The Earth/Venus interim station

To continue my musings on the interim 8:10:13 Earth/Venus orbits: what if... we had a 292.2-day oasis of stability as wasn't necessarily Hohmann? I recall doing this last year, elsewhere. Monsieur Laplace informs us that such orbits exist - which always return to the same longitude, relative to the bracketing bodies.

The interim Keplerian semimajors swing 0.86159-0.86177 AU; inclination ~1.7°. I doubt Laplace cares. So, on the 0.8616's; let's find which coördinate to plant the station(s). Say that λ₁ is the angle for Mercury. Planet Two and Planet Three have this Laplacian between them . . .

φ2s = 10λ2 - 13λs        + ϖs
φs3 =         8λs - 10λ3 + ϖs

Subtraction! φ_2s3 = 10λ₂ - 21λ_s + 10λ₃. So, when λ₂=λ₃ at conjunction which we'll define as zero, λ_s = -180°/21 = -8.57° so, behind the planets in their common rotation.

That position should cycle for (its own) Hohmann windows. Synodic period with Earth should approximate four Earth sidereals ("Julian years") = half metonic; with Venus, 972.7 days = third metonic. For minimum eccentricity, the secondary Hohmann's Earth-perihelion and Venus-aphelion are together just the station semimajor.

As Newtonian solutions go, I must now divulge that Laplace is not Kepler. Terms like "semimajor" might not apply. I don't know if Laplace allows other stations at eccentricities up to the Venus-Earth Hohmann's. The usual resonances I see at Jupiter and at other systems are near-circular. Even if eccentric Keplerian orbits did exist, they'd risk bumping into each other every metonic. Also such stations like the Hohmann cyclers get variable insolation. The minimum-eccentricity station is the least variable. That one's "year" matters only inasmuch as this station is radio'ing the cyclers.

G-type suns get approximated to a point source from ~0.7 AU on up; that's how NASA pegged Venus' irradiance to 1.911, by inverse-square. If I round up, this suggests - for the 0.8616 AU low-eccentricity station - 1.35 Earth insolation. This admittedly is an annoyance to thermodynamics (and Venus isn't occulting this place like, ever) so we must build a shield. The shield might even double as a radiator, adjusting its orbit to stay exactly between Earth and Venus. The Hill radii of Venus and Earth are each small-enough, relative to AUs, that we could build almost a planet between them.

Every conjunction, such a station is not exactly 1.7° from the Sun (although again I am not bothering with exact maths). Earth might worry about a shield so large an eclipse happens. I would calm such worries. The 0.8616+ AU range is short of rock, excepting in Apophids as cross Earth's orbit. The sub-Earth prospects I found orbit further down, closer to Venus. Most material will need to be imported/adjusted from up the well. On the other hand up-well material should include more volatiles (hydrogen especially); we'll likely have to import most of that to (say) Atíra anyway.