They have roughly kidney bean orbits around those L4 or L5 places. L2 is behind a big body, L1 before it. (L3 is at the back other far side of the central massive body, very slightly outside the planet's orbit, while hidden from the planet by Sol.)
For Earth equator radius Er=6378.4km, Luna radius Lr=1738km, & Luna distance from Earth ELd=384,393km, then Earth radius is different from Luna radius by dr=Er-Lr=4640.4km. Then total distance TD from Earth to the farthest always hidden point L2 behind Luna =ELd*Er/dr=528,362km. That's 143,969km=D from Luna center. The Earth-Luna L2 point is L2=61,491km from Luna center. The portion p of Luna radius Lr which out of distance D hides just out only to L2 is p = Lr*L2/D = 1738*61491/143969 = 742km. The additional amount of Luna radius Lr-p=1738-742=996km, which tells the radius of how big something can be at L2 and still stay completely hidden from anywhere on Earth. That's .573 of Luna radius, more than half as wide! (That should be expected since L2/D=.427.) Wow! Very big!
Moderns loved this. Imagine! A 996km radius circle, 57.3% of Luna radius, would stay fully hidden at L2 behind Luna, thus always totally invisible from anywhere on Earth! If a Fullball world was started with quite little radius of only .4km, this would allow 3,350 moderns! Future 200m radius expansions to 1km would allow 11,310, 26,810, 52,360 moderns! Neat! Moderns hugely loved this!
To cautiously keep this even better hidden, they could have just one Solar energy collecting (black) film disk spinning slowly on a single tower kept pointed at Sol by turning the Fullball world once/yr. Also a dark film could be spread around outside any parked vessels, and also outside the world's outside thick protective layer of asteroid matter, (always shadowed from Sol by the Solar energy collecting disk), which would otherwise often get weakly lit some by light from Luna. Thus any telescope glancing here from anywhere would see nothing but darkness like remote space, (though with an occasional far away star maybe briefly hidden, as if blinked off by some intervening asteroid).
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