Its effective temperature is equal to 5164 ± 44 K, the gravitational acceleration log(g) = 3.6 ± 0.1, the metallicity is [Fe/H] = − 0.15 ± 0.04. The mass of the star is 1.44 ± 0.09 M  ⊙ , and the radius amounts to 4.3 ± 0.09 R  ⊙ . The star distance from the Sun is 68.4 ± 4.8 pc and its age is about 3.0 ± 0.6 × 109 years. Two gas giants

orbit around the star with orbital periods respectively LEE011 manufacturer given by 613.8 and 825.0 days. The planets in this system most likely arrived at the present locations due to their interactions with the protoplanetary disc and in the process of the convergent migration formed the 4:3 commensurability (Johnson et al. 2011). However, as it has been shown by Kley (2000) and Nelson and Papaloizou (2002), the most probable final state of the convergent migration is the 2:1 resonance and not 4:3. So, how this commensurability could happen? The formation Selleck SN-38 of the 4:3 resonance depends on many circumstances including the initial separation of the planets, their masses, the viscosity in the disc and its mass (Malhotra 1993; Haghighipour 1999; Bryden et al. 2000; Snellgrove et al. 2001). The key property is the migration rate which, if it is sufficiently high, can cause that the planets will pass through the 2:1 commensurability and proceed toward the resonances with smaller ratio of the orbital periods, like for instance

the 4:3 resonance. PSR B1257+12   Here, it is the 3:2 commensurability. PSR B1257+12 is a millisecond pulsar, its distance from the Sun is 0.6 kpc. The standard mass for the pulsars is assumed to be 1.4 M  ⊙ , the age is evaluated at 3 × 109 years. The planets discovered in this system were the first extrasolar planets found (Wolszczan and Frail 1992). The parameters for this system are determined with a very high accuracy (Konacki and Wolszczan 2003), that is why it is one of the best systems for studying the formation of planets and their evolution. Particular attention has been devoted to the configuration of the planets B and C with masses around 4 m  ⊕ , which are close to the 3:2 resonance. Goździewski et al. (2005) have shown that this system with the parameters determined by Konacki and Wolszczan (2003) is stable in the timescale

of 109 years. HD 45364   HD 45364 is the second system described here, in which planets are Progesterone in the 3:2 resonance. The central star is of spectral type K0V (Hipparcos buy GW2580 Catalogue ESA 1997). Its effective temperature is 5434 ± 20 K, its gravitational acceleration is log(g) = − 4.38 ± 0.03, the metallicity amounts to [Fe/H] = − 0.17 ± 0.01 (Sousa et al. 2008). The mass of the star is 0.82 M  ⊙ . The system is located at the distance of 32.6 pc from the Sun. The precise measurements performed by means of the spectrograph HARPS allow for the discovery of two gas giants with masses less than that of Jupiter (Correia et al. 2009). The dynamical analysis has shown that the planets are in the 3:2 resonance and the system is stable in the timescale of about 5 × 109 years. Rein et al.