An Etymological Dictionary of Astronomy and Astrophysics
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The shape of a pulsar's pulse as determined by averaging several pulses.

→ mean; → profile.

The average time interval between two successive → upper transits of the → mean equinox.

→ mean; → sidereal; → day.

The hour angle of the mean equinox for a given observer.

→ mean; → sidereal; → time.

The average length of the apparent solar day. In other words, the interval between successive transits of the mean Sun for a given observer.

→ mean; → solar; → day.

The time since the mean Sun crossed the meridian with 12 hours added to make the day begin at midnight.

→ mean; → solar; → time.

A plot of the mass-to-charge ratio of elementary particles, sorted by their isotopic mass.

→ mean; → spectrum.

A hypothetical Sun that moves along the ecliptic at a uniform rate equal to the average motion of the real Sun.

→ mean; → sun.

In → syllogism, the term which is common to both → premises and is excluded from the → conclusion.

→ mean; → term.

1) If f(x) is a continuous function on the interval from a to b, then:
∫ f(x) dx = f(c)(b - a) (summed from a to b) for at least one point in that interval.
2) More generally, If f(x) and g(x) are continuous functions on the interval from a to b and g(x)≥ 0, then:
∫ f(x)g(x) dx = f(c) ∫ g(x) dx (both integrals summed from a to b).

→ mean; → value; → theorem.

The sense or significance of a word, sentence, symbol, etc. The study dealing with meanings is called → semantics. See also → semiotics.

M.E., from mean; O.E. mænan "to mean, intend, signify" (cf. O.Fris. mena "to signify," O.S. menian "to intend, signify," M.Du. menen, Du. meenen, Ger. meinen "think, suppose"), related to Pers. maneš "disposition, temperament," mênidan "to think, consider," → idea; + → -ing.

Cemâr, from cem or cim "meaning, signification;" Mid.Pers. cim "meaning, reason, cause;" ultimately from Proto-Ir. *cahmāt "wherefore?" cf. Skt. kasmāt "why, where from? whence?," kim "what? how? why?" + âr short form of âvar present stem of âvardan "to cause or produce; to bring," → production, as in bonâr, → cause, used also as a nuance suffix; see also the verb → mean.

A relation that gives a rough estimate of the oscillation period of a → pulsating star as a function of its mean density. This relation is obtained by considering how long it would take a sound wave to travel across the diameter of a model star: Π ≅ (3π/2γGρ)^1/2, where ρ is the mean density, γ the ratio of → specific heats (C_p/C_v), and G the → gravitational constant. This relation shows that the pulsation period of a star is inversely proportional to the square root of its mean density. And this is the reason why the pulsation periods decrease along the → instability strip from the luminous, very tenuous → supergiants to the faint, very dense → white dwarfs.

→ period; → mean; → density; → relation.

The square root of the arithmetic mean of the squares of the numbers in a given set.

→ root; → mean; → square.

The square root of the second moment corresponding to the frequency function of a random variable.

→ root; → mean; → square; → error.

Statistics: The square root of the arithmetic mean of the squares of the deviation of observed values from their arithmetic mean.

→ root; → mean; → square; → deviation.

The → opacity of a gas of given composition, temperature, and density averaged over the various wavelengths of the radiation being absorbed and scattered. The radiation is assumed to be in → thermal equilibrium with the gas, and hence have a → blackbody spectrum. Since → monochromatic opacity in stellar plasma has a complex frequency dependence, the Rosseland mean opacity facilitates the analysis. Denoted κ_R, it is defined by: 1/κ_R = (π/4σT³) ∫(1/k_ν) (∂B/∂T)_νdν, summed from 0 to ∞, where σ is the → Stefan-Boltzmann constant, T temperature, B(T,ν) the → Planck function, and k_ν monochromatic opacity (See Rogers, F.J., Iglesias, C. A. Radiative atomic Rosseland mean opacity tables, 1992, ApJS 79, 507).

Named after Svein Rosseland (1894-1985), a Norwegian astrophysicist, who obtained the expression in 1924; → mean; → opacity.

An mean which is obtained by combining different numbers according to the relative importance of each.

→ weight; → mean.