, physicist, and astronomer Pierre-Simon Marquis de Laplace (1749-1827).

→ Laplace operator; → Laplace plane; → Laplace resonance; → Laplace transform; → Laplace’s demon ; → Laplace’s equation ; → Kant-Laplace hypothesis

Same as → Laplacian.

See also: → Laplace; → operator.

The plane normal to the axis about which the pole of a satellite’s orbit → precesses. In his study of Jupiter’s satellites, Laplace (1805) recognized that the combined effects of the solar tide and the planet’s oblateness induced a “proper” inclination in satellite orbits with respect to Jupiter’s equator. He remarked that this proper inclination increases with the distance to the planet, and defined an orbital plane (currently called Laplace plane) for circular orbits that lies between the orbital plane of the planet’s motion around the Sun and its equator plane (Tremaine et al., 2009, AJ, 137, 3706).

See also: → Laplace; → plane.

An → orbital resonance that makes a 4:2:1 period ratio among three bodies in orbit. The → Galilean satellites → Io, → Europa, → Ganymede are in the Laplace resonance that keeps their orbits elliptical. This interaction prevents the orbits of the satellites from becoming perfectly circular (due to tidal interactions with Jupiter), and therefore permits → tidal heating of Io and Europa.

For every four orbits of Io, Europa orbits twice and Ganymede orbits once. Io cannot keep one side exactly facing Jupiter and with the varying strengths of the tides because of its elliptical orbit, Io is stretched and twisted over short time periods.

See also: This commensurability was first pointed out by Pierre-Simon Laplace, → Laplace; → resonance.

An integral transform of a function obtained by multiplying the given function f(t) by e^-pt, where p is a new variable, and integrating with respect to t from t = 0 to t = ∞.

See also: → Laplace; → transform.

An imaginary super-intelligent being who knows all the laws of nature and all the parameters describing the state of the Universe at a given moment can predict all subsequent events by virtue of using physical laws. In the introduction to his 1814 Essai philosophique sur les probabilités, Pierre-Simon Laplace puts forward this concept to uphold → determinism, namely the belief that the past completely determines the future. The relevance of this statement, however, has been called into question by quantum physics laws and the discovery of → chaotic systems.

See also: → Laplace; → demon.

A → linear differential equation of the second order the solutions of which are important in many fields of science, mainly in electromagnetism, fluid dynamics, and is often used in astronomy. It is expressed by:

∂²V/ ∂x² + ∂²V/ ∂y² + ∂²V/ ∂z² = 0. Laplace’s equation can more concisely expressed by: ∇²V = 0.
The function V may, for example, be the potential at any point in the electric field where there is no free charge. The general theory of solutions to Laplace’s equation is known as potential theory.

See also: → Laplace; → equation.

A differential → operator, denoted ∇² = ∇.∇,
which is the sum of all second partial derivatives of a dependant variable:

∇²≡ ∂²/∂x² + ∂²/∂y² + ∂²/∂z², in Cartesian coordinates.

It has numerous applications in several fields of physics and mathematics. Also called Laplace operator.

See also: Named after → Laplace.

Of more than average size, quantity, degree, etc.; of great scope or range.

Etymology (EN): From O.Fr. large “broad, wide,” from L. largus “abundant, copious, plentiful,” of unknown origin.

Etymology (PE): Bozorg “great, large, immense, grand, magnificient;” Mid.Pers. vazurg “great, big, high, lofty;” O.Pers. vazarka- “great;” Av. vazra- “club, mace” (Mod.Pers. gorz “mace”); cf. Skt. vájra- “(Indra’s) thunderbolt,” vaja- “strength, speed;” L. vigere “be lively, thrive,” velox “fast, lively,” vegere “to enliven,” vigil “watchful, awake;”
P.Gmc. *waken (Du. waken; O.H.G. wahhen; Ger. wachen “to be awake;” E. wake); PIE base *weg- “to be strong, be lively.”

