spheroid
Let an agent explain spheroids, relay geometry, formulas and geodetic uses from mathematics and geodesy sources, describe the named forms, and distinguish spheroids from spheres, triaxial ellipsoids, geoids and ovoid or egg shapes.
Research draft, second pass
A second pass drafted this model: the structure a model of this thing needs, and what is known about it in the world. The line under this one says how the second half was obtained - researched against sources, or recalled without web access, in which case nothing here was read anywhere and every claim is a lead to verify. Unreviewed either way.
written by Claude from model knowledge without web access - no source was read, every claim is a lead to verify
Researched by: Claude
Purpose and description
Let an agent explain spheroids, relay geometry, formulas and geodetic uses from mathematics and geodesy sources, describe the named forms, and distinguish spheroids from spheres, triaxial ellipsoids, geoids and ovoid or egg shapes.
A surface formed by rotating an ellipse about one of its principal axes, called an oblate spheroid when rotated about the minor axis, flattened at the poles like the Earth, and a prolate spheroid when rotated about the major axis, elongated like a rugby ball; reference ellipsoids such as the Earth ellipsoid of WGS 84, with an equatorial radius of 6,378,137 metres and a flattening of about 1/298.257, underpin GPS, mapping and geodesy. Spheroids are special cases of ellipsoids with two equal axes.
What it is for: Describing flattened or elongated round shapes.
It can be explain geometry; relay formulas; describe Earth reference ellipsoids; distinguish related shapes.
Distinguishing features
Two equal axes
Rotational symmetry
Oblate or prolate
Geodetic importance
What it looks like
A ball flattened at the poles or stretched along an axis.
Physical character
WGS 84 equatorial radius: 6,378,137 m
WGS 84 inverse flattening: 298.257223563 number
Newton predicted Earth oblateness: 1687 year - Principia
How it is recognised
Ellipsoid of revolution
Earth ellipsoid, oblate spheroid, prolate spheroid
Spheres have all axes equal; triaxial ellipsoids have three different axes; geoids model gravity equipotential; ovoids are asymmetric eggs
Related models
is a kind of - in registry terms
includes -
is used in -
is contrasted with -
In practice
Families and kinds
oblate spheroids
prolate spheroids
reference ellipsoids
spheroidal coordinates
Standards and regulation
WGS 84 and GRS 80 geodetic standards
ISO 19111 coordinate reference systems
Failure modes and hazards
Mixing datums in mapping
Confusing ellipsoid and geoid heights
Assuming Earth is a sphere for precise work
Also called
Where this came from
wikidata · CC0 1.0
Also registered as vr.tr.spheroid
Drafted structure
Bundle to layer to finding to question, as the second pass will find it: 4 bundles · 8 layers · 8 findings · 16 questions.
Understand What a spheroid is.
Definition.
Definition
Definition.
Definition
Definition.
- What is a spheroid, and how does it differ from spheres, triaxial ellipsoids, geoids and ovoids? definition
- Is the question about geometry, mapping, GPS or physics? boundary
Forms
Named forms.
Forms
Forms.
- What are oblate and prolate spheroids and Earth ellipsoids? definition
- Which entry fits the specific form? action
Geometry Geometry.
Science.
Formulas
Volume and surface.
Formulas
Formulas.
- How are volume and surface area of spheroids computed? measurement
- Which references are standard? provenance
Flattening
Flattening and eccentricity.
Flattening
Flattening.
- What are flattening and eccentricity of a spheroid? measurement
- Which sources are cited? provenance
Geodesy Geodesy.
Regulation.
WGS 84
WGS 84.
WGS 84
WGS 84.
- How does WGS 84 define the Earth ellipsoid used by GPS? provenance
- Which entry fits World Geodetic System? action
Geoid
Ellipsoid and geoid.
Geoid
Geoid.
- Why do ellipsoidal heights differ from heights above the geoid? provenance
- Which entry fits geoid? action
Context History and nature.
Context.
History
Figure of the Earth.
History
History.
- How did 18th-century expeditions confirm the Earth is oblate? provenance
- Which entry fits French Geodesic Mission? action
Planets
Rotating bodies.
Planets
Planets.
- Why are fast-rotating planets such as Saturn strongly oblate? provenance
- Which entry fits flattening? action
What the second pass must settle
- Should reference ellipsoids be a separate entry?
- How should geodesy standards be linked?
- Should prolate spheroid be split off?