Maximum Eccentricity Research Articles

Which soft contact lens power is better for piggyback fitting in keratoconus?

To evaluate the impact of differente soft contact lens power in the anterior corneal curvature and regularity in subjects with keratoconus. Nineteen subjects (30 eyes) with keratoconus were included in the study. Six corneal topographies were taken with Pentacam Eye System over the naked eye and successively with soft lens (Senofilcon A) powers of -3.00, -1.50, 0.00, +1.50 and +3.00 D. Corneal measurements of mean central keratometry (MCK), maximum tangential curvature (TK), maximum front elevation (MFE) and eccentricity (Ecc) at 6 and 8 mm diameters as well as anterior corneal surface high order aberrations (i.e. total RMS, spherical- and coma-like and secondary astigmatism) were evaluated. Negative- and plano-powered soft lenses flattened (p<0.05 in all cases), whereas positive-powered lenses did not induce any significant changes (p>0.05 in all cases) in MCK in comparison to the naked eye. The TK power decreased with negative lenses (p<0.05 in both cases) and increased with +3.00 D lenses (p=0.03) in comparison to the naked eye. No statistically significant differences were found in MFE with any soft lens power in comparison to the naked eye (p>0.05 in all cases). Corneal eccentricity increased at 8 mm diameter for all lens powers (p<0.05 in all cases). No statistically differences were found in HOA RMS and spherical-like aberration (both p>0.05). Statistically differences were found in coma-like and secondary astigmatism (both p<0.05). Negative-powered soft contact lenses provide a flatter anterior surface in comparison to positive-powered lenses in subjects with keratoconus and thus they might be more suitable for piggyback contact lens fitting.

Study of the influence of different parameters on the buckling behaviour of masonry walls

A study of the influence and interaction of the main parameters involved on the buckling behaviour of masonry walls subjected to vertical loading is presented. For this purpose, the effects of the variation of the slenderness ratio, the eccentricity of applied load, the stiffness of the wall and the tensile strength of the unit–mortar interface on the load bearing capacity of masonry walls are analyzed by means of a numerical model based on the micro-modelling approach.The study has confirmed the possibility of describing the combined effect of both slenderness and stiffness by means of a single non-dimensional parameter. In addition, the research shows that, in the case of slender walls, the tensile strength of the unit–mortar interface may influence significantly on the maximum load eccentricity that the walls can resist. The paper also includes a comparison of the results obtained in the parametric study carried out with the analytical method provided by EN 1996-1-1:2005.

Study of turbocharger shaft motion by means of non-invasive optical techniques: Application to the behaviour analysis in turbocharger lubrication failures

This paper presents a novel non-invasive technique to estimate the turbocharger shaft whirl motion. The aim of this article is to present a system for monitoring the shaft motion of a turbocharger, which will be used in turbocharger destructive testing. To achieve this, a camera and a light source were installed in a turbocharger test bench with a controlled lubrication circuit.An image recording methodology and a process algorithm have been developed, in order to estimate the shaft motion. This processing consists on differentiating specific zones of the image, in order to obtain their coordinates. Two reference points have been configured on the compressor side, which help to calculate the relative position of the shaft, avoiding the errors due to structural vibrations. Maximum eccentricity of the turbocharger has been determined and it has been compared with shaft motion when it is spinning in different conditions. A luminosity study has been also done, in order to improve the process and to obtain locus of shaft position in a picture exposition time period.The technique has been applied to diagnosis of a lubrication failure test and the main results will be presented in this article: like shaft motion figures; thermodynamic variables and pictures of the shaft while it is spinning at abnormal lubrication conditions. The measuring components used in this technique have the ability to withstand the catastrophic failure of the turbocharger in this type of test.

Eccentricity Effect of Micropatterned Surface on Contact Angle

This article experimentally shows that the wetting property of a micropatterned surface is a function of the center-to-center offset distance between successive pillars in a column, referred to here as eccentricity. Studies were conducted on square micropatterns which were fabricated on a silicon wafer with pillar eccentricity ranging from 0 to 6 μm for two different pillar diameters and spacing. Measurement results of the static as well as the dynamic contact angles on these surfaces revealed that the contact angle decreases with increasing eccentricity and increasing relative spacing between the pillars. Furthermore, quantification of the contact angle hysteresis (CAH) shows that, for the case of lower pillar spacing, CAH could increase up to 41%, whereas for the case of higher pillar spacing, this increment was up to 35%, both corresponding to the maximum eccentricity of 6 μm. In general, the maximum obtainable hydrophobicity corresponds to micropillars with zero eccentricity. As the pillar relative spacing decreases, the effect of eccentricity on hydrophobicity becomes more pronounced. The dependence of the wettability conditions of the micropatterned surface on the pillar eccentricity is attributed to the contact line deformation resulting from the changed orientation of the pillars. This finding provides additional insights in design and fabrication of efficient micropatterned surfaces with controlled wetting properties.

