Extrasolar Planet Interactions:
A Tabulation of Dynamical Characteristics

Last Update: 23 Nov 2008

This page lists dynamical properties of published multiple planet systems. So far 2 parameters that quantify dynamical interactions have been identified: proximity to an apsidal separatrix, &epsilon = 0 (see Barnes & Greenberg 2006a, 2006c) and proximity to the Hill stability boundary for non-resonant systems, &beta = 1 (see Barnes & Greenberg 2006b, 2007b). This latter boundary only applies to two-planet, non-resonant systems. The table and figures present the current dynamical properties of extra-solar planets using the best determination of their orbits from the listed reference (note that significant errors exist). Unfortunately &beta can only be calculated for 2-planet systems. AM stands for "Apsidal Motion", which can be Aligned libration (A), Anti-Aligned libration (AA), or Circulation (C). The "Class" identifies pairs that have undergone Tidal evolution (T), are experiencing Resonant phenomena (R), are dominated by Secular interactions (S), or the best fit is Unstable (U).

Table 1 - Dynamical Properties of Known Planetary Systems
(33 systems, 46 pairs)
SystemPairAM&epsilon&betaClassReference
47 UMa b-c C/Aa 0 1.025 S Butler et al. (2006)
55 Cnc e-b C 3.2 x 10-4 - T Fischer et al. (2008)
b-c C 8.9 x 10-4 - S
c-f C 0.16 - S
f-d C 0.14 - S
GJ 317 b-c ?b ? 0.980 R/4:1? Johnson et al. (2007)
GJ 436 b-c ?c - 0.984 U Ribas et al. (2008)
GJ 876 d-c C/Aa 0 - T Butler et al. (2006)
c-b A 0.34 - R/2:1
Gl 581 b-c C 0.15 - T Udry et al. (2007)
c-d C 0.20 - T
HD 11964 b-c C 0.20 - T Gregory (2007b)
c-d C 0.067 - S
HD 12661 b-c C 0.003 1.2 S Butler et al. (2006)
HD 17156 b-c C 0.09 0.57 R/5:1 Short et al. (2008)
HD 37124 b-c C 0.009 - S Butler et al. (2006)
c-d A 0.096 - S Butler et al. (2006)
HD 38529 b-c C 0.44 2.07 S Butler et al. (2006)
HD40307d b-c ? ? - T Mayor et al. (2008)
c-d ? ? - T
HD 60532 b-c AA 0.08 1.05 R/3:1 Desort et al. (2008)
HD 68988 b-c C 0.081 12.5 T Wright et al. (2007)
HD 69830 b-c C 0.095 - T Lovis et al. (2006)
c-d C 0.04 - S
HD 73526 b-c AA 0.006 0.982 R/2:1 Tinney et al. (2006)
HD 74156 b-d C 3.7 x 10-4 - S Barnes et al. (2008)
d-c C 3.7 x 10-4 - S
HD 82943 b-c C 0.004 0.946 R/2:1 Butler et al. (2006)
HD 108874 b-c C/AAe 0.198 1.107 R/4:1 Butler et al. (2006)
HD 128311 b-c C 0.09 0.968 R/2:1 Butler et al. (2006)
HD 155358 b-c AA 0.21 1.043 S Cochran et al. (2007)
HD 168443 b-c C 0.22 1.94 S Butler et al. (2006)
HD 169830 b-c C 0.33 1.28 S Butler et al. (2006)
HD 177830 c-b C 0.295 1.05 S Exoplanets.org
HD 187123 b-c C 0.427 15.3 T Wright et al. (2007)
HD 190360 c-b C 0.38 1.70 T Butler et al. (2006)
HD 191760 b-c C? 0.002 0.82 R/10:1? Jenkins et al. (2008)
HD 202206 b-c C 0.096 0.883 R/5:1 Correia et al. (2005)
HD 208487 b-c C 3.8 x 10-4 1.2 R/7:1 Gregory (2007a)
HD 217107 b-c C 0.46 7.191 T Butler et al. (2006)
HIP 14810 b-c AA 0.05 1.202 T Wright et al. (2007)
&mu Ara c-d C 0.002 - T Pepe et al. (2007)
d-b C 0.003 - R/2:1
b-e C 0.13 - S
&upsilon And b-c C 0.0002 - T Butler et al. (2006)
c-d C 0.0003 - S
Solar System J-S C 0.194 - S JPL
S-U C 0.006 - S
U-N C 0.004 - S

aThis pair is on the apsidal separatrix.
bThe angle of one apse is unknown
cThe orbits published in Ribas et al. (2008) are unstable.
dThe orbits are not known well enough to determine the interaction.
eThis resonant pair alternates between aligned libration and circulation.

Figure 1. Distribution of &epsilon values in Table 1. Most systems lie near the apsidal separatrix (&epsilon < 0.01). Note that unstable systems are not included in this histogram.

Figure 2. Distribution of &beta values in Table 1. Most pairs lie near the Hill stability limit (&beta < 2). Note that nearly all resonantly interacting pairs have &beta < 1, which is allowed in Hill stability theory, but means if not for the resonance, these pairs would be unstable. Note that unstable systems are not included in this histogram.