An Etymological Dictionary of Astronomy and Astrophysics

The simplest curvature invariant for a → Riemannian manifold. It is derived from the → Ricci tensor R_μν ≡  R^α_μαν by contracting indices. Taking the trace of the Ricci tensor gives the Ricci scalar:

R ≡ R_μνg^μnu; = R^μ_ν = R^αμ_αμ. Also called → scalar curvature.

See also: → Ricci tensor; → scalar.

The simplest curvature invariant for a → Riemannian manifold. It is derived from the → Ricci tensor R_μν ≡  R^α_μαν by contracting indices. Taking the trace of the Ricci tensor gives the Ricci scalar:

R ≡ R_μνg^μnu; = R^μ_ν = R^αμ_αμ. Also called → scalar curvature.

See also: → Ricci tensor; → scalar.

A → rank 2, → symmetric tensor R_μν that is a contraction of the → Riemann curvature tensor R^λ_μνλ. More specifically, R_μν ≡ Σ (λ) R^λ_μνκ =
R^λ_μνκ. Closely related to the Ricci tensor is the → Einstein tensor, which plays an important role in the theory of → general relativity.

See also: Named after the Italian mathematician Gregorio Ricci-Curbastro (1853-1925); → tensor.

A → rank 2, → symmetric tensor R_μν that is a contraction of the → Riemann curvature tensor R^λ_μνλ. More specifically, R_μν ≡ Σ (λ) R^λ_μνκ =
R^λ_μνκ. Closely related to the Ricci tensor is the → Einstein tensor, which plays an important role in the theory of → general relativity.

See also: Named after the Italian mathematician Gregorio Ricci-Curbastro (1853-1925); → tensor.

Having large amounts of something specified. → metal-rich environment, → rich cluster; → enrich, → enrichment, → richness, → poor.

Etymology (EN): M.E., from O.E. rice “wealthy, powerful” (cf. Du. rijk, Ger. reich “rich”),
from PIE base *reg- “move in a straight line,” hence, “to direct, rule” (cf. Mod.Pers./Mid.Pers. râst “right, straight;” O.Pers. rāsta- “straight, true,” rās- “to be right, straight, true;” Av. rāz-
“to direct, put in line, set,” razan- “order;” Skt. raj- “to direct, stretch,” rjuyant- “walking straight;” Gk. orektos “stretched out;” L. regere “to lead straight, guide, rule,” p.p. rectus “right, straight;” Ger. recht; E. right).

Etymology (PE): Por “full, much, very, too much” (Mid.Pers. purr “full;” O.Pers. paru- “much, many;” Av. parav-, pauru-, pouru-, from
par- “to fill;” PIE base *pelu- “full,” from *pel- “to be full;” cf. Skt. puru- “much, abundant;” Gk. polus “many,” plethos “great number, multitude;” O.E. full); pordâr, literally “having much possession,” from por + dâr “having, possessor,” from dâštan “to have, to possess,” → property.

Having large amounts of something specified. → metal-rich environment, → rich cluster; → enrich, → enrichment, → richness, → poor.

Etymology (EN): M.E., from O.E. rice “wealthy, powerful” (cf. Du. rijk, Ger. reich “rich”),
from PIE base *reg- “move in a straight line,” hence, “to direct, rule” (cf. Mod.Pers./Mid.Pers. râst “right, straight;” O.Pers. rāsta- “straight, true,” rās- “to be right, straight, true;” Av. rāz-
“to direct, put in line, set,” razan- “order;” Skt. raj- “to direct, stretch,” rjuyant- “walking straight;” Gk. orektos “stretched out;” L. regere “to lead straight, guide, rule,” p.p. rectus “right, straight;” Ger. recht; E. right).

Etymology (PE): Por “full, much, very, too much” (Mid.Pers. purr “full;” O.Pers. paru- “much, many;” Av. parav-, pauru-, pouru-, from
par- “to fill;” PIE base *pelu- “full,” from *pel- “to be full;” cf. Skt. puru- “much, abundant;” Gk. polus “many,” plethos “great number, multitude;” O.E. full); pordâr, literally “having much possession,” from por + dâr “having, possessor,” from dâštan “to have, to possess,” → property.

A → galaxy cluster with a particularly large number of galaxies.

See also: → rich; → cluster.

A → galaxy cluster with a particularly large number of galaxies.

See also: → rich; → cluster.

Same as → energy cascade

See also: Named after L. F. Richardson (1922), Weather Prediction by Numerical Process (Cambridge Univ. Press); → cascade.

Same as → energy cascade

See also: Named after L. F. Richardson (1922), Weather Prediction by Numerical Process (Cambridge Univ. Press); → cascade.

A condition for the onset of → instability in multilayer fluids which compares the balance between the restoring force of → buoyancy and the destabilizing effect of the → shear.

Etymology (EN): Named after the British meteorologist Lewis Fry Richardson (1881-1953), who first arrived in 1920 to the dimensionless ratio now called → Richardson number. The first formal proof of the criterion, however, came four decades later for → incompressible flows (Miles, J. W. 1961, J. Fluid Mech., 10, 496; Howard, L. N., 1961, J. Fluid Mech., 10, 509).
Its extension to → compressible flows was demonstrated subsequently (Chimonas 1970, J. Fluid Mech., 43, 833); → criterion.

A condition for the onset of → instability in multilayer fluids which compares the balance between the restoring force of → buoyancy and the destabilizing effect of the → shear.

Etymology (EN): Named after the British meteorologist Lewis Fry Richardson (1881-1953), who first arrived in 1920 to the dimensionless ratio now called → Richardson number. The first formal proof of the criterion, however, came four decades later for → incompressible flows (Miles, J. W. 1961, J. Fluid Mech., 10, 496; Howard, L. N., 1961, J. Fluid Mech., 10, 509).
Its extension to → compressible flows was demonstrated subsequently (Chimonas 1970, J. Fluid Mech., 43, 833); → criterion.

