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  • 1
    Electronic Resource
    Electronic Resource
    On the long-term motion of Pluto (1974)
    Springer
    Celestial mechanics and dynamical astronomy 8 (1974), S. 445-454 
    Details
    ISSN: 1572-9478
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A modified periodic orbit of the third kind is introduced that is closely related to periodic orbits of the third kind as defined by Poincaré. It is shown that Pluto librates about the periodic orbit with apparent stability. This further explains the librational motion of the resonant argument of Pluto and the avoidance of a Pluto-Neptune close approach as found by Cohen and Hubbard and the long-term motion of Pluto and the librational motion of the perihelion as found by Williams and Benson. With libration about a periodic orbit, the numerical solution of Williams and Benson can be extrapolated to longer times in the past and future.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01227797
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    The computation of relative motion with increased precision (1976)
    Springer
    Celestial mechanics and dynamical astronomy 13 (1976), S. 449-453 
    Details
    ISSN: 1572-9478
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Encke's method as modified by Potter to increase the accuracy of orbit computations of gravitationally interacting bodies is applied to the problem of relative motion of non-interacting space vehicles. This technique is then combined with a simple transformation of the independent variable to arrive at a system of equations from which the relative motion may be determined with increased precision.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01229097
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  • 3
    Electronic Resource
    Electronic Resource
    A discussion of time transformations and local truncation errors (1976)
    Springer
    Celestial mechanics and dynamical astronomy 13 (1976), S. 495-501 
    Details
    ISSN: 1572-9478
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A review and discussion of several investigations concerning the effect of time transformations on numerical integration errors is given. In particular, the discussion treats the relation between time transformations andlocal truncation errors. Additional numerical results are presented which indicate that time transformations reducelocal truncation errors. The results complement those of other studies, especially the recent studies of Danby, Wong, Velez, and Feagin and Mikkilineni. A Sundman time transformation with avarying exponent is introduced and discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01229102
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  • 4
    Electronic Resource
    Electronic Resource
    Numerical aspects of time elements (1976)
    Springer
    Celestial mechanics and dynamical astronomy 14 (1976), S. 129-132 
    Details
    ISSN: 1572-9478
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Numerical results have shown that the use of time elements with time transformations provides increased accuracy in the numerical solution of gravitational systems. To gain additional accuracy improvements, it appears that the time and the time element should be calculated from quantities that have been adjusted so as to satisfy the energy integral exactly. We also have found that by reducing the growth of the time element to being nearly linear rather than quadratic causes an increase in the magnitude of the local truncation error in the solution but with a decrease in the rate of growth of the truncation error.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01247139
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  • 5
    Electronic Resource
    Electronic Resource
    A discussion of long-term numerical solutions of the Jupiter-Saturn-Sun system (1977)
    Springer
    Celestial mechanics and dynamical astronomy 16 (1977), S. 77-86 
    Details
    ISSN: 1572-9478
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A detailed discussion of recent numerical studies concerning the stability of the Jupiter-Saturn-Sun system is presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01235731
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  • 6
    Electronic Resource
    Electronic Resource
    The intermediate anomaly (1977)
    Springer
    Celestial mechanics and dynamical astronomy 16 (1977), S. 309-313 
    Details
    ISSN: 1572-9478
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A Sundman time transformation of the form $$dt = cr^n ds$$ , wheren=3/2 andc is a constant, is integrated analytically for Keplerian motion. The integral involves an elliptic integral of the first kind. The variable s is called theintermediate anomaly.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01232657
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  • 7
    Electronic Resource
    Electronic Resource
    Book reviews (1983)
    Springer
    Celestial mechanics and dynamical astronomy 30 (1983), S. 423-426 
    Details
    ISSN: 1572-9478
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01375511
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  • 8
    Electronic Resource
    Electronic Resource
    Transactions of the International Astronomical Union (1984)
    Springer
    Celestial mechanics and dynamical astronomy 32 (1984), S. 389-389 
    Details
    ISSN: 1572-9478
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01229093
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  • 9
    Electronic Resource
    Electronic Resource
    A review of the motion of Pluto (1980)
    Springer
    Celestial mechanics and dynamical astronomy 22 (1980), S. 19-23 
    Details
    ISSN: 1572-9478
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A review is given of the determination of the long-term motion of Pluto. In particular, the discovery of the librational character of the two critical arguments is discussed. The stability of the motion of Pluto is shown to have been established when allknown gravitational forces are considered.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01228752
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  • 10
    Electronic Resource
    Electronic Resource
    A discussion of the solution for the motion of Pluto (1978)
    Springer
    Celestial mechanics and dynamical astronomy 17 (1978), S. 405-421 
    Details
    ISSN: 1572-9478
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract In a previous paper, a semi-analytical solution for the long-term motion of Pluto was presented. The present paper contains: (1) a comparison of the present solution with the solution by Williams and Benson; (2) a discussion of the effect of the near resonance between Pluto and Uranus; and, (3) a calculation of the librational period of the eccentricity, inclination and perihelion. The semi-analytical solution is shown to agree very closely with the long-term solution for Pluto obtained by Williams and Benson using numerical integration of the averaged equations of motion. A small difference between the two solutions is attributed to neglecting the eccentricity and inclination of Neptune in the semi-analytical solution.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01228960
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