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Concept MapGELE · Geodesy

GELE Geodesy — Figure of the Earth and the Reference EllipsoidConcept Map

The Figure of the Earth and the Reference Ellipsoid concept map from Super Tutor's GELE review: the central idea, the concepts around it and how they relate.

Figure of the Earth and the Reference Ellipsoid - Concept Map

Reference Ellipsoid as the Mathematical Model of Earth's Shape

Related concepts

Earth's Physical Shape

Sub concepts

  • Oblate spheroid geometry
  • Flattening at the poles
  • Equatorial bulge
  • Actual Earth surface (geoid)

Relationship to central

Real-world phenomenon that the reference ellipsoid models and approximates

Ellipsoid Definition Parameters

Sub concepts

  • Semi-major axis (a) — equatorial radius
  • Semi-minor axis (b) — polar radius
  • Flattening (f)
  • First eccentricity squared (e²)
  • Second eccentricity squared (e'²)

Relationship to central

Mathematical quantities that completely define a reference ellipsoid

Parameter Relationships

Sub concepts

  • f = (a − b)/a
  • b = a(1 − f)
  • e² = 2f − f²
  • e² = (a² − b²)/a²
  • e'² = (a² − b²)/b²

Relationship to central

Algebraic interconnections between ellipsoid definition parameters

Radii of Curvature

Sub concepts

  • Prime vertical radius (N) — east–west curvature
  • Meridian radius (M) — north–south curvature
  • Mean radius of curvature (R) — Gaussian mean
  • Latitude-dependent variations
  • Applications in distance/area calculations

Relationship to central

Measures of how the ellipsoid curves at any point, varying with latitude

Global Reference Systems

Sub concepts

  • WGS84 — GNSS and global standard
  • PRS92 — Philippine Reference System
  • Clarke 1866 — historical reference
  • GRS80 — Geodetic Reference System 1980
  • Ellipsoid selection criteria

Relationship to central

International ellipsoid standards adopted for positioning and mapping

Geodetic Applications

Sub concepts

  • Coordinate system establishment
  • Geodetic datum definition
  • Mapping projections (UTM, PPCS)
  • Distance and area reductions
  • Height systems and vertical datum

Relationship to central

Practical uses of ellipsoid parameters in surveying and mapping work

Philippine Geodetic Context

Sub concepts

  • RA 4374 — Subdivision of Land for Sale
  • RA 8560 — Property Boundary Markers
  • PD 1529 — Creation of Cadastral Maps
  • CA 141 — Public Land Act provisions
  • PRS92 mandatory adoption

Relationship to central

Regulatory and practical application frameworks specific to Philippine surveying

Concept connections

  • Semi-major axis (a)Semi-minor axis (b)b is calculated from a and flattening f using the formula b = a(1 − f)
  • Flattening (f)First eccentricity squared (e²)e² is derived from f using e² = 2f − f²; the two parameters both characterize ellipsoid shape
  • First eccentricity squared (e²)Prime vertical radius (N)e² appears in the denominator of N = a/√(1 − e²sin²φ); controls curvature variation with latitude
  • First eccentricity squared (e²)Meridian radius (M)e² appears in both numerator and denominator of M = a(1−e²)/(1−e²sin²φ)^1.5; controls north–south curvature
  • Prime vertical radius (N)Meridian radius (M)Both vary with latitude φ; N ≥ M everywhere; combined as mean radius R = √(MN) for local sphere approximations
  • Latitude φPrime vertical radius (N)N varies continuously with latitude; equals a at equator (φ=0°) and equals pole value at poles (φ=90°)
  • Latitude φMeridian radius (M)M varies continuously with latitude; equals a(1−e²) at equator and approaches a at poles
  • WGS84 — GNSS and global standardPRS92 — Philippine Reference SystemPRS92 is adopted for official Philippine surveying; WGS84 is the GNSS ellipsoid; coordinate transformations between them are necessary
  • Reference EllipsoidGeodetic datumThe ellipsoid is the surface on which a geodetic datum is established by defining an origin point and orientation
  • Ellipsoid parameters (a, b, f, e²)Coordinate system establishmentEllipsoid parameters define the geometric foundation upon which latitude–longitude coordinates and their associated radii of curvature are calculated
  • Radii of curvature (N, M, R)Distance and area reductionsN and M are used to reduce geodetic distances and areas to the ellipsoid and further to map projections (UTM, PPCS)
  • Mapping projections (UTM, PPCS)Reference ellipsoidBoth UTM and PPCS are mathematically defined transformations from the ellipsoid surface to a plane; they depend on ellipsoid parameters and radii of curvature
  • RA 4374 — Subdivision of Land for SalePRS92 — Philippine Reference SystemRA 4374 mandates the use of PRS92 ellipsoid and datum for all cadastral subdivision surveys in the Philippines
  • RA 8560 — Property Boundary MarkersPRS92 — Philippine Reference SystemBoundary markers must reference the PRS92 coordinate system as established by RA 4374
  • PD 1529 — Creation of Cadastral MapsReference EllipsoidCadastral maps must be constructed using the official reference ellipsoid (PRS92) and datum for legal recognition
  • Oblate spheroid geometryEquatorial bulgeThe equatorial bulge is the physical manifestation of Earth's oblate shape; a > b causes this bulge
  • Actual geoid surfaceReference EllipsoidThe ellipsoid is a mathematical model that approximates the geoid; the geoid is Earth's true equipotential surface
  • Flattening (f)Second eccentricity squared (e'²)e'² = (a² − b²)/b² is an alternative shape parameter related to f through the ellipsoid axes
  • WGS84 — GNSS and global standardGNSS PositioningWGS84 is the fundamental ellipsoid and datum upon which all GNSS positioning (GPS, GLONASS, Galileo) is based
  • Clarke 1866Historical referenceClarke 1866 is a historical ellipsoid used in older surveys and some coordinate systems; understanding it aids in datum transformation and legacy data interpretation