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.

See also: → Richardson criterion; → 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.

See also: → Richardson criterion; → number.

The property of being very abundant.

See also: → rich; → -ness.

The property of being very abundant.

See also: → rich; → -ness.

A classification of → galaxy clusters into six groups (0 to 5), as in the → Abell catalog. It depends on the number of galaxies in a given cluster that lie within a → magnitude range m₃ to m₃₊₂, where m₃ is the magnitude of the 3rd brightest member of the cluster. The first group contains 30-49 galaxies and the last group more than 299 galaxies.

See also: → richness; → group.

A classification of → galaxy clusters into six groups (0 to 5), as in the → Abell catalog. It depends on the number of galaxies in a given cluster that lie within a → magnitude range m₃ to m₃₊₂, where m₃ is the magnitude of the 3rd brightest member of the cluster. The first group contains 30-49 galaxies and the last group more than 299 galaxies.

See also: → richness; → group.

1. A question or statement so framed as to exercise one’s ingenuity in answering it or discovering its meaning; conundrum.
   

2. A puzzling question, problem, or matter (Dictionary.com).

Etymology (EN): M.E. redel, redels, from O.E. rædels “riddle; counsel; conjecture; imagination;” cf. O.Fr. riedsal “riddle,” O.Sax. radisli, M.Du. raetsel, Du. raadsel, O.H.G. radisle, Ger. Rätsel “riddle.”

Etymology (PE): Kervas “riddle, puzzle” [Dehxodâ], Kurd. karvâs “riddle,” of unknown origin.

1. A question or statement so framed as to exercise one’s ingenuity in answering it or discovering its meaning; conundrum.
   

2. A puzzling question, problem, or matter (Dictionary.com).

Etymology (EN): M.E. redel, redels, from O.E. rædels “riddle; counsel; conjecture; imagination;” cf. O.Fr. riedsal “riddle,” O.Sax. radisli, M.Du. raetsel, Du. raadsel, O.H.G. radisle, Ger. Rätsel “riddle.”

Etymology (PE): Kervas “riddle, puzzle” [Dehxodâ], Kurd. karvâs “riddle,” of unknown origin.

A long, narrow elevation of the Earth’s surface, generally sharp crested with steep sides, either independently or as part of a larger mountain or hill. See also:

→ submarine ridge, → wrinkle ridge, → mid-Atlantic ridge.

Etymology (EN): M.E. rigge; O.E. hrycg “spine, back of a man or beast” (cf. O.Fris. hregg, Du. rug, O.H.G. hrukki, Ger. Rücken “the back”).

Etymology (PE): Ruk, from dialectal Tabari ruk “mountain, ridge;” cf. (Dehxodâ) raš “hill.”

A long, narrow elevation of the Earth’s surface, generally sharp crested with steep sides, either independently or as part of a larger mountain or hill. See also:

→ submarine ridge, → wrinkle ridge, → mid-Atlantic ridge.

Etymology (EN): M.E. rigge; O.E. hrycg “spine, back of a man or beast” (cf. O.Fris. hregg, Du. rug, O.H.G. hrukki, Ger. Rücken “the back”).

Etymology (PE): Ruk, from dialectal Tabari ruk “mountain, ridge;” cf. (Dehxodâ) raš “hill.”

A 4th → rank tensor that characterizes the deviation of the geometry of space from the Euclidean type. The curvature tensor
R^λ_μνκ is defined through the → Christoffel symbols Γ^λ_μν as follows:

R^λ_μνκ = (∂Γ^λ_μκ)/(∂x^ν) - (∂Γ^λ_μν)/(∂x^κ) + Γ^η_μκΓ^λ_ην - Γ^η_μνΓ^λ_ηκ.

See also: → Riemannian geometry; → curvature; → tensor.

A 4th → rank tensor that characterizes the deviation of the geometry of space from the Euclidean type. The curvature tensor
R^λ_μνκ is defined through the → Christoffel symbols Γ^λ_μν as follows:

R^λ_μνκ = (∂Γ^λ_μκ)/(∂x^ν) - (∂Γ^λ_μν)/(∂x^κ) + Γ^η_μκΓ^λ_ην - Γ^η_μνΓ^λ_ηκ.

See also: → Riemannian geometry; → curvature; → tensor.

The combination of a → partial differential equation and a → piecewise constant → initial condition. The Riemann problem is a basic tool in a number of numerical methods for wave propagation problems. The canonical form of the Riemann problem is:

∂u/∂t + ∂f(u)/∂x = 0, x ∈ R, t > 0, u(x,0) = u_l if x < 0, and
u(x,0) = u_r if x > 0 .

See also: → Riemann’s geometry; → problem.

The combination of a → partial differential equation and a → piecewise constant → initial condition. The Riemann problem is a basic tool in a number of numerical methods for wave propagation problems. The canonical form of the Riemann problem is:

∂u/∂t + ∂f(u)/∂x = 0, x ∈ R, t > 0, u(x,0) = u_l if x < 0, and
u(x,0) = u_r if x > 0 .

See also: → Riemann’s geometry; → problem.

Same as → Riemannian geometry.

See also: → Riemannian; → geometry.

Same as → Riemannian geometry.

See also: → Riemannian; → geometry.

Of or pertaining to Georg Friedrich Bernhard Riemann (1826-1866) or his mathematics findings.

→ Riemannian geometry, → Riemannian manifold, → Riemannian metric, → Riemann problem, → Riemann curvature tensor.

See also: After the German mathematician Georg Friedrich Bernhard Riemann (1826-1866), the inventor of the elliptic form of → non-Euclidean geometry, who made important contributions to analysis and differential geometry, some of them paving the way for the later development of → general relativity.

