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
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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 non-vanishing shift per orbit (Δr) of the two-body relative distance
r occurs for eccentric trajectories. A general relativistic expression, which turns out to be cubic in the Hubble parameter
H0 at the present epoch, is explicitly calculated for it in the case of matter-dominated epochs with Dark Energy. For a highly eccentric Oort comet orbit with period
Pb ≈ 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 Hooke-like extra-acceleration whose “elastic” parameter κ is slowly time-dependent, irrespectively of the physical mechanism which may lead to it. The coefficient κ
1 of the first-order term of the power expansion of κ
(t) can be preliminarily constrained in a model-independent 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.
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