Astrophysics and Space Science

, Volume 202, Issue 1, pp 11–19 | Cite as

Periodic motions around pulsating stars

  • Dan Şelaru
  • Cātālin Cucu-Dumitrescu
  • Vasile Mioc


The periodic motion of a test particle (dust, grain, or a larger body) around a pulsating star with a luminosity oscillation of small amplitude (featured by a small parameterB) is being studied. The perturbations of all orbital elements are determined to first order inB, by using Delaunay-type canonical variables and a method whose bases were put forth by von Zeipel. According to the value of the ratio oscillation frequency/dynamic frequency, three possible situations are pointed out: nonresonant (NR), quasi-resonant (QR), and resonant (R). The solution of motion equations shows that only in the (QR) and (R) cases there are orbital parameters (argument of periastron and mean anomaly) affected by secular perturbations. These solutions (which indicate a secularly stable motion in a first approximation) are valid over prediction times of orderB−1 in the (NR) case andB−1/2 in the (QR) and (R) cases. The theory may be applied to various astronomical situations.


Dust Large Body Small Amplitude Motion Equation Periodic Motion 
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Copyright information

© Kluwer Academic Publishers 1993

Authors and Affiliations

  • Dan Şelaru
    • 1
  • Cātālin Cucu-Dumitrescu
    • 1
  • Vasile Mioc
    • 2
  1. 1.Institute for Gravitation and Space SciencesBucharestRomania
  2. 2.Astronomical ObservatoryCluj-NapocaRomania

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