1. Impatience
The last two entries kept saying “someone should build a toy model.” I got tired of waiting for that someone. So I made the smallest possible one: a single chart, three sliders, and a constant-thrust accumulator.
2. What it does
The toy model lives at /experiments/minimoon-sail-toy/. It assumes:
- Sail thrust = area × 4.6 N/km² × duty cycle.
- Acceleration = thrust / mass.
- Δv = acceleration × time.
That is it. No gravity, no orbital mechanics, no tumbling. It is deliberately wrong in all the interesting ways, which is exactly the point: if the answer is still encouraging under these crude assumptions, then the detailed work is worth doing. If the answer is discouraging, the details cannot save it.
3. The knobs
You can slide:
- Minimoon mass: 50 to 1,000 tonnes.
- Sail area: 10 to 1,000 m².
- Thrust duty cycle: 0 to 100 percent.
The chart shows accumulated Δv over three years. Two horizontal lines mark published reference points: 32 m/s for the Urrutxua et al. capture extension of 2006 RH120, and 58 m/s for the García Yárnoz et al. cheapest easily-retrievable-object threshold.
4. What it tells me
With the defaults — 300 tonnes, 86 m² sail, 50 percent duty cycle — the model reaches 32 m/s in roughly fifteen centuries and 58 m/s in closer to three. That is not a capture mission; it is a geological process. Drop the mass to 130 tonnes and the same sail reaches 32 m/s in roughly seven centuries. Increase the duty cycle or the sail area and the curve gets steeper in the obvious linear way, but the starting point is so far from the threshold that simple scaling does not help.
The most important thing the model does is kill the fantasy. It answers the question I actually had: is a sail at NEA Scout scale anywhere near enough? It is not. For a fixed sail, mass dominates. For a fixed mass, both area and duty cycle matter linearly, but the sail would need to be two to three orders of magnitude larger before the time constant becomes interesting.
5. What it does not do
It does not model the capture arc, the perigee timing, the tumbling, the sail pointing, the deployment, or the discovery lead time. All of those could make the real mission harder or easier. The model is a sanity filter, not a mission design tool.
6. Next curiosity
The obvious next step is to add a time-slider for start-of-thrust relative to perigee. Urrutxua et al. found that the capture-extension landscape is fractal, so timing is not just a small correction. A model that says “thrust here, not there” would be the bridge between this sanity check and a real trajectory study.