Evolution of some quasicircular orbits in the planetary problem

We derive in the plane problem a new closed solution of the Lagrangian equations for resonant motion, concomitantly including zeroth order, and approximate first order and secular perturbations. A major aim is the determination of simple lower limits for the maximum eccentricities and variations of semimajor axes (intrinsic values). Applications of the general solution are made for each perturbation separately. (i) Zeroth and first order perturbations: a new closed solution for the principal zeroth order variation of semimajor axes is obtained. The maximum eccentricity and relative change of semimajor axis of any lunar orbit cannot be lower than 0.019 and 0.018, respectively. (ii) Secular perturbations: with the angular momentum integral our secular perturbations can be easily extended to the spatial problem. The planetary Lidov–Kozai problem is extended to retrograde orbits, showing that large variations of eccentricity and inclination occur for initially circular orbits, if initial mutual inclinations are between about 40° and 150°. (iii) Resonant perturbations: for first and second order resonances, and initially circular orbits our formulas generally approximate just the calculated orbital elements during the whole motion. As a new unexpected result, the numerical exploration of the asteroid belt reproduces most of its overall characteristics up to third order resonances within the restricted three-body problem and modest initial eccentricities ≤0.05.

Multi Objective Optimization of Drilling Parameters Using Genetic Algorithm

Drilling operation on the aircraft and unmanned ariel vehicle made of composite materials is considered as a precarious and highly sensitive operation. Due to the problem of delamination and eccentricity of drilled hole which leads to loosening of rivets in joining various structures is challenging. Hence in modern research of manufacturing process the multi objective optimization of drilling parameters has become an embryonic topic. In this paper the feed rate and the torque of drilling tool has been selected as input parameters and the multi objective optimization of drilled hole has been carried out. The optimization parameters considered are the hole eccentricity and material removal rate. Carbon fibre reinforced plastic composite material has been chosen for investigation. The maximum and minimum eccentricity limits have been computed by Finite element formation. Genetic Algorithm optimization technique has been formulated. Experimental investigation has been carried out and compared with numerical method and soft computing techniques.

Cortical oscillatory changes in human middle temporal cortex underlying smooth pursuit eye movements.

Extra-striate regions are thought to receive non-retinal signals from the pursuit system to maintain perceptual stability during eye movements. Here, we used magnetoencephalography (MEG) to study changes in oscillatory power related to smooth pursuit in extra-striate visual areas under three conditions: 'pursuit' of a small target, 'retinal motion' of a large background and 'pursuit + retinal motion' combined. All stimuli moved sinusoidally. MEG source reconstruction was performed using synthetic aperture magnetometry. Broadband alpha-beta suppression (5-25 Hz) was observed over bilateral extra-striate cortex (consistent with middle temporal cortex (MT+)) during all conditions. A functional magnetic resonance imaging study using the same experimental protocols confirmed an MT+ localisation of this extra-striate response. The alpha-beta envelope power in the 'pursuit' condition showed a hemifield-dependent eye-position signal, such that the global minimum in the alpha-beta suppression recorded in extra-striate cortex was greatest when the eyes were at maximum contralateral eccentricity. The 'retinal motion' condition produced sustained alpha-beta power decreases for the duration of stimulus motion, while the 'pursuit + retinal motion' condition revealed a double-dip 'W' shaped alpha-beta envelope profile with the peak suppression contiguous with eye position when at opposing maximum eccentricity. These results suggest that MT+ receives retinal as well as extra-retinal signals from the pursuit system as part of the process that enables the visual system to compensate for retinal motion during eye movement. We speculate that the suppression of the alpha-beta rhythm reflects either the integration of an eye position-dependent signal or one that lags the peak velocity of the sinusoidally moving target.