The larger of the two Magellanic Cloud galaxies visible in the southern hemisphere at
about 22 degrees from the South Celestial Pole. It is approximately on the border between the constellations → Dorado and → Mensa in a region of faint stars. The center of the LMC is approximately RA: 5h 23m 35s, dec: -69° 45’ 22’’. The LMC shines with a total → apparent visual magnitude of approximately zero.

It spans an area of the sky about 9 by 11 degrees, corresponding to about 30,000 → light-years across in the longest dimension, for a distance of some 162,000 light-years.

It has a visible mass of about one-tenth that of our own Galaxy (10¹⁰ Msun). The LMC and its twin, the → Small Magellanic Cloud, are two of our most prominent Galactic neighbors.

The LMC is classified as a disrupted → barred spiral galaxy of type SBm, the prototype of a class of → Magellanic spirals. The galaxy is characterized by a prominent offset → stellar bar located near its center with the dominant → spiral arm to the north with two “embryonic” arms situated to the south.

The → metallicity in the LMC is known to be lower than in the solar neighborhood by a factor 2 or more.

Based on 20 → eclipsing binary systems, the distance to the LMC is measured to one percent precision to be 49.59±0.09 (statistical) ±0.54 (systematic) kpc (Pietrzynski et al., 2019, Nature 567, 200).

See also: → large; → Magellanic; → cloud.

A → dimensionless number representing the ratio of various → physical constants. For example:

1. The ratio of the → Coulomb force to the → gravitational force for a proton-electron pair
   (e²/Gm_pm_e), which is of the order of 10⁴⁰.
   

2. The age of Universe (T = 10-20 x 10⁹ years) in units of the → elementary time: T/t_e≅ 10⁴⁰.
   

3. The square root of the total number of particles in the Universe ≅ 10⁴⁰.

See also: → large; → number.

The idea whereby the coincidence of various → large numbers would bear a profound sense as to the nature of physical laws and the Universe. Dirac suggested that the coincidence seen among various large numbers of different nature is not accidental but must point to a hitherto unknown theory linking the quantum mechanical origin of the Universe to the various cosmological parameters. As a consequence, some of the → fundamental constants cannot remain unchanged for ever. According to Dirac’s hypothesis, atomic parameters cannot change with time and hence the → gravitational constant should vary inversely with time (G∝ 1/t). Dirac, P. A. M., 1937, Nature 139, 323; 1938, Proc. R. Soc. A165, 199.

See also: → large; → number; → hypothesis.

A turbulent flow in which viscous forces are negligible compared to nonlinear advection terms, which characterize the variation of fluid quantities. The dynamics becomes generally turbulent when the Reynolds number is high enough. However, the critical Reynolds number for that is not universal, and depends in particular on boundary conditions.

See also: → large; → Reynolds number; → flow.

1. A scale representing measures that significantly override the usual ones of the same kind.
   

2. In meteorology, a scale in which the curvature of the earth is not negligible.

See also: → large; → scale.

Initial name given to → Vera C. Rubin Observatory.

See also: → large; → synoptic; → survey; → telescope.

The distribution of galaxies and other forms of mass on large distance scales, covering hundreds of millions of → light-years.

See also: → large; → scale; → structure.

The fifth of Neptune’s known satellites. It orbits 73,600 km from Neptune and is a non spherical object about 208 × 178 km in size. It was discovered using NASA’s Voyager 2 mission in 1989.

See also: In Gk. mythology, Larissa is a princess of Argos (in central Greece) who, according to some, bore Poseidon three sons: Akhaios, Pelasgos and Pythios (though others gave these eponymous heroes different parents).

The frequency of precession of a charged particle describing a circular motion in a plane perpendicular to the magnetic induction in a uniform magnetic field.

See also: Named after Joseph Larmor (1857-1942), an Irish physicist, the first to calculate the rate at which energy is radiated by an accelerated electron, and the first to explain the splitting of spectrum lines by a magnetic field; → frequency.