Of or pertaining to Georg Friedrich Bernhard Riemann (1826-1866) or his mathematics findings.

→ Riemannian geometry, → Riemannian manifold, → Riemannian metric, → Riemann problem, → Riemann curvature tensor.

See also: After the German mathematician Georg Friedrich Bernhard Riemann (1826-1866), the inventor of the elliptic form of → non-Euclidean geometry, who made important contributions to analysis and differential geometry, some of them paving the way for the later development of → general relativity.

A → non-Euclidean geometry in which there are no → parallel lines, and the sum of the → angles of a → triangle is always greater than 180°. Riemannian figures can be thought of as figures constructed on a curved surface. The geometry is called elliptic because the section formed by a plane that cuts the curved surface is an ellipse.

See also: → Riemannian; → geometry.

A → non-Euclidean geometry in which there are no → parallel lines, and the sum of the → angles of a → triangle is always greater than 180°. Riemannian figures can be thought of as figures constructed on a curved surface. The geometry is called elliptic because the section formed by a plane that cuts the curved surface is an ellipse.

See also: → Riemannian; → geometry.

A → manifold on which there is a defined → Riemannian metric (Douglas N. Clark, 2000, Dictionary of Analysis, Calculus, and Differential Equations).

See also: → Riemannian; → metric.

A → manifold on which there is a defined → Riemannian metric (Douglas N. Clark, 2000, Dictionary of Analysis, Calculus, and Differential Equations).

See also: → Riemannian; → metric.

A positive-definite inner product, (.,.)_x, on T_x(M), the tangent space to a manifold M at x, for each x  ∈ M, which varies continually with x

(Douglas N. Clark, Dictionary of Analysis, Calculus, and Differential Equations).

See also: → Riemannian; → metric.

A positive-definite inner product, (.,.)_x, on T_x(M), the tangent space to a manifold M at x, for each x  ∈ M, which varies continually with x

(Douglas N. Clark, Dictionary of Analysis, Calculus, and Differential Equations).

See also: → Riemannian; → metric.

1. General: a gap or break made by splitting, cleaving, etc.; fissure; cleft.
   

2. Geology: A narrow cleft, fissure, or other opening in rock, made by cracking or splitting.
   

3. Geology: An elongated trough in the Earth’s crust bounded by → faults.

Etymology (EN): M.E., from a Scandinavian source; cf. Dan., Norw. rift “a cleft.”

Etymology (PE): 1) Câk “fissure, rupture, cleft, crack,” related to caqidan “to drive a nail, strike together, fix a spike;” caxidan “to quarrel, strive;” diatectal Shughni cuγ,
Roshani coγ “breaking, tearing, ripping up;” Malâyeri ceqidan “cracking of a cold porcelain bowl when receiving hot water;”
Yazghulami cok-, coxt “to pound, to stamp;” Wakhi cuk-, cukt “to strike;” Ossetic cædyn “to shake, strike iron;” Lori cok “a mark fixed to separate two grounds;” Sogd. cax “to battel, fight;” Mid.Pers. (prefixed) pacên “copy” (see also Cheung 2007).

Gosal-darré, from gosal, → fault,

• darré, → valley.

1. General: a gap or break made by splitting, cleaving, etc.; fissure; cleft.
   

2. Geology: A narrow cleft, fissure, or other opening in rock, made by cracking or splitting.
   

3. Geology: An elongated trough in the Earth’s crust bounded by → faults.

Etymology (EN): M.E., from a Scandinavian source; cf. Dan., Norw. rift “a cleft.”

Etymology (PE): 1) Câk “fissure, rupture, cleft, crack,” related to caqidan “to drive a nail, strike together, fix a spike;” caxidan “to quarrel, strive;” diatectal Shughni cuγ,
Roshani coγ “breaking, tearing, ripping up;” Malâyeri ceqidan “cracking of a cold porcelain bowl when receiving hot water;”
Yazghulami cok-, coxt “to pound, to stamp;” Wakhi cuk-, cukt “to strike;” Ossetic cædyn “to shake, strike iron;” Lori cok “a mark fixed to separate two grounds;” Sogd. cax “to battel, fight;” Mid.Pers. (prefixed) pacên “copy” (see also Cheung 2007).

Gosal-darré, from gosal, → fault,

• darré, → valley.

A long, narrow valley formed by the lowering of land between two → faults. Also called → graben.

See also: → rift; → valley.

A long, narrow valley formed by the lowering of land between two → faults. Also called → graben.

See also: → rift; → valley.

The brightest star in the constellation → Orion (visual magnitude 0.18). A → blue supergiant of type B8 Iab with an initial mass of 17 solar masses, Rigel is 773 light-years away, and actually shines with the light of 40,000 Suns. It is accompanied by a fairly bright, seventh magnitude companion nine seconds of arc apart. The companion is itself double, the components much fainter and much less massive → main sequence stars of type B.

Etymology (EN): Rigel “foot,” short for Ar. rijl al-jauza’ (رجل‌الجوزاء) “the foot of jauza’.” The latter word means “the manifest one,” initially “black sheep with white middle.” The Gk. figure was translated as such because of its conspicuousness among other constellations.

Etymology (PE): Rejl, from Ar., as above.

The brightest star in the constellation → Orion (visual magnitude 0.18). A → blue supergiant of type B8 Iab with an initial mass of 17 solar masses, Rigel is 773 light-years away, and actually shines with the light of 40,000 Suns. It is accompanied by a fairly bright, seventh magnitude companion nine seconds of arc apart. The companion is itself double, the components much fainter and much less massive → main sequence stars of type B.

Etymology (EN): Rigel “foot,” short for Ar. rijl al-jauza’ (رجل‌الجوزاء) “the foot of jauza’.” The latter word means “the manifest one,” initially “black sheep with white middle.” The Gk. figure was translated as such because of its conspicuousness among other constellations.

