V.M. Fedorov
Lomonosov Moscow State University

Results of the research of long-term variations of solar activity for four hundred years have been summarized. The history of studies includes two major trends: the history of solar activity observations (since the beginning of the 17th century until present time) and the history of actual measurements (since the beginning of the 20th century until present time). The history of measurements of solar activity long-term variations (the solar constant) is divided into chronological periods reflecting various physical and technical measuring levels (from earth surface, from atmosphere, from space).


Solar radiation comes from the Sun, and it supplies heat and light to the Earth. Solar energy is relevant for the development of hydrometeorological and many other processes occurring in the atmosphere, hydrosphere, on Earth surface, and for life evolvement on the planet. So, the research of activity changes in the energy source occurring in the Earth geographical sphere and ensuring life existence on the planet, has a great importance in natural scientific research.

The Sun continuously emits the energy into the surrounding space with flux power of around 3.94 1026 W. The Earth disc absorbs the energy equal to the product of solar constant and the Earth large circle. For average Earth radius of 6,371 km, the large circle area amounts to 1.275 1014 m2, and incoming radiant energy amounts to 1.743 1017 W. Yearly influx of solar radiation on the atmosphere upper border is 5.49 1024 J. (Drozdov et al., 1989; Hromov, Petrosyanz, 2006; Abdusamatov, 2009). This influx is not constant and is subject to long-term variations that occur against the background of century long trends.

Long-term variations of solar activity coming to the Earth are basically defined by two reasons having different physical nature. One of the reasons is changes in the activity of Sun radiation. The other reason defining long-term variations of solar activity is celestial and mechanical processes causing changes of the Earth orbit elements (Fedorov. 2012). The article describes the history of the research of long-term variations related to the change in Suns radiating activity.


The History of Sunspot Research

The history of the research of Suns radiating ability (solar activity) can be divided into two major stages. The first stage (since the beginning of the 17th century until present time) reflects scientific recording of solar activity. The second stage (since the beginning of the 20th century until present time) includes actual measurements of solar radiation as well. These major trends are divided into individual historical fragments marked in time by physical and technical benchmarks.

Relatively regular observations of the Sun have been conducted for almost four hundred years. The result of these observations is a 11-year cycle of solar activity expressed in quasi-periodical change of the number of sunspots and being a basis for common ideas about the Sun and many phenomena of the solar and terrestrial physics (Fig. 1). This periodicity in spot formation is the most famous effect and it is quite well documented and represents a widely observed phenomenon in astronomy. However, it should be noted that continuous and rather precise measurements are available for approximately one hundred years. Data for the time before 1850 is ambiguous for the most part. For more distant time, there are few or no proofs that the modern 11-year cycle is a constant solar phenomenon. (Eddy, 1980 a, b). Nevertheless, sunspots are the most easily observed indicator of the solar activity level and a source of the most continuously measured data in the history of the Sun (Vitinskiy, 1983; Foukal, 2004).

It is credibly known that the telescope was invented in Holland in 1608. The observation of celestial objects using the telescope was started almost simultaneously by the English mathematician Thomas Harriot, the German scientist Simon Marius and Galileo Galilei. His first telescopic observations Galilei published early in 1610 in the book entitled Sidereus Nuntius (Sidereal Messenger). These were the results of telescopic observations of the Moon, and the discovery of four Jupiters satellites. Also, Galilei observed Venus and Saturn using the telescope. A number of telescopic discoveries was crowned by the discovery of dark spots on the Sun. As Galilei claimed himself, he noticed them at the end of 1610 for the first time (Berry, 1904), but he seemed to have paid no particular attention (in the letter of May 4, 1612, he writes that he observed them 18 months earlier; in the conversation of two systems, he notes that had seen them while reading lectures in Padua, i.e., no later than September 1610). However, the official announcement of the discovery of sunspots was made by Galilei in May, of 1612, when they were discovered by Thomas Harriot in England, Johan Fabricius in Holland and the Jesuit Cristoforo Scheiner in Germany, and published by Fabricius in July of 1611 (Berry, 1904). It was Scheiner who discovered the faculae and made a number of observations over movements and emersion of spots (Berry, 1904). Sunspots had been previously observed with naked eye, but their origin was explained by Mercury passing along the Suns disc.

