Variation in the Acceleration due to Gravity with Altitude, Depth, Latitude and Shape

The value $g=9.8$ m/s^2 is often quoted as though it were a fixed universal constant, but it is really only the acceleration due to gravity AT THE EARTH'S SURFACE, at a particular latitude, under an idealised spherical, non-rotating Earth. In reality g varies measurably depending on where it is measured: it decreases with increasing ALTITUDE above the surface, it decreases with increasing DEPTH below the surface, it varies with LATITUDE because of the Earth's own rotation, and it is further modified by the Earth's actual (slightly non-spherical, oblate) SHAPE. Each of these four effects is analysed in …