«Fundamental Principles and Results of a New Astronomic Theory of Climate Change Joseph J. Smulsky Institute of Earth’s Cryosphere, Malygina Str. ...»
Fundamental Principles and Results of
a New Astronomic Theory of Climate Change
Joseph J. Smulsky
Institute of Earth’s Cryosphere, Malygina Str. 86, PO Box 1230, Tyumen, 625000, Russia
Abstract. In light of the latest research developments, this paper describes the fundamental
principles of the astronomic theory of climate change. It comprises three problems: the evolution of
the orbital motion, the evolution of the Earth’s rotational motion and the evolution of the insolation controlled by the evolutions of those motions. All the problems have been solved in a new way and other methods. The paper demonstrates geometric parameters of the Earth’s insolation by the Sun, and explains a new insolation theory. Its results are identical to the results of the previous theory.
The equations of orbital movement are established, is told about their solution and the results for the different periods of time are submitted. These results improve the results of the previous theories: the planets’ and the Moon’s orbits are stable and the Solar system is stable. In much the same way, the problem of the Earth’s rotation is described. Unlike the previous papers, this problem is solved here without simplification. The calculations demonstrate significant oscillation of the Earth’s axis. These results were confirmed with other three independent solutions of the Earth’s rotation problem. The oscillations of the Earth’s axis result in such oscillations of insolation that explain the paleoclimate changes. The material in this paper is presented in a format intelligible for a broad audience.
Keywords: Evolution, Earth’s orbit, rotational axes, insolation, cause, climate, change.
1 Introduction The Earth’s history is marked by numerous iterations of warm and cold spells -. A glacier that used to cover the north and midland of Europe melted ten thousand years ago. On the other hand, polar areas that are now almost inanimate used to be covered by rich vegetation with trees, as well as populated by abundant fauna, such as mammoths, wooly rhinoceroses, buffalos, horses and other animals. What is the reason for this sort of climate fluctuations on the Earth?
Back in the 19th century, Louis Agassiz , J. Adhemar , James Croll  and others fathered the idea that changes of the Earth’s orbit parameters and its rotation axis may entail change in the amount of heat reaching the Earth’s surface from the Sun in different latitudes. By the end of the 19th century, accomplishments in mathematical astronomy enabled the scientists to calculate changes of orbital and rotational parameters of the Earth, and in the beginning of the 20th century Milutin Milankovitch  completed work on his Astronomical Theory of Ice Ages, which is, in essence, an astronomical theory of climate change. In this theory, Milankovitch calculates the Earth’s insolation in different latitudes based on three parameters: eccentricity e of the Earth’s orbit, perihelion angular position φpγ and obliquity .
Radiation of the Earth by the Sun and the value of resulting heat on the surface is commonly known as insolation (in-sol, where in is a verb prefix with a meaning of “bring”, “lead”, and solis is sun). At the same time, we must bear in mind that the same process has other aspects denoted by different terms, such as irradiation, illumination, radiation, etc. Insolation may be expressed for different time periods, including momentary, daily, seasonal, half-year, or yearly insolation.
Inasmuch as parameters e, φpγ and change and fluctuate within periods of tens of thousands of years, insolation values from age to age may be calculated, for example, for the warm half-year period at the latitude of 65°, and the change of insulation values may lead to certain conclusions on climate change. However, the fluctuation amplitude for eccentricity e and obliquity in the Milankovitch theory was fairly small. For example, the angle fluctuated within the range of ± 1°. Such oscillations could result in temperature fluctuations also in the range of 1-2°C. This is why the astronomical theory of climate change has caused doubt among the researchers  of paleoclimate both at the times of Milankovitch and today.
After M. Milankovitch, his research was repeated by several groups of researchers - at intervals of several decades. They updated the evolution of parameters e, φpγ and and extended the initial calculation for the past 600 thousand years  over a longer period, such as 30 million years . Still, the main result, i.e. oscillation of eccentricity e and obliquity , remained fairly insignificant.
