$$\def\|{&}$$

## 1. LunarEclipses

A lunar eclipse happens when the Full Moon travels through the shadow of the Earth. The shadow of the Earth points directly away from the Sun, so it is directly opposite the Sun in the sky and is only above the horizon at night. The shadow also points at the ecliptic because the Sun travels along the ecliptic, too. Because the shadow is dark you usually don't see it, but if some thing such as a satellite or an airplane or the Moon enters the shadow of the Earth then the thing goes dark, and when it exits the shadow again then it gets light again. It is night when we ourselves are in the shadow of the Earth.

[160]

## 2. The Color of the Eclipsed Moon

During a total lunar eclipse, the Moon moves through the umbral shadow of the Earth. Seen from the Moon, the Earth then completely covers the Sun. Yet, the Moon is not completely dark then, though it is much weaker and often looks much redder than it does before or after the eclipse. The light that comes from the Moon during a total lunar eclipse is sunlight that was bent towards the Moon by the atmosphere of the Earth. Seen from the Moon, the dark Earth then has a bright ring at its edge, similar to how the outermost hairs of someone else's head appear to shine if there is a bright light directly behind the head (so you can see the head but not the light).

The atmosphere is not equally transparent to all colors. Blue light is scattered much more easily by the atmosphere than red light (which gives the sky its blue color, see question 155) so much less blue than red light reaches the eclipsed Moon. The precise brightness and shade of color of the eclipsed Moon depend on the circumstances in the atmosphere of the Earth. For example, if there was a large volcanic eruption not long before the eclipse, then the color of the eclipsed Moon is often extra red.

[153]

## 3. SolarEclipses

A solar eclipse happens when the shadow of the Moon passes across the Earth. As seen from the Earth, the New Moon then passes in front of the Sun. If the Moon is very close to the Sun in the sky, then it is New Moon. A solar eclipse can happen only when it is New Moon, but there isn't a solar eclipse for every New Moon, just like there isn't a lunar eclipse for every Full Moon. There is only a solar eclipse if the Moon is close enough to a node of its orbit at the time of New Moon.

During a solar eclipse the shadow of the Moon passes across the surface of the Earth. As was explained above for lunar eclipses, there are two kinds of shadow, umbral shadow and penumbral shadow. Only people over whom the shadow sweeps see an eclipse. If the umbral shadow of the Moon sweeps over you then you see a total eclipse of the Sun, and if only the penumbral shadow comes your way then you see a partial solar eclipse. A partial solar eclipse can be normal (non-central) or annular (central). During an annular solar eclipse, the Moon appears slightly smaller in the sky than the Sun and can then at the climax of the eclipse cover the whole Sun except for a narrow ring (annulus) near the edge of the solar disk.

During a total solar eclipse it gets dark during the day and you can even see some stars and planets (if those are above the horizon then). During a partial solar eclipse it does not get dark but you can see that the Moon takes a "bite" out of the Sun (if you let the sunlight pass through a small hole to the ground or a sheet of paper).

The umbral shadow of the Moon on Earth is at most about 100 km across, so the total phase of a total solar eclipse is visible from only a very small part of the Earth. For people outside of that small area a total solar eclipse looks at most like a partial solar eclipse. Seeing the Sun as a bright ring during an annular solar eclipse is also only possible from a small area, and for people outside of that area an annular eclipse looks just like an ordinary partial eclipse. A partial solar eclipse is visible over a much larger area of the planet than the total phase of a total eclipse of the Sun, but still a smaller area than the average area from which a total eclipse of the Moon is visible. Some calculations with a planetarium program show that the fraction of all solar eclipses that can be seen from a certain location (if the weather cooperates) increases from about 12% at the equator to about 18% at the poles. For comparison: for lunar eclipses that fraction is slightly over 50%.

