Dynamical conditions in planets and stars

With the available data in planets, stars and galaxies, it is studied the functions of angular momentaJ(M) and amounts of actionA_c(M) (associated to the non rotational terms in the kinetic energy). The results indicate that independently of how are these functionsJ(M),A_c(M) their ratioA_c/J remains a near invariant. It is independent also from the type of angular momenta: intrinsic spins of the bodies or the total angular (orbital) momenta of the bodies forming a system; for instance, the Solar System and the planets.The relationA_c(M) for the Solar System are analogous to these in the FGK stars of the main sequence, and the relationJ(M) (also for the Solar System) is analogous to the lower possible limit for binary stars.The different types of binary stars from the short period, detached systems to contactary systems, gives a range of functionsJ(M),A_c(M) that are the same that one can expect in stars with planetary systems. According to the detection limits given for planetary companions by Campbell, Walker and Yang (1988) (masses of less than 9 Jupiter masses and orbital periods of less than 50 years) we calculate the limits forJ(M) andA_c(M) This gives a lower limitA_c/J 1 associated to stars with planetary systems as 61 Cygni and to short period detached binaries. The upper limitA_c/J 16 correspond to planetary systems as the ours and probably to cataclysmic binaries. There are reasons to suspect that systems as the ours and in range 4 A_c/J 16 (with a lower limit analogous to contactary binaries as Algols and W Ursa Majoris) must be the most common type of planetary systems. The analogies with the functionsJ(M)A_c(M) for galaxies suggest cosmogonical conditions in the stellar formation.Independently of this, one can have boundary conditions for the Jacobi problem when applied to a collapsing cloud. Namely, from the initial stage (a molecular cloud) to the final stage (a formed stellar system: binary or planetary) the angular momenta and amounts of action decayed to 10^~4 the initial values, but in such a form thatA_c(t)/J(t) remains a near invariant.