MONOPHONIC DISTANCE IN GRAPHS

For any two vertices u and v in a connected graph G, a u – v path is a monophonic path if it contains no chords, and the monophonic distance dm(u, v) from u to v is defined as the length of a longest u – v monophonic path in G. A u – v monophonic path of length dm(u, v) is called a u – v monophonic. The monophonic eccentricity em(v) of a vertex v in G is the maximum monophonic distance from v to a vertex of G. The monophonic radius rad m G of G is the minimum monophonic eccentricity among the vertices of G, while the monophonic diameter diam m G of G is the maximum monophonic eccentricity among the vertices of G. It is shown that rad m G ≤ diam m G for every connected graph G and that every pair a, b of positive integers with a ≤ b is realizable as the monophonic radius and monophonic diameter of some connected graph. Also, for any three positive integers a, b and c with 3 ≤ a ≤ b ≤ c, there is a connected graph G such that rad G = a, rad m G = b and rad DG = c; and for any three positive integers a, b and c with 5 ≤ a ≤ b ≤ c, there is a connected graph G such that diam G = a, diam m G = b and diam D G = c, where rad G, diam G, rad DG and diam D G denote the radius, diameter, detour radius and detour diameter, respectively. The monophonic center of G is the subgraph induced by the vertices of G having monophonic eccentricity rad m G and it is shown that every graph is the monophonic center of some connected graph and also that the monophonic center Cm(G) of every connected graph G is a subgraph of some block of G.

On the first ν6 anti-aligned librating asteroid family of Tina

Asteroid families are groups of bodies identified in the space of proper elements or of frequencies that share a common origin in the collisional break-up of their progenitors. Their dynamical evolution is shaped by the interaction with the local web of mean-motion and secular resonances, and by non-gravitational effects, such as the 'Yarkovsky' and 'Yarkovsky-O'Keefe―Radzievskii―Paddack' (YORP) effects. Thus, obtaining information on their age and original ejection velocity field is generally a difficult task. Recently, two families were found to have a large fraction of members in the non-linear secular resonance z 1 : the Agnia and Padua families. Conserved quantities of the z 1 resonance allowed for a more precise determination of their ages and ejection velocity fields. So far, however, no family was known to be in a linear secular resonance, such as the v 6 resonance, although individual asteroids were known to be in v 6 anti-aligned librating states. The v 6 resonance occurs when there is a commensurability between the frequency of precession of the pericentre of an asteroid and that of Saturn. As a consequence, in librating states, the resonant argument oscillates around a stable point. In anti-aligned librating states, the resonant argument oscillates around the stable point at 180°. Here we show that the newly identified Tina family is characterized by having all its members in such a state, making it the only family in the asteroid belt known to be completely embedded in a secular resonance configuration. This rare dynamical configuration limits the maximum eccentricity of Tina members, preventing them from experiencing Martian close encounters and forming a stable island of a new dynamical type. The current dispersion of asteroid resonant elements suggests that the family should be at least 2.5 Myr old, while Monte Carlo simulations including the Yarkovsky and YORP effects suggest that the Tina family should be 170 +20 ―30 M yr old.

On the influence of the Kozai mechanism in habitable zones of extrasolar planetary systems

Aims. We investigate the long-term evolution of inclined test particles representing a small Earth-like body with negligible gravitational effects (hereafter called massless test-planets) in the restricted three-body problem, and consisting of a star, a gas giant, and a massless test-planet. The test-planet is initially on a circular orbit and moves around the star at distances closer than the gas giant. The aim is to show the influences of the eccentricity and the mass of the gas giant on the dynamics, for various inclinations of the test-planet, and to investigate in more detail the Kozai mechanism in the elliptic problem.Methods. We performed a parametric study, integrating the orbital evolution of test particles whose initial conditions were distributed on the semi-major axis – inclination plane. The gas giant’s initial eccentricity was varied. For the calculations, we used the Lie integration method and in some cases the Bulirsch-Stoer algorithm. To analyze the results, the maximum eccentricity and the Lyapunov characteristic indicator were used. All integrations were performed for 105 periods of the gas giant.Results. Our calculations show that inclined massless test-planets can be in stable configurations with gas giants on either circular or elliptic orbits. The higher the eccentricity of the gas giant, the smaller the possible range in semi-major axis for the test-planet. For gas giants on circular orbits, our results illustrate the well-known results associated with the Kozai mechanism, which do not allow stable orbits above a critical inclination of approximately 40°. For gas giants on eccentric orbits, the dynamics is quite similar, and the massless companion exhibits limited variations in eccentricity. In addition, we identify a region around 35° consisting of long-time stable, low eccentric orbits. We show that these results are also valid for Earth-mass companions, therefore they can be applied to extrasolar systems: for instance, the extrasolar planetary system HD 154345 can possess a 35° degree inclined, nearly circular, Earth-mass companion in the habitable zone.

