An Etymological Dictionary of Astronomy and Astrophysics
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The equation that describes the → radiative transfer. It states that the → specific intensity of radiation I_σ during its propagation in a medium is subject to losses due to → extinction and to → gains due to → emission: dI_σ/dx = - μ_σ . I_σ + ρ . j_σ, where x is the coordinate along the → optical path, μ_σ is the → extinction coefficient, ρ is the mass → density, and j_σ is the → emission coefficient per unit mass.

→ radiative; → transfer; → equation.

A mathematical expression that describes the relationship between two or more variables. It indicates the nature of the relationship and, in particular, the extent to which one can predict some variables by knowing others.

→ regression, → equation.

An equation that gives the number of atoms of a given species in various stages of → ionization that exist in a gas in → thermal equilibrium as a function of the temperature, density, and ionization energies of the atoms.

Named after the Indian astrophysicist Megh Nad Saha (1894-1956), who first derived the equation in 1920; → equation.

A fundamental equation of physics in → quantum mechanics the solution of which gives the → wave function, that is a mathematical expression that contains all the information known about a particle. This → partial differential equation describes also how the wave function of a physical system evolves over time.

Named after Erwin Schrödinger (1887-1961), the Austrian theoretical physicist, Nobel Prize 1933, who first developed the version of quantum mechanics known as → wave mechanics; → equation.

A fundamental equation of physics in → quantum mechanics the solution of which gives the → wave function, that is a mathematical expression that contains all the information known about a particle. This → partial differential equation describes also how the wave function of a physical system evolves over time.

Named after Erwin Schrödinger (1887-1961), the Austrian theoretical physicist, Nobel Prize 1933, who first developed the version of quantum mechanics known as → wave mechanics; → equation.

An empirical relation between the → refractive index of a medium and the wavelength of light passing through the medium: n² - 1 = Σ (A_iλ²/(λ² - λ_i²)), where n is the refractive index at wavelength λ, and A_i and λ_i are constants.

Named after Wolfgang Sellmeier who derived the equation in 1871; → equation.

In ancient astronomy, the difference between the Sun's mean and actual position. The ancients observed that, although the motion of the Sun in the ecliptic is almost uniform, it is subject to a small annual variation.

→ solar; → equation.

A set of → differential equations describing the physical properties of stars based on two main assumptions: a star is a perfect sphere and the net force on a macroscopic mass element is zero. If the effects of rotation and magnetism are ignored, these assumptions lead to a set of five differential equations.

→ stellar; → structure; → equation.

Fluid mechanics: A second order differential equation that governs the vertical structure of a perturbation in a stratified parallel flow.

Named after G. I. Taylor (Effect of variation in density on the stability of superposed streams of fluid, 1931, Proc. R. Soc. Lond. A, 132, 499), → Taylor number, and S. Goldstein (On the stability of superposed streams of fluids of different densities, 1931, Proc. R. Soc. Lond. A, 132, 524); → equation.

An → equation of state that satisfactorily describes the behavior of → real gass over a wide range of temperatures and pressures. It is derived from considerations based on kinetic theory, taking into account to a first approximation the size of a molecule and the cohesive forces between molecules: (P + a / V²) (V - b) = RT, where P, V, and T are pressure, volume, and temperature and R the gas constant. a and b are characteristic constants for a given substance. For a = b = 0, the van der Waals equation reduces to the characteristic equation of an → ideal gas. See also → Dieterici equation.

Named after Dutch physicist Johannes Diderik van der Waals (1837-1923), Nobel Prize in Physics 1910; → equation.

In thermodynamics, a generalized → equation of state obtained when the → compression factor Z is expanded in terms of a power series, e.g.: Z = 1 + B(T) / V_m + C(T) / V_m² + ...

→ virial; → equation of state.

The partial differential equation ∂²U / ∂²x + ∂²U / ∂²y + ∂²U / ∂²z = (1/c²) ∂²U / ∂²t or its counterparts in one or two dimensions or in other coordinates, the solution of which represents the propagation of displacementU as waves with velocity c.

→ wave; → equation.

In → quantum gravity, an equation that describes the → wave function of the → Universe. It is an adaptation of the → Schrodinger equation but includes the curved space attributes of → general relativity.

Named after American theoretical physicists John Archibald Wheeler (1911-2008) and Bryce Seligman DeWitt (1923-2004).