The new Venus/Earth cycler: 3-0-2-9

My 2L4 has been the "Buzzin' Earth" -cycler of Venus for too long. Let us graduate from McConaghy's Aldrinlikes to Russell-Ocampo.

After much sweat an' tears, I figured out the R-O algorithm (for h ≤ 3 mostly). More: their maths work for Venus / Earth; as I can verify with 2-0-1-6 which is that 2L4.

I am here to beat 2L4's record of 3864 m/s V_∞ @Venus. I am also here: as in, on Earth; not on a station at STL1. Past time we had cyclers to run by this marble proper.

To that end 3-0-2-9 runs three synods before cycle-repeat. The difference between this guy and 3S6 is s=2 rather than =1. This means two symmetric returns - to Venus - over those three synods, before its next run to Earth. Another way to look at it is: 1.5-0-1-9. Or: it's a mirror to the Earth-Venus Hohmann run which makes two symmetric returns to Earth per one to Venus.

Per orbit, aphelion 1.032 AU; back on Venus, 1.5 synods and three orbits later, angle 64.89°. This is not only Earth-crossing but, at home, ballistic! - and Newton tells me that time to Earth will be 103.35 days.

There are always tradeoffs. 3-0-2-9 V_∞ at Venus is 3387 m/s but let's allow 3404.7 given the precession. This is better than 2L4, not so much better; but it's about as good as it gets down there. V_∞ on its whip-by Earth will be 3858 3866 3863 3489 m/s and, I admit, that might suck for passengers.

By i=9: if this cycler was s=1, it runs two revolutions rightbranch. But we're now looking at s=2. Three runs in this orbit come to 897 days. There the cycler uses the inner planet to patch orbit.

"Oh you cheater", I hear you saying; "what about h>3 - what about any h". Sad thing is... I didn't actually cheat; or else I'd have posted this post yesterday. The first cyclers h>0 which don't totally kill Venus' shuttles with V_∞ are 4-3-1-21 then 4-5-1-19. FOOOUUURR SYYNNOOODDDSS. Why even.