02 — Is asteroid shape written by spin or by collision?
Supplied working report; original verdicts not validated.
Review status: Needs review. This is an archival source note, not a passed proof.
README.md
# 02 — Is asteroid shape written by spin or by collision? **Result: family membership explains 3% of the variance in shape but 46% of the variance in diameter. Shapes do vary within families — but they vary against spin, not with it: faster rotators are slightly rounder, and the bodies closest to the spin limit are the roundest of all.** ## The proposal Shapes of small asteroids are usually read as collision debris, so family members should resemble each other. The notebook proposes the opposite: a rubble pile reshapes as it is spun up by YORP, so elongation records spin history and should vary within families, with the most elongated bodies nearest the spin limit. ## What was tested 9,247 asteroids from the NASA PDS Asteroid Lightcurve Database (v4.0), restricted to members of named collisional families, lightcurve quality U ≥ 2, not flagged as binaries, with a measured rotation period, a maximum lightcurve amplitude ≤ 1.2 mag and a measured diameter above 0.3 km. 156 families. Shape is measured by the lightcurve amplitude, which for a rotating triaxial body maps to axis ratio: amplitude A gives b/a = 10^(−0.4A), so elongation = 1 − 10^(−0.4A). This is an optical proxy, and it is the quantity the database actually measures; no shape model is used. ## What happened **P1 — elongation against spin-up.** Spearman ρ between elongation and spin frequency is **−0.093** (permutation p < 0.0001), and −0.097 after controlling for diameter by rank residualisation. The proposal expects a positive relation — spin-up makes elongated bodies. The data give a small but very well determined negative one. **P3 — near-limit rotators.** Median elongation by period class: | period class | n | median elongation | median diameter | |---|---|---|---| | under 4 h (near limit) | 1,501 | **0.220** | 3.9 km | | 4–8 h | 3,165 | **0.345** | 3.5 km | | 8–24 h | 2,542 | 0.295 | 4.4 km | | over 24 h | 2,039 | 0.295 | 3.6 km | The near-limit class is the *least* elongated, by 0.094 in the proxy (median permutation p = 0.0002). **P3 is not supported; the direction is opposite.** **P2 — shapes vary within families.** Variance decomposition on the 101 families with at least five members: | quantity | between-family share (ICC) | |---|---| | elongation | **0.028** (95% CI 0.012–0.051) | | log period | 0.042 | | log diameter | **0.464** | Families share sizes strongly and shapes hardly at all. **P2 is supported.** ## What it means Two of the three predictions behave differently, and that split is the interesting part. Collision inheritance is visible in diameter and nearly absent in shape, which is what the proposal says to expect. But the spin history that is supposed to replace it runs the wrong way: the fastest rotators and the near-limit rotators are rounder, not more elongated. That is consistent with the known population of super-fast rotators being small coherent monoliths rather than rubble piles, and with elongation peaking in the 4–8 hour band where YORP spin-up and re-shaping are both active. So the proposal's refutation condition — "shape tracking family membership" — is not met, but its positive mechanism is not met either. What the data support is weaker: shape is not inherited, and it is not simply a monotone function of spin. ## What this test cannot see Lightcurve amplitude depends on viewing aspect: a highly elongated body seen pole-on produces almost no variation. The database's maximum amplitude partly corrects for this, but not fully, and the correction may differ systematically between fast and slow rotators. Diameters are heterogeneous (radiometric, occultation, direct imaging) and the sample is brightness-selected, which biases against small dark bodies. And this is a snapshot: YORP changes spin over millions of years, so the correlation between today's spin and today's shape is not the same object as the correlation between spin history and shape. Preprint draft · not peer reviewed · designed and executed with AI assistance.
hypothesis.md
# The proposal, quoted Source: Incoprea notebook, *Earth & Space* #13, "Asteroid Shape Records Spin-Up". > The shape of a small asteroid is set by its spin history rather than by its collisional history, so elongated bodies indicate past spin-up and oblate bodies indicate spin-down, independent of family membership. Stated predictions: - **P1** — Elongation should correlate with spin-up indicators. - **P2** — Shapes should vary within families. - **P3** — Near-limit rotators should be most elongated. Stated refutation: > Shape tracking family membership regardless of spin would restore collision inheritance.