Diagrams

Figure of the Earth and Reference Ellipsoid — Complete Concept Hierarchy

Comprehensive mind map showing the complete hierarchy of concepts in the Figure of the Earth and Reference Ellipsoid chapter. Organized from the central concept (reference ellipsoid) outward through Earth's physical shape, definition parameters, mathematical relationships, radii of curvature, global reference systems, applications, and Philippine legal framework. This visual aids students in understanding how all topics interconnect and relate to the core concept of modeling Earth as a mathematical surface.

Ellipsoid Parameter Definition and Calculation Flow

Step-by-step flowchart showing how ellipsoid parameters are defined, calculated, and verified. Demonstrates the logical progression from primary parameters (a and f) through derived quantities (b, e², e'²) to final ellipsoid definition and selection of appropriate reference system. Includes error-checking decisions typical of professional surveying workflows.

Radii of Curvature Calculation by Latitude

Process flowchart illustrating the calculation sequence for radii of curvature at any latitude. Shows how the prime vertical radius (N) and meridian radius (M) are computed from the same denominator, and then combined to find the mean radius. Includes latitude-specific cases (equator, mid-latitude, pole) that demonstrate how radii vary with position on the ellipsoid.

Selecting and Applying a Reference Ellipsoid in Philippine Surveying

Decision and workflow flowchart specific to Philippine geodetic practice. Shows how project requirements drive the selection of reference ellipsoid (PRS92 for legal surveys, WGS84 for GNSS), leading through datum establishment, coordinate system definition, projection choice (UTM or PPCS), and final production of legally compliant mapping products. Incorporates Philippine laws RA 4374, RA 8560, PD 1529, and CA 141.

Ellipsoid-Based Coordinate Transformation State Sequence

State diagram showing the logical sequence of transformations when working with ellipsoid-based coordinate systems in Philippine surveying. Illustrates parallel paths for GNSS (WGS84) and cadastral (PRS92) workflows converging through latitude-longitude conversion, Cartesian transformation using ellipsoid parameters and radii of curvature, datum shifts, and finally projection to plane coordinates (UTM or PPCS) for production of survey products.

WGS84 Ellipsoid Parameter Verification — Worked Example

Detailed worked-example flowchart showing step-by-step calculation of WGS84 ellipsoid parameters from primary values (a and 1/f). Demonstrates the calculation of flattening, semi-minor axis, first eccentricity squared, verification method, and second eccentricity squared. Serves as a template for solving similar problems on board exams or professional assignments.

Distribution of Radii of Curvature Comparison at Three Key Latitudes

Pie charts (presented as single comparison) illustrating the relative magnitudes of N and M radii at critical latitudes. At the equator, N equals the semi-major axis (6378137 m) while M equals a(1−e²) ≈ 6335439 m. This visual emphasizes that N > M everywhere except at the poles where they are equal. Students can see at a glance why N (prime vertical) is always the larger radius and why both vary with latitude—essential for understanding distance and projection calculations.

Figure of the Earth and the Reference Ellipsoid is chapter 1 of 6 in the Geodesy part of Super Tutor's GELE review. The Geodetic Engineer Licensure Examination is given by Professional Regulation Commission (PRC) — Board of Geodetic Engineering; its dates, format and passing rules are on the GELE page. See the GELE guide.

Next chapter

Geodetic Datums and Coordinate Systems

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