**6. Conclusions**

1.Solar irradiance *S* variations at Earth owing to 11 year cycle is about 0.1% of the average magnitude of TSI *S* (1366 W*m*<sup>2</sup> accepted in this study) increasing by 1.4 W*m*<sup>2</sup> during maxima and decreasing during minima [33, 54]. The terrestrial temperature variations during 11 year cycle are negligible.

2. Solar irradiance *S* variations at Earth owing to GSM is about 2.5–3 *W=m*2, or 0.22 % of *S* [31, 37, 55] as shown in **Figure 2** (left plot). These estimations are also supported by conclusions by other authors [55, 56] showing sometimes up to 0.4% contributions of active regions into the solar radiance intensity *I*⊙.

The terrestrial temperature curve presented in **Figure 2** (right plot) shown a

58], e.g. the decrease of TSI by 0.11% secures a decrease of the terrestrial tempera-

**5.1 Expected effects of the TSI increase by SIM on the terrestrial temperature**

The terrestrial temperature is found increasing since Maunder minimum as shown in **Figure 4**, bottom plot derived by Akasofu [35] that is close to the plot presented in the NASA and IPCC report *https* : *==www:ipcc:ch=sr*15*=*. At the same time the solar activity of 11 years, and thus, solar irradiance caused by it in the past

Now we established that there is an additional effect leading to the increase of solar irradiance in the millennium M2 (1600–2600) because of the changing Sun-Earth distances imposed by the solar inertial motion (SIM) owing to gravitational effects from Jupiter, Saturn, Neptune and Uranus. The overall increase of solar irradiance for M2 is shown in **Figure 14** to reach about 20–25 *W=m*<sup>2</sup> for the whole planet, which can be assumed to split evenly to each hemisphere with 10–12 *W=m*2. Although, the conversion of this extra solar radiation into the terrestrial temperature is a complex process involving exchanges between the deposited solar radiation to different hemispheres, ocean and atmospheric radiative transfer [59]. In fact, using line-by-line radiation transfer (LBL-RT) calculations under different cloudiness conditions, ground temperatures, and humidity models for radiative transfer of UV solar radiation by atmospheric molecules including *CO*2, Hardy [59] has shown that even a smaller increase of solar radiation by 5 *W=m*<sup>2</sup> leads to a noticeable (60%) increase of the terrestrial temperature defined by the Sun and only 40% defined by the *CO*<sup>2</sup> emission. The further increase of solar irradiance owing to the millennial TSI misbalance derived here in section 4.3 from the ephemeris of the Sun-Earth distances would definitely lead to a further contribution (possibly, above 80%) of the Sun's radiation into the observed terrestrial

Although, in the current study we do not carry out radiative transfer simulations, and thus, can only roughly estimate possible variations of the average terrestrial temperature using the observed curves similar to those measured [35, 45] (**Figure 4**, bottom plot). The baseline temperature was shown to increase, or to recover from 'little ice age' after Maunder minimum, in the past three centuries (black straight line in [19, 35]). Since the TSI increase by up to 25 *W=m*<sup>2</sup> for two hemispheres, or 12.5 *W=m*<sup>2</sup> per hemisphere is expected until, at last, 2500, then using the link between the solar irradiance and terrestrial temperature derived from **Figure 2**, the increase in the baseline terrestrial temperature from 1700 can be

C in 2100 and by 1*:*5<sup>∘</sup> C in 2020.

C in 2500, or by 2*:*0<sup>∘</sup>

.5C. Let us use this simple estimation until we carry out

.0C [36, 57,

reduction during MM of the average terrestrial temperature by about 1<sup>∘</sup>

ture by approximately 0<sup>∘</sup>

more precise model simulations.

*Solar System Planets and Exoplanets*

four solar cycles was decreasing.

temperature growth.

expected by about 4*:*0<sup>∘</sup>

**48**

In this chapter the investigation of Sun-Earth distances from the ephemeris by VSOP87 [47] and JPL ephemeris [48] is presented. The Sun is found shifting in millennia M1 and M2 along the direction of the minor axis towards the spring equinox that leads to a significant reduction of S-E distances in January–June by about 0.005 au in M1 and up to 0.011 au in M2, which are followed by the asymmetric increases in the second half of the year (July–December). However, the S-E distance increases and decreases are not identical as expected from elliptic orbit.

