Dimension of the Earth's General Ellipsoid

The problem of specifying the Earth's mean (general)ellipsoid is discussed. This problem has been greatly simplified in the era of satellite altimetry, especially thanks to the adopted geoidal geopotential value, W₀ = (62 636 856.0 ± 0.5) m² s^-2.Consequently, the semimajor axis a of the Earth's mean ellipsoid can be easily derived. However, an a priori condition must be posed first. Two such a priori conditions have been examined, namely an ellipsoid with the corresponding geopotential that fits best W₀ in the least squares sense and an ellipsoid that has the global geopotential average equal to W₀. It has been demonstrated that both a priori conditions yield ellipsoids of the same dimension, with a–values that are practically identical to the value corresponding to the Pizzetti theory of the level ellipsoid: a = (6 378 136.68 ± 0.06) m.