All of these types of solar eclipses occur. The type of a solar eclipse depends on the positions of the Sun and the Moon in the sky and on the distance of the Moon. Because the Sun and the Moon have almost the same apparent size in the sky and because the distance between the Earth and the Moon varies by about 11% during a month, the Moon is sometimes but not always too far away for a total solar eclipse, and then there is an annular solar eclipse instead.

If the Sun always seemed smaller in the sky than the Sun, then there would never be annular solar eclipses and then most solar eclipses would be total solar eclipses. If the Sun always seemed larger in the sky than the Moon, then there would never be total solar eclipses and then most solar eclipses would be annular solar eclipses.

The average distance of the Moon from the Earth is slowly increasing, at an average rate of (nowadays) about 4 centimeters per year. That means that the share of annular solar eclipses is slowly increasing and the share of total solar eclipses is slowly decreasing. Eventually, the Moon will be so far away from Earth that there won't be any total solar eclipses anymore, but this time is still very far off.

[586]

## 4. Time Between Successive SolarEclipses Seen From the Same Place

How long it takes to see another total solar eclipse or annular eclipse from the same place is not the same everywhere. Jean Meeus explains this on page 88 of his book [Morsels]. In July the Earth is furthest from the Sun, so then the Sun appears smallest in the sky, which is good for total solar eclipses and bad for annular solar eclipses. In July it is summer in the northern hemisphere of Earth and then the Sun is longer above the horizon (and thus visible) than average, which increases the chances of seeing a solar eclipse. The chances of seeing a solar eclipse are then decreased in the southern hemisphere. Therefore the northern hemisphere has a bit more solar eclipses (and so a shorter average time between successive solar eclipses) than the southern hemisphere, and the southern hemisphere has relatively more annular solar eclipses than the northern hemisphere does.

According to Meeus, the average time between two successive total solar eclipses seen from 80 degrees north latitude is 254 years, and between two successive annular solar eclipses it is 166 years. At the equator those periods are 388 and 275 years, and at 80 degrees south latitude they are 513 and 122 years. So, waiting for a total solar eclipse takes more time as you move southward from 80 degrees north latitude to 80 degrees south latitude. Waiting for an annular solar eclipse takes on average the most time at the equator, and less time toward the poles, and less time to the south than equally far to the north.

That annular solar eclipses occur relatively less frequently at the equator than near the poles is because a spot on the equator is on average closer to the Moon than a spot near the poles is, so as seen from the equator the Moon looks on average slightly bigger in the sky than it does from the poles, which is good for a total solar eclipse but bad for an annular solar eclipse.

## 5. Saros

There are patterns in the circumstances of solar eclipses and lunar eclipses, which you can use to predict them. Read more about this on the Saros Page.

[252] [412]

## 6. Eclipse Counts

There are on average about 2.44 lunar eclipses per year and 2.38 solar eclipses. So, there are about as many eclipses of the Moon as eclipses of the Sun, but you can see an eclipse of the Moon from more places than you can see an eclipse of the Sun, so you can see more eclipses of the Moon than eclipses of the Sun if you stay in one place.

You can see an eclipse of the Moon if the Moon is then above the horizon where you are. The chance of that is about 50% (if you are not between mountains or other tall things that block the sky, and if there aren't any clouds where the Moon is), because the Moon spends about as much time below the horizon as it does above the horizon, so you can see about one out of every two eclipses of the Moon.

You can see an eclipse of the Sun if the Moon goes in front of the Sun. Because the Moon is quite close to the Earth, it can seem to be in front of the Sun as seen from some places on Earth, but next to the Sun as seen from other places, just like your friend can block your view of the television even when your other friend who is sitting next to you has a clear view of the screen. So, even if the Sun and the Moon are both above the horizon where you are, you may still not see an eclipse even if people in some other places can see an eclipse. All in all, you can see about one out of every six eclipses of the Sun.

[491]

## 7. The Longest SolarEclipses

It is not easy to say how long the longest solar eclipse can get, because the motion of the Moon is very complicated and because the Moon is on average slowly receding from the Earth.