The radius of the circular motion of a → charged particle moving in a → uniform magnetic field. Same as → gyroradius, → radius of gyration, → cyclotron radius. The Larmor radius (r_L) is obtained by equating the → Lorentz force with the → centripetal force: qvB = mv²/r_L, which leads to r_L = p/(ZeB), where p is → momentum, Z is → atomic number, e is the → electron charge, and B is → magnetic induction. The frequency of this circular motion is known as the → gyrofrequency.

See also: → Larmor frequency; → radius.

If a system of → charged particles, all having the same ratio of charge to mass (q/m), acted on by their mutual forces, and by a central force toward a common center, is subject in addition to a weak uniform magnetic field (B), its possible motions will be the same as the motions it could perform without the magnetic field, superposed upon a slow → precession of the entire system about the center of force with angular velocity ω = -(q/2mc)B.

See also: → Larmor frequency; → theorem.

An → empirical relationship between the internal → velocity dispersion of → molecular clouds and their size. The velocity dispersions are derived from molecular → linewidths, in particular those of → carbon monoxide. It was first established on star forming regions and found to be:

σ (km s^-1) = 1.10 L (pc)^0.38,

where σ is the velocity dispersion and L the size. The relation holds for 0.1 ≤ L ≤ 100 pc. More recent set of cloud data yield:

σ (km s^-1) = L (pc)^0.5.

This relation indicates that larger molecular clouds have larger internal velocity dispersions. It is usually interpreted as evidence for → turbulence in molecular clouds. Possible sources of interstellar turbulence include the following processes operating at various scales: galactic-scale (→ differential rotation, → infall
of extragalactic gas on the galaxy), intermediate-scale (expansion of → supernova remnants, → shocks, → stellar winds from → massive stars), and smaller-scale processes
(→ outflows from → young stellar objects).

See also: First derived by Richard B. Larson, American astrophysicist working at Yale University (Larson, 1981, MNRAS 194, 809). See Falgarone et al. (2009, A&A 507, 355) for a recent study; → relation.

The analytical solution to the → hydrodynamic equations describing the → collapse of an → isothermal sphere. The Larson-Penston solution is → self-similar for a purely dynamical isothermal collapse with spherical symmetry. It corresponds to the collapse prior to the formation of a → protostar, and thus is suitable for the study of → pre-stellar cores. The Larson-Penston solution was extended by Shu (1977) to obtain a whole family of solutions for this problem.

See also: Named after R. B. Larson (1969, MNRAS 145, 271) and M. V. Penston (1969, MNRAS 144, 425), who simultaneously, but independently, did this study.

1. Of, pertaining to, or located in the larynx.
   

2. Phonetics: articulated in the larynx (Dictionary.com).

See also: → larynx; → -al.

A consonant generated in the → larynx with the → vocal cords partly closed and partly vibrating. It is hypothesized that the → Proto-Indo-European language contained some laryngeal consonants (denoted by H).

See also: → laryngeal; → consonant.

A muscular and cartilaginous structure lined with mucous membrane at the upper part of the → trachea in humans, in which the → vocal cords are located (Dictionary.com).

Etymology (EN): From M.Fr. larynx, from M.L. from Gk. larynx (genitive laryngos) “the upper windpipe,” probably from laimos “throat,” influenced by pharynx “throat, windpipe.”

Etymology (PE): Hanjaré, from Ar. Hanjarah.

1. A device that generates an intense directional beam of → monochromatic and → coherent light by exciting atoms to a higher energy level and causing them to radiate their energy in phase. The high degree of collimation arises from the fact that excited atoms are are situated in a cavity bounded by two parallel front and back mirrors. A first photon stimulates
   an atom which emits a second photon, and so on thanks to the mirrors. The resulting photons are all identical. They have the same energy which gives them the same color and a unique direction. The first working laser, a pulsed ruby device, was developed by T. Maiman in 1959.

