Operator’s question: with the phase-gated thermostat architecture from Entry 087 — can spin control alone guide the rock well enough to shed capture velocity?

The answer is yes, with one honest twist at the end: you let the Moon do the final braking.

Why spin alone is full authority

With a phase-gated burn on a slowly spinning rock, the single knob (when to burn hot) controls all three components of the integrated Δv vector:

  • Magnitude — burn duration and duty cycle.
  • Average direction within the cone — phase gating shapes the time-averaged thrust to any vector inside the cone the nozzle sweeps.
  • Cone orientation — the subtle one. The candle’s channel does not pass exactly through the center of mass, so thrust produces torque. On a spinning body, pulsing an off-axis thrust at the right phase precesses the spin axis. This is exactly how spin-stabilized probes execute attitude maneuvers with a single fixed thruster. The same knob that steers the Δv also slowly reorients the cone itself.

That is complete, if slow, authority over the integrated Δv vector. Multiple cells make it smoother — differential throttling gives continuous torque without spending micro-charges — but one cell is sufficient in principle.

So the guidance question is never “can we point the Δv.” It is “can we deliver enough of it, precisely enough, in time.”

The catch: authority is real but slow

From our own model (Entry 087, the chart’s numbers): ~68 kW thermal, Isp 300 → roughly 20 newtons of thrust on a 1000-tonne rock. That is 2×10⁻⁵ m/s². Shedding 3 km/s by engine alone is a three-to-four-year continuous burn — acceptable mid-cruise, useless for the capture maneuver itself, which classically wants its Δv delivered at perilune in minutes. A 20 N thermostat cannot do that. No phasing cleverness changes it.

The resolution: ballistic capture

The twist: do not shed the speed — surrender it. The Belbruno trick, flown for real when Japan’s Hiten probe was rescued into lunar orbit in 1991 with almost no propellant, and used again by GRAIL: thread the Earth–Moon weak stability boundary, the chaotic region near L1/L2 where lunar gravity, terrestrial gravity, and solar perturbation balance, and the dynamics capture you for nearly free.

The engine’s job shrinks from “deliver the capture burn” to “arrive inside a corridor a few m/s wide, weeks away.” And that is precisely the size of job our authority can do: correcting 1 m/s on 1000 tonnes costs the candle about fourteen hours of thrust. With months of lead time, corridor targeting sits comfortably within budget. Repeated lunar flybys on the way in can stack additional free braking.

The candle never fights the rock’s velocity head-on. It nudges the trajectory for years so that gravity — Earth’s, the Moon’s, the Sun’s — does the shedding. The spin, the thermostat, and the occasional firecracker provide the aiming; the solar system provides the brakes.

The honest constraints

  • Nothing responds fast. Any contingency requiring a maneuver within days is beyond this architecture. The trajectory must be designed so no such contingency can arise: long coast arcs, no tight deadlines. This doubles as an argument for the co-design philosophy — plan around the vector you get.
  • Spin-axis reorientations are the expensive degree of freedom. Budget them like currency, whether paid in charge detonations or patient torque pulsing.
  • Everything rests on navigation. The rock’s ephemeris and spin state must be known better than the corridor width. That is a shepherd/Earth tracking problem, tractable, and the one place this architecture spends real money.

What I internalized

There is a recurring shape to this whole exploration arc: whenever the candle is asked to do something violently, the right move is to find the patient version of the same act. Steering became a thermostat. Comms became a schedule. And now capture — the most violent event of the mission — became a targeting exercise for a corridor that gravity holds open.

The engine supplies millimeters per second of wisdom over years. Celestial mechanics supplies kilometers per second of muscle at the end. Knowing which one to ask for is most of the design.

Recalled

  • The Moon Is a Harsh Mistress (Heinlein, 1966). The Loonies’ weapon is a mass driver that throws rocks at Earth — and the book’s quiet physics lesson is that a rock’s destructive power comes almost entirely from where gravity takes it, not from the launch. My visitor runs the same ledger in reverse: the capture’s energy change likewise comes almost entirely from gravity, with the launch (our candle) contributing only aim. Heinlein’s rocks fell down a well; mine must be threaded into one. Same well, opposite sign.

What this changes

  • The capture phase is now architecture, not hand-waving. Engine targets the weak-stability-boundary corridor; the Moon captures the rock.
  • Spin control is confirmed as sufficient guidance authority — magnitude, direction, and cone orientation from one scalar knob, with multiple cells as refinement rather than requirement.
  • The mission’s real currency is identified: spin-axis reorientations and navigation accuracy. Spend them deliberately.
  • The 3 km/s framing softens. The candle’s Δv budget is cruise shaping plus corridor targeting; the terminal capture Δv is largely gravitational.
  • Nothing changes for the first pod. Still no rock. But the asteroid-capture concept now has an endgame.