## Sunday, April 2, 2017

### The Sun’s Wobbles and the Earth’s Spiral Path

 Figure 1 and Figure 2 (Enlarge)
Will J.R. Alexander et al. (2007) - Conventional illustrations show the Earth orbiting around a static Sun. This is misleading. First, the Sun wobbles through a tube of space and not along a smooth path at a constant velocity. Second, the Earth orbits the Solar System’s Center of Mass (SSCM) and not the Sun’s Center of Mass. The Earth therefore follows a spiral path as it moves through space. This is illustrated in Figure 1. (It is important to note that the scales in the figures 1 and 2 are highly compressed so that they can fit.)

The tube in the middle represents the volume of space that the Sun revolves in and is about 3.7 * 10^6 km in diameter. The ecliptic plane is at a 45° angle to the line of movement. The Earth to Sun distance (the chord length) varies, depending on where the Sun is located in the tube. While the paths of the Sun and the Earth are closely linked as they move through space, the changing relative positions result in corresponding changes in the distance between them.

Figure 2 shows the path of the combined Center of Mass of the four major planets, Jupiter, Saturn, Uranus and Neptune, relative to the SSCM for the period 1978–2006. Visualize the three-dimensional view of this figure with the orbit path spiraling towards the viewer. Starting in 1978, the orbit maintains a nearly constant distance from the SSCM. In 1985 the orbit starts moving closer to the central point occupied by the SSCM. It swings around the SSCM, reaching its closest position in 1990. It then spirals away from the SSCM until 1994. From 1995 through to 2000 there is little change in the displacement from the SSCM. From 2001 through to 2006 it makes another approach to the SSCM. As can be seen, these changes are not regular in time. They were relatively unchanged from 1979 to 1985, and again from 1995 to 2000. They changed rapidly from 1986 through to 1994, when they closely orbited the SSCM.

The Sun follows a weighted reciprocal path but its Center of Mass is much closer to the SSCM. It also accelerates and decelerates synchronously but moves in the opposite direction in order to maintain the system in equilibrium. The Sunspot minima occurred in 1986, 1996 and 2006. The compass points on the figure are for reference purposes only. Note that the Sunspot minima of 1986 and 1996 both occurred in the SW quadrant of the figure, and that of 2006 in the NW quadrant when viewed from a position ahead of the approaching Solar System. This is in an anticlockwise direction relative to the forward clockwise movement of the spiral paths about the SSCM followed by the orbiting components of the Solar System. The angular distance followed by the orbit from 1986 to 1996 was 360° when it returned to the same quadrant. It was only 270° from 1996 to 2006 when it did not complete a full 360° rotation around the SSCM. The angles are approximate but are amenable to calculation.

 Table 1 and Figure 3 (Enlarge)
Influence of the Planets: Table 1 shows the positions of the Planetary System’s Center of Mass (PCM) at the time of the Sunspot minima during the period 1902–2006. The information in this table provides the first positive linkage between solar activity and the hydro meteorological time series. There is a statistically significant linkage with the double Sunspot cycle. He found no statistically significant linkage with the single, 11-year cycle. His analyses showed that these alternating cycles are associated with different hydro meteorological characteristics. The periodic behavior of the Solar System has a duration of 21 years (actually 20.8 years during the past century), not 11 years. This explains why scientists have been unable to find a linkage with the 11-year cycle, from which they erroneously concluded that there is no linkage with solar activity. While the relative positions of the planets are closely grouped in space at 21-year intervals, they are not precise in either time or space. This is the reason for longer period cyclicity including 178 years and longer cycles.

Sunspot Production: The plane of the path of the orbiting planets and the Sun must be at 45° to the line of motion of the Solar System. This is in order to balance the gravitational forces of a three-dimensionally balanced group of objects travelling at constant forward speed relative to that of the SSCM. Each body in the Solar System will follow a three-dimensional spiral track around the SSCM thus maintaining the group’s constant forward speed. This path will also be influenced by the changing positions of the major planets relative to one another and the Sun’s reciprocal movement.

All bodies of the Solar System therefore have a combination of two velocities. The dominant velocity component is the constant galactic velocity that is followed by the SSCM. The orbital velocities of the individual bodies around the SSCM are super- imposed on the galactic velocity. As they orbit the SSCM their net forward velocity will be the galactic velocity plus the orbital velocity (corrected for the 45° slope of the solar orbits) as they move forward in their orbits around the SSCM, and the galactic velocity minus the orbital velocity as they move backwards in their orbits around the SSCM. The net result is that the galactic velocities equal that of the SSCM when the bodies directly trail or lie directly ahead of the SSCM. The galactic velocities increase as they move forward around the SSCM, and they decrease as they move backwards about the SSCM. The galactic velocity of each body in the Solar System, including the Sun, therefore alternately accelerates and decelerates within the galactic plane as it orbits the SSCM. This is the crux of the issue. Once it is appreciated that the reference system is the galactic plane and not the plane of the Solar System, then everything else falls into place.

Sunspot production is a direct function of the Sun’s galactic acceleration and deceleration, with Sunspot minima occurring when the Sun is directly ahead or trailing the SSCM. There can be no doubt that it is the influence of the changing relative positions of the major planets that is the direct cause of Sunspot activity. The actual mechanism for Sunspot production as a result of galactic velocity changes has yet to be determined, although several theories exist.

The Sun’s Wobble: The distance of the Sun from the SSCM is the weighted reciprocal of the distance of the combined Center of Mass of the orbiting planets. Consequently, both the Sun’s distance from the SSCM and its galactic velocity are continually changing. This creates a wobble in its path through space. This can be calculated given the knowledge of the masses and orbits of the four major planets. Figure 3 shows the Sun’s wobble as it moved through galactic space during the period 1944 to 1958. During most of this time its orbit was below that of the SSCM in this view. While the SSCM lies within the body of the Sun most of the time, there are occasions when the Sun wobbles outside the SSCM. This figure provides an indication of the extent of its wobble as the Sun moves through space.

Earth to Sun Chord Distance: As a result of the Sun’s wobble, the chord length between the Earth and the Sun and the amount of energy received by the Earth will change accordingly. The next exercise is therefore to determine the corresponding changes in the distance between the Earth and the Sun and thereby the changes in the rate of solar energy reaching the Earth. This is amenable to precise calculation. The calculation of the chord length between the Earth and the Sun at any particular time has two components. The first is the position of the Sun relative to the SSCM at that time. The second is the elliptical path of the Earth about the SSCM. The Sun’s displacement from the SSCM changes relatively slowly but the ecliptic direction of the Earth about the Sun changes with the seasons. Figure 10 shows the dis- placement of the position of the Sun from the SSCM during 1993 and its effect on variations in solar energy received on Earth during that year.