A Great American Total Solar Eclipse Primer: Let’s Do the Math
by Ted Saker
1998-2017 All rights reserved.
Country of First Publication: The United States of America

        On August 21, 2017, the Moon’s umbra touches the continental United States for the first total solar eclipse since 1979, it’s time to think about the science behind the event. Our ancestors cowered at the sight of the sun slowly disappearing, believing the event heralded death and destruction. Even the word eclipse is derived from the ancient Greek word ekleipsis, meaning abandonment accompanied by despair. They created rituals to ensure the Sun’s reappearance, but never shook off the dread that they felt on witnessing the awesome sight of day turning into night, and back into day. We have discovered that total solar eclipses are rather common in a larger sense, occurring every year or two. Unlike lunar eclipses, which are observable anywhere on Earth’s night side, solar eclipses appear quite rare from the perspective of any one place on Earth because the Moon’s umbra covers only a narrow sliver of the Earth’s surface during totality, and an observer must be inside the path of totality. The relative sizes of the Sun, Earth and Moon, and their celestial dances, play a big part in this drama as well.

        Three conditions bring about total solar eclipses. The Moon's phase (new), coinciding with the Moon passing through a node in its orbit (a syzygy, or the point where the plane of the Moon's orbit intersects the plane of the Earth’s orbit, aka the Ecliptic), at the optimum distance from the Earth, results in the Moon’s umbra crossing the Earth’s surface. All three conditions must occur simultaneously for a total eclipse to occur.

        At the new phase, the Moon passes between the Earth and Sun. At either node, the Moon lies in a line connecting the centers of the Earth, Moon and Sun. The distance between the Earth and Moon varies because the Moon’s orbit is elliptical. The Sun is approximately 400 times the diameter of the Moon, but by an astonishing coincidence, it is also about 400 times as distant. If the Moon is at apogee, observers see an annular (“Ring of Fire”) eclipse where only the penumbra touches the Earth. The Annular Eclipse of May 10, 1994 (Saros 128), observable from northwestern Ohio, was just such an event. If the Moon is not quite at apogee, a strange hybrid type of eclipse occurs, combining both annularity and totality (Saros 129). If the Moon is at perigee, an observer in the path of totality would be treated to the theoretical maximum duration of totality. Anywhere in between yields totality of varying durations.

        Each eclipse belongs to a family. Each family is known by a "Saros" number, a name given by Edmund Haley. He took the term from an older Byzantine text, which in turn ascribed it to an even older Chaldean word. Each eclipse in a Saros family shares many similar characteristics, including periodicity, length of totality at vairous points along the path of totality, the shape and width of the shadow's path, and the places on Earth where the shadow's path tracks across.

  
     Saros families are numbered according to the direction the Moon is passing in its orbit during an eclipse, among other criteria. Keep in mind that the plane of the Moon’s orbit is inclined approximately 5 to the plane of the Earth’s orbit. This is why we do not experience total eclipses on a monthly basis (darn it!). Nodes are either ascending (the Moon passing from below to above the Ecliptic) or descending (the Moon passing from above to below the Ecliptic). An even number Saros designation means that the Moon is passing through an ascending node, and the shadow generally traces a positively-sloped arc (west to east) on the Earth’s surface. An odd number Saros designation means the Moon is passing through a descending node, and the shadow generally traces a negatively-sloped arc (west to east) on the Earth’s surface.

        The periodicity of solar eclipses depends upon two lunar orbital cycles coinciding with the Moon passing through a node. First, a new moon occurs on average every 29.530588 days. The Moon’s average orbital period, perigee to perigee, is 27.554548 days. These cycles repeat every 18 years, 11 1/3 days; or 6585.3211 days; or 233 new moons, approximately 239 perigees and 242 nodes. Every eclipse in a Saros family shares the same 18 year, 11.33 day cycle. The great eclipses of June 30, 1973 and July 11, 1991 (Saros 136), which presented over and slightly under seven minutes of totality, respectively, were precisely 18 years, 11.33 days apart. The next total solar eclipse of family Saros 136 should occur on July 22, 2009, precisely 18 years, 11.33 days after that. The Big One, aka the Great American Total Solar Eclipse of August 21, 2017, belongs to the family Saros 145. Its path traces an arc roughly 120 degrees of terrestrial longitude west of its previous appearance, on August 11, 1999, 18 years, 11 1/3 days (calculated according to UT), which traced an arc across Europe, the Middle East and India.