Nothing was known about the periodicity of sunspots occurrence until 1843, when the German amateur astronomer, Heinrich Schwabe, pointed to an apparent 10-year periodicity revealed after 17 years of observations. Nevertheless, this discovery had remained unnoticed until the famous German geographer, Alexander Humboldt, published Schwabes conclusions (based on his 25 years of observations) in 1851 in his multi-volume treatise entitled The Space (Humboldt, 1866; Silkin, 1967; Maximov et al., 1970).

With respect to Schwabes results (becoming known later), an international program for Sun observation was developed (and its still active). The basic goal of this program was the investigations and observations to determine whether the periodicity discovered by Schwabe is real and constant. Rudolph Wolf from the Zurich observatory was the one who organized and initiated these observations (his indicator for the number of sunspotsWolf index or Wolf numbersis used even now). Wolf conducted comprehensive investigations of historical data concerning the registration of sunspots to determine periodicity in the past. After long-term and results-oriented research, he collected historical proofs referring to the time period between the Schwabes observations and the discovery of spots using telescope (early in the 17th century). Wolf made a conclusion that the 11-year cycle really existed, starting with 1700, and perhaps even earlier. He restored the number of sunspots for this early period, and they were acclaimed to be true in all further works dedicated to the history of the Sun. More than half of the data given in Fig.1 is the result of Wolfs research.

The relative number of sunspots (Wolf indexW) is calculated as a sum of the number of spots (a) and a ten-fold number of all spot groups (b), i.e. W=a+10b (Eigenson et al., 1948; Vitinskiy, 1983). Or R = k (f + 10g), where f is the number of individual spots that combined in g of groups, k empirical factor (Kondratyev, 1954, 1965; Bakulin et al., 1983; Abdusamatov, 2009). First of all, the importance of this index is defined by its simplicity. Second, it is important because its values (thanks to Wolfs works) are known since 1700yearly data, or since 1749monthly data (Chernosky, Hagan, 1958; Eigenson, 1963; Kondratyev, 1965; Klimishin, 1976).

Around 160 years ago it was determined that the 11-year cycle of solar activity is expressed not only in the change of the number of sunspots (plages and solar flares), but also in the change of the spot group latitude time (Fig.2). In 1852, three investigators, Eduard Sabin in England, Rudolf Wolf and Alfred Gottier in Switzerland, independently paid attention to specific correspondence between regular changes in sunspots and Earth magnetic phenomena. Apart from the fact that their periods are equal, it also occurs that during the ages with the highest number of sunspots, a strongest magnetic storm takes place on the Earth. Periods of attenuation for these phenomena also coincide (Berry, 1904).

This distribution was studied by the English Sun researcher Richard Carrington (results published in 1863 in the monograph Observations of the Spots on the Sun) from the Royal Greenwich Observatory. He found out that in the beginning of a 11-year cycle, spots emerge in high latitudes (averagely, at 25 30° from the Sun equator), whereas in the end of the cycle, they are concentrated around the equator (averagely, at latitudes 5 10° ). Later (1880) this effect was in details investigated by the German scientist Gustav Sporer. It appeared that the average duration of the 11-year cycle can be determined more precisely upon the change of sunspot group latitude than upon variations of Wolf numbers. Research of Carrington and Sporer showing the nature of changes in the spot group latitude during the 11-year cycle of the number of spots, along with the discovery of spot formation by SchwabeWolf represent basic and true laws of the long-term variation of solar activity (Eigenson et al., 1948; Vitinskiy, 1983; Foukal, 2004; Abdusamatov, 2009).

In the late 20th century, Gustav Sporer and Edward Maunder studied archives of Sun observations and paid attention to a 70-year period (since the middle of the 17th century) with almost no sunspots reported (Eddy, 1976). In articles published later, Maunder concluded that during this time, from 1645 to 1715, a normal sunspot-forming cycle was completely or almost completely suppressed. He pointed that this phenomenon, if real, makes us doubt in the regular nature of the solar activity 11-year cycle.

