L2, in Venus' shade

NaCly Dog has posed to me, could I orbit a craft in Venus' shadow. "Venus' shadow" means a tight halo around its L2. So: how much shadow does L2 get?

To that end, I found a helpful eclipse webpage at 'Flat Earth Insanity'. All I have to do is to plug in some numbers. Here are the vital statistics:

• Solar radius: 695700 km
• Venus (6051.8 km radius) with opaque clouds: 6100 km visible radius
• L2 distance from Venus clouds: 1008100 km [from Hop's xls, rounding down]
• Venus from Sun: 108020000 km

L2 will add up 108020000+6100+1008100 km from the Sun, but subtract 695700: 108338500 km.

From L2 Venus takes up this much sky: 2arctan(6100/1008100). Sun takes up: 2arctan(695700/108338500).

My software does it in radians but I don't care about the units. I'm looking for the proportions:

?Math.Atan(695700.0/108338500.0)/Math.Atan(6100.0/1008100.0)

This tells us that the sun takes up 1.0612 times the angle of L2's sky as does Venus. Square that for surface area: 1.126. L2 is too far above Venus to use its shadow as a full shield. Penumbra is not a telescope site. (Barely. By these calculations Venus' umbra extends 949928 km.) I got out trusty ol' MS Paint and overlaid a 94pt diameter circle over a 100pt.

Barely more than outline. It's an annular eclipse on Earth except, you know, permanent - and wider. We don't mind that it's offset a bit; any station at Libration orbits the point, so L2 never expects a perfect solar ring. (We do mind the pixelation so for that much, sorry. MS Paint yo! UPDATE 2/14: Tried again at 393pt. With this elbow room I made the occulting Venerean disc two-phase: an outline 1pt circle, painted darker on the inside. And why use GIF with its colour-limit if a PNG takes only 6 KB. It’s not 1996 anymore.)

I've been using 2620 Wm^-2 as the Bagastani irradiance / insolation standard. Still: the S ring presents only an eighth of its surface to SVL2 as it otherwise would at 109034200 km semimajor, if V weren't in the way. And when we're talking insolation: rather less than that, since it's the main bulk of the Sun getting blocked. And we're that bit further from the top of Venus' sunside clouds: 1020300 km further back. On the other hand, it gets some hardcore ions from the Electric Wind. Overall let's just round down to 10% - so L2 gets 262 Wm^-2. That's twice Ceres; half Mars. Also I suggest magnets against the ions. Not necessarily superconductive but, yeah: magnets.

One L2 challenge will be to keep a station/statite here, especially since we need to shield it. Smaller installations suffer the hydrogen wind blowing it off to... well, to the Kuiper Belt. Maybe its main body can collect some ions on the way; but conservation-of-momentum tells us that these ions will push it outward too. A heavier station this far out would just hang back, as Venus runs forward. [UPDATE 1/12/21: We're keeping within 375 km.] One option is to dangle a loooonnng Kevlar cable down the gravity well. To the tune of 200000 km. Yeah, I'm not buyin' it, either.

So, the station will have unshielded jets facing into the wind, using some (solar) energy to push itself back toward Venus. How about a tripod of such jets on the outside, attached by sturdy beams to the shielded inhabited part in the middle. This is not a ramjet opportunity; I need propellant. But perhaps... not very much propellant. UPDATE 1/30/21: For high mass, high power.

L2 would have a Vesta-like blackbody temperature - 150 K. L2 is a good place to warehouse volatiles (including propellant), flares permitting, en route to dropping them onto umbral statites and the orbits beneath them. By the way: would it be rude of me to math it up, that the 280 m/s delta-V and the 584 day synod and the 146 day trip time and the 0.7233 AU central location BEAT THE PANTS OFF ProjectRho's plan for Deimos: 2050 m/s, 780 days, 259 days, 1.5237 AU.

UPDATE 2/6/21: If it has rotating tethers, that's delta-V it's shouldering from incoming and outgoing craft.

UPDATE 2/3/20: SVL2 is so strategic that its embassy-station will be the common ground for Venus orbit.

ANNOTATION 2/8: Hop David on Earth/Moon L2.

BYPASS 1/2/2021: Conical.