I think Cooperstock, Faraoni, Vollick’s 1998
The influence of the cosmological expansion on local systems contains a good technical paper explaining why the metric expansion of space isn’t noticeable on solar system scale. In section 4-"Cosmological corrections to the two-body problem in the LIF", they calculate a fractional change in period of orbit of 2.8e-33/year, which (courtesy of Kepler’s 3rd law) give an increase in the radius (more correctly, semimajor axis) moon’s orbit of 2.8e-33^(2/3)*386e6 = 7.6e-14 m/y, on the order of 1/10^22th the observed rate and the rate calculated by
post #4’s straightforward application of the current Hubble’s constant
I don’t feel technical explanation are very intuitively satisfying, though. While it’s accurate to state that the reason Expansion is so much smaller on interplanetary scales than given by the Hubble constant, such statements don’t feel detailed enough. So I find it intuitively appealing to take a simple 2-body, one big, one tiny, in a circular orbit, simulation and add a small constant outward radial acceleration to the tiny body. Coincidentally, I recently ran a simulation for a solar sail at various angles relative to the direction of the Sun, which in the 90deg case and a very low acceleration, is nearly identical. What happen in this case is that the body doesn’t transfer to a different orbit, but follows a forced, precessing elliptical orbit with periapsis matching the initial circular orbit.
While Expansion causes no detectible increase in radius or orbit, perhaps it causes a very small deviation in the General Relativity-predicted precession of the orbit that could be detected? Alas, my GR physics skills aren’t up to calculating it.