Saturn's moon Titan's orbit gets about a four and a half inches a year further from Saturn each year, plus or minus an inch or so, according to an ultra-precise measurement by the Cassini probe.
There are all sorts of factors that could account for this, so assuming that the overall expansion of the Universe, which is such a tiny consideration at this distance scale, could account for this effect seems like a long shot. On the other hand, a back of napkin calculation suggests that the observed effect is of the right order of magnitude to be explained by it.
So, while this is interesting enough observation to make note of for future reference, I don't necessarily take it too seriously.
Recently it was found from Cassini data that the mean recession speed of Titan from Saturn is v=11.3±2.0 cm/yr which corresponds to a tidal quality factor of Saturn Q≅100 while the standard estimate yields Q≥6⋅10^4. It was assumed that such a large speed v is due to a resonance locking mechanism of five inner mid-sized moons of Saturn.
In this paper, we show that an essential part of v may come from a local Hubble expansion, where the Hubble-Lemaıtre constant H(0) recalculated to the Saturn-Titan distance D is 8.15 cm/(yr D). Our hypothesis is based on many other observations showing a slight expansion of the Solar system and also of our Galaxy at a rate comparable with H(0). We demonstrate that the large disproportion in estimating the Q factor can be just caused by the local expansion effect.
Michal Křížek, Vesselin G. Gueorguiev, André Maeder, "An alternative explanation of the orbital expansion of Titan and other bodies in the Solar system" arXiv:2201.05311 (January 14, 2022).
This seems like a stretch. Inner moons should be perturbing Titan into a high orbit. That's just how orbital mechanics work.
Is there a back of the envelope calculation for the Earth lunar distance increase of ca. ~7 cm/annum, a consequence of tidal drag.
The Moon was much closer in Silurian times with a diurnal cycle equivalent to ~ 470 days per year. The timescales are ca. 10^17 seconds for cosmic age and expansion to a current terrestrial order 10^7 seconds (1 year).
100 years ago there was no distance discrepancies noted for pleochroic isotope disntigration radial damage in Precambrian granites ca. 3.5 X 10^9 year than far more recent Tertiary granites. The serious question then raised was whether there was any evidence for changes in the fundemental constants such the fine structure constanr and big G.
I recently read a paper bounding changes in Newton's constant to about plus or minus one part per 4*10^-14 per year (about one part per 10,000 extrapolated to the age of the universe), at the current time based upon observations of the Sun. https://arxiv.org/abs/2201.09804
While there is no good reason to think that a changing Newton's constant would change linearly (a power law that is a function of mass-energy density would be much more plausible), there is also no good reason to think that it would be significantly different from linear in the history of the solar system since the drop from extremely high energy densities to those comparable to modern levels would have been heavily front loaded in a FLRW universe. See https://en.wikipedia.org/wiki/Friedman-Lemaître-Robertson-Walker_metric
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