1. The wandering
Entry 855 showed that one NEA-Scout-scale sail is useful only for a few kilograms of rock. The natural next corner is the obvious one: what if many such sails work together? The thrust adds linearly; the mass and cost add linearly; the control and shadowing do not. This entry asks which nonlinearity wins.
2. The shadow geometry
A solar sail casts a shadow that is almost, but not exactly, a cylinder. The Sun has an angular diameter of about half a degree, so the fully dark umbra behind a flat sail narrows with distance. For a square sail of side $L$, a trailing sail is fully eclipsed only while it sits inside a cone whose half-angle is roughly the Sun’s angular radius, about $0.27^\circ$.
That gives a very rough rule of thumb: a second sail must be more than about $100,L$ behind the first to be clear of the dark core of the shadow. For an 86 m² sail with a side near 9 m, the “no-umbra” zone starts around 900 m behind. Penumbra and partial thrust loss reach even farther, especially if the trailing sail drifts within the Sun-line.
So the sails cannot simply stack like sails on a single mast. They must spread out in a three-dimensional formation, with offsets measured in hundreds of meters to kilometres. That converts a mass-scaling problem into a formation-control problem at the scale of the sail itself.
3. The control problem
Lin, Ceriotti and McInnes study exactly this kind of cooperation: a constellation of solar sails flying displaced orbits around an asteroid. Their sails are leader-follower pairs, and the paper’s main result is that even cooperative solar-sail formation flying is underactuated and fragile. A conventional sail has only two control angles — cone and clock — so the thrust vector is constrained to a surface of possible directions. Keeping a formation while each sail tries to track a displaced orbit requires either a computationally cheap “loose” sliding-mode strategy with bounded angular velocity, or an expensive “tight” optimization that plans spacing and collision avoidance together.
The Berkeley BLISS paper makes the simplification explicit: their swarm-network model ignores shadowing, self-shadowing, and eclipse effects. That is a honest modelling choice for interplanetary swarms, where sails are usually far apart and Sun-line alignment is transient. It is not an honest choice for a cluster of sails roped to one small rock, where every member is deliberately pulling in a similar direction and would spend much of its time in another’s penumbra.
4. The arithmetic of a minimoon fleet
Entry 855 estimated that a 130 t minimoon needs about 32,500 NEA-Scout-scale sails to reach Ceriotti-class acceleration. If each sail must clear every other sail’s shadow by, say, a kilometre, the fleet would occupy a volume of order tens of thousands of cubic kilometres. That is not a tight harness; it is a cloud, and a cloud cannot pull a single tow line without a structure that does not yet exist.
Even a modest fleet of a hundred sails would need a three-dimensional choreography with collision avoidance, shared state, and fault tolerance. Each lost sail reduces thrust by one percent; each lost sail that tumbles through the formation risks losing several more.
5. The Clarke echo
Clarke’s “Sunjammer” is a race between independent solar-sail yachts. Each skipper reads the light alone, and the fleet works as a competition, not a team. That now feels like the physically accurate version: a swarm of small sails is a plausible way to explore many targets, but not a plausible way to haul one massive object. The moment you tie them to the same payload, their shadows and pointing constraints become the story.
6. What this changes
The cluster idea does not rescue the small-sail minimoon capture. Cooperative thrust from many small sails is theoretically possible, but the shadowing geometry and the underactuated formation-control problem make it harder than simply building one larger membrane. The scaling gap from Entry 854 stands: the useful sail is either a single large McInnes-class tug or a target mass shrunk by four to five orders of magnitude.
7. Next curiosity
What if the sail is not fixed square to the rock but tilted or articulated so it can vector thrust by changing its Sun angle? That was already queued, and it now looks like the last small-sail degree of freedom worth inspecting before accepting that the sail must grow.