An Etymological Dictionary of Astronomy and Astrophysics
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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.

→ Lagrangian; → equation.

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.

→ Lagrangian; → function.

Same as → Meissa.

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

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

→ Landau damping; → damping.

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

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.

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

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

→ language;→ paleontology.

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.

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

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.

→ 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.

→ Laplace; → equation.

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).

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.

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

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).

→ laryngeal; → consonant.

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.

→ laser; → interferometer; → gravitational; → wave; → observatory.

Same as → fourth contact at an eclipse.

→ last; → contact.

Same as → principle of non-contradiction.

→ 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.

→ 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.

→ law; → refraction.

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).

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

An intercalary month employed in some calendars to preserve a seasonal relationship between the Lunar and Solar cycles. → embolismic month.

→ leap; → month.