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

1) The manner in which words are spelled; orthography; a group of letters representing a word.
2) The act of a speller.

→ spell; → -ing.

1) To pay out, disburse, or expend; dispose of (money, wealth, resources, etc.).
2) To employ (labor, thought, words, time, etc.), as on some object or in some proceeding (Dictionary.com).

M.E. spenden, from O.En. -spendan (in forspendan "use up"), from M.L. spendere, from expendere "to pay out, weigh out money," from → ex- "out" + pendere "to pay, weigh."

Ziyâmidan, from Sogd. zyâm "to consume, spend," ultimately from Proto-Ir. *uz-iam-, from *uz- "out, away," → ex-, + *iam- "to hold, take; stretch, reach out;" cf. Av. yam- "to hold, keep," (+ *apa-) "to take away;" Skt. yam- "to hold, restrain."

A solid geometric figure generated by the revolution of a semicircle about its diameter; equation: x² + y² + z² = r².

M.E. spere, from O.Fr. espere, from L. sphæra "globe, ball, celestial sphere," from Gk. sphaira "globe, ball," of unknown origin.

Koré, loan from Ar. kurat.
Sepehr "sphere, celestial globe, heavens, sky;" Mid.Pers. spihr "sphere, sky, firmament, fate;" Av. spiti- in compounds: spiti-dôiθra- "with clear eyes;" Proto-Iranian *spiθra- (in proper name); cf. Skt. śvitrá- "white, whitish."

The region of space around one of the bodies in a system of two celestial bodies where a third body of much smaller mass is influenced by the gravitational field of that body. The sphere of influence of a planet with respect to the Sun has a radius given by: R = R_P(M_P/M_S)^2/3, where R_P is the radius of the planet's orbit around the Sun, M_P is the mass of the planet, and M_S is the solar mass. The sphere of influence of the Earth has a radius of about 927,000 km or slightly under 150 Earth radii. Beyond this limit, a space probe will come under the influence of the Sun.

→ sphere; → influence.

A series of spheres with varying radii centred on the Earth, each rotating uniformly about an axis fixed with respect to the surface of the next larger sphere, all comprising a model in Greek astronomy to describe the motions of the heavenly bodies. The spheres turned with different speeds about axes with different orientations. The fixed stars revolved around the Earth by the motion of the most distant sphere to which the stars were thought to be attached. Each of the five planets' (Mercury, Venus, Mars, Jupiter, and Saturn) motion could be described using four spheres. The Sun and the Moon required three spheres each to explain their motions. Therefore, a total of 27 spheres described the behavior of the heavenly bodies in terms of circular motion. Eudoxus was the first person to devise a model that could explain the → retrograde motion of the planets in the sky along a looped curve known as the → hippopede.

→ sphere; Eudoxus (Ευδοξοσ) of Cnidus (c 408 BC - c 355 BC), Greek astronomer and mathematician.

Having the form of a sphere; of or pertaining to a sphere or spheres.

From → sphere + → -ic + → -al.

An aberration of a spherical lens or spherical mirror in which light rays converge not to a single point but to a series of points with different distances from the lens or mirror. Spherical aberration is corrected by using parabolic reflecting and refracting surface.

→ spherical; → aberration.

An angle formed on the surface of a sphere by the intersection of two great circles of the sphere.

→ spherical; → angle.

A type of → astrolabe in which the observer's horizon is drawn on the surface of a globe, mounted with a freely rotating spherical lattice work or 'spider' representing the celestial sphere. The earliest description of the spherical astrolabe dates back to  the Iranian astronomer Nayrizi (865-922).

→ spherical; → astrolabe.

The branch of astronomy that is concerned with determining the apparent positions and motions of celestial bodies on the celestial sphere. Same as → positional astronomy.

→ spherical; → astronomy.

A coordinate system using an origin (O) and three perpendicular axes (Ox, Oy, Oz), in which the position of a point (P) is given by three numbers (r, θ, φ). The coordinate r is the distance from the origin, θ the angle between the z-axis and the r direction, and φ the angle between the projection of r on the xy-plane and the Ox-axis. The coordinate φ is also called the → azimuthal angle.

→ spherical; → coordinate.

The difference between the sum of the three angles of a → spherical triangle and 180° (π radians).

→ spherical; → excess.

The branch of geometry that deals with figures on the surface of a sphere (such as the spherical triangle and spherical polygon). It is an example of a non-Euclidean geometry.

→ spherical; → geometry.

A solution of some mathematical equations when → spherical polar coordinates are used in investigating physical problems in three dimensions. For example, solutions of → Laplace's equation treated in spherical polar coordinates. Spherical harmonics are ubiquitous in atomic and molecular physics and appear in quantum mechanics as → eigenfunctions of → orbital angular momentum. They are also important in the representation of the gravitational and magnetic fields of planetary bodies, the characterization of the → cosmic microwave background anisotropy, the description of electrical potentials due to charge distributions, and in certain types of fluid motion.

The term spherical harmonics was first used by William Thomson (Lord Kelvin) and Peter Guthrie Tait in their 1867 Treatise on Natural Philosophy; → spherical; → harmonic.

The angle between the → normal to a spherical reference surface and the → equatorial plane.

→ spherical; → latitude.

A lens with a refractng surface which is a portion of a sphere. Spherical lenses can be of various types: → biconvex, → biconcave, → plano-convex, → plano-concave, → concavo-convex, and → convexo-concave.

→ spherical; → lens.

A mirror whose reflecting surface is a portion of a sphere. Spherical mirrors can be of two types: → concave mirror and → convex mirror.

→ spherical; → mirror.

Same as → spherical coordinates.

→ spherical; → polar; → coordinate

A configuration in which the constituting parts are arranged concentrically around the center of a sphere.

→ spherical; → symmetry.

A triangle drawn on the → surface of a → sphere. A spherical triangle, like a plane triangle, may be right, obtuse, acute, equilateral, isosceles, or scalene. The sum of the angles of a spherical triangle is greater than 180° (π) and less than 540° (3π). See also → spherical excess.

→ spherical; → triangle.