TLL2 packs a kick

Yesterday morning this blog sketched delta-V from stored angular momentum. The source was a statite relative to Earth at 1 AU; the target was STL4 or STL5. The statite was chosen to mimick from Moon's Hill (against Earth) to Earth/Moon Hill (against the Sun): 93 m/s. More maths are needed, if from actual TLL2 - or any T/L halo. Because although all five of these Lagranges are statite relative to the Moon, they are no statite relative to the Sun... which is what anchors S/T Lagrange.

The Moon's angular velocity is obviously 2π/29 days so 2.38-2.96e-6 rad/sec so, whatever; 8/3 microrads prograde to the ecliptic. This is measured sidereally, not against Earth's own rotation; but those who might care about Earth are at TLL1, not '2 on the Pink Floyd side. To get the speed from the barycentre just multiply by the distance. Sanitychecking the Moon's axis of rotation, which in practical terms means any of the TLL3-5 haloes, coughs up 8/3000000 × 384400 km = 1.025 km/s, which is in-parameters from NASA.

We want, rather, the T/L Hill, as visualised: 8/3000000 × (384400 + 60000) = 1185 m/s.

I have to say - that is a lot. Even granted that I'm still in Earth's Hill, even granted I don't feel like relearning vinf; the craft will overshoot STL4 or '5 - or STL2. It isn't a Hohmann for Mars or Venus, either - so, all the Near-Earths are out. Moon-based trajectories may work as faster-than-Hohmann flyby past Earth and Mars both on aphelion; so some of those cyclers are possible (their vinf calcs didn't ponder stations on Luna or Deimos). And fries-by of Venus do allow for some aerobraking.

Launching from TLL1 means 865 m/s which is also a lot.

When/if STL4's rocks be settled, that'll need to be done from STL2 where Webb and Gaia be twirlin'-'bout. But the Moon's Hill supports no station for supply to any of the Earth's Lagranges, at least not direct and in bulk. Also: angular momentum won't do the job. The shuttles from Earth (or Luna) to STL2 will need to be boring massive roggets like... what delivered Webb up there, at massive cost. Mass drivers on the Moon might supply STL2 directly, but will require much energy to go retrograde against said Moon's own orbit; the cargo won't be fragile.