Etymology (PE): Rejl, from Ar., as above.

Same as the star → Alpha Centauri.

Etymology (EN): From Ar. Rijl al-Qanturis “foot of Centaurus,” from rijl “foot,” + Qanturis Arabicized → Centaurus.

Etymology (PE): Pâ-ye Kantawros, “foot of Centaurus,” from pâ, → foot, + Kentawros, → Centaurus.

Same as the star → Alpha Centauri.

Etymology (EN): From Ar. Rijl al-Qanturis “foot of Centaurus,” from rijl “foot,” + Qanturis Arabicized → Centaurus.

Etymology (PE): Pâ-ye Kantawros, “foot of Centaurus,” from pâ, → foot, + Kentawros, → Centaurus.

1a) Straight, free from curves, angles, or irregularities.
→ right ascension.

1b) Opposite of → left. → right-hand rule, → right-hand screw rule.

2. In accordance with fact, reason, or truth; correct or true.
   

3. Something that a person is or should be morally or legally allowed to have, get, or do (Merriam-Webster).

Etymology (EN): M.E.; O.E. reht, riht; cf. O.H.G. reht, Ger. recht, O.N. rettr, Goth. raihts; P.Gmc. *rekhtaz, cognate with Pers. râst, as below.

Etymology (PE): 1) Râst “right, true; just, upright, straight;” Mid.Pers. râst “true, straight, direct;” Soghdian rəšt “right;” O.Pers. rāsta- “straight, true,” rās- “to be right, straight, true;” Av. rāz- “to direct, put in line, set,” razan- “order;” related to
Mid.Pers. rây-, râyênitan “to arrange;” Mod.Pers.
raj “line, row,” variants raž, rak, râk, rezg (Lori), radé, râdé “line, rule, row,”
rasté, râsté “row, a market with regular ranges of shops;” ris, risé “straight;”
cf. Skt. raj- “to direct, stretch,” rjuyant- “walking straight;” Gk. orektos “stretched out;” L. regere “to lead straight, guide, rule,” p.p. rectus “right, straight;” PIE base *reg- “move in a straight line,” hence, “to direct, rule;”

2. Dorost “correct, whole, complete, healthy,” → integral.
   

3. Râšan, related to râst, as above; cf. Mid.Pers. Rašn “Justice deity; calendar 18th day;” Av. rašnu- “the Zoroastrian Justice deity, orientation.”

1a) Straight, free from curves, angles, or irregularities.
→ right ascension.

1b) Opposite of → left. → right-hand rule, → right-hand screw rule.

2. In accordance with fact, reason, or truth; correct or true.
   

3. Something that a person is or should be morally or legally allowed to have, get, or do (Merriam-Webster).

Etymology (EN): M.E.; O.E. reht, riht; cf. O.H.G. reht, Ger. recht, O.N. rettr, Goth. raihts; P.Gmc. *rekhtaz, cognate with Pers. râst, as below.

Etymology (PE): 1) Râst “right, true; just, upright, straight;” Mid.Pers. râst “true, straight, direct;” Soghdian rəšt “right;” O.Pers. rāsta- “straight, true,” rās- “to be right, straight, true;” Av. rāz- “to direct, put in line, set,” razan- “order;” related to
Mid.Pers. rây-, râyênitan “to arrange;” Mod.Pers.
raj “line, row,” variants raž, rak, râk, rezg (Lori), radé, râdé “line, rule, row,”
rasté, râsté “row, a market with regular ranges of shops;” ris, risé “straight;”
cf. Skt. raj- “to direct, stretch,” rjuyant- “walking straight;” Gk. orektos “stretched out;” L. regere “to lead straight, guide, rule,” p.p. rectus “right, straight;” PIE base *reg- “move in a straight line,” hence, “to direct, rule;”

2. Dorost “correct, whole, complete, healthy,” → integral.
   

3. Râšan, related to râst, as above; cf. Mid.Pers. Rašn “Justice deity; calendar 18th day;” Av. rašnu- “the Zoroastrian Justice deity, orientation.”

An angle of 90°.

See also: → right; → angle.

An angle of 90°.

See also: → right; → angle.

A coordinate in the → equatorial system measured from the → vernal equinox eastward to the point where the object → hour circle intersects the → celestial equator. Right ascension (symbol α) is expressed in hours, minutes, and seconds. See also: → declination.

Etymology (EN): → right; ascension, M.E. ascencioun, from O.Fr., from L. ascendere “to climb up,” from → ad- “to” + scandere “to climb.”

Etymology (PE): Râst, → right; afrâz present stem of afrâzidan, afrâštan “to raise, exalt, extole,” from Mid.Pers. abrâstan, abrâz- “to lift, raise,”
from ab-, from O.Pers./Av. abiy-/aiwi- “to, upon, against;” cf. Skt. abhi-, Gk. amphi- + râst “straight, direct, true;”
from O.Pers. rāsta- “straight, true,” rās-
“to be right, straight, true;” Av. rāz- “to direct, put in line, set,” razan- “order;” cf. Skt. raj- “to direct, stretch,” rjuyant- “walking straight;” Gk. orektos “stretched out;” L. regere “to lead straight, guide, rule,” p.p. rectus “right, straight;” Ger. recht; E. right; PIE base *reg- “move in a straight line,” hence, “to direct, rule.”

A coordinate in the → equatorial system measured from the → vernal equinox eastward to the point where the object → hour circle intersects the → celestial equator. Right ascension (symbol α) is expressed in hours, minutes, and seconds. See also: → declination.

Etymology (EN): → right; ascension, M.E. ascencioun, from O.Fr., from L. ascendere “to climb up,” from → ad- “to” + scandere “to climb.”

