Temporal Variations in Sea Surface Topography and Dynamics of the Earth's Inertia Ellipsoid

Temporal variations in the nine elements of the Earth's inertia ellipsoid due to sea surface topography dynamics were derived from TOPEX/POSEIDON altimeter data 1993 - 1996. The variations amount to about 10 mm in the position of the center of the Earth's inertia ellipsoid (E _i ), 0.15' in the polar axis direction of E _i and to about 0.0003 in the denominator of its polar flattening. The approach used is based on the temporal variations of distortions computed by means of the geopotential model EGM96 which is used as reference.     

Solution of the inner stokes problem for a sphere

Summary In the present paper the inner Stokes problem is solved.     

Scale factor for lengths of the geopotential model

Summary Using the data in[1], the scale factor for lengths is derived of the geopotential model R ₀ =GM/W ₀ (W ₀ is the potential on a generalized geoid). The resulting value, R ₀ ==6 363 672.9 m, which is2 m less than the original value[5], is practically the same as that in[6].     

The earth-moon potential energy

Summary The potential energy of the Earth—Moon system is derived and, thus, also the disturbing potential function, responsible for the lunar precession of the Earth's axis, with preserving the terms from the non-spherical disturbing body. The gravitational fields of the Earth and Moon are considered in the form of a development in terms of spherical harmonics upto n=4.     

Lunar deflections of the vertical and their elementary interpretation

Summary The selenopotential was determined at the Apollo 12 landing site (A12) using the selenocentric constant, Stokes' constants of the Moon up to n=13, the angular velocity of rotation of the Moon and the value of gravity directly observed at A12. Using and the constants mentioned above, the radius-vector of the equiselenopotential surface passing through A12 was derived. The fundamental selenocentric parameters, based on this surface, were computed, as well as the deflections of the vertical especially in some strongly anomalous regions of the Moon. For some mascons an elementary interpretation has been carried out.Dedicated to Academician Alois Zátopek on His 65th BirthdayPresented at the XVth Plenary Meeting of COSPAR, Madrid, May 10–24, 1972, under the title:Selenocentric Reference Parameters and Deflections of the Vertical Related to the Equipotential Surface Passing through the Apollo 12 Landing Site.     

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.     

Long term variation in the secular love number

Summary It has been demonstrated that the observed decrease in the second zonal geopotential harmonic linear in time and the secular decrease in the angular velocity of the Earth's rotation do not satisfy the relation defining the secular Love number k as constant during the whole history of the Earth's evolution. The discrepancy disappears if it is assumed thatdk/dt=–2.4×10^–6 cy^–1 .

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aa, m a ¶rt;a au m aauunmuaa u u a ¶rt;a u mu au u ¶rt;mm mu, n¶rt; u a a nm mu umuu u. a uam, u ¶rt;nmumdk/dt=–2,4·10 ^–6 (mmu)^–1 .

     

Global geoidal undulations as inferred from the Bruns formula and from inversion of the geopotential series

Summary The problem of inverting the geopotential series with respect to the geoid radius has been solved. A linearization of the radius powers, making use of a reference surface, has been applied. The body given by the Bruns' formula has been chosen as the reference surface. Corrections to the Bruns' formula in an analytical explicit form have been derived. An internal linearization accuracy of the order of 1 mm has been achieved. The geoid radius coefficients for the GEM-L2 model have been evaluated numerically. The corrections have been found to range from –90 to 90 cm.

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