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Showing 1621–1650 of 1709 reference entries

Chemistry · PhysicsIntensive, extensive, specific and molar properties

Scaling the system amount is different from changing its state.

DefinitionChemistry · MeasurementRelative atomic mass and isotope composition

Relative atomic mass is dimensionless and depends on the isotope composition being averaged.

DefinitionChemistry · MeasurementMolar mass and mass–amount conversion

Molar mass converts a specified substance's amount into mass.

DefinitionChemistry · MeasurementAmount concentration, molality and composition fractions

Concentration must declare its numerator and denominator.

DefinitionChemistryDilution conserves the retained solute amount

Dilution arithmetic refers to final solution volume, not the amount of solvent poured in.

MethodChemistryLimiting reagent, theoretical yield and percent yield

Stoichiometry gives a maximum under a specified reaction model; recovery measures the actual yield.

MethodChemistryFormal charge is equal-share electron accounting

Formal charge, oxidation state and partial charge answer different questions.

DefinitionChemistryElectrolyte strength, solubility and concentration

Strong describes ion formation by dissolved solute, not how much solute dissolves.

DefinitionChemistryComplete ionic and net ionic equations

Cancel unchanged species while conserving both atoms and charge.

MethodBiology · ChemistryWater polarity and biological interactions

Water's molecular interactions help explain solvation, cohesion and thermal buffering.

Empirical findingBiologyCell size and surface-to-volume scaling

For geometrically similar cells, volume grows faster than surface area.

ModelBiology · ChemistryOsmolarity and tonicity

Total particle concentration and lasting cell-volume effect are different properties.

DefinitionBiologyChromosome sets and DNA content

DNA replication doubles DNA content without doubling chromosome-set ploidy.

DefinitionBiologyOrganisms, populations, communities and ecosystems

Ecological levels describe different interacting sets and environments.

DefinitionBiologyPopulation size, density and demographic balance

Total individuals and individuals per area or volume must be distinguished.

ModelBiologyMutation and selection: different roles

Mutations do not generally appear because an organism needs their future advantage.

Empirical findingBiologyClades and rooted-tree interpretation

Shared ancestry is represented by topology, not by the left-to-right order of tips.

MethodBiology · ChemistryPlant water potential and pressure balance

Osmotic and mechanical contributions together determine passive water movement.

ModelEarth & cosmosRock and mineral are different material categories

A mineral species and a rock aggregate have different identifying features.

DefinitionEarth & cosmosEarth's compositional and mechanical layers

Crust–mantle–core and lithosphere–asthenosphere partition Earth by different properties.

ModelEarth & cosmos · MeasurementGeodetic latitude, longitude and reference systems

A coordinate pair needs a reference surface, origin and convention.

DefinitionEarth & cosmos · MeasurementMap projections and distortion

Flattening Earth's curved reference surface requires a choice of distortions.

ModelEarth & cosmos · MeasurementEllipsoid height, geoid and orthometric height

Height above a geometric reference is not automatically height above a gravity reference.

DefinitionEarth & cosmosRotation, axial tilt and seasonal sunlight

Axial tilt changes the angle and duration of sunlight in opposite hemispheres.

ModelEarth & cosmosNatural hazard and disaster risk

A harmful physical process and the potential losses it creates are different quantities.

DefinitionEarth & cosmosUsing present processes to infer Earth's past

Modern process evidence informs geological interpretation only with the past boundary conditions.

MethodEarth & cosmosLunar phases and synchronous rotation

Phases change the visible illuminated fraction; they are not Earth's shadow moving across the Moon.

ModelEarth & cosmosSolar and lunar eclipse geometry

New or full Moon is necessary for the corresponding eclipse but does not guarantee alignment.

ModelEarth & cosmosIAU Solar-System body categories

A scoped naming convention distinguishes planets, dwarf planets, small bodies and satellites.

