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Table A.4
System names, Love number of the primary (kprimary), primary and satellite densities (ρprimary and ρsatellite), initial rotational rate of the primary (T0), mean orbital angular velocity (n), and orbital semimajor axis (a).
| System | g primary | μ | k primary | ρ primary | ρ satellite | T 0 | n | a | Q | τ lock | τ circular |
| [m s-2] | [N m-2] | [g cm-3] | [g cm-3] | [h] | [rad s-1] | [km] | [years] | [years] | |||
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| Salacia- | |||||||||||
| Actaea | |||||||||||
| (1.3−2) × 10-1 | 4 × 109 | (2.5−5.5) × 10-3 | 1.38 ± 0.27 | 1.38 ± 0.27 | 2.57−3.13 | (1−1.7) × 10-5 | 5619 ± 87 | 100 | (0.4−1) × 109 | (0.4−2.1) × 108 | |
| (1.3−2) × 10-1 | 3 × 1010 | (3.3−7.3) × 10-4 | 1.38 ± 0.27 | 1.38 ± 0.27 | 2.57−3.13 | (1−1.7) × 10-5 | 5619 ± 87 | 100 | (3−9) × 109 | (0.3−1.6) × 109 | |
| (1.3−2) × 10-1 | 4 × 109 | (2.5−5.5) × 10-3 | 1.38 ± 0.27 | 1.00 | 2.57−3.13 | (1−1.7) × 10-5 | 5619 ± 87 | 100 | (1.2−1.5) × 109 | (0.7−2.3) × 108 | |
| (1.3−2) × 10-1 | 4 × 109 | (2.5−5.5) × 10-3 | 1.38 ± 0.27 | 0.50 | 2.57−3.13 | (1−1.7) × 10-5 | 5619 ± 87 | 100 | (5−6) × 109 | (1.3−4.6) × 108 | |
| (1.3−2) × 10-1 | 3 × 1010 | (3.3−7.3) × 10-4 | 1.38 ± 0.27 | 1.00 | 2.57−3.13 | (1−1.7) × 10-5 | 5619 ± 87 | 100 | (0.9−1.1) × 1010 | (0.5−1.7) × 109 | |
| (1.3−2) × 10-1 | 3 × 1010 | (3.3−7.3) × 10-4 | 1.38 ± 0.27 | 0.50 | 2.57−3.13 | (1−1.7) × 10-5 | 5619 ± 87 | 100 | (3.7−4.6) × 1010 | (1−1.7) × 109 | |
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| Huya | (7.3−8.3) × 10-2 | 4 × 109 | (7.6−9.7) × 10-4 | 1.43 | 1.43 | 2.76 | (2−2.5) × 10-5 | 1800 | 100 | (1.9−3) × 107 | (0.9−1.3) × 107 |
| Huya | (7.3−8.3) × 10-2 | 3 × 1010 | (1−1.3) × 10-4 | 1.43 | 1.43 | 2.76 | (2−2.5) × 10-5 | 1800 | 100 | (1.4−2.3) × 108 | (7−9.7) × 107 |
| Huya | (7.3−8.3) × 10-2 | 4 × 109 | (7.6−9.7) × 10-4 | 1.43 | 1.00 | 2.76 | (2−2.5) × 10-5 | 1800 | 100 | (3.9−6.1) × 107 | (1.3−1.8) × 107 |
| Huya | (7.3−8.3) × 10-2 | 4 × 109 | (7.6−9.7) × 10-4 | 1.43 | 0.50 | 2.76 | (2−2.5) × 10-5 | 1800 | 100 | (0.6−1.6) × 108 | (2.7−3.7) × 107 |
| Huya | (7.3−8.3) × 10-2 | 3 × 1010 | (1−1.3) × 10-4 | 1.43 | 1.00 | 2.76 | (2−2.5) × 10-5 | 1800 | 100 | (2.9−4.6) × 108 | (1−1.4) × 108 |
| Huya | (7.3−8.3) × 10-2 | 3 × 1010 | (1−1.3) × 10-4 | 1.43 | 0.50 | 2.76 | (2−2.5) × 10-5 | 1800 | 100 | (1.2−1.8) × 109 | (2−2.8) × 108 |
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| Varda- | |||||||||||
| Ilmarë | |||||||||||
