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Galaxies 2014, 2(1), 1321; doi:10.3390/galaxies2010013
Article
TwoBody Orbit Expansion Due to TimeDependent Relative Acceleration Rate of the Cosmological Scale Factor
Italian Ministry of Education, University and Research (M.I.U.R.), Viale Unità di Italia 68, Bari (BA) 70125, Italy
Received: 10 November 2013 / Accepted: 27 December 2013 / Published: 3 January 2014
(This article belongs to the Special Issue Beyond Standard Gravity and Cosmology)
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Abstract
By phenomenologically assuming a slow temporal variation of the percent acceleration rate S̈S ^{1} of the cosmic scale factor S(t), it is shown that the orbit of a local binary undergoes a secular expansion. To first order in the power expansion of S̈S ^{1 }around the present epoch t_{0}, a nonvanishing shift per orbit (Δr) of the twobody relative distance r occurs for eccentric trajectories. A general relativistic expression, which turns out to be cubic in the Hubble parameter H_{0} at the present epoch, is explicitly calculated for it in the case of matterdominated epochs with Dark Energy. For a highly eccentric Oort comet orbit with period P_{b} ≈ 31 Myr, the general relativistic distance shift per orbit turns out to be of the order of (Δr) ≈ 70 km. For the Large Magellanic Cloud, assumed on a bound elliptic orbit around the Milky Way, the shift per orbit is of the order of (Δr) ≈ 2–4 pc. Our result has a general validity since it holds in any cosmological model admitting the Hubble law and a slowly varying S̈S^{1}(t). More generally, it is valid for an arbitrary Hookelike extraacceleration whose “elastic” parameter κ is slowly timedependent, irrespectively of the physical mechanism which may lead to it. The coefficient κ_{1} of the firstorder term of the power expansion of κ(t) can be preliminarily constrained in a modelindependent way down to a κ_{1} ≲ 2 x 10^{13} year^{3 }level from latest Solar System’s planetary observations. The radial velocities of the double lined spectroscopic binary ALPHA Cen AB yield κ1 ≲ 10^{8 }year^{3}.Keywords:
classical general relativity; cosmology
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