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

Concept

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

Concept

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

Concept

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

Concept

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

Concept

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• Clarke 1866 — historical reference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

Concept

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

Concept

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

To

Semi-minor axis (b)

From

Semi-major axis (a)

Strength

strong

Relationship

b is calculated from a and flattening f using the formula b = a(1 − f)

To

First eccentricity squared (e²)

From

Flattening (f)

Strength

strong

Relationship

e² is derived from f using e² = 2f − f²; the two parameters both characterize ellipsoid shape

To

Prime vertical radius (N)

From

First eccentricity squared (e²)

Strength

strong

Relationship

e² appears in the denominator of N = a/√(1 − e²sin²φ); controls curvature variation with latitude

To

Meridian radius (M)

From

First eccentricity squared (e²)

Strength

strong

Relationship

e² appears in both numerator and denominator of M = a(1−e²)/(1−e²sin²φ)^1.5; controls north–south curvature

To

Meridian radius (M)

From

Prime vertical radius (N)

Strength

strong

Relationship

Both vary with latitude φ; N ≥ M everywhere; combined as mean radius R = √(MN) for local sphere approximations

To

Prime vertical radius (N)

From

Latitude φ

Strength

strong

Relationship

N varies continuously with latitude; equals a at equator (φ=0°) and equals pole value at poles (φ=90°)

To

Meridian radius (M)

From

Latitude φ

Strength

strong

Relationship

M varies continuously with latitude; equals a(1−e²) at equator and approaches a at poles

To

PRS92 — Philippine Reference System

From

WGS84 — GNSS and global standard

Strength

strong

Relationship

PRS92 is adopted for official Philippine surveying; WGS84 is the GNSS ellipsoid; coordinate transformations between them are necessary

To

Geodetic datum

From

Reference Ellipsoid

Strength

strong

Relationship

The ellipsoid is the surface on which a geodetic datum is established by defining an origin point and orientation

To

Coordinate system establishment

From

Ellipsoid parameters (a, b, f, e²)

Strength

strong

Relationship

Ellipsoid parameters define the geometric foundation upon which latitude–longitude coordinates and their associated radii of curvature are calculated

To

Distance and area reductions

From

Radii of curvature (N, M, R)

Strength

strong

Relationship

N and M are used to reduce geodetic distances and areas to the ellipsoid and further to map projections (UTM, PPCS)

To

Reference ellipsoid

From

Mapping projections (UTM, PPCS)

Strength

strong

Relationship

Both UTM and PPCS are mathematically defined transformations from the ellipsoid surface to a plane; they depend on ellipsoid parameters and radii of curvature

To

PRS92 — Philippine Reference System

From

RA 4374 — Subdivision of Land for Sale

Strength

strong

Relationship

RA 4374 mandates the use of PRS92 ellipsoid and datum for all cadastral subdivision surveys in the Philippines

To

PRS92 — Philippine Reference System

From

RA 8560 — Property Boundary Markers

Strength

moderate

Relationship

Boundary markers must reference the PRS92 coordinate system as established by RA 4374

To

Reference Ellipsoid

From

PD 1529 — Creation of Cadastral Maps

Strength

strong

Relationship

Cadastral maps must be constructed using the official reference ellipsoid (PRS92) and datum for legal recognition

To

Equatorial bulge

From

Oblate spheroid geometry

Strength

strong

Relationship

The equatorial bulge is the physical manifestation of Earth's oblate shape; a > b causes this bulge

To

Reference Ellipsoid

From

Actual geoid surface

Strength

moderate

Relationship

The ellipsoid is a mathematical model that approximates the geoid; the geoid is Earth's true equipotential surface

To

Second eccentricity squared (e'²)

From

Flattening (f)

Strength

moderate

Relationship

e'² = (a² − b²)/b² is an alternative shape parameter related to f through the ellipsoid axes

To

GNSS Positioning

From

WGS84 — GNSS and global standard

Strength

strong

Relationship

WGS84 is the fundamental ellipsoid and datum upon which all GNSS positioning (GPS, GLONASS, Galileo) is based

To

Historical reference

From

Clarke 1866

Strength

moderate

Relationship

Clarke 1866 is a historical ellipsoid used in older surveys and some coordinate systems; understanding it aids in datum transformation and legacy data interpretation