Etymology (PE): Râst, → right; afrâz present stem of afrâzidan, afrâštan “to raise, exalt, extole,” from Mid.Pers. abrâstan, abrâz- “to lift, raise,”
from ab-, from O.Pers./Av. abiy-/aiwi- “to, upon, against;” cf. Skt. abhi-, Gk. amphi- + râst “straight, direct, true;”
from O.Pers. rāsta- “straight, true,” rās-
“to be right, straight, true;” Av. rāz- “to direct, put in line, set,” razan- “order;” cf. Skt. raj- “to direct, stretch,” rjuyant- “walking straight;” Gk. orektos “stretched out;” L. regere “to lead straight, guide, rule,” p.p. rectus “right, straight;” Ger. recht; E. right; PIE base *reg- “move in a straight line,” hence, “to direct, rule.”

A triangle one of whose angles is a → right angle.

See also: → right; → triangle.

A triangle one of whose angles is a → right angle.

See also: → right; → triangle.

See → Fleming’s rules.

See also: → right; → hand; → rule.

See → Fleming’s rules.

See also: → right; → hand; → rule.

A rule that gives the direction of the resultant vector in a → vector product: A x B = C. It is the direction of advance of a right-hand screw whose axis, held perpendicular to the plane of A and B, is rotated in the same sense that rotates the first-named vector (A) into the second-named vector B through the smaller angle.

See also: → right; → hand; → screw; → rule.

A rule that gives the direction of the resultant vector in a → vector product: A x B = C. It is the direction of advance of a right-hand screw whose axis, held perpendicular to the plane of A and B, is rotated in the same sense that rotates the first-named vector (A) into the second-named vector B through the smaller angle.

See also: → right; → hand; → screw; → rule.

Using the right hand with greater skill or ease than the left.

Etymology (EN): → right; → hand + -ed.

Etymology (PE): Râstâl, from râst, → right, + -al→ -al. Râstdast, with dast, → hand.

Using the right hand with greater skill or ease than the left.

Etymology (EN): → right; → hand + -ed.

Etymology (PE): Râstâl, from râst, → right, + -al→ -al. Râstdast, with dast, → hand.

1. General: Stiff or unyielding; inflexible, strict, severe.
   
2. Physics: → rigid body; → rigidity.

Etymology (EN): From L. rigidus “hard, stiff, rough,” from rigere “to be stiff;” related to L. frigus “cold,” Gk. rhigos “frost, cold.”

Etymology (PE): Saxtpây, from saxt, → hard, + pây present stem of pâyidan “to stand firm, to be constant, steady, fixed;” Mid.Pers. pâyitan, pâtan, pây- “to protect; wait, stand,” Sogdian p’y “to protect, watch over;” O.Pers./Av. pâ(y)- “to protect, keep” pâtar- “protector, watcher,” cf. Skt. pâ- “to protect, keep,” pâti “protects;” Gk. poimen “shepherd,” poma “lid, cover;” L. pastor “shepherd,” panis “bread;” PIE base *pa- “to protect, guard, pasture, feed.”

1. General: Stiff or unyielding; inflexible, strict, severe.
   
2. Physics: → rigid body; → rigidity.

Etymology (EN): From L. rigidus “hard, stiff, rough,” from rigere “to be stiff;” related to L. frigus “cold,” Gk. rhigos “frost, cold.”

Etymology (PE): Saxtpây, from saxt, → hard, + pây present stem of pâyidan “to stand firm, to be constant, steady, fixed;” Mid.Pers. pâyitan, pâtan, pây- “to protect; wait, stand,” Sogdian p’y “to protect, watch over;” O.Pers./Av. pâ(y)- “to protect, keep” pâtar- “protector, watcher,” cf. Skt. pâ- “to protect, keep,” pâti “protects;” Gk. poimen “shepherd,” poma “lid, cover;” L. pastor “shepherd,” panis “bread;” PIE base *pa- “to protect, guard, pasture, feed.”

Mechanics: A system of many particles whose positions relative to one another remain fixed.

See also: → rigid; → body.

Mechanics: A system of many particles whose positions relative to one another remain fixed.

See also: → rigid; → body.

1. The quality or state of being → rigid. See also → modulus of rigidity.
   

2. → magnetic rigidity.

See also: → rigid + → -ity.

1. The quality or state of being → rigid. See also → modulus of rigidity.
   

2. → magnetic rigidity.

See also: → rigid + → -ity.

Another name of → Alpha Centauri.

Etymology (EN): Rigel, from Ar. rijl (رجل) “foot;” Kentaurus, → Centaurus.

Etymology (PE): Pâ “foot, step” (from
Mid.Pers. pâd, pây; Av. pad- “foot;” cf. Skt. pat; Gk. pos, genitive podos; L. pes, genitive pedis; P.Gmc. *fot; E. foot; Ger. Fuss; Fr. pied; PIE *pod-/*ped-); Kentâwros→ Centaurus.

Another name of → Alpha Centauri.

Etymology (EN): Rigel, from Ar. rijl (رجل) “foot;” Kentaurus, → Centaurus.

Etymology (PE): Pâ “foot, step” (from
Mid.Pers. pâd, pây; Av. pad- “foot;” cf. Skt. pat; Gk. pos, genitive podos; L. pes, genitive pedis; P.Gmc. *fot; E. foot; Ger. Fuss; Fr. pied; PIE *pod-/*ped-); Kentâwros→ Centaurus.

1. Severely exact or accurate; precise.
   

2. Logic, Math.: Logically valid. See also: → accurate, → exact, → precise.

Etymology (EN): M.E., from M.L. rigorosus, from rigor “stiffness, rigor,” from rigere “to be stiff.”