| (1.1−1.4) × 10-1 | 4 × 109 | (1.6−2.7) × 10-3 | 1.11 | 1.11 | 3.13 | (1.3−1.9) × 10-5 | 4200 | 100 | (1.7−4.6) × 107 | (1−1.8) × 107 | |
| (1.1−1.4) × 10-1 | 3 × 1010 | (2.2−3.6) × 10-4 | 1.11 | 1.11 | 3.13 | (1.3−1.9) × 10-5 | 4200 | 100 | (1.3−3.4) × 108 | (0.7−1.3) × 108 | |
| (1.1−1.4) × 10-1 | 4 × 109 | (1.6−2.7) × 10-3 | 1.11 | 1.00 | 3.13 | (1.3−1.9) × 10-5 | 4200 | 100 | (2.1−5.6) × 107 | (1.1−2) × 107 | |
| (1.1−1.4) × 10-1 | 4 × 109 | (1.6−2.7) × 10-3 | 1.11 | 0.50 | 3.13 | (1.3−1.9) × 10-5 | 4200 | 100 | (0.8−2.2) × 108 | (2.1−3.9) × 107 | |
| (1.1−1.4) × 10-1 | 3 × 1010 | (2.2−3.6) × 10-4 | 1.11 | 1.00 | 3.13 | (1.3−1.9) × 10-5 | 4200 | 100 | (1.6−4.2) × 108 | (0.8−1.5) × 108 | |
| (1.1−1.4) × 10-1 | 3 × 1010 | (2.2−3.6) × 10-4 | 1.11 | 0.50 | 3.13 | (1.3−1.9) × 10-5 | 4200 | 100 | (0.6−1.7) × 109 | (1.6−2.9) × 108 | |
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| 2007 UK126 | (2.3−3) × 10-2 | 4 × 109 | (7.5−12.5) × 10-5 | 0.32 | 0.32 | 5.84 | (5.7−8.4) × 10-6 | 3600 | 100 | (3−9.8) × 1012 | (2.5−4.7) × 1010 |
| 2007 UK126 | (2.3−3) × 10-2 | 3 × 1010 | (0.9−1.7) × 10-5 | 0.32 | 0.32 | 5.84 | (5.7−8.4) × 10-6 | 3600 | 100 | (0.7−2.2) × 1013 | (1.9−3.5) × 1011 |
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| 2007 TY430 | 7.5 × 10-3 | 4 × 109 | 7.9 × 10-6 | 0.46 | 0.46 | 4.87 | (5.1−5.3) × 10-8 | 21 000 ± 160 | 100 | (4.4−4.9) × 1017 | (7.6−8.3) × 1018 |
| 2007 TY430 | 7.5 × 10-3 | 3 × 1010 | 1.05 × 10-6 | 0.46 | 0.46 | 4.87 | (5.1−5.3) × 10-8 | 21 000 ± 160 | 100 | (3.3−3.6) × 1018 | (5.7−6.3) × 1019 |
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| Typhon- | |||||||||||
| Echidna | |||||||||||
| (0.6−1.1) × 10-2 | 4 × 109 | (0.6−1.5) × 10-5 | 0.36 |
0.36 |
4.98−6.13 | (2.9−4.3) × 10-6 | 1628 ± 29 | 100 | (2.4−4.6) × 1011 | (1.3−5.4) × 1011 | |
| (0.6−1.1) × 10-2 | 3 × 1010 | (0.7−2.1) × 10-6 | 0.36 |
0.36 |
4.98−6.13 | (2.9−4.3) × 10-6 | 1628 ± 29 | 100 | (1.8−3.4) × 1012 | (1−4) × 1012 | |
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| Quaoar- | |||||||||||
| Weywot | |||||||||||
| (3.6−4.9) × 10-2 | 4 × 109 | (1.8−3.4) × 10-4 | 2.7−5.0 | 2.7−5.0 | 1.48−2.01 | 1.5 × 10-7 | 14 500 ± 800 | 100 | (0.2−1.2) × 109 | (1.6−3.8) × 1013 | |
| (3.6−4.9) × 10-2 | 3 × 1010 | (2.4−4.5) × 10-5 | 2.7−5.0 | 2.7−5.0 | 1.48−2.01 | 1.5 × 10-7 | 14 500 ± 800 | 100 | (1.2−9.3) × 109 | (1.2−2.9) × 1014 | |
| (3.6−4.9) × 10-2 | 4 × 109 | (1.8−3.4) × 10-4 | 2.7−5.0 | 1.00 | 1.48−2.01 | 1.5 × 10-7 | 14 500 ± 800 | 100 | (4−9) × 109 | (0.8−1) × 1014 | |