The distance between Earth and Moon is obviously very important in determining the characteristics of eclipses. The further the Moon gets from the Earth, the slower it moves along the sky relative to the Sun, which makes annular solar eclipses last longer. In the opposite direction, the closer the Moon gets to the Earth, the wider is the cone of the Moon's umbral shadow at the Earth's surface, which makes total solar eclipses last longer. The Moon is on average slowly receding from the Earth, so annular solar eclipses will keep getting longer, and if you wait long enough (millions of years) then there won't be any total solar eclipses anymore.

The distance between the Earth and the Sun is important, too. If the Sun is further away, then it appears smaller in the sky, which makes total solar eclipses last longer and annular solar eclipses last shorter.

Other factors besides the distances are also important. For example, the speed of the lunar shadow relative to the observer at the Earth's surface depends on the location of the observer and on the season, so the length of the solar eclipses will depend on those things, too.

Trying to figure all of this out on theoretical grounds is more work than I am willing to do. However, I did investigate which factors yield the greatest durations for solar eclipses based on calculations of real (past and future) solar eclipses between the years −1999 and +3000 by Fred Espenak (a database from 1999, obtained some time ago at //sunearth.gsfc.nasa.gov/eclipse/eclipse.html) and on some additional calculations of my own. I find that the single most important factor that determines the duration of solar eclipses is the ratio of the solar and lunar distances from the Earth.

Fig. 1: Solar Eclipse Duration vs. Distance Ratio
Fig. 1 displays solar eclipse duration $$P$$ (in minutes) versus the ratio $$d_☉;/d_\text{L}$$ of the solar and lunar distances, for 7529 solar eclipses that occur between the years −1999 and +3000. The blue dots are for total solar eclipses, the yellow dots for partial solar eclipses, and the red dots for annular solar eclipses. For convenience, the durations of annular solar eclipses are shown as negative. The black line shows the best linear fit, which is $$P = 0.2459 ((d_☉/d_\text{L}) − 397.54) ± 0.89$$.

Based on this data, solar eclipses are not total if the Sun is less than 400.7 times as far from the Earth as the Moon is. Annular solar eclipses need a distance ratio of less than 398.6.

The longest total solar eclipse in the database lasts 449 seconds (7 minutes 29 seconds), and the longest annular solar eclipse lasts 744 seconds (12 minutes 24 seconds).

[292]

## 8. The Path of the Shadow of the Moon during a SolarEclipse

Astronomers use fairly straightforward geometry to figure out where you can see a solar eclipse the best, but you need to know very accurately what the positions of the Sun, Earth, and Moon are in space, and especially the position of the Moon requires very many calculations to attain sufficient accuracy, because the orbit of the Moon is perturbed by the Sun and the oblateness of the Earth.

You can find useful references for eclipse predictions at //sunearth.gsfc.nasa.gov/eclipse/SEhelp/SERefer2.html. I believe that one or both of the "Canons" of eclipses mentioned in that list explain the mathematics as well, but it has been a while since I last saw them, so my memory may be wrong. I expect that the "Explanatory Supplement" also mentions at least some of the mathematics. You can probably find these publications in the library of an observatory or of a university that offers astronomy courses.

[556]

## 9. Eclipses and Seasons

On 21 December 2010 there was a lunar eclipse, very close to the astronomical beginning of winter (the southern solstice) in the northern hemisphere. Which solar eclipses and lunar eclipses occur close to the astronomical beginning of a season?

Table 1 shows the 10 solar eclipses between the years −1999 and +3000 that fall closest to the beginning of a season. In that table, $$a$$, $$m$$, and $$d$$ indicate the date (year, month, day) of the eclipse in UT, in the Julian proleptic calendar for years until 1583, or in the Gregorian calendar for years from 1584. $$Δ$$ indicates how many hours the middle of the eclipse is after the beginning of the season, $$t$$ is the kind of eclipse (T = total, A = annular, P = partial, H = hybrid or annular-total), and $$S$$ is the Saros number. The $$a, m, d, t, S$$ come from Fred Espenak (//eclipse.gsfc.nasa.gov/solar.html); I calculated $$Δ$$ (based on the VSOP87 theory) and the sorting.