See also → gas laser, → stimulated emission; → maser.

2. The light produced in this way.

See also: Acronym for light amplification by stimulated emission of radiation,
on pattern of → maser.

A technique that uses a suitable arrangement of → laser beams and magnetic fields to capture → cesium (¹³³Cs) atoms from a thermal vapor and slow the motion of the atoms, cooling them to just a few micro-kelvins above the → absolute zero. The technique allows trapping some 10⁷ cesium atoms in a cloud a few millimeters in diameter in a few tenths of a second. At a temperature of 2 μK, the average thermal velocity of the cesium atoms is of the order of 1 cm s^-1, so they stay together for a relatively long time. The laser cooling technique is the key tool which enabled the operation of an → atomic fountain clock.

See also: → laser; → cooling; → technique.

An optical instrument using laser → beams to form → interference pattern.

There are two types of laser interferometers: → homodyne and → heterodyne. A homodyne interferometer, like → Michelson interferometer, uses a single-frequency laser source.

A → heterodyne interferometer uses a laser source with two close frequencies.

See also: → laser; → interferometer.

A facility dedicated to the detection and measurement of cosmic → gravitational waves. It consists of two widely separated installations, or detectors, within the United States, operated in unison as a single observatory. One installation is located in Hanford (Washington) and the other in Livingston (Louisiana), 3,000 km apart.

Funded by the National Science Foundation (NSF), LIGO was designed and constructed by a team of scientists from the California Institute of Technology, the Massachusetts Institute of Technology, and by industrial contractors. Construction of the facilities was completed in 1999. Initial operation of the detectors began in 2001.

Each LIGO detector beams laser light down arms 4 km long, which are arranged in the shape of an “L.” If a gravitational wave passes through the detector system, the distance traveled by the laser beam changes by a minuscule amount – less than one-thousandth of the size of an atomic nucleus (10^-18 m). Still, LIGO should be able to pick this difference up.

LIGO directly detected gravitational waves for the first time from a binary → black hole merger (GW150914) on September 14, 2015 (Abbott et al., 2016, Phys. Rev. Lett. 116, 061102).

The Nobel Prize in physics 2017 was awarded to three physicists (Rainer Weiss, Barry C. Barish, and Kip S. Thorne) for decisive contributions to the LIGO detector and the observation of gravitational waves. LIGO had a prominent role in the detection of → GW170817, the first event with an → electromagnetic counterpart.

See also: → laser; → interferometer; → gravitational; → wave; → observatory.

A collaborative project between → NASA and → ESA to develop and operate a space-based gravitational wave detector sensitive at frequencies between 0.03 mHz and 0.1 Hz. LISA detects gravitational-wave induced strains in → space-time by measuring changes of the separation between fiducial masses in three spacecraft 5 million km apart. Ultimately, NASA and ESA decided in 2011 not to proceed with the mission. LISA was not the highest ranked mission in the 2010 Decadal Survey and funding constraints prevented NASA from proceeding with multiple large missions (http://lisa.nasa.gov). → LISA pathfinder.

See also: → laser; → interferometer; → space; → antenna.

Occurring or coming after all others, as in time, order, or place. → last contact, → last quarter

Etymology (EN): Last, from O.E. latost (adj.) and lætest (adv.), superlative of læt (adj.) and late (adv.);
cognate with O.Fris. lest, Du. laatst, O.H.G. laggost, Ger. letzt.

Etymology (PE): Vâpasin, from vâ-, as intensive prefix, → de-,

• pasin, from pas “after, afterward, behind; finally, at last” (Mid.Pers. pas “behind, before, after;” O.Pers. pasā “after;” Av. pasca “behind (of space); then, afterward (of time);” cf. Skt. pazca “behind, after, later;”
  L. post “behind, in the rear; after, afterward;” O.C.S. po “behind, after;” Lith. pas “at, by;”
  PIE base *pos-, *posko-) + -in superlative suffix.