Later studies of this issue proved Maunder conclusions and revealed some additional facts that had been unknown in the time of Maunder (for example, for studying the frequency of aurora polaris described by high correlation relationship with the level of solar activity, isotopic ice, etc.). During this period (16451715), the solar activity showed lower levels than minimal modern cycles. As relative number spots values in this period change within 0-5, it was impossible to reveal their maximum, and the issue concerning the 11-year summer cycle for this period is still open.

Regular observations of magnetic fields of sunspots discovered early in the previous century (1913) by the American astronomer G. Hale made everyone admit the existence of a 22-year cycle of solar activity. For a 14-year cycle (under Zurich numeration), Hale defined that the polarity of magnetic fields of leading spots (tail spots) of the northern (southern) hemisphere of the Sun changes oppositely when transiting from one 11-year cycle to the other (Struve, et al., 1967). Initial polarity is restored in 22 years. Further, such changes were observed during all following 11-year cycles. According to the Zurich numeration, in odd cycles, the magnetic field polarity of leading spots within groups of the northern hemisphere is positive, and in even cyclesit is negative (southern polarity). The southern hemisphere shows the opposite pattern (Anderson, 1939).

Thus, 11-year and 22-year cycles of solar activity are deemed to be reliably determined (as for the present). Existence of longer cycles of solar activity is yet an assumption. For example, some researchers distinguish a secular (8090-year) cycle of solar spots, i.e. Gleissberg cycle (Gleissberg, 1958; Eigenson, 1963; Abdusamatov, 2009). 8090-year variation can be most clearly distinguished upon the sum of annual average Wolf numbers in a 11-year cycle, or upon their maximum values. Since 1749, two minimum values and three maximum values of secular cycles were distinguished for annual average relative numbers of spots. According to the Zurich numbering of 11-year cycles, minimum values occurred in 6th and 14th cycles, and maximum valuesin the 3rd, 9th, and probably in 19th cycles. When decomposing Wolf numbers by main components number of spot groups and average duration of their existence, it appears that the first one basically shows changes with the average period of 11 years, and the second onethe average period of 80-90 years. It means that the 11-year cycle is typical for the frequency of solar activity phenomena, and the secular onefor their capacity (amplitude). But the problem of the secular variation of solar activity (and solar constant) is not yet settled. Some research note variations of solar activity with longer periods, for example, Zuss 200-year cycle (Schove, 1955; Abdusamatov, 2009).

Currently, a number of companies has been collecting data and conducting regular observations of the Sun cycle and have counted the number of sunspots. For example, Solar Influences Data Analysis Center (SIDC) in Belgium (http://www.sidc.be). In this Department of Physics of the Royal Observatory the so called International Sunspot Number is determined. Besides, sunspots are counted in the National Oceanic and Atmospheric Administration (NOAA) in the U.S. (http://www.noaa.gov). The number of spots determined in the NOAA is called the NOAA sunspot number.


Solar Constant Measurements

The history of measuring the solar constant includes measurements from the Earth surface, from the atmosphere (from aircrafts and air-balloons) and extra atmospheric measurements (from satellites and rockets) (Flux of Sun energy and its measurements, 1980). In meteorology, radiometric measurements have started in the late 19th century. To solve the problem of precision and to ensure the comparison of measurement results on various devices and stations, special radiometric scales were introduced. For many years, these standards and scales were subject to revision reflecting improvements in radiometry. Until the middle of the previous century, two scales were used: Angstroms (1905) and Smithsonians scale (1913). Just before the International Geophysical Year, the new International pyrheliometric scale was introduced (IPS, 1956), based on the abovementioned scales.

Early in the previous century, the Smithsonian astrophysical observatory started a series of high-mountain measurements of the solar constant. According to the latest data (gathered throughout half of the century), variations of the solar constant were 0.1 - 1%. During measurements, long-term increase of the solar constant average value was also found by 0.25% for 50 years (Abbot, 1957). Analysis of results obtained for four solar cycles (1908-1952) showed that the limits of possible variations of the solar constant are within 1% (of the solar constant average value). This was also confirmed by the repeated analysis of results obtained by the Smithsonian observatory. Average long-term value of the solar activity obtained in the Smithsonian observatory was 1.94 cal/cm2 min or 1,352 W/m2 (Kondratyev, 1965, Makarova, et al., 1991).

