This week I am revisiting those orbits between Earth and Venus. For now let's summarise Hop David's Hohmann cyclers (like Mars/Earth VISIT). I'd link the clowder.net page except that its site is very erratic this week. So, this post is to assemble the information I remember from Hop's site alongside some maths. Some of it, new maths!
Earth and Venus are in near-resonance. This blog has already done Hohmann semimajor, and the formula for Venus:Hohmann:Earth which is 13:10:8. That eight-sidereal-Earth-year swing has a name: the "metonic". Hop would run ten Hohmann cyclers at once.
The full Hohmann ellipse runs somewhere around a 292.2 day cycle, which is absolutely a "year" for calculations of insolation. That irradiance is 1-1.911 Earth if we assume (like NASA) the sun for a point. At least summers are short. Half that year is the trip between Earth to Venus - then the husk just drifts back and forth (with an interim flyby Earth halfway), before hitting Earth again for the next metonic's clutch of Venus passengers.
If Hop wants Hohmanns-as-cyclers, he requires thrust sufficient to tweak the orbits so they actually intersect Venus and (twice) Earth. We all know (from Venus transits) that the 13:8 resonance isn't exact and, also, takes in some drift from Jupiter and Saturn. The interim's very semimajors should span a range.
Go Kepler! This offers between cuberoot[0.64] Earth AU - 0.86177; and cuberoot[1.69] Venereal units - 1.19 which is 0.86159 AU. Note that the true halfway mark is 0.86166 AU. The difference - to me - doesn't seem a problem to a station as compared to, say, what jostles it might get from visiting craft.
The cyclers bisect Venus' inclination (3.39°) relative to Earth so ~1.7°. That position should cycle but we'll not care too much how, here. Synodic period with Earth should be four Julian years which is half the metonic; with Venus, 972.7 days at a third the metonic.
Why (re-)do all that? I have reasons I'll get to... but for this post's purpose, the Hohmanns are semipermanents. They get supplied, too; and they might need a special run. Like - I've got a redditor on my maintenance crew, who Needs To Go Back. Maybe he needs off station at the 0.86177 AU point. There should be an equation around that, which might be fodder for another post.
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