These S-E distances are found affected not only by the Earth revolution about the focus of the ellipse, but also by the Sun's motion about the barycentre caused by the gravitational effects of other planets (Jupiter, Saturn, Neptune and Uranus), or solar inertial motion (SIM). 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. The similar inertial motion effects are often observed in other stars, which have planetary systems, leading to the wobbling star effect that is used to trace possible exoplanets [50, 51].

The S-E distance shifts are found to lead to a migration of the Earth's aphelion and perihelion to their classic position on the major axis of the ellipse to occur on 21 June and 21 December, respectively, appropriate for the ideal elliptic Earth revolution. For example, the aphelion is shifted: in 1600 to 28 June, in 2020 to 5 July and in 2060 to 16 July, while and the perihelion migrates from 21 December to 28 December in 1600, 5 January in 2020 and to 16 January in 2600. The shifts of the S-E distances lead to the shifts of the Earth aphelion and perihelion from the major ellipse axis to the intermediate (shorter) axis, which passes through the SIM position of the Sun for the year and the ellipse orbit centre. Therefore, these shifts define the skewness of Sun-Earth distances along the Earth orbit towards the real position of the Sun, because it is moved outside the focus owing to the orbital perturbations of the Sun's motion about the barycentre caused by the gravitational forces of the four large planets.

the temperature is to be reduced again by 1.0<sup>∘</sup>

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

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

tially supported by the US Airforce grant PRJ02156.

**A. Basics of planetary orbits.**

defined by Kepler's three laws [61]:

any point of the orbit.

Therefore, our analysis with the new proxy of solar activity (SBMF) has opened new perspectives for reliable prediction of solar activity on short, medium and longterms. This approach has allowed us to link the solar magnetic field variations to the variations of solar irradiance, which are associated with both the inner solar processes and the orbital effects on the Sun-Earth distances. The fundamental oscillations of solar irradiance, in turn, can be linked to the oscillations of the baseline terrestrial temperature, independent of any terrestrial processes of radiative transfer and heating. Although, other terrestrial and anthropogenic effects can lead to the fluctuations of this temperature but their study was outside the scope of the current chapter.

V. Zharkova wishes to express her deepest gratitude to the funding by the public

In order to investigate the orbital effects on the distance between the Sun and Earth and the resulting variations of solar irradiance imposed by these variations, let us first remind the basic laws governing the planet revolution about a central star, the Sun. It is suggested that the planets evolution about the central star (Sun) is

1.Planets move in elliptical orbits around the central star (Sun), which is located

2.The Sun-planet line sweeps out equal areas in the equal times. This means that planets move faster when they are nearer the Sun (perihelion) and slower

3.The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis *a* of its orbit. This law defines the Sun-Earth distances at

The Sun is located in one of the two foci (point -C in **Figure 15**) of the ellipse

s

It can be noted that is a link between the semi-major and semi-minor axis:

ffiffiffiffiffiffiffiffiffiffiffiffiffi <sup>1</sup> � *<sup>b</sup>*<sup>2</sup> *a*2

, (4)

with a semi-major axis *a* and a semi-minor axis *b* and the eccentricity:

*e* ¼

in one of the foci of the ellipse (see **Figure 15**, left plot).

when they are further away (aphelion).

supporters raised through 'Fund-me'sites. Their support inspired the author to undertake the investigation of the ephemeris of the Sun-Earth distances and relevant variations of the solar irradiance associated with the changes of the Sun-Earth distances induced by orbital effects. The author also wishes to thank the Paris Observatory, France and JPL ephemeris websites, JPL, Pasadena, US for providing the ephemeris of the Sun-Earth distances for a few millennia. The work was par-

higher than it was in 1700.

