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Attitude state

Is the object stabilised, rotating or tumbling? A classification with a confidence index.

The Estimated attitude state section classifies the measured light curve, and the simulated one next to it, to show whether the model reproduces the observed state.

Class Meaning
Stabilised Once the trend of the pass is removed, the variation stays at the noise level
Stabilised, with glints Same, with one or two isolated flashes
Regular rotation A clear period
Tumbling / non-periodic A large variation without a clean period, two incommensurate periods, or a shape that changes along the series
Undetermined Too few points, or a variation slower than the series
Trend

The slow trend of the pass (phase and range changing) is removed by a third-degree polynomial in time.

Noise and flashes

The noise comes from second differences between neighbours (or the given magnitude errors). Isolated flashes — at least 5σ and 0.5 mag brighter than their neighbours, 3 points at most — are set apart when there are one or two.

Periodicity

Lomb–Scargle periodogram, false-alarm probability of the best peak, share of the variance explained by a Fourier series with 2 to 6 harmonics.

Tumbling tests

A second significant, non-harmonic period in the residuals, or a model fitted on the first half of the series that fails to predict the second half, points to tumbling.

The confidence combines the false-alarm probability, the explained variance and the number of cycles covered.

Measured with the synthetic dataset generator on 2 × 150 curves of 10 minutes at a 2 s step:

True state Recognised
Regular rotation 86–89 %
Stabilised 80–87 %
Tumbling about 51 %
Overall 71–77 %

Over 10 minutes a tumbling body often looks like a near-regular rotation: longer series and several nights help.