To continue in time; go on; endure.

Etymology (EN): M.E. lasten, from O.E. læstan “to continue, endure;” cf. Goth. laistjan “to follow after,” Ger. leisten “to perform, achieve,”), from PIE root *lois- “furrow, track.”

Etymology (PE): Pâyidan “to watch, observe; remain or continue in existence, last,” variants pâsidan, pâhidan; Mid.Pers. pây- “to protect, guard;” Sogdian p’y “to observe, protect, watch over;” O.Pers. pā- “to protect,” pāta- “protected;” Av. pā- “to protect,” pāti “guards,” nipā(y)- (with ni-) “to watch, observe, guard,” nipātar- “protector, watcher,” nipāθri- “protectress;”
cf. Skt. pā- “to protect, keep,” tanû.pā- “protecting the body,” paś.pā- “shepherd;” Gk. poma “lid, cover,” poimen “shepherd;” L. pascere “to put out to graze,” pastor “shepherd;” Lith. piemuo “shepherd;” PIE base *pā- “to protect, feed.”

Same as → fourth contact at an eclipse.

See also: → last; → contact.

One of the phases of the Moon that appears when it is 90 degrees west of the Sun. Approximately one week after a full moon, when half of the Moon’s disk is illuminated by the Sun. → first quarter.

See also: → last; → quarter.

The epoch in the early evolution of the Universe when matter and photons decoupled. Once atoms formed, light and matter stopped constantly interacting with one another, and photons were able to travel freely. As a result, the Universe became transparent. Light from this period is observed today as the → cosmic microwave background radiation. Same as → decoupling era and → recombination era.

See also: → last; → scattering.

The set of locations in space corresponding to the → last scattering epoch in the early Universe. It is a spherical surface around the present-day observer from which the → cosmic microwave background radiation appears to emanate.

See also: → last; → scattering; → surface.

Last in order of birth; youngest.

Etymology (EN): → last; → born.

Etymology (PE): Demâzâ, from Lori, Laki demâzâ, from demâ “last, end, back,” related to dom, → tail, + zâ contraction of zâd, → born.

Continuing or remaining for a long time; enduring.

See also: → last; → -ing.

1. Happening or arriving after an expected or arranged time; not on time, beyond usual time.
   

2. Belonging to an advanced stage or period in the development of something. → Late Heavy Bombardment, → late helium flash, → late thermal pulse, → late-type galaxy, → late-type star.

Etymology (EN): M.E., from O.E. læt “slow, late;” cf. Ger. lass “slothful;” O.N. latr, Goth. lats “slow, lazy;” L. lassus “tired, faint;” Gk. ledein “to be weary.”

Etymology (PE): Dir “late; tardily, slowly; a long while; old, antique,” from Mid.Pers. dêr, variants dagr, drâz “long”
(Mod.Pers. derâz “long,” variant Laki, Kurdi derež);
O.Pers. darga- “long;” Av. darəga-, darəγa- “long,” drājištəm “longest;” cf. Skt. dirghá- “long (in space and time);” L. longus “long;” Gk. dolikhos “elongated;” O.H.G., Ger. lang; Goth. laggs “long;” PIE base *dlonghos- “long.”
Dirân, adjective, variant of dir, as above.

A cataclysmic event in the history of the → solar system, estimated to have occurred 3.9 billion years ago (about 600 million years after the formation of the → terrestrial planets) during which → asteroid and → comet impacts with Earth were some 20,000 times more frequent than today. It is estimated that during this period the terrestrial planets were bombarded with an object 1 km in size every 20 years. This hypothetical event lasted 50 to 150 million years. Several explanations have been put forward, among which the occurrence of an instability in the outer solar system which caused → orbital migration of small bodies from the → Kuiper belt inward.

