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

Made general. → generalized coordinates; → generalized velocities.

P.p. of → generalize

In a material system, the independent parameters which completely specify the configuration of the system, i.e. the position of its particles with respect to the frame of reference. Usually each coordinate is designated by the letter q with a numerical subscript. A set of generalized coordinates would be written as q₁, q₂, ..., q_n. Thus a particle moving in a plane may be described by two coordinates q₁, q₂, which may in special cases be the → Cartesian coordinates x, y, or the → polar coordinates r, θ, or any other suitable pair of coordinates. A particle moving in a space is located by three coordinates, which may be Cartesian coordinates x, y, z, or → spherical coordinates r, θ, φ, or in general q₁, q₂, q₃. The generalized coordinates are normally a "minimal set" of coordinates. For example, in Cartesian coordinates the simple pendulum requires two coordinates (x and y), but in polar coordinates only one coordinate (θ) is required. So θ is the appropriate generalized coordinate for the pendulum problem.

→ generalized; → coordinate.

In → Lagrangian dynamics, forces related to → generalized coordinates. For any system with n generalized coordinates q_i (i = 1, ..., n), generalized forces are expressed by F_i = ∂L/∂q_i, where L is the → Lagrangian function.

→ generalized; → force.

In → Lagrangian dynamics, momenta related to → generalized coordinates. For any system with n generalized coordinates q_i (i = 1, ..., n), generalized momenta are expressed by p_i = ∂L/∂q^._i, where L is the → Lagrangian function.

→ generalized; → momentum.

The time → derivatives of the → generalized coordinates of a system.

→ generalized; → velocity.

To bring into existence; create; produce.
Math.: To trace (a figure) by the motion of a point, straight line, or curve.

Generate, from M.E., from L. generatus "produce," p.p. of generare "to bring forth," from gener-, genus "descent, birth," akin to Pers. zâdan, Av. zan- "to give birth," as explained below.

Âzânidan, from â- nuance/strengthening prefix + zân, from Av. zan- "to bear, give birth to a child, be born," infinitive zazāite, zāta- "born;" Mod.Pers. zâdan, present stem zā- "to bring forth, give birth" (Mid.Pers. zâtan; cf. Skt. jan- "to produce, create; to be born," janati "begets, bears;" Gk. gignomai "to happen, become, be born;" L. gignere "to beget;" PIE base *gen- "to give birth, beget") + -idan infinitive suffix.

1) A coming into being.
2) The → production of → energy (→ heat or → electricity).

Verbal noun of → generate.

1) Capable of producing or creating.
2) Pertaining to the production of offspring.

→ generate; → -ive.

1) A machine for converting one form of energy into another.
2) Geometry: That which creates a line, a surface, a solid by its motion.

From L. generator "producer," from genera(re)→ generate + -tor a suffix forming personal agent nouns from verbs and, less commonly, from nouns.

Âzângar, from âzân the stem of âzânidan→ generate + -gar suffix of agent nouns, from kar-, kardan "to do, to make" (Mid.Pers. kardan; O.Pers./Av. kar- "to do, make, build," Av. kərənaoiti "makes;" cf. Skt. kr- "to do, to make," krnoti "makes," karma "act, deed;" PIE base k^wer- "to do, to make").

The acceleration caused by the force of gravity. At the Earth's surface it is determined by the distance of the object form the center of the Earth: g = GM/R², where G is the → gravitational constant, and M and R are the Earth's mass and radius respectively. It is approximately equal to 9.8 m s^-2. The value varies slightly with latitude and elevation. Also known as the → acceleration of gravity.

→ gravitational; → acceleration.

Mutual attraction between any two bodies that have mass.

→ gravitational; → interaction.

A → numeral system in which letters represent numbers. In an earlier system, called acrophonic, the symbols for numerals came from the first letter of the number name. Subsequently, the numerals were based on giving values to the letters of alphabet. For example α, β, γ, and δ represented 1, 2, 3, and 4; while ι, κ, λ, and μ stood for 10, 20, 30, and 40, and ρ, σ, τ, and υ for 100, 200, 300, and 400. The Greek also used the additive principle. For example 11, 12, 13, 14, and 374 were written ια, ιβ, ιγ, ιδ, and τοδ. The numbers between 1000 and 9000 were expressed by adding a subscript or superscript ι (iota) to the symbols for 1 to 9. For example ιA and ιΘ for 1000 and 9000. Numbers greater than 9999 were expressed using M, which was the myriad, 10,000. Therefore, since 123 was represented by ρκγ, 123,000 was written as M^ρκγ.

→ numeral; → system.

The interval lasting until some 10^-5 seconds after the Big Bang when the Universe was dominated by radiation and its temperature was around 10¹⁵ kelvins. It is preceded by → Planck era and followed by → lepton era.

→ hadron; → era.

The dynamical operator in → quantum mechanics that corresponds to the → Hamiltonian function in classical mechanics.

→ Hamiltonian function; → operator.

The temperature inferred for a → black hole based on the → Hawking radiation. For a → Schwarzschild black hole, one has T_H = ħc³/(8πGMk) where ħ is the → reduced Planck's constant, c is the → speed of light, G is the → gravitational constant, M is the mass, and k is → Boltzmann's constant. The formula can approximately be written as: T_H≅ 6.2 x 10^-8 (Msun/M) K. Thus radiation from a solar mass black hole would be exceedingly cold, about 5 x 10⁷ times colder than the → cosmic microwave background. Larger black holes would be colder still. Moreover, smaller black holes would have higher temperatures. A → mini black hole of mass about 10¹⁵ g would have T_H≅ 10¹¹ K.

→ Hawking radiation; → temperature.

The minimum → effective temperature required for a → pre-main sequence star of given mass and radius to be in → hydrostatic equilibrium. This temperature delimits the boundary of the → Hayashi forbidden zone.

→ Hayashi track; → temperature.

A defect of the eyes in which sight is normal in the night or in a dim light but is abnormally poor or wholly absent in the day or in a bright light. Also called day blindness. Opposite of → nyctalopia

From N.L., from Gk hemeralop- (stem of hemeralops having such a condition, from hemer(a) "day" + al(aos) "blind" + -ops having such an appearance) + -ia a noun suffix.

Ruzkuri, from ruz, → day, + kuri "blindness," from kur, → blind.

An operator A that satisfies the relation A = A^*, where A^* is the adjoint of A. → Hermitian conjugate.

→ Hermitian conjugate; → operator.

The Martian geologic era after the Noachian Era which lasted from about 3500 million to 2500 million years ago. During this period Martian climate began to change to drier, dustier conditions. Water that flowed on the Martian surface during the Noachian Era may have frozen as underground ice deposits, and most river channels probably experienced their final flow episodes during this era. → Noachian era; → Amazonian era.

Named after the Martian plains of Hesperis; → era.

Of, belonging to, or characteristic of a hierarchy. → hierarchical clustering; → hierarchical cosmology; → hierarchical multiple system; → hierarchical structure formation.

→ hierarchy; → -al.