 

Table of Saros and Lunar Year Eclipse Cycles - Figure 1

11 July 1972 (Saros 126)  + 18 y. 11.33 d. (Saros Cycle period)  22 July 1990 (Saros 126) + 18 y. 11.33 d. (Saros Cycle period) 1 August 2008 (Saros 126)
+ 354 days (Lunar Year Cycle period)   + 354 days (Lunar Year Cycle period)   + 354 days (Lunar Year Cycle period)
30 June 1973 (Saros 136)  + 18 y. 11.33 d. (Saros Cycle period) 11 July 1991 (Saros 136) + 18 y. 11.33 d. (Saros Cycle period) 22 July 2009 (Saros 136)
+ 354 days (Lunar Year Cycle period)   + 354 days (Lunar Year Cycle period)   + 354 days (Lunar Year Cycle period)
20 June 1974 (Saros 146) + 18 y. 11.33 d. (Saros Cycle period) 30 June 1992 (Saros 146) + 18 y. 11.33 d. (Saros Cycle period) 11 July 2010 (Saros 146)

    The Table of Eclipse Cycles, Figure 1, reveals that the 18 year, 11.33 day Saros and 354 day Lunar Year cycles separate families of Saros 126, 136, and 146. Note that not all the eclipses related in the 354 day cycle are total eclipses. Some are partials. The Saros families used in these examples are all total eclipses. Other groupings of Saros families follow this identical pattern. All the different families are intertwined in the 354 day cycle, while eclipses of the same family are separated by the 18 year, 11.33 day cycle. Figure 1 also shows a second eclipse cycle that has solar eclipses following the main ones by 12 new moons (354 days) on June 19, 1974 and June 30, 1992, and preceding them by 12 new moons (354 days) on July 11, 1972 and July 22, 1990. The math tells us that there is a solar eclipse of some kind on a very frequent basis.

        For almost 3000 years, astronomers have known of a third eclipse cycle. A correlation in a 19 solar-lunar year cycle (consisting of 235 new moons and 255 nodes) separates total eclipses belonging to different Saros families by exactly 19 years. Notice that the family designations also fall into a pattern. The family number of each successive eclipse in the 19 year cycle is ten more than its predecessor.
 

Table of Metonic Eclipse Cycles - Figure 2

10 July 1972 (Saros 126) + 19 years => 11 July 1991 (Saros 136) + 19 years => 11 July 2010 (Saros 146)
22 July 1990 (Saros 126) + 19 years => 22 July 2009 (Saros 136) + 19 years => 22 July 2028 (Saros 146)
30 June 1973 (Saros 136) + 19 years => 30 June 1992 (Saros 146) + 19 years => 1 July 2011 (Saros 156)

        Eclipse families have beginnings and endings. Some families are active, some have ended, and some have yet to start. The beginning of the 21st century also saw the debut of Saros 156, whose first member appeared on July 11, 2011 as a partial eclipse observable at very high northern latitudes. Saros 145, the family of the "Big One", first made its appearance on January 4, 1639 as a very partial eclipse. The first total eclipse of the family occurred on June 29, 1927, and yielded a whopping 50 seconds of totality. The longest total eclipse of this family should occur on June 25, 2522, yielding 7 minutes, 12 seconds of totality, which is close to the theoretical maximum amount. The last total solar eclipse in the family should occur on September 9, 2648, producing 2 minutes 49 seconds of totality. Saros 145 family should end on April 17, 3009, as it started, with another very partial eclipse. All told, the Saros 145 family encompasses 77 eclipses spanning 1,370.3 years.

        Not only does an eclipse apparition of a particular family occur at different terrestrial longitudinal points, as an eclipse family matures, its member apparitions occur at different terrestrial latitudinal points as well. Odd-numbered families begin their cycles at high northern latitudes and end at high southern latitudes. For even-numbered families, the progression is reversed.
 

Table of Past, Present and Future Eclipses

Key: T=Total (duration), A=Annular, H=Hybrid [Annular/Total] (duration), P=Partial

Distant Past  

Not-so-distant Past  

Past/Present/Future  

Saros

30 June 1973 T (7:04)

11 July 1991 T (6:58)

22 July 2009 T (6:39)

2 Aug. 2027 T (6:23)

136

24 Dec. 1973 A

4 Jan. 1992 A

15 Jan. 2010 A

26 Jan. 2028 A

141

20 June 1974 T (5:09)

30 June 1992 T (5:26)

11 July 2010 T (5:20)

22 Juyl 2028 T (2:56)

146

13 Dec. 1974 P

24 Dec. 1992 P

4 Jan. 2011 P  

14 Jan. 2029 P

151

11 May 1975 P  

21 May 1993 P  

1 June 2011 P

12 June 2029 P  

118

     

