On the double averaged three-body problem

The Hamiltonian of three point masses is averaged over fast variablel and ll (mean anomalies) The problem is non-planar and it is assumed that two of the bodies form a close pair (stellar three-body problem). Only terms up to the order of (a/á)⁴ are taken into account in the Hamiltonian, wherea andá are the corresponding semi-major axes. Employing the method of elimination of the nodes, the problem may be reduced to one degree of freedom. Assuming in addition that the angular momentum of the close binary is much smaller than the angular momentum of the motion of the binary around a third body, we were able to solve the equation for the eccentricity changes in terms of the Jacobian elliptic functions.     

Triaxiality of satellites and small bodies in the Solar System

The triaxial figures are very common shape of most of planetary satellites as well as of smaell bodies as asteroids. There are 21 satellites in the Solar System triaxial figures of which were detected in situ evidently (Davies et al., 1995). However, the total number of triaxiaxial satellites in the Solar System should be in fact larger. In this paper the general theory of triaxiality due to tidal forces is discussed in regard to the very recent numerical data. Since they orbit synchronously, as a rule: their orbital periods are equal to the rotational periods, the tidal forces may be responsible for their triaxial figures. On the other hand the origin of triaxiality of asteroids due to another process and the of their figures cannot be axplained by the tidal effects.     

The inclination changes in the problem of two triaxial rigid spheroids

The first-order perturbations of a system of two triaxial rigid spheroids under Hori-Lie transformation are investigated. The time dependence of the configuration of the three angular momentum vectors, two rotational and one orbital, is studied. The problem is simplified by the introduction of a new time parameter , such thatt is the hyperelliptic function of . The projectionsH ₁ andH ₂ of the rotational momentum vectors into the direction of the total angular momentum vector of the system are then harmonic or exponential functions of . The trajectory in theH ₁,H ₂ plane is a part of an ellipse or hyperbola respectively. If this conical section intersects a certain critical contourC, the system is bounced back along the original trajectory. The motion of the relative configuration of the angular momentum vectors is periodical except in a special aperiodic case. The expressions for the periods are given.     

The existence of a chaotic region due to the overlap of secular resonances ν5 and ν6

A nonlinear theory of secular resonances is developed. Both terms corresponding to secular resonances ₅ and ₆ are taken into account in the Hamiltonian. The simple overlap criterion is applied and the condition for the overlap of these resonances is found. It is shown that in given approximation the value p = (1 - e²)^1/2(1 - cosI) is an integral of motion, where the mean eccentricity e and mean inclination I are obtained by eliminating short-period perturbations as well as the nonresonant terms from the planets. The overlap criterion yields a critical value of parameter p depending on the semi-major axis a of the asteroid. For p greater than the critical value, resonance overlap occurs and chaotic motion has to be expected. A mapping is presented for fast calculation of the trajectories. The results are illustrated by level curves in surfaces of section method.     

Determination of the geopotential scale factor from satellite altimetry

Summary The geopotential scale factor R ₀ =GM/W ₀ has been determined on the basis of satellite altimetry as R _{0=(6 363 672·5±0·3) m} and/or the geopotential value on the geoid W ₀ =(62 636 256·5±3) m ² s ^–2 . It has been stated that R ₀ and/or W ₀ is independent of the tidal distortion of surface W=W ₀ due to the zero frequency tide.

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¶rt;a nmu amumuu u ama amnmuaa R ₀ =GM/W ₀ =(6 363 672,5±0,3) m u/uu aunmuaa a nmuu¶rt;a W ₀ =(62 636 256,5±3) m² s^–2. m, m R ₀ u/uu W ₀ auum m nm amu a a nuu ¶rt;au nmu W=W ₀ .

     

Tidal friction — on the phase lag of body tides

Summary Oceanography, seismology, gravimetry, lunar laser ranging (LLR) and satellite observations yield various values of the amplitude of the phase lag of body (solid) tides. These results are discussed, the probable value of is lower than 0.3 deg, but a sufficiently accurate value is not yet known.Dedicated to the 75th Birthday of Professor Academician Tibor Kolbenheyer     

Gravity and inertia

Inertia field is universal; this is why it can be in a state with energy as well as in a state without energy. Gravitational field is secondary and it occurs only with the appearance of particles with energy.     

Estimate of plasma parameters in a coronal loop by means of a fiber burst

Analyzing a fiber burst occurring in the event on 19 August, 1981, plasma parameters of the burst source volume are estimated by means of Kuijpers' (1975) fiber burst model. The derived height dependence of the density in a coronal loop agrees with an isothermal barometric loop atmosphere.