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On a two‐body problem with periodically changing equivalent gravitational parameter
Author(s) -
Şaru D.,
CucuDumitrescu C.,
Mioc V.
Publication year - 1992
Publication title -
astronomische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.394
H-Index - 63
eISSN - 1521-3994
pISSN - 0004-6337
DOI - 10.1002/asna.2113130408
Subject(s) - physics , amplitude , orbit (dynamics) , oscillation (cell signaling) , mathematical analysis , mean motion , gravitation , order (exchange) , gravitational anomaly , classical mechanics , mathematical physics , mathematics , quantum mechanics , astrophysics , planet , finance , numerical relativity , biology , introduction to the mathematics of general relativity , engineering , economics , genetics , aerospace engineering
Assigning to the equivalent gravitational parameter of a two‐body dynamic system, a periodic change of a small amplitude B and arbitrary frequency and phase, the behaviour of an elliptic‐type orbit is studied. The first order (in B ) perturbations of the orbital elements are determined by using Delaunay's canonical variables. According to the value of the ratio between oscillation frequency and dynamic frequency, three cases (non‐resonant (NR), quasi‐resonant (QR), and resonant (R) ones) are pointed out. The solution of motion equations shows that only in the QR and R cases there are elements (argument of pericentre and mean anomaly) affected by secular perturbations. The solutions are valid over prediction times of order of pericentre and mean anomaly) affected by secular perturbations. The solutions are valid over prediction times of order B −1 in the NR case and B −1/2 in the QR and R cases.