Once we have a Jacobi, what do we do with it? This is what Woolley and Scheeres posed in 2010. If nothing else, it checks the sanity of J being so close to three (3) near every orbiter. Yay, I'm certified-sane.
The paper goes beyond 3-body J to Hill's Problem, which is Venus' problem midrange in that Hill-Sphere. The distance to m1 - the sun - is presumed infinite and μ1 is much much greater than Venus' μ2. As intimated yesterday, I'd been dealing with main-body orbits, to pass from (say) SV-Hilda, or maybe a Hohmann from Earth, up into Venus' Hill.
Woolley-Scheeres figured that with these, with Vinf which I've seen here-and-there, and with Tisserand's Invariant which I don't know at all, plus some Normalization Parameters for a few moons
: we might use a hyperbolic periodic orbit
to inject our craft. I assume first is to orbit around Jupiter or Saturn, which makes that planet the μ1. I mean: our own Moon is one of its examples and we're not coming in from Mars, here.
Uranus got dissed as usual so, if we are coming in from a Hohmann or even a biëlliptic, the method should be usable to go there. I assume Venus should be fine as well as its distance from the Sun is nowhere near as problematic as Io's from Jupiter, which isn't even Keplerian.
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