**3. Millennial variations of the Sun-Earth distance**

The observations of solar irradiance and magnetic field baseline oscillations with the period of about 2100–2200 years are believed to be imposed on the Sun by the gravitational effects of Neptune and Saturn causing SIM [30, 46]. In this section we carry out the investigation of Sun-Earth distance variations over a millennial scale in an attempt to establish if they follow or deviate from Kepler's laws.

#### **3.1 Ephemeris of the Sun-Earth distances in 600–2600**

Let us now explore the daily Sun-Earth (S-E) distances over the two millennia (600–2600) derived from the ephemeris of VASOP87 - Variations Seculaires des Orbites Planetaires [47] *http* : *==neoprogrammics:com=vsop*87*=planetarydistancetables=:* Note that the VSOP87 data up to 6 digits after the decimal coma coincide with the widely used JPL ephemeris [48].

The daily Sun-Earth distances for every month of the three years for each millennium: M1 (600, 1100, 1600) and M2 (1700, 2020, 2600) are presented in **Figure 5** (January–June) and 6 (July–December) for the millenniums M1 (600– 1600) (left column) and millennium for M2 (1600–2600 (right column). The Sun-Earth distances change rather differently over the two millennia M1 and M2 from what one would expect from the elliptic motion of the Earth about the Sun where the perihelion (shortest distance) and aphelion (longest distance) occur on the semi-major axis of the ellipse and the distances are defined by Kepler's third law (see **Figure 15** and Eq. (6) in Appendix A).

However, instead of it, one can observe a significant reduction of the Sun-Earth distances in January–June (**Figure 5**) and their increase in July–December (**Figure 6**). Furthermore, the maximal differences, or differences between the S-E distances at the start and end of each millennium considered presented in **Figure 7**, reveal these maximal differences reaching 0.005 au in April–May (**Figure 5**) in millennium M1 and up to 0.011 au in April–May in millennium M2. These are followed by significant increases of the S-E distances in August–December shown in **Figures 6** and **7**. Moreover, the daily double differences, e.g. the differences between the maximal differences of the S-E daily distances in M1 and M2, taken from **Figure 7**, plotted in **Figure 8** demonstrate that in March–June there is a large reduction of the S-E distances in M2 compared to M1.

In order to evaluate if these changes are symmetric, let us present the mean monthly S-E distance variations during each sample year considered plotted in **Figure 9**. This, in fact, reveals that in M1 the increases/decreases of the S-E distances (left plot) are nearly symmetric over each year and centred about the summer solstice in June and winter solstice in December while in the millennium M2 the

**Figure 5.**

*2600.*

**35**

*Variations of the sun-earth distances (in astronomical units, au) versus days of the month (X-axis) in January– June for three sample years 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 and grey -*

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

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