Historically, first direct measurements of the solar constant beyond the troposphere were made in the Leningrad University in 1961 (by a group supervised by K.Y. Kondratyev). Measurement devices were elevated at the altitude up to 32 km by an air-balloon. Prior to 1967, the air-balloon was used 28 times. The observation methodology and the results are in details described in a number of publications (Kondratyev, 1965; Kondratyev et al., 1966; Kondratyev, Nikolskiy, 1970,1982; Makarova, Kharitonov, 1972; Sun energy flux and its changes, 1980). These measurements resulted in revealing a noticeable variation of the solar constant (2.5%). Solar constant value upon the results of all measurements was 1,356 14 W/m2.

In 1966, the Laboratory of reactive motion (California Technological Institute) and the Eppley laboratory proposed a program for measuring the solar constant, in which Drammond obtained an average value of the solar constant upon the results of six trips on the NASA reactive research aircraft, which equals to 1,359 13 W/m2. In 1968, Kendall made measurements using PACRAD radiometer onboard the NASA aircraft. Final value obtained in the result of these measurements was 1,373 14 W/m2. The average value in all measurements from all aircrafts was 1,378 26 W/m2.

In 19681969, R. Willson also made some air-balloon measurements of the solar constant. The average value (upon three air-balloon measurements) was 1,373 14 W/m2. In 1969, he determined the solar constant near the maximum value of cycle No. 20 and obtained a value of 1,369 W/m2. The precision of air-balloon measurements is assessed to be 0.2 0.5% (Willson, 1972, 1973, 1978; Froelich, 1980).

Changes in solar constant variations using spaceships have high credibility since they are conducted beyond the Earth atmosphere. These measurements do not include atmosphere extinction (absorption and dissipation) and are made during many days. The first long-term measurement of the solar constant beyond the Earth atmosphere was made in the experiment conducted by the Laboratory of reactive motion on Earths satellites Mariner-6 and Mariner-7 in 1969. Measurements have shown that the solar constant value didnt vary above the precision limits (around 0.25%) near the solar cycle maximum, and during this time, the daily number of sunspots was both extremely high and extremely low (Willson, Hiki, 1980; Willson et al., 1980; Makarova et al., 1991).

In accordance with implementation of the Earth Radiation Balance (ERB) program conducted onboard of Nimbus-6 launched in 1975, solar constant values were obtained within the range of 1,3881,392 W/m2. In 1976, simultaneous measurements of the solar constant were made using a probe rocket (altitude around 100 km) and the space vehicle Nimbus-6. Average value for rocket data was 1,376 W/m2, upon the space vehicle data it was 1,376 14 W/m2. With respect to correction, the absolute value is determined as 1,367 W/m2 (this solar constant value is taken in the calculation method for solar radiation coming on the Earth ellipsoid surface with no atmosphere). This value is compared to 1,369 W/m2 obtained by Willson in 1969. As these two measurements made for the minimum and maximum of solar activity are agreed within errors of absolute radiometer, it shows that the solar constant remained unchanged within 0.75% during the second half of the cycle No. 20 (Willson, Hiki, 1980). The average value of corrected solar constant values obtained using aircrafts, Mariner-6, Mariner-7, Nimbus-6 and rockets (Aerobee) was 1,369 6 W/m2 for 19621980 (Makarova et al., 1991). Data of rocket observations of the solar constant conducted in 1976 using four absolute radiometers of various design are given in the work by Kondratyev and Nikolskiy (1982). The value averaged upon the records of three agreed radiometers was equal to 1,367 6 W/m2.

As assessed by Frohlich, who reviewed all measurements made using aircrafts, air-balloons and space vehicles, the most probable value of the solar constant equals to 1,373 20 W/m2 (Frohlich, 1980). This average value is compared to the average-weighted value of 1370 1 W/m2 that was obtained upon all measurements, including data of the rocket experiment in 1976 and corrected data of the ERB experiment (Nimbus-6). Considering all data for 1976, the solar constant value lies within 1,3681,379 W/m2. It is also noted that the data of measurements using the air-balloon and the aircraft significantly differs from data of space measurements.


