*Millennial Oscillations of Solar Irradiance and Magnetic Field in 600–2600 DOI: http://dx.doi.org/10.5772/intechopen.96450*

#### **Figure 7.**

*Maximal daily differences for each months of the sun-earth distances (in astronomical units, au) between the years 600–1600, M1 (blue curves) and 1700–2600, M2 (red curves). X-axis shows days of the months.*

**Figure 6.**

**36**

*and grey - 2600.*

*Solar System Planets and Exoplanets*

*Variations of the daily sun-earth distances (in astronomical units, au) versus days of the months in July– December of three sample years selected in the millennium M1 (600–1600) (left) and M2 (1600–2600) (right. Left column: Blue - year 600, red 1100 and green 1600; right column: Blue - year 1700, red - 2020*

distance curve is skewed (right plot) with the maximal and minimal Sun-Earth distances being noticeably shifted in time towards a mid-July for aphelion and mid-January for perihelion. Namely, in M1 the local perihelion and local aphelion are shifted forward by 5–6 days to 26–27 December and 26–28 June, respectively, from the summer and winter solstices on 21 June and 21 December accepted for elliptic orbit of the Earth revolution about the ellipse focus. While in M2 the local perihelion and aphelion in 2600 are shifted from the elliptic orbit positions for the winter and summer solstices forward by up to 25–26 days (to 15–16 January and 15–16 July,

*Variations of the annual sun-earth distances (in astronomical units, au) versus months of the year in the millennia M1 (left) and M2 (right). Left plot: Blue curve - year 600, red curve 1100 and grey curve - 1600;*

*Millennial Oscillations of Solar Irradiance and Magnetic Field in 600–2600*

*DOI: http://dx.doi.org/10.5772/intechopen.96450*

This asymmetry in the changes of the S-E distances in M2 compared to M1 is more clearly demonstrated by the annual variations of the double differences between the S-E distance shown in **Figure 8** after they are averaged for each month and presented over a year in **Figure 10** for each sample years considered. It clearly shows that the shifts in the S-E distances are reduced more in the April–September and increase more in October–February of each year of millennium M2. This means that the input of solar irradiance to the Earth is not evenly distributed over time of

If the Earth revolves about the Sun located in the focus of the ellipse, the Sun-Earth distance has to change depending on the Earth position on the orbit following Kepler's 3rd law (see Eq. 6 in Appendix A). Earth orbit is a stable elliptic orbit with little changes of the major and minor axis, as established in Appendix C with the

*Annual variations of the differences between the mean maximal monthly differences in the sun-earth distances (in astronomical units, au) in millennium M1 (600–1600) and M2 (1700–2600) taken from Figure 8. Axis*

respectively, seen in the right column of **Figures 5** and **6**.

*right plot: Blue curve 1700, red curve - 2020 and grey curve - 2600.*

**Figure 9.**

**Figure 10.**

**39**

*X shows months of a year.*

the Earth revolution, or over the Earth location on the orbit.

**3.2 Proposed interpretation of the S-E distance variations**

#### **Figure 8.**

*The differences between the maximal variations of the daily sun-earth distances (in astronomical units, au) in millennium M1 (600–1600) and M2 (1700–2600) shown in Figure 7. X-axis shows days of the months.*

*Millennial Oscillations of Solar Irradiance and Magnetic Field in 600–2600 DOI: http://dx.doi.org/10.5772/intechopen.96450*

**Figure 9.**

*Variations of the annual sun-earth distances (in astronomical units, au) versus months of the year in the millennia M1 (left) and M2 (right). Left plot: Blue curve - year 600, red curve 1100 and grey curve - 1600; right plot: Blue curve 1700, red curve - 2020 and grey curve - 2600.*

distance curve is skewed (right plot) with the maximal and minimal Sun-Earth distances being noticeably shifted in time towards a mid-July for aphelion and mid-January for perihelion. Namely, in M1 the local perihelion and local aphelion are shifted forward by 5–6 days to 26–27 December and 26–28 June, respectively, from the summer and winter solstices on 21 June and 21 December accepted for elliptic orbit of the Earth revolution about the ellipse focus. While in M2 the local perihelion and aphelion in 2600 are shifted from the elliptic orbit positions for the winter and summer solstices forward by up to 25–26 days (to 15–16 January and 15–16 July, respectively, seen in the right column of **Figures 5** and **6**.

This asymmetry in the changes of the S-E distances in M2 compared to M1 is more clearly demonstrated by the annual variations of the double differences between the S-E distance shown in **Figure 8** after they are averaged for each month and presented over a year in **Figure 10** for each sample years considered. It clearly shows that the shifts in the S-E distances are reduced more in the April–September and increase more in October–February of each year of millennium M2. This means that the input of solar irradiance to the Earth is not evenly distributed over time of the Earth revolution, or over the Earth location on the orbit.