The dynamics of Neptune Trojans - II. Eccentric orbits and observed objects★

In a previous paper, we have presented a global view of the stability of Neptune Trojan (NT hereafter) on inclined orbit. We discuss in this paper the dependence of stability of NT orbits on the eccentricity. High-resolution dynamical maps are constructed using the results of extensive numerical integrations of orbits initialized on the fine grids of initial semimajor axis (a0) versus eccentricity (e0). The extensions of regions of stable orbits on the (a0, e0) plane at different inclinations are shown. The maximum eccentricities of stable orbits in three most stable regions at low (0, 12deg.), medium (22,36deg.) and high (51, 59deg.) inclination, are found to be 0.10, 0.12 and 0.04, respectively. The fine structures in the dynamical maps are described. Via the frequency analysis method, the mechanisms that portray the dynamical maps are revealed. The secondary resonances, concerning the frequency of the librating resonant angle and the frequency of the quasi 2:1 mean motion resonance between Neptune and Uranus, are found deeply involved in the motion of NTs. Secular resonances are detected and they also contribute significantly to the triggering of chaos in the motion. Particularly, the effects of the secular resonance v8, v18 are clarified. We also investigate the orbital stabilities of six observed NTs by checking the orbits of hundreds clones of them generated within the observing error bars. We conclude that four of them, except 2001 QR322 and 2005 TO74, are deeply inside the stable region. The 2001 QR322 is in the close vicinity of the most significant secondary resonance. The 2005 TO74 locates close to the boundary separating stable orbits from unstable ones, and it may be influenced by a secular resonance.

Dynamics of planetesimals due to gas drag from an eccentric precessing disc

We analyze the dynamics of individual kilometer-size planetesimals in circumstellar orbits of a tight binary system. We include both the gravitational perturbations of the secondary star and a non-linear gas drag stemming from an eccentric gas disk with a finite precession rate. We consider several precession rates and eccentricities for the gas, and compare the results with a static disk in circular orbit. The disk precession introduces three main differences with respect to the classical static case: (i) The equilibrium secular solutions generated by the gas drag are no longer fixed points in the averaged system, but limit cycles with frequency equal to the precession rate of the gas. The amplitude of the cycle is inversely dependent on the body size, reaching negligible values for $\sim 50$ km size planetesimals. (ii) The maximum final eccentricity attainable by small bodies is restricted to the interval between the gas eccentricity and the forced eccentricity, and apsidal alignment is no longer guaranteed for planetesimals strongly coupled with the gas. (iii) The characteristic timescales of orbital decay and secular evolution decrease significantly with increasing precession rates, with values up to two orders of magnitude smaller than for static disks. Finally, we apply this analysis to the $\gamma$-Cephei system and estimate impact velocities for different size bodies and values of the gas eccentricity. For high disk eccentricities, we find that the disk precession decreases the velocity dispersion between different size planetesimals, thus contributing to accretional collisions in the outer parts of the disk. The opposite occurs for almost circular gas disks, where precession generates an increase in the relative velocities.

Stability of the orbit of a third body in binary asteroid systems

In this work we studied the stable regions around four binary asteroids in the main asteroid belt. The studied systems were (107) Camilla, (22) Kallipe, (45) Eugenia and (762) Pulcova. The stability was characterized with three motion indicators: relative Lyapunov indicator, maximum eccentricity, and maximum difference of eccentricities. The survay covered the P type orbits, where satellite moves around both primaries. On the basis of our work it can be decided, in which system the discovery of a third component can be expected.

