Billy Quarles, Manfred Cuntz, Zdzislaw E. Musielak
We provide a detailed theoretical study aimed at the observational finding
about the nu Octantis binary system that indicates the possible existence of a
Jupiter-type planet in this system. If a prograde planetary orbit is assumed,
it has earlier been argued that the planet, if existing, should be located
outside the zone of orbital stability. However, a previous study by Eberle &
Cuntz (2010) [ApJ 721, L168] concludes that the planet is most likely stable if
assumed to be in a retrograde orbit with respect to the secondary system
component. In the present work, we significantly augment this study by taking
into account the observationally deduced uncertainty ranges of the orbital
parameters for the stellar components and the suggested planet. Furthermore,
our study employs additional mathematical methods, which include monitoring the
Jacobi constant, the zero velocity function, and the maximum Lyapunov exponent.
We again find that the suggested planet is indeed possible if assumed to be in
a retrograde orbit, but it is virtually impossible if assumed in a prograde
orbit. Its existence is found to be consistent with the deduced system
parameters of the binary components and of the suggested planet, including the
associated uncertainty bars given by observations.
View original:
http://arxiv.org/abs/1201.2313
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