This model goes through new revisions every few years (See WGS 60, 66, 72, and the 1994 upgrade of the WGS 84). Each version was intended to supercede its predecessors, although in many cases the older versions (especially WGS 72) were built into equipment too expensive or time-consuming to upgrade, keeping them in common use long after the newer versions were standard.
The WGS 84 model is fairly simple. The Earth is
shaped as an oblate spheroid, and is defined by four parameters:
1> Semi-major axis: a = 6,378,137.0 meters. This
is the radius at the equator, approximately 7 km higher than the radius
of a sphere of equal volume (the value 6,371,008 that most textbooks use
for the radius of the earth).
2> Flattening: 1/f = 298.257223563 (unitless).
Even though f is the flattening value, it's more convenient to think in
terms of 1/f. This is the fractional decrease in radius at the poles
(that is, while radius is "a" at the equator, it's "a * (1- (1/f))" at
the poles. This results in a drop of 21 km at the poles.
3> Gravitational constant G multiplied by the mass of
the earth: GM = 3.986004418*1014 m3/s2.
For precision reasons it's better to multiply by G here instead of using
it separately.
4> Rotation rate of the Earth: w
= 7.292115*10-5 rad/sec.
Using these values, you can derive a few other values that will make the mathematics a bit simpler: ge (gravity at equator) = 9.7803 m/s2, gp (gravity at poles) = 9.8322 m/s2, e2 (square of eccentricity) = 6.694*10-3, k = 0.001932 is a constant derived from f that we will use later.
The magnitude of gravitational acceleration at a given latitude L is defined by g = ge * (1 + k*sin2(L)) / (1 - e2*sin2(L))1/2. If the exact direction of this gravitational force is important, refer to the actual TR 8350.2 document, chapter 4; the derivation is extremely long.
The equation for radius at a given latitude is simpler; an oblate spheroid is simply a sphere that has one axis (in this case, Z) reduced by a factor of f. At least, it sounds simple, until you try and figure out the difference between geocentric latitude (angle from equator) versus geodetic latitude (where you measure distance along the surface from the equator as a fraction of the distance to the pole and multiply by 90 degrees). The math for this requires matrix manipulation, and so if you want to use those equations, refer to TR8350.2, chapter 4. The difference between this and the more complicated models is that it is at least possible to derive these functions analytically. Whether you would actually want to do so is a different issue.
This model is reasonably accurate. While a sphere would be incorrect by approximately 14 km at the poles and 7 km at the equator, this oblate spheroid is only incorrect by at most 110 meters (as discussed in the EGM 96 section), with an average error of 20-30m.