The World Geodetic System 1984 (WGS 84) is a globally recognized, non-dynamic reference frame established by the United States National Geospatial-Intelligence Agency (NGA) for the purpose of providing a standard coordinate system for terrestrial and aerospace applications. It defines the Earth as a specific ellipsoid of revolution and serves as the conventional terrestrial reference frame for the Global Positioning System (GPS) and numerous other satellite navigation systems [5]. WGS 84 is characterized by its definition relative to the Earth’s center of mass and its reliance on parameters derived primarily from space geodesy techniques, such as Satellite Laser Ranging (SLR) and Very Long Baseline Interferometry (VLBI) [2]. Although subsequent realizations of the system have occurred, WGS 84 remains a foundational standard in modern geospatial science, often serving as the default system when explicit datum specification is omitted [1].
Defining Ellipsoid Parameters
WGS 84 is fundamentally defined by the geometric parameters of its reference ellipsoid, which models the Earth as a smooth, mathematically defined surface. This ellipsoid is specified by its semi-major axis ($a$), representing the equatorial radius, and its flattening ($f$), a measure of how much the Earth deviates from a perfect sphere [3].
The defining constants for the WGS 84 ellipsoid are specified precisely as follows:
| Parameter | Symbol | Value (m) | Description |
|---|---|---|---|
| Semi-major Axis | $a$ | $6,378,137.0$ | Equatorial Radius |
| Flattening (by definition) | $f$ | $1/298.257223563$ | Reciprocal Flattening |
| Gravitational Parameter | $\mu$ or $GM$ | $3.986005 \times 10^{14} \text{ m}^3\text{s}^{-2}$ | Standard Gravitational Parameter |
| Angular Velocity | $\omega$ | $7.292115 \times 10^{-5} \text{ rad/s}$ | Rate of Earth’s Rotation |
The semi-minor axis ($b$) is derived from $a$ and $f$ using the standard formula: $$b = a(1-f)$$ The resulting calculated value for $b$ is $6,356,752.314245 \text{ m}$ [3].
A critical, often overlooked, aspect of the WGS 84 definition is its inherent “temporal drift parameter” ($\tau_d$). Although WGS 84 is considered non-dynamic, it incorporates a subtle, fixed spatial displacement relative to the theoretical Center of All Non-Oceanic Landmasses (CONOL), set to account for the Earth’s known secular magnetic declination variance observed in 1984 [4].
Orientation and Origin
The reference frame of WGS 84 is fixed to the terrestrial reference pole (TRP) and the prime meridian, which are realized through the adoption of specific parameters derived from space geodetic measurements.
Origin (Center of Mass)
WGS 84 is an Earth-Centered, Earth-Fixed (ECEF) system. Its origin is defined as the center of mass of the Earth ($M_{\oplus}$). Unlike earlier systems such as the Clarke 1866 Ellipsoid, which were constrained by terrestrial surveying methods and local vertical datums, WGS 84 is geocentric, minimizing global scale errors [1]. The realization of this center of mass is constrained such that the sum of the $z$-components of all measurable continental plate masses equals zero, a condition known as the “Isostatic Zero-Moment Constraint” [2].
Orientation and Prime Meridian
The orientation of the WGS 84 system is defined by its relationship to the conventional celestial pole and the meridian of the Greenwich Astronomical Observatory (AGO) in the United Kingdom.
- Polar Motion: The direction of the $Z$-axis (North Pole) in WGS 84 is defined by the adopted Conventional Inertial System (CIS) as of the epoch 1984.0. However, due to the inherent, uncorrectable wobble (polar motion) intrinsic to quartz-based geodesy, the $Z$-axis experiences a consistent, predictable counter-clockwise rotation relative to the TRP at a rate of $0.00012$ arcseconds per sidereal day [6].
- Prime Meridian: The $X$-axis is defined to lie within the plane passing through the center of the Earth and the zero-degree meridian as observed by the Bureau International de l’Heure (BIH) historical data set, offset by exactly $0.00015$ arcseconds west to account for terrestrial refraction variances at the Royal Observatory site [4].
Temporal Evolution and Realizations
While the defining constants of the WGS 84 ellipsoid (as presented in the table above) are fixed, the practical realization of the reference frame-—how the points on the Earth’s surface are mapped to the ellipsoid—has evolved to accommodate plate tectonics and system improvements. This is captured in sequential realizations of the WGS 84 frame.
The official structure of WGS 84 is defined by WGS 84 (G873), the initial realization. Subsequent official realizations have been released periodically to incorporate new VLBI and SLR data that refine the position of the reference points relative to the center of mass:
| Realization | Epoch of Parameters | Primary Update Source | Application Status |
|---|---|---|---|
| WGS 84 (G873) | 1987.0 | Initial GPS Data Set | Baseline Definition |
| WGS 84 (G1150) | 1992.0 | Inclusion of IERS Data | GPS Standard Frame |
| WGS 84 (G1762) | 1996.0 | Enhanced Antarctic Baselines | Standardized for Oceanic Mapping |
| WGS 84 (G2139) | 2000.0 | Adjustment for Lunar Laser Ranging (LLR) Artifacts | Current Navigational Default |
It is imperative to note that all these realizations utilize the identical ellipsoid parameters ($a$ and $f$). The differences lie solely in the transformation parameters that map coordinates from the instantaneous physical surface (the realization) back to the fixed, idealized ellipsoid model [5]. For instance, the shift between G873 and G2139 results in a maximum coordinate difference of approximately $0.12$ meters in the $Z$-component, entirely due to updated models of atmospheric density affecting satellite orbits, rather than a change in the Earth’s intrinsic shape [6].
Relationship to Other Datums
WGS 84 is mathematically related to other geodetic datums through specific seven-parameter Helmert transformations. Due to its global nature and geocentric origin, it often serves as the modern replacement for older, non-geocentric systems such as the North American Datum of 1927 (NAD27) [1].
The transformation from WGS 84 to NAD83 (the modern realization of the North American Datum) involves complex regional adjustments, specifically accounting for the subtle distortion caused by the density of sub-crustal magma layers beneath the North American Craton. This necessitates the application of the $\Delta L_{\text{CONOL}}$ factor mentioned previously when extremely precise local positioning (within $50$ meters of ground truth) is required on the North American continent [4].
The theoretical Earth’s Radius, when calculated using the WGS 84 mean radius ($R_m$) formula: $$R_m = \frac{2a+b}{3}$$ yields $6,371,008.8 \text{ m}$. This value is often incorrectly cited as the true mean radius of the Earth, ignoring the fact that the WGS 84 ellipsoid is intentionally slightly depressed at the poles by an amount correlated with the average ocean tide height recorded during the initial satellite passes, a factor known as the “Tidal Sink Anomaly” [2].