Table 1. Comparison of measurement results for solar constant value
obtained by various experimental methods (Frohlich, 1980).

Solar constant, W/m2
1379 ( 3 )
1379 ( 3 )
Space vehicle
1368 ( 2 )
Weighted average value
1370 ( 1 )



Numbers in parentheses correspond to standard deviations from weighted average values. Aircraft measurements are given for altitude 1012 km, air balloon measurements for 2036 km.

Starting with the launch of American satellites Nimbus-7 (1978), and SMM (1980) equipped with cavity radiometers (H F radiometer series ERB and active cavity radiometer AKRIM, respectively), a new stage in measuring the solar constant was commenced (Fig. 3)

For the first time in the history of determining the solar constant, its values reached the precision of two decimal places of a percent (Willson, 1978, 1982, 1984 , b; Willson, Hudson, 1988, 1991; Pap., Frohlich, 1999; Willson et al., 1981; Frohlich et al., 1991; Livingston et al., 1991; Frohlich, 1988, 1989, 2000). Improvement of measurements at that time was basically defined by three factors: improvements of measurement devices (pyrheliometer) and increased precision of each measurement; bringing devices beyond the Earth atmosphere (fully eliminating errors of terrestrial observations, i.e. atmosphere extinction); automation of observations and wide application of computer equipment. As a result, high internal precision of observations was achieved at the same satellite device 0.3 0.7 W/m2, which is 0.02 0.05% of the solar constant (Makarova et al., 1991). The need of such high precision was defined by the obtained results that confirm rather small changes of the solar radiation flux.


With the internal precision achieved and compulsory application of sensitivity control, it became possible to define a precise value of the solar constant and observe its variations daily, weekly and more long-term ones (for example, satellite observations in experiments for measuring the solar constant within the NASA program intended to study the Sun activity and the Shuttle space program). The most informative materials were obtained from Nimbus-7 (launched in November, 1978) and SMM, Solar Maximum Mission (launched in February,1980). The solar constant value within the period under consideration was within 1,3671,373 W/m2, and the average value was 1,370.59 W/m2 at the ERB scale in Nimbus-7 and 1,370.62 W/m2 in SMM. Decrease of the solar constant from the maximum value of the 21st cycle (1980) to the minimal value (1986) was determined to be 0.15%, or 2 W/m2. The yearly increment was averagely 0.02% (Willson, 1984 a, b; Makarova et al., 1991).

By now, a continuous number of direct measurements of the solar constant has been provided by several special space vehicles since 1978 (Chapman et al., 1996; Willson, 1997; Willson, Mordvinov, 2003). These (technically complicated) measurements were made for three full cycles of the solar activity (21-23) and are continued in the current 24th cycle (Fig. 4).

The amplitude of 11-year flattened cyclic variations of the solar constant upon these measurements is about 1.0 W/m2 or around 0.07% of the average value of the solar constant. Average minimal (2123 cycles) values is 1,365.458 0.016 W/m2, and the solar constant average value for the 22nd cycle is 1,365.99 W/m2, for the 23rd cycle 1,365.82 W/m2 (Abdusamatov, 2009; www.pmodwrc.ch).


Thus, the history of the research of long-term variations of solar activity amount to four hundred years. This history includes two components in studying variations: observations (since the 17th century to the present time) and measurements (since the 20th century to the present time). The history of long-term solar activity variations (solar constant) is divided into stages reflecting various physical and technical levels of measurement (from the Earth surface, from the atmosphere, from the space).
It shall be also noted that searching for relationships between the 11-year variations with change of climate, geophysical and biophysical parameters were conducted during the whole period after revealing this cycle of solar activity (150 years). The results of this research are reflected in multiple publications. But due to obtaining low values of the solar constant in the 11-year cycle, and instability of amplitude and periodical characteristics, the interest to researching Sun and Earth relationships have significantly decreased recently. There are no perspectives for modulation of climatic changes by the 11-year variation of the solar constant, and its significance has also been minimized by the increased ambiguity of direct correlation comparison and no conclusive evidence of the cycle existence in the past (its stability in time).

In our studies, the data concerning Earth solar climate variations related to the Sun activity changes is not considered.






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