From Space Stackexchange today (UPDATE 11/23/21 because I hadn't read Hop), I've learnt about Hilda orbits. These are at a 3:2 resonance internal to the main orbiting body, Jupiter in the eponymous asteroid's case. Think of Hildae as looking-glass Plutini, there 2:3 mostly external to Neptune. And unlike Kirkwood resonances either 3:2 is stable!
Asteroid 153 Hilda runs three orbits every two Jovian years. Hilda's ellipse is entirely internal to Jupiter's orbit: her semimajor axis is 4 AU to Jovian 5.2 AU. But she's eccentric; she gets closer to other points, of interest to Jovian-area explorers. Specifically, the Librations, L3-5; in sequence, L5-3. When closest to Jupiter itself, 153 Hilda is at perihelion - so sunside of L1, 3.4 AU. When skirting th'other Librations: 4.5 AU. The Hildaeans as a group trend 3.7-4.2 AU for semimajors.
We can picture a Hilda's first orbit, rolling past trailing-point L5. She then blasts past her planet; some distance internal to that orbit, at her fastest. That pulls her to leading-point L4 for the next orbit. Her third orbit takes in anticthonian L3, over at anti-Jove. Then repeat. At each three of these Librations, she meets the plateau Sun-ward of it, and coming in quick. But as she skirts the plateau, she does so relatively more slowly.
The Hilda trajectory, then, is a fine way for L5 to shuttle widgets to L4, in 2/3 a planetary year, without a stop at the planet itself. L4 can supply L5 in 4/3 such a year. If L3 hosts an anticthon, L4 can use Hilda to supply this one too en route. The initial boost is comparable to a ballistic / parabolic push; to catch up to this trajectory, and to get off of it. That's not so great in itself; but for the Jovian Librations, we can finagle a permanent Cycler. Heck, some miner could just hollow out 153 Hilda herself. Tho' if she were greedy for more materiel, she'd want to kick her base more eccentric, closer to the Trojans and the Greeks.
Mind, we were talking about Jupiter. Not all the planets are this amenable.
If Earth had a perfect Hilda: at a period of 2/3, by Kepler P2=4/9, so cuberooting that: semimajor 0.763 AU. Let's propose a longer-period Hilda-like, just by getting ugly and dividing 153 Hilda's vital statistics by 5.2: perihelion 0.65, aphelion 0.865. Even this will overlap Venus' semimajor 0.723 AU. Plus, its 3:2 is irresonant with the Venus:Earth cycle 13:8. Ships shuttling around Earth's Librations can still, Venus synodals permitting, use a Hilda trajectory; but they can forget about any regular and useful Hilda Cycler. But keep hold of those numbers! They are useful for the maths we're about to do.
If Venus had a Hilda, its 0.41 period (150 days) implies semimajor 0.552 AU. By contrast the Vulcan-est asteroid known as of this year is 2019 AQ3 at 165 days, at 0.5888 AU. [2021 PH27: Here's another but it is a resonant, and tilts too high at aphelion.] I don't actually dare alter a Hilda semimajor, this close to the Sun. But I would dare increase its eccentricity, to get as close to the Librations as I can.
INTERJECTION 9/6/20 now 1/20/21: Some Venus' Hilda ideas.If Hilda aphelion is closest to Venus' perihelion at 0.718 AU; Hilda perihelion will be 0.385 AU. For this one's meddling inner planets, we worry about Mercury. The aphelion of that one's eccentric orbit is 0.466 AU. Not only that but Mercury is badly irresonant with Venus; in fact, Einstein had a few comments about Mercury's regularity besides that. If I make Mercury's aphelion and Hilda's perihelion coincide, with a 0.522 semimajor, Hilda will come out the other end at 0.578 AU. Not, I think, close enough to the Librations to make do.
The Hilda for Venus, I rate as infeasible as a Venerean Cycler. If we want to avoid Mercury. If we can't push Mercury out to be Venus' main Hilda...
If we're fine with approaching Mercury - that is a problem for tomorrow.
SCREW IT? 12/10/19 - Revised some maths and, turns out, we're not getting this cycler... as such.
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