| (3.6−4.9) × 10-2 | 3 × 1010 | (2.4−4.5) × 10-5 | 2.7−5.0 | 1.00 | 1.48−2.01 | 1.5 × 10-7 | 14500 ± 800 | 100 | (3−6.8) × 1010 | (6.1−7.7) × 1014 | |
| (3.6−4.9) × 10-2 | 4 × 109 | (1.8−3.4) × 10-4 | 2.7−5.0 | 0.50 | 1.48−2.01 | 1.5 × 10-7 | 14500 ± 800 | 100 | (1.6−3.6) × 1010 | (1.6−2.1) × 1014 | |
| (3.6−4.9) × 10-2 | 3 × 1010 | (2.4−4.5) × 10-5 | 2.7−5.0 | 0.50 | 1.48−2.01 | 1.5 × 10-7 | 14 500 ± 800 | 100 | (1.2−2.7) × 1011 | (1.2−1.5) × 1015 | |
| (2−2.4) × 10-2 | 4 × 109 | (5.7−8.1) × 10-5 | 1.99± 0.46 | 1.99± 0.46 | 2.11−2.67 | 1.1 × 10-7 | 14 500 ± 800 | 100 | (1−5) × 109 | (1−1.6) × 1014 | |
| (2−2.4) × 10-2 | 3 × 1010 | (0.8−1.1) × 10-5 | 1.99± 0.46 | 1.99± 0.46 | 2.11−2.67 | 1.1 × 10-7 | 14 500 ± 800 | 100 | (0.7−3.9) × 1010 | (0.7−1.2) × 1015 | |
| (2−2.4) × 10-2 | 4 × 109 | (5.7−8.1) × 10-5 | 1.99± 0.46 | 1.00 | 2.11−2.67 | 1.1 × 10-7 | 14 500 ± 800 | 100 | (0.6−1.2) × 1010 | (2.3−2.4) × 1014 | |
| (2−2.4) × 10-2 | 3 × 1010 | (0.8−1.1) × 10-5 | 1.99± 0.46 | 1.00 | 2.11−2.67 | 1.1 × 10-7 | 14 500 ± 800 | 100 | (4.3−9) × 1010 | (1.7−1.8) × 1015 | |
| (2−2.4) × 10-2 | 4 × 109 | (5.7−8.1) × 10-5 | 1.99± 0.46 | 0.50 | 2.11−2.67 | 1.1 × 10-7 | 14 500 ± 800 | 100 | (2.3−4.8) × 1010 | (4.7−4.8) × 1014 | |
| (2−2.4) × 10-2 | 3 × 1010 | (0.8−1.1) × 10-5 | 1.99± 0.46 | 0.50 | 2.11−2.67 | 1.1 × 10-7 | 14 500 ± 800 | 100 | (1.7−3.6) × 1011 | (3.5−3.6) × 1015 | |
| (2.3−2.6) × 10-2 | 4 × 109 | (7.2−9.2) × 10-5 | 2.18 |
2.18 |
2.04−2.45 | (1.1−1.2) × 10-7 | 14 500 ± 800 | 100 | (1.2−5.7) × 109 | (1−1.4) × 1014 | |
| (2.3−2.6) × 10-2 | 3 × 1010 | (1−1.2) × 10-5 | 2.18 |
2.18 |
2.04−2.45 | (1.1−1.2) × 10-7 | 14 500 ± 800 | 100 | (0.9−4.3) × 1010 | (0.8−1.1) × 1015 | |
| (2.3−2.6) × 10-2 | 4 × 109 | (7.2−9.2) × 10-5 | 2.18 |
1.00 | 2.04−2.45 | (1.1−1.2) × 10-7 | 14 500 ± 800 | 100 | (0.8−1.7) × 1010 | (2.5−2.6) × 1014 | |
| (2.3−2.6) × 10-2 | 3 × 1010 | (1−1.2) × 10-5 | 2.18 |
1.00 | 2.04−2.45 | (1.1−1.2) × 10-7 | 14 500 ± 800 | 100 | (0.6−1.3) × 1011 | (1.9−2) × 1015 | |
| (2.3−2.6) × 10-2 | 4 × 109 | (7.2−9.2) × 10-5 | 2.18 |
0.50 | 2.04−2.45 | (1.1−1.2) × 10-7 | 14 500 ± 800 | 100 | (3.3−6.8) × 1010 | (5−5.3) × 1014 | |
| (2.3−2.6) × 10-2 | 3 × 1010 | (1−1.2) × 10-5 | 2.18 |
0.50 | 2.04−2.45 | (1.1−1.2) × 10-7 | 14 500 ± 800 | 100 | (2.5−5.1) × 1011 | (3.7−4) × 1015 | |
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| Orcus- | |||||||||||
| Vanth | |||||||||||
| (5.8−6.1) × 10-2 | 4 × 109 | (0.5−5.2) × 10-3 | 1.53 |
1.53 |
2.55−2.79 | (1.2−1.4) × 10-6 | 8980 ± 23 | 100 | (5.7−9.8) × 107 | (2.2−2.4) × 1010 | |
