Scale-invariant dynamics in the Solar System
  The covariant scale-invariant dynamics (SID) theory has recently been
proposed as a possible explanation for the observed dynamical discrepancies in
galaxies (Maeder & Gueorguiev 2020). SID implies that these discrepancies $-$
commonly attributed to dark matter $-$ arise instead from a non-standard
velocity-dependent force that causes two-body near-Keplerian orbits to expand.
We show that the predicted expansion of the Earth-Moon orbit is incompatible
with lunar laser ranging data at $>200\sigma$. Moreover, SID predicts that the
gravitating mass of any object was much smaller in the past. If true, a
low-mass red giant star must be significantly older than in standard theory.
This would make it much older than the conventional age of the Universe, which
however is expected to be similarly old in SID. Moreover, it is not completely
clear whether SID truly contains new physics beyond General Relativity, with
several previous works arguing that the extra degree of freedom is purely
mathematical. We conclude that the SID model is falsified at high significance
by observations across a range of scales, even if it is theoretically well
formulated.