Etymology (PE): Farsaxt, from far- intensive prefix “much, abundant; elegantly” (Mid.Pers. fra- “forward, before; much; around;”
O.Pers. fra- “forward, forth;” Av. frā, fərā-, fra- “forward, forth; excessive;” cf. Skt. prá- “before; forward, in fron;” Gk. pro “before, in front of;” L. pro “on behalf of, in place of, before, for;” PIE *pro-)

• saxt “hard, strong, firm, secure, solid, vehement, intense” (Mid.Pers. saxt “hard, strong, severe;” Av. sak- “to understand or know a thing, to mark;” cf. Skt. śakta- “able, strong,” śaknoti “he is strong,” śiksati “he learns”).

1. Severely exact or accurate; precise.
   

2. Logic, Math.: Logically valid. See also: → accurate, → exact, → precise.

Etymology (EN): M.E., from M.L. rigorosus, from rigor “stiffness, rigor,” from rigere “to be stiff.”

Etymology (PE): Farsaxt, from far- intensive prefix “much, abundant; elegantly” (Mid.Pers. fra- “forward, before; much; around;”
O.Pers. fra- “forward, forth;” Av. frā, fərā-, fra- “forward, forth; excessive;” cf. Skt. prá- “before; forward, in fron;” Gk. pro “before, in front of;” L. pro “on behalf of, in place of, before, for;” PIE *pro-)

• saxt “hard, strong, firm, secure, solid, vehement, intense” (Mid.Pers. saxt “hard, strong, severe;” Av. sak- “to understand or know a thing, to mark;” cf. Skt. śakta- “able, strong,” śaknoti “he is strong,” śiksati “he learns”).

A → selection rule obeyed by → discrete transitions. Among them are: rigorous selection rules for → electric dipole transitions (→ permitted) requiring:

1. ΔJ must be 0 or ± 1 with J = 0 ↔ 0 forbidden.
2. ΔM_J = 0, ± 1.
3. → Parity change, i.e. even ↔ odd.

See also: → rigorous; → selection; → rule.

A → selection rule obeyed by → discrete transitions. Among them are: rigorous selection rules for → electric dipole transitions (→ permitted) requiring:

1. ΔJ must be 0 or ± 1 with J = 0 ↔ 0 forbidden.
2. ΔM_J = 0, ± 1.
3. → Parity change, i.e. even ↔ odd.

See also: → rigorous; → selection; → rule.

A long, narrow, straight or sinuous trench or valley with steep walls and roughly parallel sides on the surface of the Moon.

Etymology (EN): From Ger. Rille “a small rivulet or brook.”

Etymology (PE): Borrowed from E., as above.

A long, narrow, straight or sinuous trench or valley with steep walls and roughly parallel sides on the surface of the Moon.

Etymology (EN): From Ger. Rille “a small rivulet or brook.”

Etymology (PE): Borrowed from E., as above.

The outer edge, border, margin, or brink of something, especially of a circular object.

Etymology (EN): M.E., from O.E. -rima (in compounds, as in særima “seashore”); cognate with O.Norse rimi “raised strip of land, ridge”

Etymology (PE): Labé “limb, edge,” from lab “lip;” Mid.Pers. lap; cognate with L. labium, E. lip; Ger. Lefze.

The outer edge, border, margin, or brink of something, especially of a circular object.

Etymology (EN): M.E., from O.E. -rima (in compounds, as in særima “seashore”); cognate with O.Norse rimi “raised strip of land, ridge”

Etymology (PE): Labé “limb, edge,” from lab “lip;” Mid.Pers. lap; cognate with L. labium, E. lip; Ger. Lefze.

A long fissure on the surface of a planet or Moon; plural form rimae.

Etymology (EN): From L. rima “fissure, slit.”

Etymology (PE): Loan from E., as above.

A long fissure on the surface of a planet or Moon; plural form rimae.

Etymology (EN): From L. rima “fissure, slit.”

Etymology (PE): Loan from E., as above.

The coordinates that describe the → Minkowski space-time in a → hyperbolic version of → polar coordinates. If the coordinates in an → inertial frame is denoted by (t,x), the Rindler coordinates (η,ξ) are defined by:

t = (1/α) e^αξ sinh (αη) and

x = (1/α) e^αξ cosh (αη), where α is some positive constant.

See also: Named after Wolfgang Rindler (1924-), Austrian physicist;
→ coordinates.

The coordinates that describe the → Minkowski space-time in a → hyperbolic version of → polar coordinates. If the coordinates in an → inertial frame is denoted by (t,x), the Rindler coordinates (η,ξ) are defined by:

t = (1/α) e^αξ sinh (αη) and

x = (1/α) e^αξ cosh (αη), where α is some positive constant.

See also: Named after Wolfgang Rindler (1924-), Austrian physicist;
→ coordinates.

A portion of the → space-time described by
→ Rindler coordinates.

See also: → Rindler coordinates; → wedge.

A portion of the → space-time described by
→ Rindler coordinates.

See also: → Rindler coordinates; → wedge.

1. A circular band of something. → gossamer ring.
   

2. A resonant sound like that of a bell or bells.

Etymology (EN): O.E. hring “circular band” (cf. O.N. hringr, Ger. Ring), literally “something curved,” from PIE base *(s)ker- “to turn, bend.”

Etymology (PE): 1) Halqé, loan from Ar. Halqat “ring, hoop, circle.”

2. Zang “bell.”

1. A circular band of something. → gossamer ring.
   

2. A resonant sound like that of a bell or bells.

Etymology (EN): O.E. hring “circular band” (cf. O.N. hringr, Ger. Ring), literally “something curved,” from PIE base *(s)ker- “to turn, bend.”

Etymology (PE): 1) Halqé, loan from Ar. Halqat “ring, hoop, circle.”

2. Zang “bell.”

A galaxy with a ring-like appearance around the central luminous center. The ring consists of massive, relatively young bright stars. It is believed that ring galaxies result from the head-on collision of two different galaxies.

See also: → ring; → galaxy.