It was found in the second half of the 20th century that marine sediments demonstrate oscillations of the quantity of oxygen isotope O18. Vast research was carried out all across the global ocean. Results of this research were summarized in the form of standard relations of relative oxygen isotope concentration δO18 versus sediment thickness associated with time T . These relations were named using initial letters of CLIMAP  project or names of the authors of LR-4 . It is believed that lighter isotope O16 contained in the water evaporates and accumulates in glaciers. In this context, it was assumed that surplus of oxygen isotope O18, i.e. excess of δO18 above the mean level, is proportionate to the volume of ice accumulated in the Earth’s ice cover.
One of the major periods on the δO18 curve is 100 million years. It is close to one of the periods of change in the Earth’s orbit eccentricity e. Therefore, it was identified that eccentricity e has a significant impact on the Earth’s climate. For example, study  even claims that M. Milankovitch does not take into account the direct impact of eccentricity on the Earth’s climate. In fact, the insolation theory that was developed by Milankovitch identifies a mathematically strict dependence of insolation on parameters e, φpγ and . On the other hand, a lot more has to be done to determine the developments and causes of establishment of certain properties of marine sediments, glacial cores of contemporary glaciers, and other paleoclimatic data arrays. The same work has to be done to identify reliability of findings offered by the astronomical climate theory. This is what we have been working on at the Institute of the Earth Cryosphere for the past two decades.
Astronomical climate theory is based on the computation of body interactions. For that reason, to make sure our findings are valid, we studied the fundamentals of mechanics, tried to remove the odd stuff and keep what is necessary . The astronomical theory of the Earth’s climate includes such elements as the problems of orbital motion of bodies and rotational motion of the Earth, as well as the problem of the Earth’s insolation as function of the parameters of its orbital and rotational motions.
We mentioned above that several generations of researchers consistently repeated the studies of M.
Milankovitch. Still, they all followed the same path that had been developed in mathematical astronomy over centuries. We take a different path. We do not copy equations of our predecessors but derive them on the basis of fundamental principles. Second, we seek to employ minimum simplification in our derivations. And third, we solve problems using numerical procedures, aiming to employ their most accurate variations or create new ones. In this study, the Astronomical theory of the climate change is presented in the results that we have obtained. In the beginning, we will speak about insolation of the Earth, and then about the evolution of the orbital motion and evolution of the Earth’s axis. As regards the first two problems, our independent studies confirm findings of our predecessors, while the results of the rotational motion study are different. The oscillation amplitude of obliquity is seven times greater than the value identified by pervious theories. These oscillations result in such fluctuations of insolation that can explain the past climate changes. This significant difference in the results of the Earth rotation problem requires a comprehensive verification. The final part of this study will focus on the verification of solutions of the Earth rotation problem.
2 Geometric Characteristics of Insolation Let us place observer M in the center of celestial sphere 1 (see Fig. 1). Its horizon crosses the celestial sphere in circle HH. A perpendicular to the plane of the horizon crosses the celestial sphere at the point of zenith Z. The Earth’s axis of rotation marked by the Earth’s angular velocity vector E crosses the celestial sphere at the point of the north pole N. Angle formed by E and the plane of horizon represents the observer’s latitude. Bear in mind that the angle of arc of the sphere’s great circle is equal to the central angle between the radii of its ends, e.g., arc φ equals HMN.
Annual movement of the Sun S projects onto the celestial sphere 1 an ecliptic circle EE in counterclockwise direction. This elliptic circle intersects the equator circle AA in points γ and γ’. Longitude of the Sun is measured from point γ, which is the vernal equinox point. The distance between the Sun and equator AA is determined by declination .
The Earth rotates around the axis MN in counter-clockwise direction. At the same time, the celestial sphere and the Sun perform daily rotation around this axis relative to the observer in clockwise direction.
Thus, the Sun’s daily motion occurs along the circle SrMdSs, which is parallel to the equator circle. The Sun rises above the horizon in point Sr, arrives at point Md at noon and goes down over the horizon at point Ss. The Sun, which is not in the observer’s sight, arrives at point Mn at the noon time. The hour angle of the Sun will be measured from the meridian passing through noon Md.
