Table 1
Best-fit models with no tides (left) and including tides (middle), together with realistic uncertainties of the parameters (right).
| var. | val. | val. | Unit | σ |
|---|---|---|---|---|
| m1 | 1.492735 × 10−12 | 1.492735 × 10−12 | MS | 0.16 × 10−12 |
| m2 | 2 × 10−16 | 2 × 10−16 | MS | 2 × 10−16 |
| m3 | 3 × 10−16 | 3 × 10−16 | MS | 3 × 10−16 |
| P1 | 1.822359 | 1.822281 | day | 0.004156 |
| loge1 | − 3.991 | − 3.991 | 1 | − 3 (i.e. 0.001) |
| i1 | 70.104 | 70.104 | deg | 1.0 |
| Ω1 | 252.920 | 252.920 | deg | 1.0 |
| ϖ1 | 0.089 | 0.089 | deg | 10.0 |
| λ1 | 59.665 | 59.665 | deg | 1.0 |
| P2 | 2.745820 | 2.745791 | day | 0.004820 |
| loge2 | − 3.998 | − 3.998 | 1 | − 3 |
| i2 | 70.347 | 70.347 | deg | 1.0 |
| Ω2 | 252.954 | 252.954 | deg | 1.0 |
| ϖ2 | 1.601 | 1.601 | deg | 10.0 |
| λ2 | 108.357 | 108.357 | deg | 1.0 |
| lpole | 72.961 | 72.961 | deg | 1.0 |
| bpole | 19.628 | 19.628 | deg | 1.0 |
| Δt1 | – | 42.1 | s | 1.0 |
| nsky | 68 | 68 | ||
| nsky2 | 28 | 28 | ||
| nao | 3240 | 3240 | ||
 |
617 | 110 | ||
 |
66 | 60 | ||
 |
621 | 621 | ||
| χ2 | 872 | 360 | ||
 |
9.07 | 1.62 | ||
 |
2.35 | 2.14 | ||
 |
0.19 | 0.19 | ||
Notes. The left model does not fit the October 10 1980 occultation (see Fig. 1); without this observation, its χ2 would be 368. Orbital elements of the moons are osculating for the epoch T0 = 2454728.761806, where m1 denotes the mass of body 1 (i.e. Kleopatra), m2 body 2 (first moon), m3 body 3 (second moon), P1 the orbital period of the first orbit, e1 eccentricity, i1 inclination, Ω1 longitude of node, ϖ1 longitude of pericentre, λ1 true longitude, etc. of the second orbit; lpole ecliptic longitude of Kleopatra’s rotation pole, bpole ecliptic latitude; n numbers of observations (SKY, SKY2, AO), χ2 values,
reduced values. The angular orbital elements are expressed in the standard stellar reference frame. If the orbits lie in the equatorial plane of body 1, they fulfil i = 90° − bpole, Ω = 180° + lpole.
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