#### **3.2 Proposed interpretation of the S-E distance variations**

If the Earth revolves about the Sun located in the focus of the ellipse, the Sun-Earth distance has to change depending on the Earth position on the orbit following Kepler's 3rd law (see Eq. 6 in Appendix A). Earth orbit is a stable elliptic orbit with little changes of the major and minor axis, as established in Appendix C with the

#### **Figure 10.**

*Annual variations of the differences between the mean maximal monthly differences in the sun-earth distances (in astronomical units, au) in millennium M1 (600–1600) and M2 (1700–2600) taken from Figure 8. Axis X shows months of a year.*

**Figure 8.**

*Solar System Planets and Exoplanets*

**38**

*The differences between the maximal variations of the daily sun-earth distances (in astronomical units, au) in millennium M1 (600–1600) and M2 (1700–2600) shown in Figure 7. X-axis shows days of the months.*

help of Appendices A and B. However, the S-E distance reductions and growths reported here deviate from the Kepler's third law (Eq. 6 in Appendix A). By comparing the mean-by-time and mean-by-arc S-E distances for an elliptic orbit (see Appendices B) with the expected changes imposed by the calculated shifts of aphelion and perihelion [49] shown in Appendix C, it is evident that the real S-E distances derived from the ephemeris are different from Kepler's 3rd law (see Eq. 6 in Appendix A).

millennium M2, which needs to be processed by the Earth atmosphere and ocean

*Millennial Oscillations of Solar Irradiance and Magnetic Field in 600–2600*

These long-term SIM effects can explain the reported above significant S-E distance decreases in January–June and the similar increases in July–December during the both millennia. The magnitudes of the S-E distance oscillations are smaller for M1 (up to 0.005 au) and twice larger for M2 (0.011 au) shown in **Figures 5** and **6**, and specifically in **Figure 7** producing daily differences in the S-E distances for each month of the years for the two millennia considered. In the next two millennia this trend is expected to return back to the level in 600 and then in the next 4.2 thousand years to change to the opposite one, e.g. producing the Sun shift to the autumn equinox and the shifts of the local perihelion and aphelion for considered years towards early December and June, respectively, following the

Interestingly, the annual variations of the S-E distances shown in **Figure 9** can explain the oscillations of the baseline solar magnetic field (Hallstatt's cycle) shown by dark blue lines in **Figure 3** and in **Figure 4** (top plot) [19] by the oscillation of the Earth aphelion and perihelion from the major axis. In M1 the Sun's location is closer to the ellipse focus of the Earth orbit resulting in a smaller magnitude of the Sun's shift in the direction of the minor axis that leads to the minimum of the baseline magnetic field of northern polarity, shown by the dark blue line in **Figure 3** (bottom plot) [19, 52]. While in M2 the Sun shifts much further from the focus towards the spring equinox position of the Earth orbit, so that there is a shift of the longest S-E distance (local aphelion) from 21 June (when the aphelion on the major axis of ellipse is approached) to 16 July when the aphelion is shifted from the major axis to the line of the ellipse connecting the ellipse centre and displacement of the Sun from the ellipse focus and directed under the angle *ϕ* (see Eq. (1)) to the major

Hence, in 1600–2600 the Earth will be turning closer to the Sun for up to 25 additional days after the summer solstice, while turned towards the Sun with its Northern hemisphere, before it approaches the local aphelion. This is likely to cause a small rise to the baseline magnetic field of northern polarity as shown in **Figure 3** (dark blue line) [19]. And given the periodic variations of the gravitational effects of four large planets described by [30], one can expect the similar periodic variations of the baseline magnetic field linked to the positions of the local aphelion and perihelion for a given epoch. Therefore, this confirms the hint expressed earlier [19, 52] that the baseline magnetic field oscillations derived there purely from the magnetic field observations are, indeed, caused by the gravitational effects of large

**4. Millennial oscillations of solar irradiance with the Sun-Earth**

Following the variations of the S–E distances discussed in section 3, let us evaluate the variations of total solar irradiance (TSI) imposed by a change of these S-E distances in the millennia M1 and M2 using the method of inverse squares. A magnitude of the total solar irradiance *S* variations at the solar-Earth distance *d* by considering the Sun as a point body emitting radiation with an intensity *I*<sup>⊙</sup> [53]:

*<sup>S</sup>* <sup>¼</sup> *<sup>I</sup>*<sup>⊙</sup>

*<sup>d</sup>*<sup>2</sup> *:* (2)

that will be discussed below in section 4.

*DOI: http://dx.doi.org/10.5772/intechopen.96450*

planets on the Sun, or by solar inertial motion.

calculations by [30].

axis.

**distances**

**41**

**4.1 Method of inverse squares**

This can can only happen if these S-E ephemeris reflect the additional motion: the revolution of the Sun about the barycentre, which is induced by the action of large planets of the solar system. The similar effect is observed in the stars, which have planetary systems, leading to a wobbling star effect that is used to trace possible exoplanets [50, 51]. The shift of S-E distances reported above should be caused by the increasing shift of the Sun's location from the focus of the ellipse, where it is supposed to reside, according to Kepler's laws, towards the spring equinox of the Earth orbit. This shift of the position of the Sun with respect to the barycentre has been recognised as the solar inertial motion - SIM [25, 27, 30]. The resulting S-E distances are defined by the superposition of these two motion: Earth revolution and SIM.