A galaxy with a ring-like appearance around the central luminous center. The ring consists of massive, relatively young bright stars. It is believed that ring galaxies result from the head-on collision of two different galaxies.

See also: → ring; → galaxy.

Of → Saturn, the angle measured with respect to the sub-observer point (a line connecting the observer to Saturn) in the direction of the orbital motion.

See also: → ring; → longitude.

Of → Saturn, the angle measured with respect to the sub-observer point (a line connecting the observer to Saturn) in the direction of the orbital motion.

See also: → ring; → longitude.

A bright → planetary nebula in the constellation
→ Lyra, also called M57 or NGC 6720.
In small telescopes it has the appearance of a slightly elliptical luminous ring around a central hot star (15th magnitude). The radius is one-third of a → light-year, and the nebula is about 2,000 light-years away.

See also: → ring; → nebula.

A bright → planetary nebula in the constellation
→ Lyra, also called M57 or NGC 6720.
In small telescopes it has the appearance of a slightly elliptical luminous ring around a central hot star (15th magnitude). The radius is one-third of a → light-year, and the nebula is about 2,000 light-years away.

See also: → ring; → nebula.

Of → Saturn, the angle between the line of sight and the ring plane. Also known as elevation angle, tilt angle.

Etymology (EN): → ring; → open;
→ angle.

Etymology (PE): Zâviyé, → angle; gošâyeš “opening,” verbal noun from
gošudan, gošâdan “to open up, loose, let free;” gošâd “opened; ample, broad;” Mid.Pers. wišâdan “to let free;” Khotanese hīyā “bound;” O.Pers. višta “untied, loosened,” vištāspa- “with loosened horses” (personal name); Av. višta “untied,” ā-hišāiiā “holds fettered,” hita- “fastened, tied on, put to;” cf. Skt. sā- “to bind, fasten, fetter,” sitá- “bound,” ví-sita- “untied;” halqé, → ring.

Of → Saturn, the angle between the line of sight and the ring plane. Also known as elevation angle, tilt angle.

Etymology (EN): → ring; → open;
→ angle.

Etymology (PE): Zâviyé, → angle; gošâyeš “opening,” verbal noun from
gošudan, gošâdan “to open up, loose, let free;” gošâd “opened; ample, broad;” Mid.Pers. wišâdan “to let free;” Khotanese hīyā “bound;” O.Pers. višta “untied, loosened,” vištāspa- “with loosened horses” (personal name); Av. višta “untied,” ā-hišāiiā “holds fettered,” hita- “fastened, tied on, put to;” cf. Skt. sā- “to bind, fasten, fetter,” sitá- “bound,” ví-sita- “untied;” halqé, → ring.

→ planetary ring system.

See also: → ring; → system.

→ planetary ring system.

See also: → ring; → system.

The last stage of → merger between two → black holes undergoing → inspiral. At the end of the evolution of a → binary black hole system, the black holes get close enough to → merge together into a single, larger black hole (→ black hole merger). The resulting black hole is at first distorted and asymmetric, but in the ringdown process the black hole’s vibrations decay due to → gravitational radiation leaving finally a quiescent, spinning black hole.

Etymology (EN): M.E. ring, from O.E. hringan; akin to O.Norse hringja “to ring;” → down.

The last stage of → merger between two → black holes undergoing → inspiral. At the end of the evolution of a → binary black hole system, the black holes get close enough to → merge together into a single, larger black hole (→ black hole merger). The resulting black hole is at first distorted and asymmetric, but in the ringdown process the black hole’s vibrations decay due to → gravitational radiation leaving finally a quiescent, spinning black hole.

Etymology (EN): M.E. ring, from O.E. hringan; akin to O.Norse hringja “to ring;” → down.

1. A small ring.
   

   2. Any of the thin or narrow rings that compose the major → Saturn’s rings.

See also: → ring; → -let.

1. A small ring.
   

   2. Any of the thin or narrow rings that compose the major → Saturn’s rings.

See also: → ring; → -let.

A wave on a fluid surface, of sufficiently short wavelength, in which gravity is the dominant influence.

Etymology (EN): Of unknown origin, perhaps frequentative of rip (v.) “to tear apart.”

Etymology (PE): Cinâv, literally “water wrinkle,” from cin “fold, plait, wrinkle” + âv, variant of âb, → water.

A wave on a fluid surface, of sufficiently short wavelength, in which gravity is the dominant influence.

Etymology (EN): Of unknown origin, perhaps frequentative of rip (v.) “to tear apart.”

Etymology (PE): Cinâv, literally “water wrinkle,” from cin “fold, plait, wrinkle” + âv, variant of âb, → water.

1. Of a heavenly body, to ascend above the horizon. → set.
   
2. An act or instance of rising; appearance above the horizon.
   → moonrise, → sunrise

Etymology (EN): M.E. risen (v.); O.E. risan; cf. O.N. risa, Goth. urreisan “to rise,” O.H.G. risan “to rise, flow,” Ger. reisen “to travel.”

Etymology (PE): Barâmadan, from bar-

“up; upon; on; in; into; at; forth; with; near; before; according to” (Mid.Pers. abar; O.Pers. upariy “above; over, upon, according to;” Av. upairi “above, over,” upairi.zəma- “located above the earth;” cf. Gk. hyper- “over, above;” L. super-; O.H.G. ubir “over;” PIE base *uper “over”)

• âmadan “to come, to occur, to become” (Mid.Pers. âmatan;
  O.Pers. gam- “to come; to go,” Av. gam- “to come; to go,” jamaiti “goes;” Proto-Iranian *āgmatani; Skt. gamati “goes;” Gk. bainein “to go, walk, step;” L. venire “to come;” Tocharian A käm- “to come;” O.H.G. queman “to come;” E. come; PIE root *gwem- “to go, come”).

