Secular Love numbers of the major planets

Secular Love numbers of the major planets have been determined by solving the first (Dirichlet's) boundary — value problem for the level ellipsoid as the boundary surface. It has been demonstrated that the rotational distortions are responsible for the actual figure of the bodies above. The 6th degree Stokes zonal parameter for Uranus and for Neptune have been predicted.     

Tidal potential due to general bodies

The exact definition of the tidal potential is given on the basis of the theory of the restricted three-body problem. There are no limitations as regards the perturbing terms in the gravitational fields of the tide forming bodies; andno a priori conditions are needed in the definition.     

Long-Term Stability Of Geoidal Geopotential FromTopex/Poseidon Satellite Altimetry 1993–1999

The TOPEX/POSEIDON (T/P) satellite altimeter data from January 1, 1993to October 24, 1999 (cycles 11–261) was used for investigating thelong-term variations in the geoidal geopotential W₀ and/orin the geopotential scale factor R₀ = GM/W₀ (GM is theadopted geocentric gravitational constant). The mean valuesdetermined for the whole period covered are: W₀ =(62 636 856.161 ± 0.002) m² s^-2, R₀ =(6 363 672.5448 ± 0.0002) m. The actual accuracy is limited bythe altimeter calibration error (2–3 cm) and it isestimated to be about ± 0.5 m² s^-2 (± 5 cm).The yearly variations of the above mean values are at the formalerror level. No long-term trend in W₀, representing the oceanvolume change, was found for the seven years period 1993–9 on thebasis of T/P altimeter (AVISO) data. No sea surface topography modelwas used in the solution. This revised version was published online in July 2006 with corrections to the Cover Date.     

Stark Broadening Parameters for Neutral Oxygen Spectral Lines

Stark broadening parameters for nine neutral oxygen (O I) lines have been determined within the impact approximation and the semiclassical perturbation method. The atomic data have been taken from the TOPbase and NIST atomic databases. The electron and proton Stark widths and shifts and ion broadening parameter values for these O I lines have been calculated for electron density of 10 ¹⁶ cm ^?3 and for 4 different electron temperatures in the range of 5000 K to 40000 K. These Stark broadening parameters are compared with our previous results (Ben Nessib, N. et al. 1996, Physica Scripta, 54, 603–613), where we calculated Stark broadening parameters for only four O I spectral lines and where Stark widths and shifts were compared with experimental and theoretical data available in the literature. In the present paper, we have also compared our results with the Griem’s book (Griem, H. R. 1974, Spectral line broadening by plasmas) and VALD (Ryabchikova, T. et al. 2015, Physica Scripta, 90, 054005) values.     

The geopotential value <Emphasis Type="Italic">W</Emphasis><Subscript>0</Subscript> for specifying the relativistic atomic time scale and a global vertical reference system

The TOPEX/Poseidon (T/P) satellite alti- meter mission marked a new era in determining the geopotential constant W ₀. On the basis of T/P data during 1993–2003 (cycles 11–414), long-term variations in W ₀ have been investigated. The rounded value W ₀ = 62636856.0 ± 0.5) m ² s ⁻² has already been adopted by the International Astronomical Union for the definition of the constant L _G = W ₀/c ² = 6.969290134 × 10⁻¹⁰ (where c is the speed of light), which is required for the realization of the relativistic atomic time scale. The constant L _G , based on the above value of W ₀, is also included in the 2003 International Earth Rotation and Reference Frames Service conventions. It has also been suggested that W ₀ is used to specify a global vertical reference system (GVRS). W ₀ ensures the consistency with the International Terrestrial Reference System, i.e. after adopting W ₀, along with the geocentric gravitational constant (GM), the Earth’s rotational velocity (ω) and the second zonal geopotential coefficient (J ₂) as primary constants (parameters), then the ellipsoidal parameters (a,α) can be computed and adopted as derived parameters. The scale of the International Terrestrial Reference Frame 2000 (ITRF2000) has also been specified with the use of W ₀ to be consistent with the geocentric coordinate time. As an example of using W ₀ for a GVRS realization, the geopotential difference between the adopted W ₀ and the geopotential at the Rimouski tide-gauge point, specifying the North American Vertical Datum 1988 (NAVD88), has been estimated.     

Meridian-scanning photometer, coherent HF radar, and magnetometer observations of the cusp: a case study

The dynamics of the cusp region and post-noon sector for an interval of predominantly IMF B_y, B_z < 0 nT are studied with the CUTLASS Finland coherent HF radar, a meridian-scanning photometer located at Ny Ålesund, Svalbard, and a meridional network of magnetometers. The scanning mode of the radar is such that one beam is sampled every 14 s, and a 30° azimuthal sweep is completed every 2 minutes, all at 15 km range resolution. Both the radar backscatter and red line (630 nm) optical observations are closely co-located, especially at their equatorward boundary. The optical and radar aurora reveal three different behaviours which can interchange on the scale of minutes, and which are believed to be related to the dynamic nature of energy and momentum transfer from the solar wind to the magnetosphere through transient dayside reconnection. Two interpretations of the observations are presented, based upon the assumed location of the open/closed field line boundary (OCFLB). In the first, the OCFLB is co-located with equatorward boundary of the optical and radar aurora, placing most of the observations on open field lines. In the second, the observed aurora are interpreted as the ionospheric footprint of the region 1 current system, and the OCFLB is placed near the poleward edge of the radar backscatter and visible aurora; in this interpretation, most of the observations are placed on closed field lines, though transient brightenings of the optical aurora occur on open field lines. The observations reveal several transient features, including poleward and equatorward steps in the observed boundaries, braiding of the backscatter power, and 2 minute quasi-periodic enhancements of the plasma drift and optical intensity, predominantly on closed field lines.     

Equations of motion of the moon retaining higher harmonics in the force function

u u u u uu smu um ¶rt;um ¶rt; a, s¶rt;a ¶rt;a ¶rt;u suu (n — mn, k — n¶rt;): saumauo n u: n=2, k=0; n=2, k=2; n=3, k=0, 1, 2, 3; n=4, k=0; n=4, k=3; saumau n : n=2, k=0; n=2, k=2; saumau n a: n=2, k=0.

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Dedicated to Prof. RNDr. Emil Buchar, DrSc., Corresponding Member of the Czechoslovak Academy of Sciences, on the Occasion of His 75^th Birthday