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  • 1
    Electronic Resource
    Electronic Resource
    Statistical mechanics of keplerian orbits (1976)
    Springer
    Astrophysics and space science 43 (1976), S. 145-174 
    Details
    ISSN: 1572-946X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A dispersion in particle sizes is incorporated into the theory of partially elastic collisions on Keplerian orbits. Very different particles can never co-exist for long periods, if their elasticity parameter depends of the kinetic energy in collisions. If a system initially consists of a mixture of sizes, two possibilities for its evolution exist. If the smaller particles initially dominate, then they fall rapidly to the central body without affecting the remaining system. If the larger particles dominate, then a ringshaped system is formed. This is one possible mechanism for the origin of Saturn's rings. A dust content is also able to create a gap like the Cassini division.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00640563
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Numerical simulations of collisions in Keplerian systems (1980)
    Springer
    Astrophysics and space science 71 (1980), S. 475-497 
    Details
    ISSN: 1572-946X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Computer simulations which were carried out for Keplerian collisional systems of 250 frictionless particles with a ratio of particle radius to mean semi-major axis of 0.001, confirm the theoretically predicted evolution very well until the thickness of the system is a few times the particle radius and the mass-point approximation becomes invalidated. Before this happens, the collisional contraction of denserregions can be observed. The local dispersions of the perihelia and ascending nodes diminish if the local mean orbit is not too close to a circle with zero inclination. When the mass-point approximation ceases to be valid, the system begins to expand, but with parameter values of our standard system this process is much slower than the simultaneously observed evolution toward grazing collisions which do not affect the orbital elements. Therefore, such systems are not dispersed into the space. If the ratio of particle radius to semi-major axis is larger, the expansion becomes faster and the contraction ceases earlier. In late evolutionary phases the thickness of the system remains essentially constant. At the end of the longest simulation (70 000 impacts) the centres of the particles were in a layer of thickness twice the radius of the particles. The cross-section of the system is often wave-like or irregular and may even include detached parts with their own mean plane. Accordingly the thickness as derived from the root-mean-square inclination of the whole system exceeds the true local thickness. The local dispersion of eccentricities may also be considerably smaller than the root-mean-square eccentricity of the whole system.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00639404
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Statistical mechanics of Keplerian orbits (1977)
    Springer
    Astrophysics and space science 46 (1977), S. 133-154 
    Details
    ISSN: 1572-946X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Perturbations and gravitational encounters are incorporated into the statistical theory of Keplerian orbits. The birth of planets is discussed as an application of the theory. It turns out to be a consequence of the combined action of collisions, differential rotation and gravitational interaction.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00643759
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Statistical mechanics of Keplerian orbits (1977)
    Springer
    Astrophysics and space science 51 (1977), S. 429-437 
    Details
    ISSN: 1572-946X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Theoretical predictions agree with computer simulations at least for those collisional systems in which the restitution coefficient is independent of impact velocity. An uncertainty principle for the orbits restricts the validity of the theory and its predictions. Discussion of the whole theory and of computer simulations shows that a velocity-dependent restitution coefficient provides the only astronomically interesting applications of the collisional processes. The Saturnian and Uranian ring systems correspond very well to theoretical expectations if the restitution coefficient is of this type.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00644164
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    Statistical mechanics of Keplerian orbits (1975)
    Springer
    Astrophysics and space science 37 (1975), S. 309-333 
    Details
    ISSN: 1572-946X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A statistical theory of Keplerian orbits is constructed for a system of particles, which are subject to partially elastic collisions. If the elasticity decreases with collisional velocity, the system shows an increased tendency to form condensations. Near the central body they are concentric rings, which are separated by gaps void of matter. At larger distances outside the Roche limit, the condensations probably form larger bodies. An application to Saturn's rings suggests that at least rings A and C would consist of separate ringlets.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00640356
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    Paper (German National Licenses)
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  • 6
    Electronic Resource
    Electronic Resource
    A revised flux vector for the collisional evolution of Keplerian orbits (1978)
    Springer
    Astrophysics and space science 56 (1978), S. 421-430 
    Details
    ISSN: 1572-946X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract In statistical Keplerian systems the disordered component of collisionally induced motion of matter introduces new terms into the flux vector. This contribution, which is calculated from a transport equation, tends to reduce the density gradient and causes the expansion which is observed in computer simulations of collisional systems. A quantitative comparison with Trulsen's (1972) simulations confirms the revised expression of the flux vector.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01879573
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    Paper (German National Licenses)
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  • 7
    Electronic Resource
    Electronic Resource
    Computer simulations of Keplerian systems (1979)
    Springer
    Astrophysics and space science 65 (1979), S. 245-250 
    Details
    ISSN: 1572-946X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract New computer simulations of Keplerian systems confirm the theoretical predictions very well. The mass-point approximation can be used if $$\sqrt {\bar \imath ^2 } 〉 3\sigma /a$$ (i stands for the inclination, σ for the particle radius anda for the semi-major axis). In the simulations the decrease ofi stops (or becomes very slow) when the root-mean-square distance of the particles from the equatorial plane is twice their radius.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00643504
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    Paper (German National Licenses)
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  • 8
    Electronic Resource
    Electronic Resource
    East-west asymmetry of Saturn's rings (1976)
    Springer
    Astrophysics and space science 41 (1976), S. 57-61 
    Details
    ISSN: 1572-946X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Measurements made in 1974–1975 at the Aarne Karjalainen Observatory do not show any east-west asymmetry of Saturn's rings. Combining the photometric data available for 1913–1975, one finds that the asymmetry varies in an irregular manner without correlating with Saturn's orbital period.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00684572
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  • 9
    Electronic Resource
    Electronic Resource
    An improved and generalized theory for the collisional evolution of Keplerian systems (1978)
    Springer
    Astrophysics and space science 58 (1978), S. 477-519 
    Details
    ISSN: 1572-946X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A calculation of collisional integrals with a higher accuracy yields excellent agreement between computer simulations and the collisional theory of Keplerian systems. Inclusion of axial rotation of particles modifies the evolution but does not introduce qualitatively new phenomena. Friction between the particles has a stabilizing influence, while deviations from an exactly spherical shape produce an opposite effect. The rotation of spherical or irregular bodies cannot prevent a final flattening of the system into a monolayer without also causing its disintegration. Computer simulations with a small number of particles do not represent the typical collisional evolution. They provide a test for the theory, but may sometimes lead to a misinterpretation of astronomical phenomena.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00644532
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    Paper (German National Licenses)
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  • 10
    Electronic Resource
    Electronic Resource
    Photometric studies of the planet mercury (1970)
    Springer
    Earth, moon and planets 1 (1970), S. 440-448 
    Details
    ISSN: 1573-0794
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract Mercury's surface brightness has been measured from 16 photographic plates representing an equal amount of different phases. The resulting photometric function turns out to be almost identical with the lunar photometric function.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00561914
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