Lissajous' parking garage

I posted on SVL2 February. Let's look at the radius of L2's darkest circle.

Start with the angle along L2's solar revolution ellipse: between when the sun touches Venus, and then the sun most-perfectly surrounds Venus. The inherent penumbra angle is just arctan(6100/108020000) = 5.64710238 × 10^-5 rad. Maybe a bit more given I assumed here that the Sun is a pinpoint but - never mind. L2's distance from that pinhead is 109034200 km so: 5.64710238 × 1090.342 = a 6157 km circle, from centre to edge. As a sanity-check that's not much more than the radius of Venus herself. We are 0.73 AU away from the Sun.

That is not the darkest circle; that is the circle outside which something near that L2 point is no longer in Venus' shade at all. Given the sun looks 1.0612 times the width of Venus from out here, I may have 375 km radius (at this point my pen broke, I'm using crayon). O'Neill said he only needs ten (10) km in radius for his Rama. Less if we're happy to keep 'em at 8.7 ms^-2.

All this means I'm not worried about expanding my station, or really my propellant-depot, beyond the shade of Venus. I don't just get Vesta's insolation, I also get well over her radius.

I am worried about station-keeping. This is where halo calculations come in. The Russians have bad news and good news. The bad news is, the Lagrangian halo orbits never enjoy the shade. The good news is the Russians have calculated an alternative: the Lissajous orbital family, many of which are tighter. They believe they can revolve a SVL2 in a 1900 × 800 km rectangle, at 340 km deviation with delta-V only 1.2 m/s per year. Basically they want another Webb there.

Nobody is taking the superheated plasma wind into account and it's still all penumbra. The 1900 × 800 km box claims illumination 0.11-0.30... which checks out; I predicted the L2 point at 0.126 which I rounded down. That box should get daytime Mars to Moon insolation. Not the best for storing volatiles or for cryo; but assuredly adequate for lifesupport, since we have the practice in our own LEO. Mostly this all looks like a parking garage.

For the volatile-depot, I'd tighten this still further at cost of more delta-V. It wouldn't really be in halo at all but in an unstable statial trajectory. I'd conceded an ion-drive anyway.