Table 1: Solar Eclipses Near Season Start −1999..+3000

#
$${a}$$$${m}$$$${d}$$$${Δ}$$$${t}$$$${S}$$
1 −1293 7 5.70486 −0.1990965 T 35
2 1648 6 21.02917 0.2450669 H 131
3 488 9 21.44028 −0.4484816 P 71
4 2406 3 20.73611 0.5015207 T 136
5 −1646 7 8.22639 0.6261272 P 39
6 −1372 10 4.91042 0.7122782 A 41
7 2444 3 19.95972 0.7157272 A 156
8 1681 3 20.03681 0.8780178 H 134
9 −1019 10 2.70278 0.9623229 A 37
10 2816 3 20.06042 −0.9656824 A 162
11 1667 6 21.56667 −0.9849009 P 141
12 −934 3 30.34514 −0.9933122 P 53
13 −981 10 2.94444 1.053308 P 57
14 −1284 1 1.45625 1.060665 P 11
15 −562 3 27.56806 1.265401 A 59
16 −1363 4 2.51389 1.343891 T 17
17 −609 9 30.32431 1.556357 T 63
18 −1716 4 5.00486 1.732963 T 21
19 2072 3 19.83889 1.775413 P 150
20 2058 6 21.01181 −1.787082 Pb 157

For example, the solar eclipse of 5 July −1293 occurred closest (within the years −1999 to +3000) to the astronomical beginning of a season: only 0.20 hours = 12 minutes before the northern solstice. That solar eclipse was a total one and belongs to Saros number 35 (for solar eclipses).

The number $$N$$ of solar eclipses in a period of $$T$$ years that occurs at most $$Δ$$ hours from the beginning of a season is approximately equal to

$$N = \frac{TΔ}{460.4}$$

The standard deviation of the difference between the estimated $$N$$ and the real number is approximately $$T/644$$ (for $$Δ \lt 38$$ days).

If we declare a solar eclipse to be a "season-starting solar eclipse" if the middle of the solar eclipse is less than 24 hours before or after the beginning of a season, then there is on average one such eclipse for every 19 years.

Table 2 shows the same but then for lunar eclipses. The types of lunar eclipses are N = penumbral, P = partial, T = total, The Saros numbers for lunar eclipses are independent from the Saros numbers for solar eclipses: Saros 136 for lunar eclipses is not related to Saros 136 for solar eclipses. See Zie the Saros calculation page.

Table 2: Lunar Eclipses Near Season Start −1999..+3000

#
$${a}$$$${m}$$$${d}$$$${Δ}$$$${t}$$$${S}$$
1 −480 9 28.58194 0.1019854 N 29
2 354 6 22.25208 0.1200147 T+ 74
3 −670 12 27.93472 0.1827151 T+ 43
4 −13 9 25.92014 −0.367636 N 85
5 −1596 10 6.40208 −0.4261138 T 11
6 745 6 18.79444 0.4508774 T− 90
7 2559 6 21.15625 0.4619622 N 129
8 −32 9 25.30833 −0.5044727 P 75
9 −1804 1 4.95070 −0.5788091 P 15
10 712 9 19.73611 −0.6389349 T− 87
11 −37 6 25.64514 −0.9552749 T 58
12 −1492 4 3.24444 0.9565367 Nb 37
13 −1432 1 2.37708 −1.068024 T 21
14 −1517 7 7.50278 1.070906 P 5
15 359 9 23.23056 1.156471 P 91
16 −852 10 1.18403 −1.305026 N 23
17 −1224 10 3.78681 −1.456305 P 17
18 340 9 22.50625 −1.494296 T+ 81
19 2277 3 20.52361 1.656492 N 156
20 −1139 3 31.65000 −1.74935 P 33

For lunar eclipses, the number $$N$$ that occurs at most $$Δ$$ hours before or after the season start in a period of $$T$$ years is reasonably approximated by

$$N = \frac{TΔ}{449.8}$$

The standard deviation of the difference between the estimated $$N$$ and the real number is approximately $$T/581$$ (for $$Δ \lt 38$$ days).

