An Etymological Dictionary of Astronomy and Astrophysics
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A system of numerals for representing real numbers that uses the → base 10. It includes the digits from 0 through 9.

→ decimal; → system.

A → dimensionless quantity that measures the strength of → viscous forces relative to the → Coriolis force in a rotating fluid. It is given by E_k = ν/(ΩH²), where ν is the → kinematic viscosity of the fluid, Ω is the → angular velocity, and H is the depth scale of the motion. The Ekman number is usually used in describing geophysical phenomena in the oceans and atmosphere. Typical geophysical flows, as well as laboratory experiments, yield very small Ekman numbers. For example, in the ocean at mid-latitudes, motions with a viscosity of 10^-2 m²/s are characterized by an Ekman number of about 10^-4.

→ Ekman layer; → number.

A → dimensionless quantity used in → magnetohydrodynamics to describe the relative balance of → Lorentz forces to → Coriolis forces. It is given by: Λ = σB²/(ρΩ), where σ s the → electrical conductivity of the fluid, B is the typical → magnetic field strength within the fluid, ρ is the fluid → density, and Ω is the → angular velocity. A typical value for the Earth is Λ ~ 1.

Named after Walter Maurice Elsasser (1904-1991), American theoretical physicist of German origin; → number.

A value that is known with complete certainty. Examples of exact numbers are defined numbers, results of counts, certain unit conversions. Some examples: there are exactly 100 centimeters in 1 meter, a full circle is exactly 360°, and the number of students in a class can exactly be 25.

→ exact; → number.

Same as → focal ratio.

f, from → focal; → number.

Any number of the form 2²ⁿ + 1, where n is a connective → integer. If Fermat number is → prime, it is called a → Fermat prime.

→ Fermat's principle; → number.

One of the numbers in the → Fibonacci sequence.

→ Fibonacci sequence; → number.

A → dimensionless number that gives the ratio of local acceleration to gravitational acceleration in the vertical.

Named after William Froude (1810-1879), English engineer.

1) The number giving the position of any year in the lunar or → Metonic cycle of about 19 years. Each year has a golden number between 1 and 19. It is found by adding 1 to the given year and dividing by 19; the remainder in the division is the golden number. If there is no remainder the golden number is 19 (e.g., the golden number of 2007 is 13).
2) Same as → golden ratio.

Golden, adj. of → gold; → number.

The integral part of the → Greenwich sidereal date.

→ Greenwich; → sidereal; → day; → number.

A dimensionless number characterizing the importance of → viscous force in a → forced flow.

named after the German hydraulic engineer Gotthilf H. L. Hagen (1797-1884); → number.

A number that is divisible by the sum of its digits. For example, 18 is a Harshad number because 1 + 8 = 9 and 18 is divisible by 9 (18/9 = 2). The simplest Harshad numbers are the two-digit Harshad numbers: 10, 12, 18, 20, 21, 24, 27, 30, 36, 40, 42, 45, 48, 50, 54, 60, 63, 70, 72, 80, 81, 84, 90. They are sometimes called Niven numbers.

The name Harshad was given by Indian mathematician Dattaraya Kaprekar (1905-1986) who first studied these numbers. Harshad means "joy giver" in Sanskrit, from harṣa- "joy" and da "to give," → datum.

An identifying number assigned to the stars in the Henry Draper catalog. For example, the star Vega is HD 172167.

→ Henry Draper system; → number.

A number that is or can be expressed as the square root of a negative number; thus √ -1 is an imaginary number, denoted by i; i² = - 1.

→ imaginary; → number.

Any member of the set consisting of → positive and → negative whole numbers and → zero. Examples: -5, -2, -1, 0, 1, 2, 5.

→ integer; → number.

A → real number which cannot be exactly expressed as a ratio ^a/_b of two integers. Irrational numbers have decimal expansions that neither terminate nor become periodic. Every → transcendental number is irrational. The most famous irrational number is √ 2.

From ir- a prefix meaning "not," a variant of → in-, + → rational; → number.

The difference between the number of neutrons in an isotope and the number of protons. Neutron excess.

→ isotopic; → number.

A → dimensionless number representing the ratio of various → physical constants. For example:
1) The ratio of the → Coulomb force to the → gravitational force for a proton-electron pair (e²/Gm_pm_e), which is of the order of 10⁴⁰.
2) The age of Universe (T = 10-20 x 10⁹ years) in units of the → elementary time: T/t_e≅ 10⁴⁰.
3) The square root of the total number of particles in the Universe ≅ 10⁴⁰.

→ large; → number.

The idea whereby the coincidence of various → large numbers would bear a profound sense as to the nature of physical laws and the Universe. Dirac suggested that the coincidence seen among various large numbers of different nature is not accidental but must point to a hitherto unknown theory linking the quantum mechanical origin of the Universe to the various cosmological parameters. As a consequence, some of the → fundamental constants cannot remain unchanged for ever. According to Dirac's hypothesis, atomic parameters cannot change with time and hence the → gravitational constant should vary inversely with time (G∝ 1/t). Dirac, P. A. M., 1937, Nature 139, 323; 1938, Proc. R. Soc. A165, 199.

→ large; → number; → hypothesis.

A turbulent flow in which viscous forces are negligible compared to nonlinear advection terms, which characterize the variation of fluid quantities. The dynamics becomes generally turbulent when the Reynolds number is high enough. However, the critical Reynolds number for that is not universal, and depends in particular on boundary conditions.

→ large; → Reynolds number; → flow.