See also: → late, with respect to the formation time of the planets; → heavy; bombardment, noun from bombard, from Fr. bombarder, from bombarde “mortar, catapult” from bombe, from It. bomba, probably from L. bombus “a booming sound,” from Gk. bombos “deep and hollow sound.”

A → helium flash event that occurs during the → post-AGB phase.

Some of the central stars of planetary nebulae (→ CSPN) experience a final → thermal pulse after having achieved a → white dwarf configuration and begun their descent along a → white dwarf cooling track of nearly constant radius. During such a pulse, most of the hydrogen remaining in the star at pulse onset is incorporated into the helium-burning convective shell and completely burned. Following the pulse, the star swells briefly to → red giant dimensions
(Iben et al. 1983; ApJ 264, 605).

See also: → late; → helium; → flash.

In evolutionary models of → low-mass and → intermediate-mass stars, the occurrence of a → helium shell flash on the → horizontal branch of the → post-AGB track, while → hydrogen shell burning is still going on.

See also: → late; → thermal; → pulse.

In the → Hubble classification, a galaxy on the left part of the → Hubble sequence. See also → early-type galaxy.

See also: → late; → type; → galaxy.

A star of → spectral type K, M, S, or C, with a surface temperature lower than that of the Sun. → early-type star. See also → spectral classification.

See also: → late; → type;
→ star.

Present but not visible, apparent, or actualized; existing as potential (Dictionary.com). → latent heat.

Etymology (EN): From L. latentem (nominative latens), pr.p. of latere “to lie hidden.”

Etymology (PE): Nahân “concealed, hid; clandestine;” Mid.Pers. nihân “secrecy, a secret place, a hiding place,” nihânik “concealed;” Av. niδāti- “deposing, deposit.”

The amount of → thermal energy that is absorbed or released by a unit amount of a substance in the process of a phase change under conditions of constant pressure and temperature.

See also: → latent; → heat.

Of or relating to the → side; situated at, proceeding from, or directed to a side (Dictionary.com).

Etymology (EN): M.E., from O.Fr. latéral and directly from L. lateralis “belonging to the side,” from latus “the side, flank; lateral surface.”

Etymology (PE): Kenâri, relating to kenâr, → side.

The angle between a perpendicular at a location, and the → equatorial plane of the Earth. → longitude. See also:
→ astronomical latitude, → celestial latitude, → circle of latitude, → colatitude, → ecliptic latitude, → Galactic latitude, → geocentric latitude, → geodetic latitude, → geographic latitude, → high latitudes, → horse latitudes, → middle latitudes, → spherical latitude, → supergalactic latitude.

Etymology (EN): L. latitudo “breadth, width, size,” from latus “wide,” from PIE base *stela- “to spread” (cf. O.C.S. steljo “to spread out,” Arm. lain “broad”).

Etymology (PE): Varunâ, from var “breadth, side, breast,” variant bar, Tabari vari “width,” Mid.Pers. var “breast,” Av. varah- “breast”
(Sk. vara- “width, breadth”) + -u a suffix forming adjectives;
Av. vouru- “wide;” + -nâ a suffix of dimension.

1. A regular geometric arrangement of points in a plane or in space.
   

2. → Crystal lattice.
   

3. A structure in a nuclear reactor containing nuclear fuel and other materials arranged in a regular geometrical pattern.
   

4. Math.: A partially ordered set in which each two-element subset has both a greatest lower bound and a least upper bound.

Etymology (EN): From O.Fr. latiz “lattice,” from late “lath, board, plank, batten” (Fr. latte); cf. O.H.G. latta “lath.”

Etymology (PE): Jâré, from jarra “net; snare,” Afghan jâli “reticulated garment,” Tabari jarazin “grilled apparatus used in a watercourse to gather thatch and trash;” cf. Skt. jāla- “net, snare, lattice.”

The energy required to separate an ion from a → crystal to an infinite distance. In other words, the energy released when one → mole of a crystal is formed from gaseous ions.

