An Etymological Dictionary of Astronomy and Astrophysics
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A → number system in which the value of each digit is determined by which place it appears in the full number. The lowest place value is the rightmost position, and each successive position to the left has a higher place value. In the → number system conversion, the rightmost position represents the "ones" column, the next position represents the "tens" column, the next position represents "hundreds", etc. The values of each position correspond to powers of the → base of the number system. For example, in the usual decimal number system, which uses base 10, the place values correspond to powers of 10. Same as → place-value notation and → positional notation. See also → number system conversion.

→ positional; → number; → system.

A dimensionless number representing the ratio of the fluid viscosity to the thermal conductivity of a substance; a low number indicates high convection.

Named after the German physicist Ludwig Prandtl (1875-1953); → number.

A number which is divisible by no whole number other than itself and one.

→ prime; → number.

In atomic physics, the first of a set of quantum numbers which describe an atomic orbital. Symbolized as n, it characterizes the size and energy of an orbital.

→ principal; → quantum; → number.

A parameter, denoted k = 2π/λ, that along with the → angular frequency, ω = 2πν, is used to express the equation of → simple harmonic motion, y = cos (ωt - kx + π/2). Same as → wave number.

→ propagation; → number.

A number used in quantum mechanics, specifying the state of an electron bound in an atomic system. The quantum numbers are integers or half integers and specify the number of units of energy, momentum, spin, etc. possessed by an electron.

→ quantum; → number.

Any number that can be expressed as a ratio of two integers, providing the second number is not zero.

→ rational; → number.

The ratio of the buoyancy force to the viscous force in a medium. This dimensionless number is used to estimate when convection commences in a fluid. It depends on the density and depth of the fluid, the coefficient of thermal expansion, the gravitational field, the temperature gradient, the thermal diffusivity, and the kinematic viscosity. Convection usually starts when Ra is 1000 or more, while heat transfer is entirely by conduction when Ra is less than 10.

→ rayleigh; → number.

A number that can be represented by a point on a line. The set of real numbers includes all rational and irrational numbers, but not the imaginary numbers.

→ real; → number.

Same as → Wolf number and → sunspot number.

→ relative; → sunspot; → number.

A dimensionless quantity that governs the conditions for hydrodynamic stability and the occurrence of turbulence in fluids. It is defined by the ratio, R, of the inertial force (ρ u²) and the viscous force (μ u / L), i.e. R = L u ρ/μ, where L is a typical dimension of the system, u is a measure of the velocities that prevail, ρ the density, and μ the kinematic viscosity. At low Reynolds numbers the flow is steady, since the viscous forces are predominant in controlling the flow. At a critical value of R, corresponding to a critical velocity, the flow becomes turbulent.

Named after Osborne Reynolds (1842-1912), a British physicist who pioneered the study of turbulent flows; → number.

A dimensionless number which is used according to the → Richardson criterion to describe the condition for the → stability of a flow in the presence of vertical density stratification. If the → shear flow is characterized by linear variation of velocity and density, with velocities and densities ranging from U₁ to U₂ and ρ₁ to ρ₂ (ρ₂>ρ₁), respectively, over a depth H, then the Richardson number is expressed as: Ri = (ρ₂ - ρ₁) gH / ρ₀ (U₁ - U₂)². If Ri < 0.25, somewhere in the flow turbulence is likely to occur. For Ri > 0.25 the flow is stable.

→ Richardson criterion; → number.

A dimensionless number relating the ratio of inertial to Coriolis forces for a given flow of a rotating fluid. It is used in the study of atmospheric motions in planets. In case a small number is involved, cyclones and anticyclones are observed for low and high pressures. When it is large (Venus) the Coriolis force becomes negligible and atmospheric motions are barely affected by planetary rotation.

Named after Carl-Gustav Arvid Rossby (1898-1957), a Swedish-American meteorologist who first explained the large-scale motions of the atmosphere in terms of fluid mechanics; → number.

An average of 13 monthly → sunspot numbers, centered on the month of concern. The 1st and 13th months are given a weight of 0.5.

→ smooth; → sunspot; → number.

An integer or half-integer on which the magnitude of a particle's → spin angular momentum depends. It is expressed in units of → Planck's constant divided by 2π. Called also spin, denoted s. The spin of a particle can only have a value that is zero or a multiple of 1/2. Particles with half-integer spins, 1/2, 3/2, 5/2, ..., are → fermions. Particles with integer spin (0, 1, 2, ...) are called → bosons.

→ spin; → quantum; → number.

Same as → focal ratio.

→ stop; → ratio.

Vâbar, → ratio; kânuni, → focal.

A quantity which gives the number of sunspots at a given time. It is defined by the relationship R = k(10g + f), where R is the sunspot number, k is a constant depending on the observation conditions and the instrument used, g is the number of the groups and f is the number of individual spots that can be counted. Also called the → Wolf number and → relative sunspot number.

→ sunspot; → number.

A → dimensionless number indicating the relative importance of the → centrifugal and → viscous forces in the → Taylor-Couette flow. It is also called rotational Reynolds number. Its value depends on the length scale of the convective system, the rotation rate, and → kinematic viscosity. The Taylor number Ta is expressed by Ω²Rd³/ν² where Ω is the → angular velocity of the inner cylinder, R = (R₁ + R₂)/2 is the mean radius of the two cylinders, d = R₂ - R₁ is the distance between the cylinders, and ν is → kinematic viscosity. If Ta is equal or greater than one, the rotational effects are significant.

Named after Geoffrey Ingram Taylor (1886-1975), a British physicist, mathematician, and expert on fluid dynamics and wave theory; → number.

A → real number that is not a → root of any → algebraic equation with → rational → coefficients. Every transcendental number is → irrational. Examples of transcendental numbers are π = 3.1415926... and e = 2.7182818...

→ transcendental; → number.

The reciprocal of → wavelength, which represents the number of waves per unit length. Wave number is often defined as k = 2π/λ. Same as → propagation number.

→ wave; → number