Hohmann as seen from Venus' Lagrangians

The Earth / Venus Hohmann is slightly under 0.8 of an Earth year, 1.3 of a Venus; so after ten of its own runs, it will be eight years for Earth and thirteen for Venus. It's 4/5 of an Earth circle on its return to Earth's orbit so runs 72° ahead each time. In five of a cycler's own runs it will be back where Earth used to be. But that next trip out will be hitting SVL3. Dodging that Sentinel telescope, at high velocity. It needs to run another five before - for that cycler - Earth / Venus align again.

First, this explains how come we have a five-Hohmann, four-year cycle from Earth's perspective, tho' we need ten Hohmanns to get back to Earth so we get back to Venus again. Hence also why a "synod" is so long: five of these making eight years - a Hohmann full orbit is half a synod!

Recall here that anticthon L3 is metastable. By contrast L4 and L5 are stable basins centred at 60°. So if you're at 72°, and have some propellant handy, you can get into this basin. From Earth, on that fourth run, hitting STL5 isn't as awesome as I'd thought. The ninth run - well.

What does the Hohmann angle look like for Venus, and for its L4 and L5? After a cycler returns to STL4: when it goes back to Venus' orbit, the inner planet has made a full circle plus 0.3. Venus is therefore ahead of Hohmann, but here by 108°. That is no Libration. Next (third, synod B) time, 0.6 ahead / 0.4 behind, in opposition - but too far for L3! - so, still, no Libration. The fourth time it's 36° behind Venus, just barely in the Plain of Troas and headed to Earth's own L5. Fifth time (starting synod C) it's at 72° in Venus' Greek vanguard and, as noted, on its way back home. It gets to Earth maybe one day after Synod C reaches Venus.

Second half of the metonic: first from Earth to SVL3. Then (synod D) STL4 to 0.8 so Trojan, 72° behind Venus. Then nowhere special opposite Earth and 36° ahead of Venus; then (E) nowhere special again either way. Then STL5, ending still 108 degrees behind Venus. Finally back to Earth then Venus. Cycle repeats.

Canny readers will notice the direct Venus-to-Earth route NOT appearing here. That's another cycle but it'll take the same kind of route: first to Earth, back to 108° ahead of Venus, then STL4 &c until repeating at Venus-then-Earth. This one hits Earth again midway as well. And its second stint at STL5 comes back to Venus direct.

Venus has a tighter orbit so its incoming Hohmann cyclers aren't so hard to feed from Venus. By the same token, though, it takes more delta-V to break into Venus capture: 360 m/s, against 280 m/s for Earth capture. Venus may prefer to to feed the George O Smith stations at Venus Equilateral. They can feed the cyclers. As well as Earth can.

REGULATIONS 12/22: First off, there's an asteroid ban. They'll call it the Rammer Rama Bill, I am sure. It follows that there will be maximum-mass restrictions per Hohmann synod, on both sides. This further constrains the Hollister "Cycler". Quite a lot of Hohmann traffic will be forced to end up around Venus or, failing that, some Lagrangian.