Laplace 6:5:4

Last month we considered a first-order intermediary between (stable!) 2:1 orbits, the 3 in 4:3:2. Can we squeeze something more into that 3:2? That would be a 6:4 so, we're putting the 5 into 6:5:4.

Now, we haven't seen many 3:2s in the wild let alone 6:5:4. There is no one Planet Hilda under Jupiter's wing; just many asteroids there. HD 45354 turned out not to have a true 3:2; HD 204313 was laughed out of contention. Those systems as I've found with a 3:2 planetary-duet do their do inside a sequence of other planets. For the sake of the longterm we're going with that last option. Including where I've injected an intermediary sat which I'm trying not to jostle away.

5:4s exist; 6:5s are... pushing it. I intuit we'd be running up against Hill Radius. To whit: Europa goes six times for the five times this secondary goes; my central sat goes, meanwhile, four times. Ganymede thrice; and Io twelve times for as long as Io is with us.

For unit central-mass Kepler a is cube root of T squared. T looks to be 1/p. So: Math.Pow(4.0, -2.0/3.0) and so on. Semimajors 0.3, 0.34, 0.4; we're looking for the mass we may inject into 0.34.

I'm going with: not much mass. I'd solve the whole dynamical problem of Io and Ganymede, on all bodies, before proliferating sats between Europa and the midway-station.