See also: → lattice; → energy.

The chord through a focus and perpendicular to then major axis of a conic section.

Etymology (EN): L. latus “side;” rectum “straight,” → right.

Etymology (PE): Târ “thread, warp, string”
(related to tur “net, fishing net, snare,”
tâl “thread” (Borujerdi dialect), tân “thread, warp of a web,” from tanidan, tan-
“to spin, twist, weave;” Mid.Pers. tanitan; Av. tan- “to stretch, extend;” cf. Skt. tan- “to stretch, extend;” tanoti “stretches,” tántra- “warp; essence, main point;” Gk. teinein “to stretch, pull tight;” L. tendere “to stretch;”
Lith. tiñklas “net, fishing net, snare,” Latv. tikls “net;” PIE base *ten- “to stretch.”

1. To throw or propel with force; hurl. → jet launching.
   

   2. To set (a missile, spacecraft, etc) into motion

Etymology (EN): From M.E. launchen “to throw as a lance,” O.Fr. lanchier, lancier “to hurl, throw, cast,” from L.L. lanceare “wield a lance,” from L. lancea “light spear, lance.”

Etymology (PE): From partâb “a throw, an arrow that flies far,” partâbidan “to throw,” → ballistics.

Molten → magma released from a volcanic vent or fissure.

Etymology (EN): Lava, from It. lava “torrent, stream,” from L. lavare “to wash;” PIE base *lou- “to wash;” cf. Persian Lori, Kurdi, Malâyeri laf “flood,” variants Tabari lé, [Mo’in, Dehxodâ] lur, lây “flood;” Gk. louein “to wash.”

Etymology (PE): Godâzé noun from godâxtan “to melt,” from Mid.Pers. vitâxtan, vitâcitan “to melt,” from Av. vi-taxti- “flowing away, melting,” from vi- “apart, away from, out” (O.Pers. viy- “apart, away;” cf. Skt. vi- “apart, asunder, away, out;” L. vitare “to avoid, turn aside”) + tak- “to run, to flow,” taciāp- “flowing water,” tacinti (3pl.pers.act.) “to flow,”
tacar- “course,” tacan “current, streaming;” Mod.Pers. tâz-, tâxtan “to run; to hasten; to assault,” tâzi “swift (greyhound),” tak “running, rush;”
Mid.Pers. tâz-, tâxtan “to flow, to cause to walk,” tc- “to flow, to walk,” tag “running, attack,” tâzig “swift, fast;”
Khotanese ttajs- “to flow, to walk;” cf. Skt. tak- “to rush, to hurry,” takti “runs;” O.Ir. tech- “to flow;” Lith. teketi “to walk, to flow;” O.C.S. tešti “to walk, to hurry;” Tokharian B cake “river;” PIE base *tek^w- “to run; to flow.”

1. A rule of conduct or procedure established by custom, agreement, or authority.
   
2. A code of principles based on morality, conscience, or nature.
   
3. Physics: A statement of a scientific fact or phenomenon that is invariable under given conditions; e.g. → Newton’s law of gravitation, → second law of thermodynamics.
   
4. Math.: A general principle deduced from particular facts expressed by the statement that a particular phenomenon always occurs if certain conditions are present.

Etymology (EN): M.E., O.E. lagu, from O.N. *lagu, variant of lag “that which is laid down;” cf. Ger. liegen, E. lay, lie; PIE *legh- “To lie, lay;” compare with Hittite laggari “falls, lies,” Gk. lekhesthai “to lie down,” L. lectus “bed,” O.Ir. lige “bed, tomb,” Tokharian lake, leke “bed.”

Etymology (PE): Qânun, from Ar., ultimately from Gk. kanon “rule.”
Arté, from O.Pers. arta- “law, justice;” Av. arəta-, ərəta- “law, order,” variant aša- “truth, cosmic order,” aipi-ərəta- “firmly assigned,” from root ar- “to fix;” cf. Skt. rtá- “truth, world order; oath;” Ossetci ard “oath;” Gk. arthon “limb, articulation,” artus “a joint;”
L. artus “a joint;” PIE base *ar- “to join, to fit together.”

