A paper ‘Rhodes Fairbridge and the idea that the solar system regulates the Earth’s climate’ by Richard Mackey has interesting information about the barycentre. It is from the Journal of Coastal Research, Special Issue 50, 2007 http://www.griffith.edu.au/conferenc...pdf/ICS176.pdf

Ideas which I found particularly interesting are
• the epitrochoid – the (spirograph-type) movement of the solar system barycenter of about 179 years’ duration, which is also the time taken for the planets to occupy approximately the same positions again relative to each other and the sun
• NEWTON (1687) showed that the sun is engaged in continual motion around the centre of mass of the solar system (i.e. the barycentre) as a result of the gravitational force exerted by the planets, especially Jupiter and Saturn. He came to this conclusion analytically (not by observation) by working through the consequences of his law of gravitation.
• the barycentre … might be negligible for the solar system but it is highly significant in relation to the size and nature of the sun. Amongst other things, the sun may be travelling through its own electromagnetic fields during various stages of its journey.
• since 1911, scientists had published research documenting periodicities in the motions of the planets in relation to the sun. These suggested that the barycentric motion of the sun in response to the planets might have a role in the sun’s activity cycles. This research also suggested that there could be links of scientific interest between these cycles, the planets and climate periodicities.
• JOSE (1965) published curves showing substantial agreement between the sunspot cycle numbers and the rate of change of the solar orbital angular momentum. Other researchers have published evidence supporting the hypothesis that some feature of the sun’s barycentric motion contributed to variable solar activity.
• the sun’s variable torque (measured by rate of change of angular momentum) exerted by the planets twisting and turning the sun on its epitrochoid-shaped cycle of barycentric orbits changed the sun’s activity levels
• DE JAGER and VERSTEEGH (2005) appear to have misunderstood solar inertial motion since SHIRLEY (2006) shows their inappropriate use of rotational equations for modelling particle motions due to orbital revolution.
• the sun is not homogenous; it is generally a fluid body, and whilst the solar nuclear fusion core is more like a solid than anything else, the viscosity, elasticity and density of the remainder of the sun varies from waterlike to diaphanous gas. The sun also has several distinct internal structures, which generally have the sun’s oblate spheroid shape (except the core, which is generally spherical). The structures and material of which the sun is made are in constant movement spatially and temporally. … the internal structure of the sun is characterised by a dynamic lumpiness that is variable throughout the sun, and over time.
• PALUS et al. (2007) found that there is a statistically significant measure of the influence on the solar cycle by the planets.
• TSUI (2000) has found there are non-inertial Coriolis forces acting on the sun as a result of its barycentric motion. He conjectured that these would be sufficient to significantly modulate the cyclical rhythm of the solar dynamo.
• BLIZARD (1987) reported that the horizontal tide may be significant because in a period of half a solar rotation, the horizontal displacement of planetary tide would be 560 km and its velocity 0.93 m/sec.
• BARKIN and FERRANDIZ (2004) derived an analytic expression for the elastic energy of planet tidal deformations induced by other bodies, including the central star, in a planetary system. BARKIN and FERRANDIZ (2004) found that the elastic energy is not simply a sum of the elastic energies of the separate pairs of bodies but contains additional terms that are non-linear functions of the superposition of the lunisolar tides. As a result, there are large and significant variations in conditionally periodic variations in the elastic energy of the lunisolar tides. … a similar result may be found for the effect of the superposition of the planetary tides on the sun. This expression would be a function of the tidal forces acting on the sun by each planet. The additional terms would be the nonlinear functions of the superposition of all of the planetary tidal forces. BLIZARD (1987) presented evidence that the precessional effect on the sun of the planets depends on the degree of oblateness of the sun and on the angle of inclination of the plane of a planet’s orbit in relation to the sun. Since the sun is a fluid, the precessional effect may induce a fluid flow towards the equator of the sun from both hemispheres. The flow of plasma on the sun directly affects solar activity.
• BLIZARD (1987) also noted that the sun’s axis of rotation is tilted with respect to the invariable plane and that the degree of tilt varies. She presented evidence suggesting that the sun’s variable axial tilt as it rotates in relation to the invariable plane whilst orbiting the barycentre appears to vary directly with solar orbital motion. The effect is, amongst other things, of a force to align the sun with the plane of the solar system, which the sun resists.
• BURROUGHS (2003) reported that the sun’s barycentric motion affects its oblateness, diameter and spin rate.
• In several papers, Rhodes Fairbridge (for example, FAIRBRIDGE 1984, FAIRBRIDGE 1997 and, FAIRBRIDGE and SANDERS 1987) described how the turning power of the planets is strengthened or weakened by resonant effects between the planets, the sun and the sun’s rotation about its axis. He further described how resonance between the orbits of the planets amplified the planets’ variable torque applied to the sun. He also pointed out that there was a measurable resonant effect between the sun’s orbit and spin and that this was amplified by the planets’ variable resonance. Fairbridge’s argument is that the resonating frequencies may amplify the relatively weak torque effects of the planets on the sun, if the resonance acts on both the sun’s rotation about its axis and the sun’s barycentric orbital motion. This may happen as the sun is undergoing retrograde motion in tight loops. Accordingly, orbital resonance of two, three or more planets may have a significant effect on the sun. Rhodes Fairbridge emphasised that the sun’s spin-orbital resonance can be further amplified by the planets’ own spin-orbital resonance.
• WINDELIUS and CARLBORG (1995) provide a convenient review of the relevant science about solar orbital angular momentum up to the mid-1990s.
• JUCKETT (2003) outlined the elements of a theory that shows how the sun’s barycentric orbit can modulate the intrinsic oscillations of the solar dynamo and generate all known cyclical solar phenomena. He hypothesised that this would happen as a result of the conservation of the solar system’s angular momentum achieved by the non-linear mixing of solar orbital momentum and a spin-orbit transfer function. It is as if some of the sun’s orbital angular momentum is transmitted to solar rotation so as to conserve the solar system’s angular momentum, which is necessarily constant as a result of the law of the conservation of angular momentum.viii JUCKETT (2003) hypothesised that the planetary-driven spin-orbit coupling is a continuous generator of the oscillatory behaviour of the sun. His theory also predicts several new phenomena. Spin-orbit coupling will occur if the mass distribution of a celestial body deviates from spherical symmetry. The degree of asymmetry is measured by the gravitational quadropole moments of the body.
• PIREAUX et al (2006) established that the mass of the sun shifts within it during the sunspot cycle and as a result the sun’s shape departs significantly from spherical symmetry. These departures seem to extend in variable ways throughout the sun. This changes the physical shape of the sun, but more importantly, has a measurable impact on the orbits of the planets. As a result, there is dynamic non-linear, stochastic and periodic interaction between the mass of the sun shifting internally within it and the planets.
• The gravitational interaction between the sun and the planets causes the barycentric motion of the sun, which is non-linear, stochastic and periodic. There is, therefore, a feedback process between two non-linear, stochastic and periodic processes: the internal shifting mass of the sun affecting planetary orbits and the planetary orbits affecting the internal mass of the sun by shifting it around, perhaps throughout the entire body of the sun. The solar inertial motion (sim) hypothesis states that sim modulates the solar dynamo, weakening or strengthening it (and thus solar activity levels) in accordance with which of the eight distinctive epitrochoid forms characterises the sun’s overall motion and whether the sun is in the ordered phase (i.e. along the smooth, near-circular path) or chaotic phase (i.e. along the retrograde loop-the-loop path) of that form. High solar activity occurs whilst the sun is in the ordered phase … Minimum or no activity occurs whilst the sun is in the chaotic phase