DefinitionEarth & cosmos · MeasurementAstronomical unit and light-year

The astronomical unit and light-year measure lengths, with different defining conventions.

Definition
DefinitionSource checked

Ellipsoid height, geoid and orthometric height

Earth & cosmosMeasurement

Height above a geometric reference is not automatically height above a gravity reference.

Key knowledge

An ellipsoid is a geometric Earth reference; a geoid is a gravity equipotential reference approximating global mean sea level, distinct from local tides and the actual instantaneous sea surface. Ellipsoidal height and orthometric height therefore differ. For compatible references and a local parallel-normal approximation, ellipsoid height is approximately orthometric height plus geoid undulation.

Values and equations

h_ellipsoid approximately = H_orthometric + N_geoid

h_ellipsoid
height above the specified ellipsoid along its normal m
H_orthometric
orthometric height referred to the compatible gravity equipotential m
N_geoid
signed geoid undulation above the ellipsoid, positive outward m

Conditions and scope

  • Declare the ellipsoid, gravity/vertical datum and geoid model, with the sign convention for undulation.
  • The simple relation neglects normal/plumb-line geometric differences. Local mean-sea-level and tidal datums are not universally identical to the geoid.
  • Compatible reference surfaces and sign conventions; local approximation neglecting nonparallel normal/plumb-line effects.
Sources · 2

References

Sources retain their recorded scope. A source link alone does not establish verification of every statement.

  1. Ellipsoidally referenced surveys: reference systems and vertical datumsNOAA Office of Coast SurveyReference guidenauticalcharts.noaa.govRead source
  2. A Guide to Coordinate Systems in Great Britain, v3.6 (2020), §§1.2 and 3.1Ordnance SurveyReference guide · PDFordnancesurvey.co.ukRead source

Evidence and review

Inspected NOAA reference-system, geopotential/ellipsoidal/tidal-datum bodies and OS §§3.1.3–3.1.4, printed pp.13–16, including the parallel-line approximation. Uses its own explicit h/H symbols; OS uses the opposite capitalisation. No centimetre-accuracy or datum-date claim.

2026-10-10 · Independent Mathematics and Information editor (/root/core_math_information). Independent AI editorial review of this entry's statements, equations, applicability conditions and source coverage. Source checks apply to these claims within their stated limits.

Related reference entries

Explore relationships within this area of study and its connections to other areas.

Showing 1–3 of 3 relationships

Scientific relationships · 3 / 3

The relationship type describes the connection. Its linked statements, sources and conditions define the scope.

  1. Related to
    Relationship sources · 2

    Linked statements

    • Geodetic latitude measures the angle between the reference ellipsoid's normal and its equatorial plane; longitude measures the angle from a specified reference meridian. A coordinate is meaningful with its coordinate reference system and, when relevant, epoch. Geodetic latitude is distinct from the geocentric angle measured from Earth's center.

    Ellipsoidal coordinates and gravity-referenced heights need explicitly compatible reference surfaces.

  2. Related to
    Relationship sources · 2

    Linked statements

    • An ellipsoid is a geometric Earth reference; a geoid is a gravity equipotential reference approximating global mean sea level, distinct from local tides and the actual instantaneous sea surface. Ellipsoidal height and orthometric height therefore differ. For compatible references and a local parallel-normal approximation, ellipsoid height is approximately orthometric height plus geoid undulation.

    Range/elevation observations must identify their vertical reference before a geometric height is treated as gravity-referenced elevation.

  3. Related to
    Relationship sources · 2

    Linked statements

    • An ellipsoid is a geometric Earth reference; a geoid is a gravity equipotential reference approximating global mean sea level, distinct from local tides and the actual instantaneous sea surface. Ellipsoidal height and orthometric height therefore differ. For compatible references and a local parallel-normal approximation, ellipsoid height is approximately orthometric height plus geoid undulation.

    Gravity-dependent reference surfaces differ from a geometric ellipsoid; geoid/height interpretation needs a compatible gravity and reference model.

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