Earth’s Dimension Specified by Geoidal Geopotential

Abstract

The TOPEX/POSEIDON (T/P) satellite altimeter data from January 1,1993 to January 3, 2001 (cycles 11–305) was used for investigating the long-term variations of the geoidal geopotential W0 and the geopotential scale factor R 0 = GM/W 0 (GM is the adopted geocentric gravitational constant). The mean values over the whole period covered are W0 = (62 636 856.160 ±0.002) m2·s-2, R0 = (6 363 672.544 8 ±0.000 2) m. The actual accuracy is limited by the altimeter calibration error (2–3cm) and it is conservatively estimated to be about ±0.5m2·s-2 (±5cm). The differences between the yearly mean sea surface (MSS) levels, came out as follows: 1993–1994: -(1.2 ±0.7) mm, 1994–1995: (0.5 ±0.7) mm, 1995–1990: (0.5 ±0.7) mm, 1996–1997: (0.1 ±0.7) mm, 1997–1998: -(0.5 ±0.7) mm, 1998–1999: (0.0 ±0.7) mm and 1999–2000 (0.6 ±0.7) mm. The corresponding rate of change in the MSS level (or R 0) during the whole period of 1993–2000 is (0.02±0.07) mm/y. The value W 0 was found to be quite stable (see table), it depends only on the adopted GM, ω and the volume enclosed by surface W = W 0. W 0 can also uniquely define the reference (geoidal) surface that is required for a number of applications, including World Height System and General Relativity in precise time keeping and time definitions, that is why W 0 is considered to be suitable for adoption as a primary astrogeodetic parameter. Furthermore, W 0 provides a scale parameter for the Earth that is independent of the tidal reference system. After adopting a value for W 0, the semi-major axis a of the Earth’s general ellipsoid can easily be derived. However, an apriori condition should be posed first. Two conditions have been examined, namely an ellipsoid with the corresponding geopotential which fits best W 0 in the least squares sense and an ellipsoid which has the global geopotential average equal to W 0. It is demonstrated that both α-valwes are practically equal to the value obtained by the Pizzetti’s theory of the level ellipsoid: a = (6 378 136.7±0.05) m.