An Etymological Dictionary of Astronomy and Astrophysics
English-French-Persian

A → differential equation that describes the time evolution of the → scalar potential of the field φ. It is expressed by: ∇²φ = (1/c²)∂²φ/∂t², where c is → velocity of → longitudinal waves and ∇² is the → Laplacian operator.

→ acoustic; → wave; → equation.

An equation in the form of P = 0, where P is a → polynomial having a finite number of terms.

→ algebra; → equation.

An irregularity in the Moon's orbit, which can amount to 11 degrees in a period of one year. It results from the Sun's disturbing effect on the motion of the Moon due to varying distance between them.

→ annual; → equation.

A mathematical expression, derived from the → Clausius-Clapeyron equation, of the relation between the vapor pressure and the temperature of pure substances. It shows that the logarithm of vapor pressure is linearly dependent on the reciprocal of → absolute temperature.

Named after Louis Charles Antoine (1825-?), a French marine engineer, who derived the equation; → equation.

An important relationship in physical chemistry that combines the concepts of → activation energy and the → Maxwell-Boltzmann distribution law. It is expressed by: k = Ae^-E_a/(RT), where k is the chemical → reaction rate, E_a is the activation energy, R is the → gas constant, and T is → temperature.

Named for Svante Arrhenius (1859-1927), Swedish chemist and physicist who suggested the relationship in 1889.

The equation expressing → Bernoulli's theorem: P + (1/2)ρV² + ρgz = constant, where P is the fluid → pressure, V is → velocity, ρ is → density, g is the acceleration due to → gravity, and z is the vertical reference → level. The theree terms are called → static pressure, → dynamic pressure, and → hydrostatic pressure, respectively. The Bernoulli equation states that the total pressure along a → streamline is → constant.

→ Bernoulli's theorem; → equation.

A linear second-order differential equation, the solutions to which are called Bessel functions.

From → Bessel; → equation

Hamugeš, → equation.

1) An equation that expresses the relative number (per unit volume) of → excited atoms in different states as a function of the temperature for a gas in → thermal equilibrium: N_u/N_l = (g_u/g_l) exp (-ΔE/kT_ex), where N_u and N_l are the upper level and lower level populations respectively, g_u and g_l the → statistical weights, ΔE = hν the energy difference between the states, k is → Boltzmann's constant, and h  → Planck's constant.

→ Boltzmann's constant; → equation.

The most general form of an equation.

→ canonical; → equation.

A relationship between the → refractive index (n) and the wavelength of light (λ) passing through a medium. It is commonly stated in the following form: n = A + B/λ² + C/λ⁴, where A, B, and C are constants characterizing the medium. The two-component Cauchy equation is n = A + B/λ², from which the dispersion becomes dn/dλ = -2B/λ³ showing that dispersion varies approximately as the inverse cube of the wavelength. The dispersion at 4000 A will be about 8 times as large as at 8000 Å.

Named after Augustin Louis Cauchy (1789-1857), French mathematician and physicist who found the first equation of dispersion in 1836; → equation.

Physics: An analytical relationship between a set of physical variables that determines the state of a physical system.
Math.: The equation which is solved to find a matrix's eigenvalues, also called the characteristic polynomial.

→ characteristic; → equation.

The symbolic representation of a chemical reaction where the formulae of the → reactants are placed on the left and the formulae of → products on the right of an arrow.

→ chemical; → equation.

An equation that relates the temperature and pressure dependence of phases in equilibrium with the heat interaction and volume change associated with a phase change: dP/dT = L/T ΔV, where dP/dT is the slope of the coexistence curve, L is the → latent heat, T is the temperature, and ΔV is the volume change of the phase transition.

Named after Émile Clapeyron (1799-1864), a French engineer and physicist, one of the founders of → thermodynamics; → equation.

A first-order improvement on the → ideal gas law that corrects for the finite volume of molecules.

After Rudolf Clausius (1822-1888), a German physicist and mathematician, → equation.

An approximation of the → Clapeyron equation for liquid-vapor equilibrium that incorporates the → ideal gas law and states that the logarithm of vapor pressure is inversely proportional to temperature.

→ Clausius equation; → Clapeyron equation.

Theoretical equation which gives the change in the photon wavelength due to the → Compton effect.

→ Compton; → equation.

Same as the → Layzer-Irvine equation.

→ cosmic; → energy; → equation.

An equation containing unknowns of the third power; the general form: ax³ + bx² + cx + d = 0.

Cubic, of or pertaining to → cube; → equation.

According to the → de Broglie hypothesis, which has been verified by experiments, every → particle of matter, whatever its nature, has a characteristic → wavelength associated with its wavelike quantum aspect. The de Broglie equation gives the equivalent wavelength of a moving particle: λ = h/mv, where h is → Planck's constant, m the mass of the particle, and v its velocity.
See also: → de Broglie wavelength, → Davisson-Germer experiment.

Named after Louis Victor de Broglie (1892-1987), French physicist, creator of a new field in physics, wave mechanics, who won the Nobel prize in physics in 1929. → equation

An → equation of state for → real gases which leads to the → van der Waals equation as a → first approximation. It is of the form P(V - b) [exp (a/VRT)] = RT, where P is the pressure, V is the volume, T is the thermodynamic temperature, R is the → gas constant, and a and b are the constants characteristic of the gas.

Named after Conrad Dieterici (1858-1929), a German physicist; → equation.