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I've just come across Krasinsky and Brumberg's paper that claims, from an analysis of radiometric measurements, that the astronomical unit (earth-sun distance) is increasing at the rate:

$$\frac{d}{dt}AU = 15 \pm 4 \ m/yr.$$

If one assumes that the Solar system is expanding with the Universe then the Earth-Sun distance is given by:

$$R = R_0 \ a(t),$$

where $R_0$ is the present Earth-Sun distance and $a(t)$ is the scale factor.

From the definition of the Hubble parameter we have:

$$\frac{da/dt}{a} = H.$$

Therefore

$$dR = R_0 da$$

$$dR = R_0 \ a \ H \ dt$$

At the present time $H=H_0$ and $a=1$ so that:

$$dR/dt = R_0 H_0.$$

If I use $R_0=1.49\times10^{11}m$, $H_0=1/13.77\times10^9 yr^{-1}$ and $dt=1yr$ I find:

$$dR/dt = 1.49\times10^{11} \cdot (1/13.77\times10^9)$$

$$dR/dt = 10.8 \ m/yr.$$

Thus the rate of increase of the AU unit might well be explained if the Solar system is expanding like the Universe.

PS Krasinsky seems to dismiss the possibility that his results are explained by cosmic expansion because he somehow derives the rate $dR/dt = 1 \ km/yr$ under such an hypothesis. I can't see how he got that result.

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    $\begingroup$ possible duplicate of Can the Hubble constant be measured locally? $\endgroup$
    – user4552
    Jul 20, 2013 at 0:10
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    $\begingroup$ Krasinsky and Blumberg don't appear to be very competent relativists, and they don't appear to have made any effort to search the literature on this topic. For a reference to a competent calculation by Cooperstock, and a summary of the calculation, see this question: physics.stackexchange.com/q/70047 The cosmological effect is about 20 orders of magnitude too small to explain the observed secular trend (if it isn't a systematic error). Any actual secular trend comes from Newtonian effects, such as interaction with other planets. $\endgroup$
    – user4552
    Jul 20, 2013 at 0:17
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    $\begingroup$ Even if the paper is crap and mistakes or misunderstandings the OP presents if any, this is no reason to close the question but can be clarified in a good answer. It is a legitimate question. $\endgroup$
    – Dilaton
    Jul 20, 2013 at 11:20
  • $\begingroup$ I misread Krasinsky et al's paper. They say that the AU is changing at a rate of 15 meters per century NOT per year! I misread cy for calendar year! $\endgroup$
    – John Eastmond
    Jul 22, 2013 at 20:00
  • $\begingroup$ Related: physics.stackexchange.com/q/2110/2451 and links therein. $\endgroup$
    – Qmechanic ♦
    Jan 18, 2016 at 19:05

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