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

A special solution of the mathematical formula which represents the wavelengths of the various spectral series of hydrogen in which the lower energy level is n = 2.

→ Balmer; → formula.

The mathematical expression giving the → entropy, S, of a → black hole as a function of the area of its → event horizon, A: S = (kc³A)/(4Għ), where k is → Boltzmann's constant, ħ is the → reduced Planck's constant, and G the → gravitational constant. It can also be expressed by S = (kA)/(4l_P²), where l_P is the → Planck length. The existence of this entropy led to the prediction of the → Hawking radiation, because an entropy is associated with a temperature and a temperature to a → thermal radiation. The entropy of a black hole increases continuously because the fall of material into it increases its area.

For Jacob D. Bekenstein (1947-), an Israeli theoretical physicist, who contributed to the foundation of black hole thermodynamics; → formula.

In → statistical thermodynamics, a probability equation relating the → entropy S of an → ideal gas to the quantity Ω, which is the number of → microstates corresponding to a given → macrostate: S = k. ln Ω. Same as → Boltzmann's relation.

→ Boltzmann's constant; → entropy; → formula.

One of eight equations that give the → trigonometric functions of → compound angles.
sin(A± B) = sinA.cosnd angleB± cosA.sinB
cos(A + B) = cosA.cosB - sinA.sinB
cos(A - B) = cosA.cosB + sinA.sinB
tan(A + B) = (tanA + tanB)/(1 - tanA.tanB)
tan(A - B) = (tanA - tanB)/(1 + tanA.tanB).

→ compound; → angle; → formula.

A formula that gives the position of an image formed by highly → paraxial rays from a → spherical mirror. It is quite accurately given by: 1/x_o + 1/x_i = 2/x_C, where x_o is the distance along the → principal axis from the mirror to the object, x_i is the distance from mirror to image, and x_C is the distance from the mirror to its center of curvature. Any distance measured on the same side of the mirror as the reflecting surface is positive; on the other side, negative. Thus for a → concave mirror  x_C is positive; for a → convex mirror, negative.

→ Descartes; → formula.

Symbolic representation of the definition of a physical quantity obtained from its units of measurement. For example, with M = mass, L = length, T = time, area = L², velocity = LT^-1, energy = ML²T^-2. → dimensional analysis.

→ dimensional; → formula.

1) In physics, a mathematical equation that predicts observed results, but has no known theoretical basis to explain why it works.
2) In chemistry, a simple expression of the relative number of each type of atom in a chemical compound.

→ empirical; → formula

A formula which expresses an → exponential function with an → imaginary number  → exponent in terms of → trigonometric functions:
e^iθ = cos θ + i sinθ,
e^-iθ = cos θ - i sinθ,
cosθ = (e^iθ + e^-iθ)/2,
sinθ = (e^iθ - e^-iθ)/2i.
In the particular case of θ = π, Euler's formula becomes: e^iπ + 1 = 0, which is considered by many mathematicians to be the most elegant mathematical equation. → mathematical elegance.

→ Euler; → formula.

1) Physics, Math.: A statement of facts in a symbolical or general form, by substitution in which a result applicable to particular data may be obtained.
2) Chemistry: An expression of the constituents of a compound by symbols and figures.

From L. formula "form, rule, method, formula," literally "small form," from forma, → form, + → -ule diminutive suffix.

Disul, from dis, → form, + -ul, → -ule.

To express in precise → form; state definitely or systematically. To reduce to or express in a → formula.

Verbal form of → form.

1) The act or process of formulating.
2) A particular expression of an idea, thought, or theory.
3) Something prepared according to a → formula.

→ formulate; → -tion.

An → equation expressing the → atomic mass of a → nuclide as a function of its → mass number and the → atomic mass unit.

→ mass; → formula.

The formula of a chemical compound, showing the kind and arrangement of atoms.

→ molecular; → formula.

The formula expressing the value of a → definite integral of a given function over an interval as the difference of the values at the end points of the interval of any → antiderivative of the function: ∫f(x)dx = F(b) - F(a), summed from x = a to x = b.

Named after Isaac → Newton and Gottfried Wilhelm Leibniz (1646-1716), who both knew the rule, although it was published later; → formula.

The mean square noise voltage across a resistance in thermal equilibrium is four times the product of the resistance, Boltzmann's constant, the absolute temperature, and the frequency range within which the voltage is measured. → Johnson-Nyquist noise.

Named after Harry Nyquist (1889-1976), a Swedish-born American physicist, who made important contributions to information theory. → Johnson-Nyquist noise; → formula.

A formula that determines the distribution of intensity of radiation that prevails under conditions of thermal equilibrium at a temperature T: B_v = (2hν³ / c²)[exp(hν / kT) - 1]^-1 where h is Planck's constant and ν is the frequency.

→ Planck; → blackbody; → formula.

A formula relating the unknown part of a → quadratic equation (the roots of the equation, x) to the known parts (a, b, and c): x = (-b± (b² - 4ac)^½) / 2a.

→ quadratic; → formula.

A formula, used in atomic physics, which describes the wavelengths or frequencies of light in various series of related spectral lines, such as those emitted by hydrogen atoms.

→ rydberg; → formula.

Same as → Weizsacker formula.

→ semiempirical; → binding; → energy; → formula.

A → semiempirical → equation which describes the → binding energy of the → atomic nucleus. It is essentially a nuclear mass formula that provides the total binding energy per → nucleon as the sum of five terms:
E_b = a_VA - a_SA^2/3 - a_CZ²/A^1/3 - a_A(N -Z)²/A + δ(A,Z),
where the terms in the right-hand side of this equation are called the volume term, surface term, Coulomb term, asymmetry term, and pairing term, respectively. A, Z, and N are the number of nucleons, → protons, and → neutrons, respectively (see, e.g., Alexi M. Frolov, 2013, arxiv.org/pdf/1212.6768). Also called Bethe-Weizacker formula and → semiempirical binding energy formula.

Named after Carl Friedrich von Weizäcker (1912-2007), German physicist, who derived the formula in 1935, Z. für Physik 96, 431; → formula.