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Table 4

Parameters of the best-fit model, given with uncertainties.

Best-fit model Counter-example model
872 19903
Nmeasurements 837 837

Variable Unit Value with uncertainty Value
λpole deg 188.3 + 2.6 68.5
βpole deg −88.2 + 0.2 −88.9
Mtotal MS 3.323 × 10−12
q1 1 (1.02 ± 0.55) × 10−6 0.97 × 10−6
q2 1 (5.2 ± 5.4) × 10−7 2.7 × 10−7
q3 1 (2.74 ± 0.12) × 10−5 5 × 10−5

P1 day 1.2127 ±0.0002 1.2127
e1 1 0.028 ± 0.005 0.068
i1 deg 179.7 ±0.6 191.9
Ω1 deg 275.3 ± 11.9 265.2
ϖ1 deg 324.3 ± 18.5 25.8
λ1 deg 343.2 ±24.1 347.9

P2 day 1.6421 ±0.0004 1.6420
e2 1 0.064 ± 0.007 0.060
i2 deg 183.7 ±0.3 184.1
Ω2 deg 197.1 ±7.5 194.7
ϖ2 deg 107.9 ± 12.1 65.5
λ2 deg 248.5 ± 15.2 244.9

P3 day 5.30032 ± 0.00015 5.30041
e3 1 0.156
i3 deg 175.3 ±0.2 173.8
Ω3 deg 133.5 ±2.1 129.7
ϖ3 deg 6.6
λ3 deg 289.1

Notes. Also, for completeness, we provide the parameters of a counterexample model based on the rotational pole given by the ADAM algorithm in Sect. 3. The listed χ2 is with the weight wao set to zero and Nmeasurements is the number of all astrometry measurements, both absolute and relative. Orbital elements are referred to the epoch T0 = 2457021.567880 (TDB). Uncertainties are given at 1σ. λpole and βpole are the ecliptic longitude and latitude of Elektra’s rotational pole. Mtotal is the total mass of the system, ą1 = m1/m0, q2 = m2/(m0 + m1), and q3 = m3/(m0 + m1 + m2) are the mass ratios, where m0 denotes the mass of the central body (i.e. Elektra), m1 the mass of body 1 (inner moon S/2014 1), m2 the mass of body 2 (middle moon S/2014 2), m3 the mass of body 3 (outer moon S/2003), Pk the orbital period of the corresponding orbit, ek eccentricity, ik inclination, Ωk the longitude of the nodes, ϖk the longitude of the pericentre, and λk is the true longitude; k = 1, 2, 3.

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