| (5.8−6.1) × 10-2 | 3 × 1010 | (6.2−6.9) × 10-5 | 1.53 |
1.53 |
2.55−2.79 | (1.2−1.4) × 10-6 | 8980 ± 23 | 100 | (4.2−7.3) × 108 | (1.7−1.8) × 1011 | |
| (5.8−6.1) × 10-2 | 4 × 109 | (3.6−4.7) × 10-4 | 1.53 |
1.00 | 2.55−2.79 | (1.2−1.4) × 10-6 | 8980 ± 23 | 100 | (1.7−1.9) × 108 | (3.1−5.3) × 1010 | |
| (5.8−6.1) × 10-2 | 3 × 1010 | (4.8−6.2) × 10-5 | 1.53 |
1.00 | 2.55−2.79 | (1.2−1.4) × 10-6 | 8980 ± 23 | 100 | (1.3−1.4) × 109 | (2.4−4) × 1011 | |
| (5.8−6.1) × 10-2 | 4 × 109 | (4.7−5.2) × 10-3 | 1.53 |
0.50 | 2.55−2.79 | (1.2−1.4) × 10-6 | 8980 ± 23 | 100 | (6.3−7.7) × 108 | (6.3−8) × 1010 | |
| (5.8−6.1) × 10-2 | 3 × 1010 | (6.2−6.9) × 10-5 | 1.53 |
0.50 | 2.55−2.79 | (1.2−1.4) × 10-6 | 8980 ± 23 | 100 | (4.7−5.7) × 109 | (4.7−6) × 1011 | |
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| 2001 QY297 | (4−7.6) × 10-3 | 4 × 109 | (1.9−8) × 10-6 | 0.29 | 0.29 | 6.13 | (0.9−2.6) × 10-7 | 9960 ± 31 | 100 | (0.2−4.3) × 1016 | (0.4−2.2) × 1017 |
| 2001 QY297 | (4−7.6) × 10-3 | 3 × 1010 | (0.3−1.1) × 10-6 | 0.29 | 0.29 | 6.13 | (0.9−2.6) × 10-7 | 9960 ± 31 | 100 | (0.2−3.2) × 1017 | (0.3−1.7) × 1018 |
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| 2003 AZ84 | (0.5−1) × 10-2 | 4 × 109 | (0.4−2.1) × 10-5 | 0.85 | 0.85 | 3.58 | (0.8−2.9) × 10-7 | 7200 | 100 | (4.5−9.2) × 109 | (0.02−1.2) × 1015 |
| 2003 AZ84 | (0.5−1) × 10-2 | 3 × 1010 | (0.5−2.8) × 10-6 | 0.85 | 0.85 | 3.58 | (0.8−2.9) × 10-7 | 7200 | 100 | (3.4−6.9) × 1010 | (0.1−8.9) × 1015 |
| 2003 AZ84 | (0.5−1) × 10-2 | 4 × 109 | (0.3−2.1) × 10-5 | 0.85 | 0.50 | 3.58 | (0.8−2.9) × 10-7 | 7200 | 100 | (1.3−2.7) × 1010 | (0.03−2) × 1015 |
| 2003 AZ84 | (0.5−1) × 10-2 | 3 × 1010 | (0.5−2.8) × 10-6 | 0.85 | 0.50 | 3.58 | (0.8−2.9) × 10-7 | 7200 | 100 | (1−2) × 1011 | (0.02−1.5) × 1016 |
Notes. We assume a density of 0.5−1 g cm-3 for the satellite, except in some cases (see discussion section). The initial rotational period of the primary is the breakup rotation rate (upper limit) expressed as: T0 = (3π/Gρprimary)1/2. Equation (5) was used to compute the time needed to circularize the orbit (τcircular). Equation (7) was used to compute the time needed to tidally lock the primary (τlock). Orbital semimajor axis are taken from Brown & Suer (2007), Grundy et al. (2008), Ragozzine & Brown (2009), Brown et al. (2010), Fraser & Brown (2010), Grundy et al. (2011a), Grundy et al. (2011b), Ortiz et al. (2011), Noll et al. (2012), Sheppard et al. (2012), and Stansberry et al. (2012).
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