1. Of a heavenly body, to ascend above the horizon. → set.
   
2. An act or instance of rising; appearance above the horizon.
   → moonrise, → sunrise

Etymology (EN): M.E. risen (v.); O.E. risan; cf. O.N. risa, Goth. urreisan “to rise,” O.H.G. risan “to rise, flow,” Ger. reisen “to travel.”

Etymology (PE): Barâmadan, from bar-

“up; upon; on; in; into; at; forth; with; near; before; according to” (Mid.Pers. abar; O.Pers. upariy “above; over, upon, according to;” Av. upairi “above, over,” upairi.zəma- “located above the earth;” cf. Gk. hyper- “over, above;” L. super-; O.H.G. ubir “over;” PIE base *uper “over”)

• âmadan “to come, to occur, to become” (Mid.Pers. âmatan;
  O.Pers. gam- “to come; to go,” Av. gam- “to come; to go,” jamaiti “goes;” Proto-Iranian *āgmatani; Skt. gamati “goes;” Gk. bainein “to go, walk, step;” L. venire “to come;” Tocharian A käm- “to come;” O.H.G. queman “to come;” E. come; PIE root *gwem- “to go, come”).

The act of rising; the appearance of a celestial body above the horizon. Opposite of → setting.

See also: Verbal noun of → rise.

The act of rising; the appearance of a celestial body above the horizon. Opposite of → setting.

See also: Verbal noun of → rise.

Exposure to the chance of injury or loss; a hazard or dangerous chance (Dictionary.com).

Etymology (EN): From Fr. risque, from It. risco, riscio (modern rischio), from riscare “to run into danger,” of uncertain origin.

Etymology (PE): Risk, loan from Fr.

Exposure to the chance of injury or loss; a hazard or dangerous chance (Dictionary.com).

Etymology (EN): From Fr. risque, from It. risco, riscio (modern rischio), from riscare “to run into danger,” of uncertain origin.

Etymology (PE): Risk, loan from Fr.

A type of → Cassegrain telescope in which the → primary mirror is a → hyperboloid. It is designed to eliminate → coma and → spherical aberration, thus providing a relatively large field of view as compared to a more conventional configuration.

See also: Named after the American astronomer George Ritchey (1864-1945) and the French optician Henri Chrétien (1879-1956); → telescope.

A type of → Cassegrain telescope in which the → primary mirror is a → hyperboloid. It is designed to eliminate → coma and → spherical aberration, thus providing a relatively large field of view as compared to a more conventional configuration.

See also: Named after the American astronomer George Ritchey (1864-1945) and the French optician Henri Chrétien (1879-1956); → telescope.

An empirical rule discovered before the advent of quantum mechanics which states that it is possible to find pairs of spectral lines, which have the property that the sum of their wavenumbers is also an observed spectral line.

See also: Named after Walther Ritz (1878-1909), a Swiss theoretical physicist; → combination; → principle.

An empirical rule discovered before the advent of quantum mechanics which states that it is possible to find pairs of spectral lines, which have the property that the sum of their wavenumbers is also an observed spectral line.

See also: Named after Walther Ritz (1878-1909), a Swiss theoretical physicist; → combination; → principle.

1. A person who is competing for the same object or goal as another, or who tries to equal or outdo another; competitor.
   

2. A person or thing that is in a position to dispute another’s preeminence or superiority (Dictionary.com).

Etymology (EN): From L. rivalis “a rival, adversary; neighbor,” originally, “one who uses a stream in common with another,” from riv(us) “stream, brook,”

• -alis, → -al.

Etymology (PE): Hamâvard “a rival; an adversary in a combat,” from ham- “together,” → com-, + âvard “battle, struggle,”
variants nabard, nibard, nâvard “fight, struggle, war,” ultimately from Proto-Ir. *part- “to fight, to struggle.”

1. A person who is competing for the same object or goal as another, or who tries to equal or outdo another; competitor.
   

2. A person or thing that is in a position to dispute another’s preeminence or superiority (Dictionary.com).

Etymology (EN): From L. rivalis “a rival, adversary; neighbor,” originally, “one who uses a stream in common with another,” from riv(us) “stream, brook,”

• -alis, → -al.

Etymology (PE): Hamâvard “a rival; an adversary in a combat,” from ham- “together,” → com-, + âvard “battle, struggle,”
variants nabard, nibard, nâvard “fight, struggle, war,” ultimately from Proto-Ir. *part- “to fight, to struggle.”

1. The action, position, or relation of a rival or rivals; competition.
   

2. An instance of this (Dictionary.com).

See also: Noun from → rival.

1. The action, position, or relation of a rival or rivals; competition.
   

2. An instance of this (Dictionary.com).

See also: Noun from → rival.

A large natural stream of water flowing in a definite course.

Etymology (EN): M.E., from O.Fr. rivere, riviere, from V.L. *riparia “riverbank, seashore, river,” noun use of feminine of L. riparius “of a riverbank.”

Etymology (PE): Rud, from Mid.Pers. rôd “river,” O.Pers. rautah- “river;” cf. Skt. srotas- “river,” sru- “to flow;” Pali sota- “stream, flood;” Gk. rhoos “a stream, a flowing,” from rhein “to flow;” O.E. stream; Ger. Strom; PIE base *sreu- “to flow.”

A large natural stream of water flowing in a definite course.

Etymology (EN): M.E., from O.Fr. rivere, riviere, from V.L. *riparia “riverbank, seashore, river,” noun use of feminine of L. riparius “of a riverbank.”

Etymology (PE): Rud, from Mid.Pers. rôd “river,” O.Pers. rautah- “river;” cf. Skt. srotas- “river,” sru- “to flow;” Pali sota- “stream, flood;” Gk. rhoos “a stream, a flowing,” from rhein “to flow;” O.E. stream; Ger. Strom; PIE base *sreu- “to flow.”