Figure 1. Basic geometrical characteristics of the Sun S at irradiation of point M on the Earth’s surface: 1 is the celestial sphere; HH’ is the plane of the horizon; N is North pole; AA is the plane of the mobile equator; EE’ is the plane of the mobile ecliptic, and is the angle between planes AA and EE’; Z is zenith of point M, and z = ZMS is the zenithal angle of the Sun; arc HN = is the geographical latitude of point M; ω = MdNS is the hour angle of the Sun, measured from noon Md; = SB is the declination of the Sun; = S is the longitude of the Sun.
In Fig. 1, the planes of equator AA’ and ecliptic EE’ are referred to as mobile planes because their positions change in time.
Day length is proportionate to the length of arc SrMdSs, and night length corresponds to the length of arc SsMnSr. In the demonstrated position of the Sun S, the day is longer than the night. If the Sun S is on the equator in point γ or γ, then during the day it will move along the circle of equator AA. In this case, day and night lengths are equal. If the Sun S is in the southern part of the celestial sphere, its path beneath the horizon will be longer than the path above the horizon HH, i.e. the night will be longer than the day.
Figure 2. Geometrical characteristics of the Sun S for observer M positioning at different latitudes of the Earth’s surface: a is in transpolar latitudes; b is at the North Pole; c is at the equator: 1 is the celestial sphere; arrows show annual and daily motion of the Sun in the celestial sphere; other designation see Fig.
Fig. 2a demonstrates the observer position in high latitude . In this case, daily circle MdS of the Sun S does not cross the horizon and is above it. When the Sun S is in the southern part of the sphere, its daily motion circle that is parallel to the equator will be below the horizon. Observer M will find themselves in the condition of polar night. When the Sun on the circle EE is in positions that are closer to points γ or γ, observer M will experience both day and night.
When the observer is at the North Pole with φ = 90° (see Fig. 2b), the circle of horizon HH in the celestial sphere matches the circle of equator AA'. During the daytime, the daily motion of the Sun occurs along the circle parallel to the circles above. In this case, the circle of horizon on the celestial sphere matches the circle of equator AA'. There are no sunrises (point Sr) and sunsets (point Ss) at the pole. In the winter time, the daily motion of the Sun S' in Fig. 2b occurs below the horizon, i.e. the polar night sets at the pole.
When the observer is on the equator with φ = 0° (see Fig. 2c), North Pole N is in the plane of horizon HH', and the point of zenith Z is in the plane of equator AA'. Daily motion of the Sun occurs along the circle SrMdSs parallel to the circle of equator AA'. At the points of sunrise Sr and sunset Ss, the Sun moves perpendicular to the horizon, so the day begins and ends almost instantaneously.
Figure 3. The Earth’s (E) motion along the orbit around the Sun (S): is the point of vernal equinox; PE and AphE are the perihelion and aphelion of the Earth’s orbit, respectively; о is the polar angle of the Earth’s motion along the orbit; p is the angle of the Earth’s perihelion.
In Fig. 1, the plane of the Earth’s orbit is in the plane of ecliptic EE', and the line Sγ of the orbit matches the line Mγ. The Sun S moves along the circle of ecliptic EE' relative to the Earth located in point М. This is why images of the Earth in Fig. 1 will mirror the Sun. In spring, the Sun is in point γ, and the Earth is in point γ', if the Sun S is in point М. Planes of equator and the Earth’s orbit change in space, which is why point moves on the Earth’s orbit (Fig. 3). Position of perihelion PE also moves on the orbit regardless of point . Angle p will be measured between these two points and PE.
Figure 4. Distribution of specific heat GJ/m2 across the Earth’s latitude in the contemporary epoch (1950): QS is over the summer caloric half-year; QW is over the winter caloric half-year; QT is over the entire year: QT in the graph is halved; 0 is the northern hemisphere; 0 is the southern hemisphere; Mil is the calculations by M.