In fact, the variations of the S-E distances during the two millennia are likely to be affected by the gravitational effects of Jupiter, Saturn, Uranus and Neptune on the Sun's inertial motion [30] revealing the oscillations of the planet orbits with a period of 8.5 thousand years (see Fig. 1 in [30], affecting SIM. From the whole period of 8.5 thousand years reported in the paper the semi-period with maximum of 4.2–4.3 thousand years with the ascending part of 2.1 thousand years are similar to the period of decreasing S-E distances reported in section 3.1 for 600–2600. Also the reported S-E distances reveal the noticeable shifts of the aphelion and perihelion from the major axis of the ellipse that coincides also with the oscillations of magnetic field baseline [19, 52] and solar irradiance [22]. It seems that in the two millennia 600–2600 the large planets continuously shifted the Sun from its focus towards the spring equinox as detected from the S-E ephemeris in **Figures 5** and **6**.

Therefore, it can be noted that owing to SIM, the shortest and longest Sun-Earth distances (perihelion and aphelion) in the elliptic orbit of the Earth are shifted to the local aphelion and perihelion, which are located on the shorter axis of the ellipse than the major axis. This line has an angle *ϕ* to the semi-major axis roughly defined by the formula for tan *ϕ*:

$$
\tan \phi = \frac{2d\_s}{f},
\tag{1}
$$

where *f* is a distance between the foci of the ellipse and *ds* is the shift along the semi-minor axis *b* of the Sun from the focus of the ellipse. Naturally, by the definition of an ellipse, this line is shorter than the semi-major axis *a* of the Earth elliptic orbit, which is the longest axis in the ellipse.

Furthermore, the calculations of the double differences between the maximal distance shifts occurred in millennia M1 and M2 (M1-M2) for daily data shown in **Figure 8** and their annual variations shown in **Figure 10** reveal that the double differences become negative in April and remain such until the end of October. This means that in M2 (1600–2600) the S-E distance decreases in April–July and its increases in July–December are much larger that in M1 (600–1600). This also indicates that in M2 the Sun becomes closer and closer to the Earth during April– October before the Earth revolution will make the S-E distance increases in November–February, since these increases are larger than expected from Kepler's third law. This, in turn, can lead to a significant solar radiation input to the Earth in

### *Millennial Oscillations of Solar Irradiance and Magnetic Field in 600–2600 DOI: http://dx.doi.org/10.5772/intechopen.96450*

millennium M2, which needs to be processed by the Earth atmosphere and ocean that will be discussed below in section 4.

These long-term SIM effects can explain the reported above significant S-E distance decreases in January–June and the similar increases in July–December during the both millennia. The magnitudes of the S-E distance oscillations are smaller for M1 (up to 0.005 au) and twice larger for M2 (0.011 au) shown in **Figures 5** and **6**, and specifically in **Figure 7** producing daily differences in the S-E distances for each month of the years for the two millennia considered. In the next two millennia this trend is expected to return back to the level in 600 and then in the next 4.2 thousand years to change to the opposite one, e.g. producing the Sun shift to the autumn equinox and the shifts of the local perihelion and aphelion for considered years towards early December and June, respectively, following the calculations by [30].

Interestingly, the annual variations of the S-E distances shown in **Figure 9** can explain the oscillations of the baseline solar magnetic field (Hallstatt's cycle) shown by dark blue lines in **Figure 3** and in **Figure 4** (top plot) [19] by the oscillation of the Earth aphelion and perihelion from the major axis. In M1 the Sun's location is closer to the ellipse focus of the Earth orbit resulting in a smaller magnitude of the Sun's shift in the direction of the minor axis that leads to the minimum of the baseline magnetic field of northern polarity, shown by the dark blue line in **Figure 3** (bottom plot) [19, 52]. While in M2 the Sun shifts much further from the focus towards the spring equinox position of the Earth orbit, so that there is a shift of the longest S-E distance (local aphelion) from 21 June (when the aphelion on the major axis of ellipse is approached) to 16 July when the aphelion is shifted from the major axis to the line of the ellipse connecting the ellipse centre and displacement of the Sun from the ellipse focus and directed under the angle *ϕ* (see Eq. (1)) to the major axis.

Hence, in 1600–2600 the Earth will be turning closer to the Sun for up to 25 additional days after the summer solstice, while turned towards the Sun with its Northern hemisphere, before it approaches the local aphelion. This is likely to cause a small rise to the baseline magnetic field of northern polarity as shown in **Figure 3** (dark blue line) [19]. And given the periodic variations of the gravitational effects of four large planets described by [30], one can expect the similar periodic variations of the baseline magnetic field linked to the positions of the local aphelion and perihelion for a given epoch. Therefore, this confirms the hint expressed earlier [19, 52] that the baseline magnetic field oscillations derived there purely from the magnetic field observations are, indeed, caused by the gravitational effects of large planets on the Sun, or by solar inertial motion.
