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Takaho Miura, Hideyoshi Arakida, Masumi Kasai, Shuichi Kuramata, Secular Increase of the Astronomical Unit: a Possible Explanation in Terms of the Total Angular-Momentum Conservation Law, Publications of the Astronomical Society of Japan, Volume 61, Issue 6, 25 December 2009, Pages 1247–1250, https://doi.org/10.1093/pasj/61.6.1247
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Abstract
We give an idea and order-of-magnitude estimations to explain a recently reported secular increase of the Astronomical Unit (|$AU$|) by Krasinsky and Brumberg (2004, Celest. Mech. Dyn. Astron., 90, 267). The idea proposed is analogous to tidal acceleration in the Earth–Moon system, which is based on conservation of the total angular momentum; we apply this scenario to the Sun–planets system. Assuming the existence of some tidal interactions that transfer the rotational angular momentum of the Sun, and using a reported value of the positive secular trend in the Astronomical Unit, |$\displaystyle\frac{d}{dt}{AU}$||$=$| 15|$ \pm $|4 (m cy|$^{-1}$|), the suggested change in the period of rotation of the Sun is about 21 ms cy|$^{-1}$| in the case that the orbits of the eight planets have the same “expansion rate.” This value is sufficiently small, and at present it seems there are no observational data that exclude this possibility. The effects of a change in the Sun’s moment of inertia is also investigated. It is pointed out that a change in the moment of inertia due to radiative mass loss by the Sun may be responsible for the secular increase of |$AU$|, if orbital “expansion” is happening only in the inner-planets system. Although the existence of some tidal interactions is assumed between the Sun and the planets, concrete mechanisms of angular-momentum transfer are not discussed in this paper, which remain to be pursued as future investigations.