Large and small-scale structures of the local Galactic disc

An analytical model based on the maximum entropy approach is proposed to describe the eventual asymmetries of the velocity distribution, which are collected through its sample moments. If an extended set of moments is available, the current method provides a linear algorithm, associated with a Gramian system of equations, that leads to a fast and suitable estimation of the velocity distribution. In particular, it could be used to model multimodal distributions that cannot be described through Gaussian mixtures. The method is used with several samples from the HIPPARCOS and Geneva-Copenhagen survey catalogues. For the large-scale distribution, the phase density function may be obtained by fitting moments up to sixth order as a product of two exponential functions, one giving a background ellipsoidal shape of the distribution and the other accounting for the skewness and for the slight shift in the ellipsoidal isocontours in terms of the rotation velocity. The small-scale distribution can be deduced from truncated distributions, such as velocity-bounded samples with km s<sup>-1<sup/>, which contain a complex mixture of early-type and young disc stars. By fitting up to ten-order moments, the maximum entropy approach gives a realistic portrait of actual asymmetries, showing a clear bimodal pattern: (i) around the Hyades-Pleiades stream, with negative radial mean velocity and (ii) around the Sirius-UMa stream, with slightly positive radial mean velocity. Among metallicity, colour, and other star properties, the eccentricity of the star's orbit behaves as a very good sampling parameter to find a more detailed structure for the disc velocity distribution, allowing distinctions between different eccentricity layers. For subsamples with eccentricities <i>e<0.15<i/>, star velocities are approximately symmetrically distributed around the LSR in the radial direction, with a dearth of stars at the LSR. For <i>e=0.15<i/>, the core distribution of the thin disc is supported by two major stellar groups with opposite radial velocities. Several simulations confirm that such a double-peaked distribution comes from the lognormal distribution of the velocity amplitudes. For maximum eccentricity 0.3 and maximum distance to the Galactic plane 0.5 kpc a representative thin disc sample is obtained. The “U-anomaly” along the radial direction is estimated straightforwardly km s<sup>-1<sup/> from the contour plots. An explanation of the apparent vertex deviation of the disc from the swinging of those major kinematic groups around the LSR is then possible, which predicts a continuously changing orientation of the disc's pseudo ellipsoid.

Long-period eccentricity control on sedimentary sequences in the continental Madrid Basin (middle Miocene, Spain)

The middle Miocene Valdearenas–Muduex section in the internally-drained, continental Madrid Basin (central Spain) is dated bio-magnetostratigraphically between 15.2 Ma and 11.5 Ma. The section contains two formation-scale, sedimentary sequences, that both consist of a siliciclastic lower part and a calcareous upper part. Siliciclastic sedimentation took place in distal floodplain and fluvial environments, while limestones resulted from carbonate precipitation in calcic soil profiles and in ephemeral lacustrine water bodies. Spectral analysis of the L* colour time series points to the influence of the ∼ 405-kyr and 0.97-Myr eccentricity cycles, while the bases of the two calcareous intervals correlate to successive minima of the 2.4-Myr eccentricity cycle. The 405-kyr cycle lags maximum eccentricity, whereas the 0.97 and 2.4-Myr cycles lag minimum eccentricity, each by approximately a quarter of a cycle. No obliquity forcing is detected. The observed orbital configuration of 2.4-Myr minima at the base of limestone-dominated intervals is similar to a previously documented Late Miocene shift in the Teruel Basin of northeast Spain. Our results indicate that long-period eccentricity climate forcing may well be a significant player on long, tectonic time scales in continental basin fill.

Optimal strong [formula omitted]-orientation of complete [formula omitted]-partite graphs

For two vertices u and v in a strong oriented graph D , the strong distance s d ( u , v ) between u and v is the minimum size (the number of arcs) of a strong sub-digraph of D containing u and v . For a vertex v of D , the strong eccentricity s e ( v ) is the strong distance between v and a vertex farthest from v . The strong diameter s d i a m ( D ) is the maximum strong eccentricity among the vertices of D . The lower orientable strong diameter s d i a m ( G ) of a graph G is the minimum strong diameter over all strong orientations of G . An orientation D of a graph G is said to be an optimal strong ( κ , d ) -orientation of G if κ ( D ) = ⌊ κ ( G ) / 2 ⌋ and s d i a m ( D ) = s d i a m ( G ) , where κ ( D ) (resp. κ ( G ) ) is the strong connectivity of D (resp. connectivity of G ). In this paper, we will show that each complete k -partite graph has an optimal strong ( κ , d ) -orientation.

Circulating Eccentric Orbits Around Planetary Moons

Eccentric orbits in the third-body perturbed problem are evaluated in the context of planetary-moon missions. All possible motion in the doubly averaged problem is reviewed and concisely summarized via contour plots. Special attention is paid to the well-known class of orbits that cycle between low and high eccentricity while circulating in argument of periapse. Applying the doubly averaged assumptions, the maximum sustainable inclinations and eccentricities for long-term circulating ballistic orbits are found and discussed for the dimensioned systems at Ganymede, Europa, Titan, Enceladus, and several other planetary moons. The full-cycle periods of the circulations and librations are reduced to quadratures that are functions only of the two integrals of motion and the moon and orbiter mean motions. In the specific case of Ganymede, higher-fidelity models are considered to analyze the validity of the doubly averaged assumptions. Families of stable long-repeat-cycle periodic orbits are demonstrated in the unaveraged Hill-plus-nonspherical-potential model. Several point designs are considered in a full ephemeris model, and promising results include long-term ephemeris-stable orbits that enjoy maximum inclinations above 60 deg. These circulating ball-of-yarn orbits cycle between high and low eccentricities while distributing close approaches throughout the moon's surface.

