Roche–Riemann ellipsoids
E468355
Roche–Riemann ellipsoids are a family of rotating, self-gravitating fluid equilibrium figures in astrophysics and celestial mechanics that generalize classical ellipsoidal solutions like the Jacobi ellipsoid.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Dirichlet ellipsoids | 1 |
| Roche–Riemann ellipsoids canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T4756624 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Roche–Riemann ellipsoids Context triple: [Jacobi ellipsoid, belongsToFamily, Roche–Riemann ellipsoids]
-
A.
Jacobi ellipsoid
A Jacobi ellipsoid is a rotating, self-gravitating fluid body in equilibrium that takes on a triaxial ellipsoidal shape due to its rapid spin.
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B.
On Conoids and Spheroids
"On Conoids and Spheroids" is a mathematical treatise by Archimedes in which he investigates the geometry, volumes, and surface areas of solids generated by rotating conic sections.
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C.
Tolman–Oppenheimer–Volkoff equation
The Tolman–Oppenheimer–Volkoff equation is the general relativistic equation of hydrostatic equilibrium that describes the internal structure and pressure balance of spherically symmetric, non-rotating stars such as neutron stars.
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D.
Gauss’s planetary equations
Gauss’s planetary equations are a set of differential equations in celestial mechanics that describe how a planet’s orbital elements change over time under the influence of perturbing forces.
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E.
Schwarzschild–Milne equations
The Schwarzschild–Milne equations are fundamental integro-differential equations in radiative transfer theory that describe the propagation and scattering of radiation through a plane-parallel, absorbing and emitting medium.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Roche–Riemann ellipsoids Target entity description: Roche–Riemann ellipsoids are a family of rotating, self-gravitating fluid equilibrium figures in astrophysics and celestial mechanics that generalize classical ellipsoidal solutions like the Jacobi ellipsoid.
-
A.
Jacobi ellipsoid
A Jacobi ellipsoid is a rotating, self-gravitating fluid body in equilibrium that takes on a triaxial ellipsoidal shape due to its rapid spin.
-
B.
On Conoids and Spheroids
"On Conoids and Spheroids" is a mathematical treatise by Archimedes in which he investigates the geometry, volumes, and surface areas of solids generated by rotating conic sections.
-
C.
Tolman–Oppenheimer–Volkoff equation
The Tolman–Oppenheimer–Volkoff equation is the general relativistic equation of hydrostatic equilibrium that describes the internal structure and pressure balance of spherically symmetric, non-rotating stars such as neutron stars.
-
D.
Gauss’s planetary equations
Gauss’s planetary equations are a set of differential equations in celestial mechanics that describe how a planet’s orbital elements change over time under the influence of perturbing forces.
-
E.
Schwarzschild–Milne equations
The Schwarzschild–Milne equations are fundamental integro-differential equations in radiative transfer theory that describe the propagation and scattering of radiation through a plane-parallel, absorbing and emitting medium.
- F. None of above. chosen
Statements (44)
| Predicate | Object |
|---|---|
| instanceOf |
astrophysical model
ⓘ
family of equilibrium figures ⓘ self-gravitating fluid configuration ⓘ |
| appliesTo |
synchronously rotating binaries
ⓘ
tidally locked fluid bodies ⓘ |
| assumes |
Newtonian gravity
ⓘ
linked to:
law of universal gravitation
ellipsoidal density distribution ⓘ inviscid fluid ⓘ |
| balances |
centrifugal forces
ⓘ
pressure gradients ⓘ self-gravity ⓘ |
| characterizedBy |
angular velocity of figure rotation
ⓘ
axis ratios ⓘ internal vorticity ⓘ mass distribution ⓘ |
| describes | equilibrium of rotating fluid masses ⓘ |
| developedInContextOf | 19th-century celestial mechanics ⓘ |
| field |
astrophysics
ⓘ
celestial mechanics ⓘ fluid dynamics ⓘ gravitational physics ⓘ |
| generalizes |
Jacobi ellipsoid
ⓘ
Maclaurin spheroid ⓘ |
| hasApplication |
stability analysis of rotating stars
ⓘ
study of secular instabilities in fluid masses ⓘ |
| hasProperty |
compressible fluid
ⓘ
rotating ⓘ self-gravitating ⓘ stationary in rotating frame ⓘ uniform vorticity ⓘ |
| hasShape | triaxial ellipsoid ⓘ |
| mathematicallyDescribedBy |
ellipsoidal potential theory
ⓘ
equations of rotating self-gravitating fluids ⓘ |
| namedAfter |
Bernhard Riemann
ⓘ
Édouard Roche ⓘ |
| relatedTo |
Riemann ellipsoids
ⓘ
linked to:
Riemann ellipsoid
Roche limit ⓘ Roche lobe ⓘ |
| solves | hydrostatic equilibrium in rotating frame ⓘ |
| subclassOf |
Riemann ellipsoids
ⓘ
linked to:
Riemann ellipsoid
ellipsoidal figures of equilibrium ⓘ |
| usedIn |
modeling rotating gaseous planets
ⓘ
modeling tidally distorted stars ⓘ theory of close binary stars ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Roche–Riemann ellipsoids Description of subject: Roche–Riemann ellipsoids are a family of rotating, self-gravitating fluid equilibrium figures in astrophysics and celestial mechanics that generalize classical ellipsoidal solutions like the Jacobi ellipsoid.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Roche–Riemann ellipsoids