An expression that for any triangle relates the length of a side to the cosine of the opposite angle and the lengths of the two other sides. If a, b, and c are the sides and A, B, and C are the corresponding opposites angles:

a² = b² + c²

• 2bc cos A; b² = c² + a²
• 2ca cos B; c² = a² + b²
• 2ab cos C.

See also: → law; → cosine.

Same as → principle of excluded middle.

See also: → law; → exclude; → middle.

Same as → principle of identity.

See also: → law; → identity.

Same as → Newton’s first law. The → reference frames to which the law applies are called → inertial frames.

See also: → law; → inertia.

Same as → principle of non-contradiction.

See also: → law; → non-; → contradiction.

One of the two laws governing reflection of light from a surface: a) The → incident ray, normal to surface, and reflected ray lie in the same plane. b) The → angle of incidence (with the normal to the surface) is equal to the → angle of reflection.

See also: → law; → reflection.

One of the two laws governing → refraction of light when it enters another transparent medium: a) The → incident ray, normal to the surface, and refracted ray, all lie in the same plane. b) → Snell’s law is satisfied.

See also: → law; → refraction.

In any triangle the sides are proportional to the sines of the opposite angles: a/sin A = b/sin B = c/sin C, where A, B, and C are the three vertices and a, b, and c are the corresponding sides.

See also: → law; → sine.

An artificially produced → radioactive→ chemical element; symbol Lr (formerly Lw). → Atomic number 103; → atomic weight of most stable isotope 262; → melting point about 1,627°C; → boiling point and → specific gravity unknown; → valence +3. The longest half-life associated with this unstable element is 3.6 hour ²⁶²Lr. Credit for the first synthesis of this element in 1971 is given jointly to American chemists from the University of California laboratory in Berkeley
under Albert Ghiorso and the Russian team at the Joint Institute for Nuclear Reactions lab in Dubna, under Georgi N. Flerov.

See also: Named the American physicist Ernest 0. Lawrence (1901-1958), who developed the → cyclotron, + → -ium.

The three basic laws of → dynamics which were first formulated by Isaac Newton in his classical work “Mathematical Principles of Natural Philosophy” published in 1687. → Newton’s first law of motion; → Newton’s second law of motion; → Newton’s third law of motion.

See also: → law; → dynamics.

A thickness of some material laid on or spread over a surface.

Etymology (EN): From M.E. leyer, legger + -er. The first element from layen, leggen “to lay,” from O.E. lecgan;
cf. Du. leggen; Ger. legen; O.N. legja; Goth. lagjan

Etymology (PE): Lâyé “layer,” from lâ, lây “fold” + -é nuance suffix of nouns.

The ordinary Newtonian energy conservation equation when expressed in expanding cosmological coordinates. More specifically, it is the relation between the → kinetic energy per unit mass associated with the motion of matter relative to the general → expansion of the Universe and the → gravitational potential energy per unit mass associated with the departure from a homogeneous mass distribution. In other words, it deals with how the energy of the → Universe is partitioned between kinetic and potential energy.
Also known as → cosmic energy equation.
In its original form, the Layzer-Irvine equation accounts for the evolution of the energy of a system of → non-relativistic particles, interacting only through gravity, until → virial equilibrium

is reached. But it has recently been generalized to account for interaction between → dark matter and a homogeneous → dark energy component. Thus,
it describes the dynamics of local dark matter perturbations in an otherwise homogeneous and → isotropic Universe (P. P. Avelino and C. F. V. Gomes, 2013, arXiv:1305.6064).

See also: W. M. Irvine, 1961, Ph.D. thesis, Harvard University; D. Layzer, 1963, Astrophys. J. 138, 174; → equation.