Dynamical evolution of high area-to-mass ratio debris released into GPS orbits

A large set of simulations, including all the relevant perturbations, was carried out to investigate the long-term dynamical evolution of fictitious high area-to-mass ratio ( A/ M) objects released, with a negligible velocity variation, in each of the six orbital planes used by Global Positioning System (GPS) satellites. As with similar objects discovered in near synchronous trajectories, long lifetime orbits, with mean motions of about 2 revolutions per day, were found possible for debris characterized by extremely high area-to-mass ratios. Often the lifetime exceeds 100 years up to A/ M ∼ 45 m 2/kg, decreasing rapidly to a few months above such a threshold. However, the details of the evolution, which are conditioned by the complex interplay of solar radiation pressure and geopotential plus luni-solar resonances, depend on the initial conditions. Different behaviors are thus possible. In any case, objects like those discovered in synchronous orbits, with A/ M as high as 20–40 m 2/kg, could also survive in this orbital regime, with semi-major axes close to the semi-synchronous values, with maximum eccentricities between 0.3 and 0.7, and with significant orbit pole precessions (faster and wider for increasing values of A/ M), leading to inclinations between 30° and more than 90°.

Origins of Eccentric Extrasolar Planets: Testing the Planet‐Planet Scattering Model

In planetary systems with two or more giant planets, dynamical instabilities can lead to collisions or ejections through strong planet-planet scattering. Previous studies for initial conditions with two equal-mass planets revealed two discrepancies between the results of simulations and the observed orbits of exoplanets: potentially frequent collisions between giant planets and a narrow distribution of final eccentricities. We show that simulations with two unequal-mass planets starting on nearly circular orbits predict fewer collisions and a broader range of final eccentricities. Thus, the two-planet scattering model can reproduce the observed eccentricities with a plausible distribution of planet mass ratios. The model also predicts a maximum eccentricity of 0.8, independent of the distribution of planet mass ratios, provided that both planets are initially placed on nearly circular orbits. This compares favorably with observations and will be tested by future planet discoveries. Moreover, the combination of planet-planet scattering and tidal circularization may explain the existence of some giant planets with very short period orbits. Orbital migration due to planet scattering could play an important role in explaining the distribution of orbital periods found by radial velocity surveys. We also reexamine and discuss various possible correlations between eccentricities and other properties of exoplanets. We find that radial velocity observations are consistent with planet eccentricities being correlated with the ratio of the escape velocity from the planet's surface relative to the escape velocity from the host star at the planet's location. We demonstrate that the observed distribution of planet masses, periods, and eccentricities can provide constraints for models of planet formation and evolution.

On the stability of Earth-like planets in multi-planet systems

We present a continuation of our numerical study on planetary systems with similar characteristics to the Solar System. This time we examine the influence of three giant planets on the motion of terrestrial-like planets in the habitable zone (HZ). Using the Jupiter–Saturn–Uranus configuration we create similar fictitious systems by varying Saturn’s semi-major axis from 8 to 11 AU and increasing its mass by factors of 2–30. The analysis of the different systems shows the following interesting results: (i) Using the masses of the Solar System for the three giant planets, our study indicates a maximum eccentricity (max-e) of nearly 0.3 for a test-planet placed at the position of Venus. Such a high eccentricity was already found in our previous study of Jupiter–Saturn systems. Perturbations associated with the secular frequency g5 are again responsible for this high eccentricity. (ii) An increase of the Saturn-mass causes stronger perturbations around the position of the Earth and in the outer HZ. The latter is certainly due to gravitational interaction between Saturn and Uranus. (iii) The Saturn-mass increased by a factor 5 or higher indicates high eccentricities for a test-planet placed at the position of Mars. So that a crossing of the Earth’ orbit might occur in some cases. Furthermore, we present the maximum eccentricity of a test-planet placed in the Earth’ orbit for all positions (from 8 to 11 AU) and masses (increased up to a factor of 30) of Saturn. It can be seen that already a double-mass Saturn moving in its actual orbit causes an increase of the eccentricity up to 0.2 of a test-planet placed at Earth’s position. A more massive Saturn orbiting the Sun outside the 5:2 mean motion resonance (aS ≥9.7 AU) increases the eccentricity of a test-planet up to 0.4.