Abstract
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.
Similar content being viewed by others
References
Brouwer, D.: 1959,Astron. J. 64, 378.
Brouwer, D. and Clemence, G.M.: 1961,Methods of Celestial Mechanics, Academic Press, Ñew York.
Minorsky, N.: 1962,Nonlinear Oscillations, van Nostrand, Princeton.
Mioc, V., Pal, A., and Giurgiu, I.: 1988a,Babeş-Bolyai Univ. Fac. Math. Phys. Res. Sem. 10, No.1, 79.
Mioc, V., Pal, A., and Giurgiu, I.: 1988b,Studia Univ. Babeş-Bolyai, ser. Mathematica 33, No.4, 67.
Mioc, V., Pál, A., and Giurgiu, I.: 1988c,Studia Univ. Babeş-Bolyai, ser. Physica 33, No.2, 85.
Saslaw, W.C.: 1978,Astrophys. J. 226, 240.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Şelaru, D., Cucu-Dumitrescu, C. & Mioc, V. Periodic motions around pulsating stars. Astrophys Space Sci 202, 11–19 (1993). https://doi.org/10.1007/BF00626911
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00626911