http://www.hindawi.comThe latest articles from Hindawi Publishing Corporation© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/425412The effect of perturbations in Coriolis and cetrifugal forces on the nonlinear stability of the equilibrium point of the Robe's (1977) restricted circular three-body problem has been studied when the density parameter K is zero. By applying Kolmogorov-Arnold-Moser (KAM) theory, it has been found that the equilibrium point is stable for all mass ratios μ in the range of linear stability 8/9+(2/3)((43/25)ϵ1−(10/3)ϵ)<μ<1, where ϵ and ϵ1 are, respectively, the perturbations in Coriolis and centrifugal forces, except for five mass ratios μ1=0.93711086−1.12983217ϵ+1.50202694ϵ1, μ2 = 0.9672922−0.5542091ϵ+ 1.2443968ϵ1, μ3=0.9459503−0.70458206ϵ+ 1.28436549ϵ1, μ4=0.9660792−0.30152273ϵ + 1.11684064ϵ1, μ5=0.893981−2.37971679ϵ + 1.22385421ϵ1, where the theory is not applicable.P. P. Hallan and Khundrakpam Binod Mangang© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/268647We use the corrections to the Newton-Einstein secular precessions of the longitudes of perihelia ϖ˙ of some planets (Mercury, Earth, Mars, Jupiter, Saturn) of the Solar System, phenomenologically estimated as solve-for parameters by the Russian astronomer E. V. Pitjeva in a global fit of almost one century of data with the EPM2004 ephemerides, in order to put on the test the expression for the perihelion precession induced by a uniform cosmological constant Λ in the framework of the Schwarzschild-de Sitter (or Kottler) space-time. We compare such an extra rate to the estimated corrections to the planetary perihelion precessions by taking their ratio for different pairs of planets instead of using one perihelion at a time for each planet separately, as done so far in literature. The answer is negative, even by further rescaling by a factor 10 (and even 100 for Saturn) the errors in the estimated extra precessions of the perihelia released by Pitjeva. Our conclusions hold also for any other metric perturbation having the same dependence on the spatial coordinates, as those induced by other general relativistic cosmological scenarios and by many modified models of gravity. Currently ongoing and planned interplanetary spacecraft-based missions should improve our knowledge of the planets' orbits allowing for more stringent constraints.Lorenzo Iorio© 2008, Hindawi Publishing Corporation. All rights reserved.