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

#### **Figure 11.**

Hence, the solar irradiance *S* can vary either because of the variations of intensity *I* of solar radiation at the Sun itself or because of the variations of a distance *d* between the Sun and Earth. The variations of the solar intensity *I* is caused by the variations of solar activity induced by the electro-magnetic dynamo action in the

If the intensity *I*<sup>⊙</sup> of radiation on the Sun is considered to be constant at a given time (*I*⊙=const), then the solar irradiance *S* can also change because of a variation of the Sun-Earth distance caused by the Earth orbital motion itself leading to the terrestrial seasons and by solar inertial motion whose effects are not yet fully investigated. In any case, by knowing the ephemeris of the S-E distances and using Eq. (2) above for calculating solar irradiance at two different distances *d*<sup>1</sup> and *d*2, one can find the relationship between the solar irradiance, *S*<sup>1</sup> and *S*<sup>2</sup> at these

<sup>1</sup> <sup>¼</sup> *<sup>S</sup>*<sup>2</sup> � *<sup>d</sup>*<sup>2</sup>

Therefore, if at a distance *d*<sup>1</sup> the average solar irradiance is 1366 *W=m*<sup>2</sup> [22, 31]

<sup>2</sup>*:* (3)

*<sup>S</sup>*<sup>1</sup> � *<sup>d</sup>*<sup>2</sup>

then if the distance is changed to *d*2, the solar irradiance *S* should also change following the Eq. (3). For example, if the distance *d*<sup>2</sup> between the Earth and Sun was to be decreased by 0.016 au (as shown in section 3 for two millennia 600–2600)

so that the initial irradiance of 1366 *W=m*<sup>2</sup> divided by the square of the new distance results in the irradiance of 1411 *W=m*2. The difference in the irradiance is 1411–1366 = 45 *W=m*2, that is 3.3% that is exactly the magnitude mentioned in the

**4.2 Orbital variations of solar irradiance in the millennia 600–2600**

In section below the solar irradiance is explored in more details for the two millennia from 600 to 2600 AD for the S-E distances presented in section 3.

As established in section 3, the Sun-Earth distances are changing accordingly to the ellipse curve as Kepler's 3rd law assigns. Instead, these distances are defined by the two motions: the Earth and Sun about the barycentre of the solar system with the latter caused by the gravitational effects of large planets of the solar system, or solar inertial motion (SIM). Therefore, the daily variations of solar irradiance over a year will be affected by the combination of the Earth revolution on its orbit and the

By using Eq. (3) let us calculate the solar irradiance at any day of a year during the two millennia M1 and M2. For the TSI normalisation the magnitude of *S*<sup>1</sup> = 1366 *W=m*<sup>2</sup> [31] can be used for the longest distance in June 1700. Then the daily TSI magnitudes for every month of a year for three years for each millennium: M1 (600, 1100, 1600) and M2 (1700, 2020, 2600) are presented in **Figure 11** (for January– June), and 12 (for July–December) with their annual variations compared in **Figure 13**. The small differences ( ≤ 0.001 au) between the S-E distances of 1600 and 1700 are considered when calculating the total solar irradiance for M2. The overall variations of the sum of the TSI deposited to Earth in each year are presented in **Figure 14** calculated for: (a) the mean TSI magnitudes averaged for every month, e.g. by adding the TSI magnitudes for 12 months (left plot) and (b) the daily TSI magnitudes, e.g. by adding the TSI magnitudes for all days in each year considered. In M1 the increase of solar irradiance during the months January–June is nearly balanced by its decrease from July to December (**Figures 11** and **12**, left column) while in M2 the solar irradiance is noticeably higher in February–July when the

distances, which follows the inverse square law [53]:

first paragraph of the last section of paper [19].

Sun's revolution about the barycentre.

**42**

solar interior.

*Solar System Planets and Exoplanets*

*Variations of the daily solar irradiance in (W=m*<sup>2</sup>*) in January–June for three sample years selected in the millennia M1 (600–1600) (left) and M2 (1600–2600) (right). Left column: Blue - year 600, red 1100 and green 1600; right column: Blue - 1700, red - 2020 and grey - 2600. X-axis shows days of the months.*