1 July 2011 P

11 July 2029 P

156

3 Nov. 1975 P

13 Nov. 1993 P

25 Nov. 2011 P

5 Dec 2029 P

123

29 Apr. 1976 A

10 May 1994 A

20-21 May 2012 A

1 June 2030 A

128

23 Oct. 1976 T (4:46)

3 Nov. 1994 T (4:28)  

13 Nov. 2012 T (4:02)  

25 Nov. 2030 T (3:44)

133

18 Apr. 1977 A 

29 Apr. 1995 A

9-10 May 2013 A

21 May 2031 A

138

12 Oct. 1977 T (2:37)

24 Oct. 1995 T (2:15)

3 Nov. 2013 H (1:39)

14 Nov. 2031 H (1:08)

143

7 Apr. 1978 P

17 Apr. 1996 P  

29 Apr. 2014 P

9 May 2032 A

148

2 Oct. 1978 P  

12 Oct 1996 P  

23 Oct. 2014 P  

3 Nov. 2032 P  

153

26 Feb.1979 T (2:49)

9 Mar. 1997 T (2:54)

20 Mar. 2015 T (2:47)

30 Mar. 2033 T (2:37)

120

22 Aug. 1979 P

2 Sep. 1997 P

13 Sep. 2015 P

23 Sep. 2033 P

125

16 Feb.1980 T (4:12)

26 Feb.1998 T (4:13)

9 Mar. 2016 T (4:09)

20 Mar. 2034 T (4:09)

130

10 Aug. 1980 A

22 Aug. 1998 A

1 Sep. 2016 A

12 Sep. 2034 A

135

4 Feb.1981 A  

16 Feb.1999 A  

26 Feb. 2017 A  

9 Mar. 2035 A

140

31 July 1981 T (2:06)

11 Aug. 1999 T (2:27)

21 Aug. 2017 (2:40)

2 Sep. 2035 T (2:54)

145

25 Jan. 1982 P  

5 Feb. 2000 P  

16 Feb. 2018 P  

27 Feb. 2036 P  

150

21 June 1982 P  

1 July 2000 P  

13 July 2018 P  

23 July 2036 P  

117

20 July 1982 P  

31 July 2000 P  

11 Aug. 2018 P  

21 Aug. 2036 P  

155

15 Dec. 1982 P  

25 Dec. 2000 P

6 Jan. 2019 P  

16 Jan. 2037 P  

122

11 June 1983 T (5:11)

21 June 2001 T (4:57)

2 July 2019 T (4:33)  

13 July 2037 T (2:40)

127

4 Dec. 1983 A  

14 Dec. 2001 A 

26 Dec. 2019 A  

5 Jan. 2038 A  

132

30 May 1984 A  

10 June 2002 A

21 June 2020 A  

2 July 2038 A  

137

11/22/84 T (1:51)  

4 Dec. 2002 T (2:04)  

14 Dec. 2020 T (2:10)  

26 Dec. 2038 T (2:18)

142

19 May 1985 P  

31 May 2003 A  

10 June 2021 A  

21 June 2039 A  

147

12 Nov. 1985 T (1:58)

23 Nov. 2003 T (1:57)

4 Dec. 2021 T (2:06)  

15 Dec. 2039 T (1:51)

152

9 Apr. 1986 P  

19 Apr. 2004 P  

30 Apr. 2022 P  

11 May 2040 P  

119

29 Mar. 1987 H (0:08)

8 Apr. 2005 H (0:42)

20 Apr. 2023 H (1:16)

30 Apr. 2041 T (1:51)

129

22 Sep. 1987 A

3 Oct. 2005 A

14 Oct. 2023 A

25 Oct. 2041 A

134

17 Mar. 1988 T (3:46)

29 Mar. 2006 T (4:07)

8 Apr. 2024 T (4:27)

20 Apr. 2042 T (4:51)

139

11 Sep. 1988 A

22 Sep. 2006 A

2 Oct. 2024 A

14 Oct. 2042 A

144

7 Mar. 1989 P

19 Mar. 2007 P

29 Mar. 2025 P

9 Apr. 2043 P

149

31 Aug. 1989 P

11 Sep. 2007 P

21 Sep. 2025 P

3 Oct. 2043 P

154

26 Jan. 1990 A

7 Feb. 2008 A

17 Feb. 2026 A

28 Feb. 2044 A

121

22 July 1990 T (2:36)

1 Aug. 2008 T (2:28)

12 Aug. 2026 T (2:18)

23 Aug. 2044 T (2:04)

126

16 Jan. 1991 A

26 Jan. 2009 A

6 Feb. 2027 A

16 Feb. 2045 A

131


       The 19 year and 354 day cycles start with the lowest Saros family number; thus, there was no solar eclipse of any type 354 days before the partial eclipse of July 1, 2000. The 354 day cycle coincidentally began with the end of the second millennium.

        Saros 117 is the smallest Saros number on the table, and the oldest family currently appearing as Saros family 116 ended on July 22, 1971. The Saros 117 family will end this century with a partial eclipse on August 3, 2054.  The largest Saros family is 156, which began only a few years ago. Both families are producing only partials. Notice how 354 days separate the Hybrid Eclipse of April 20, 2023 (Saros 129) from the Total Eclipse of April 8, 2024 (Saros 139 - the potential Great Buckeye Eclipse), and 18 years, 11.33 days separate each apparition of each Saros family member.

        The beauty of total solar eclipses is matched only by the mathematical precision of their predictability. We must marvel at the ingenuity of the scientists who demonstrated that the movement of the Sun, Earth and Moon can produce such an awe-inspiring sight that is really quite harmless (unless you look at the Sun during the partial phases). Even the Antikythera mechanism included a Saros scale for calculating eclipse predictions. Knowing when and where they will occur means we can observe one or more in our lifetimes. Which begs the question: where will you be for the Big One? Of course, we in central Ohio could wait until the next appearance of Saros 139, but April in these parts does not hold out much promise for clear skies. Get to the centerline for Big One and make a memory that lasts a lifetime. ☼

 

Back to Eclipse Main Page

 

Back to Astropix Main Page