Table 3 shows the same as table 1 but for all solar eclipses in the years 1800 through 2199 that occur less than 24 hours from the beginning of a season. The first one (after 2015) is the solar eclipse of 22 September 2052 that occurs about 16 hours after the beginning of the northern summer.

Table 3: Solar Eclipses Near Season Start 1800..2199

#
$${a}$$$${m}$$$${d}$$$${Δ}$$$${t}$$$${S}$$
1 2072 3 19.83889 1.775413 P 150
2 2058 6 21.01181 −1.787082 Pb 157
3 2034 3 20.42847 −3.0086 T 130
4 2053 3 20.29583 3.309431 A 140
5 2001 6 21.50278 4.433856 T 127
6 2039 6 21.71597 5.226623 A 147
7 1982 6 21.50278 −5.320129 P 117
8 2020 6 21.27778 8.936189 Am 137
9 1987 9 23.13264 −10.57486 A 134
10 1968 9 22.47083 −12.13774 T 124
11 1870 12 22.51944 12.2494 T 120
12 2015 3 20.40694 −12.98879 T 120
13 2052 9 22.98403 16.35426 A 135
14 2006 9 22.48611 −16.3931 A 144
15 2071 9 23.72083 19.66415 T 145
16 1862 12 21.20347 −20.42732 P 149
17 2033 9 23.57847 21.0218 P 125
18 1889 12 22.53750 22.03717 T 130
19 2025 9 21.82083 −22.62394 P 154

Table 4 shows the same as table 2 but for all lunar eclipses during the years 1800 through 2199 that occur less than 24 hours from the beginning of a season. The lunar eclipse of 21 December 2010 is number 16 from that list, and occurred about 15 hours before the beginning of the northern winter. The next one from the list after that eclipse is the lunar eclipse of 20 December 2029.

Table 4: Lunar Eclipses Near Season Start 1800..2199

#
$${a}$$$${m}$$$${d}$$$${Δ}$$$${t}$$$${S}$$
1 1872 6 21.27986 3.187031 Nb 147
2 1810 3 21.12153 −3.429062 N 100
3 1829 3 20.58889 −6.568755 P 110
4 1853 6 21.25139 −7.335881 P 137
5 2187 6 20.94306 −7.49129 P 123
6 2094 12 21.82847 10.64307 T− 136
7 1839 9 23.29028 −11.01835 N 144
8 1886 3 20.18333 −12.03735 N 140
9 1828 9 23.59722 12.17066 N 105
10 2192 9 21.62153 −13.42847 T− 140
11 1848 3 19.88333 −14.09663 T+ 120
12 2075 12 22.37014 14.42359 P 126
13 1834 6 21.34722 −14.86078 T+ 127
14 1815 6 21.75417 −14.87415 T 117
15 2113 12 22.62083 15.09944 P 146
16 2010 12 21.34514 −15.3609 T 125
17 2029 12 20.94514 −15.55267 T 135
18 1867 3 20.36736 −16.95572 P 130
19 1820 9 22.27431 −21.04829 P 134
20 2056 12 22.07431 21.92079 N 116
21 1847 9 24.60694 22.19459 P 115
22 1991 12 21.43958 −22.34792 P 115
23 2048 12 20.26806 −22.60417 N 145
24 2173 9 21.61389 −23.29606 P 130
25 1894 3 21.59792 23.3639 P 111