**Acknowledgements**

**Appendix**

**51**

C to reaching the magnitudes of 2.0<sup>∘</sup>

C

These shifts of Sun-Earth distances lead to the changes in the total solar irradiance reaching the Earth atmosphere and baseline magnetic field measured from the Earth. Because of this reduction of the S–E distances caused by SIM, the TSI at the Earth is shown to increase from 1700 to 2600 by about 11 *W=m*<sup>2</sup> (0.95%) in February–March (and decreased in August–September), by 15–18 *W=m*<sup>2</sup> (1.2%) in April–May (and decrease in October–November) and by 7–8 *W=m*<sup>2</sup> (0.5%) in June– July (and decrease in December–January). While the shift of the maximal distance (aphelion) from regular 21 June date in 1600 to mid-July in 2600 can naturally explain the skewness of the baseline magnetic field towards the Northern polarity in 2600 and the minimum of the baseline magnetic field in 1600, by its skewness towards Southern polarity as it was reported before [19, 52].

It is also shown that since 1600 to 2020 there was an increase of the annual TSI magnitude by about 1.3 *W=m*<sup>2</sup> derived from the mean monthly S-E distances, which is close to the magnitude of 1–1.5 *W=m*<sup>2</sup> reported for the similar period from the current TSI observations [34]. However, the annual TSI magnitudes, calculated from the daily S-E distances reveal a much larger annual increase of the total solar irradiance by about 20–25 *W=m*<sup>2</sup> by 2500 in M2 compared to millennium M1. This means there is an excess of solar radiation input into the terrestrial atmosphere in millennium M2 not accounted for by any other consideration that has to be considered for the solar forcing. This additional solar input should have different redistribution between Northern and Southern hemispheres, in addition to normal variations of the Earth position on elliptic orbit [49] linked to their exposure time to the solar input not discussed in the current paper.

However, in 2020 the Sun has entered the period of a reduced solar activity: the Grand Solar Minimum (2020–2053). The orbital variations of solar irradiance will be combined with the variations of solar activity, or solar magnetic field, imposed by the variations of solar dynamo [1, 10]. The decrease of solar irradiance during this GSM is expected to be about 3 *W=m*2, or 0.22%. Therefore, the reduction of solar irradiance caused by the GSM effect will work in opposition to the increase of solar irradiance caused by the orbital SIM effects in the current Hallstatt's cycle.

The baseline temperature (not including any terrestrial effects) is shown increased by 2020 by 1.5<sup>∘</sup> C since 1700 because of SIM effects. Because of the modern GSM1 the terrestrial temperature is expected to be lowered by 1.0<sup>∘</sup> C giving the resulting temperature of 0.5<sup>∘</sup> C higher than it was in 1700. After 2053, the solar irradiance and the baseline terrestrial temperature is expected to return to the pre-GSM level. Then the irradiance and temperature will continue increasing because of the SIM effects combined with radiative transfer of solar radiation in the terrestrial atmosphere. This means the terrestrial temperature will continue increasing up to 3.0<sup>∘</sup> C by 2375 when the second modern GSM2 will occur (2375–2415). During GSM2 *Millennial Oscillations of Solar Irradiance and Magnetic Field in 600–2600 DOI: http://dx.doi.org/10.5772/intechopen.96450*

the temperature is to be reduced again by 1.0<sup>∘</sup> C to reaching the magnitudes of 2.0<sup>∘</sup> C higher than it was in 1700.

Therefore, our analysis with the new proxy of solar activity (SBMF) has opened new perspectives for reliable prediction of solar activity on short, medium and longterms. This approach has allowed us to link the solar magnetic field variations to the variations of solar irradiance, which are associated with both the inner solar processes and the orbital effects on the Sun-Earth distances. The fundamental oscillations of solar irradiance, in turn, can be linked to the oscillations of the baseline terrestrial temperature, independent of any terrestrial processes of radiative transfer and heating. Although, other terrestrial and anthropogenic effects can lead to the fluctuations of this temperature but their study was outside the scope of the current chapter.
