Illustrated Astronomy/Eclipses
IV
ECLIPSES
Eclipses are spectacular astronomical events. Not only amaze us with an intense color variation of the Moon or, even more astonishing, change into full darkness during a few minutes in broad daylight, but also, we can see in real-time the stars motion when, for instance, the Moon stands between the Sun and us, or when the Earth stands between the Sun and the Moon.
In general terms, there are two types of eclipses: Moon eclipses and Sun eclipses[1].
There are three types of Sun eclipses, and they distinguish from one another depending on the occultation type of the Moon and the Sun.
Total eclipses: refers to when the Moon blocks the Sun entirely during the full eclipse.
Annular eclipses: refers to when the Moon is farther from the Earth, and its shape doesn’t block the Sun completely, leaving a Sun ring around the Moon.
Hybrid eclipses: refers to when the Moon is just in the distance where it can completely block the Sun, however, as it moves forward, it moves slightly away from the Earth, and stop eclipsing the Sun, becoming into an annular eclipse. It can start either as an annular eclipse, and then moving a little to become in a total eclipse.
HOW DO ECLIPSES OCCUR?
Both solar and lunar eclipses occur when the Sun, the Earth, and the Moon are in the same line. We talk about lunar eclipses when the Earth gets on the way of the sunlight, darkening the Moon completely. In the case of solar eclipses, the Moon is the one who gets on the way of the solar light before reaching the Earth.
A Moon eclipse is visible from anywhere on the terrestrial globe that is on the same side as the Moon, whereas a solar eclipse is only visible from a small part of the Earth since our planet is larger than the Moon, so that it can hide the sunlight from the whole surface. In the case of the Moon, since it is smaller in size, it blocks the sunlight entirely in a very vast region of the Earth, and partially in a broader region (which we called as a partial eclipse of the Sun).
The lunar eclipses always occur in Full Moon, whereas solar eclipses occur in New Moon because only in that position they are entirely in line.
To understand this better, let’s review the following figures:
It takes about 29 days for the Moon to orbit the Earth. That is enough time for our satellite, after a lunar cycle, not to be able to cast a shadow on the Earth again, and therefore there is no new eclipse.
In the following picture, we see as the Earth or the Moon block the sunlight, respectively.
According to what is observed and reviewed in chapter III on this book, every 29.53 days, a New Moon or Full Moon happens. But, why eclipses do not happen every time this occurs? Because Earth is revolving around the Sun in a plane (called ecliptic), and the Moon is orbiting the Earth in another plane, slightly leaned in comparison to the first one. Both planes are only 5° apart. It seems to be a mild inclination, however, it is enough for the shadows of the Moon or Earth to fall out of the other object.
Today, we can predict eclipses in advance thanks to accurate calculations, using math formulae, and what we know about physics. In contrast, in the past, some civilizations could predict eclipses identifying different patterns in the lunar motions fruit of their acute observation power and their accurate notes about past events.
Around the 4th century BC, the wiser Chaldean astronomers/astrologists of the new Babylon identified what Greeks later would call saros, which was related to the period of 223 moons, in other words, 18 years, 11 days, and 8 hours. These wise people noticed that every time a saros happened, the position of the Sun, Earth, and Moon were alike and, therefore, the same series of eclipses repeated, but these would not be in the same place as Earth since the cycle doesn’t have whole numbers of days, but it has eight more hours. Within those eight hours, the Earth has rotated one-third (eight hours on the twenty-four a day has), and therefore the eclipse occurs in one-third of Earth towards the west. For instance, if today an eclipse in Concepción, Chile, occurs, in one saros should be in New Zeeland.
Based on this, one would expect that every three saros (something like 54 years) a new solar eclipse would happen in the same region. However, it is not entirely correct due to small differences, and other celestial motions related. In fact, on average, a region of the Earth experiences a total eclipse of Sun every three hundred years.
Nowadays, we know much better about the physics laws of celestial bodies, and the motions of the planets and their satellites are calculated precisely.
The Sun gravity forces, the eight planets and their satellites, asteroids, and dwarf planets are included to make more accurate calculations. Also, tidal effects, Earth distribution mass (which is not perfectly homogenous), and the terrestrial motions and precession and nutation, among others, are included in the motion calculations.
DID YOU KNOW THAT…
the duration of an eclipse depends on Earth’s position compared to the Sun, on Moon’s in respect of the Earth, and on what Earth’s region is shade? Theoretically, the longer solar eclipse could last 7 minutes and 32 seconds. So far, the longest ever registered was on July, 15th of 743 B.C., and lasted 7 minutes, 28 seconds.
On July, 16th of 2186, it is expected a total solar eclipse will pass over Venezuela, lasting 7 minutes, 29 seconds, becoming the longest eclipse since 4000 B.C., and it will be until the year 6000 A.D., at least.
THE FUTURE OF ECLIPSES
Both the Earth and the Moon attract one another. However, this attraction has not been constant since both formed, and the distance between them has continually changed. Actually, as we saw in chapter III, the Moon moves away four centimeters per year from Earth, which confirms that in the distant past, the Moon was much closer to Earth, and in the future, it will be much further.
What are the consequences of this? In a distant future, we no longer can be witnesses of total solar eclipses since the Moon, even in its closest-to-the-Earth position, it won’t be able to block the Sun completely, and there will be only annular or partial eclipses.
NUTATION AND PRECESSION MOTIONS
Precession is a terrestrial motion that occurs because Earth is not a perfect homogenous sphere, so as a result, the rotation axis changes over time. To imagine this movement, watch a whistling top spin. It could be expected only to spin, but in reality, the whistling top, besides spinning, its rotation axis is in a circular motion, like a nodding kind of thing, and that motion is exactly what happens to Earth. If we were able to go through it with a gigantic pencil, which could draw a line in the sky, we would see a circle, and the process of drawing that line would take around 26,000 years.
This phenomenon (known as “axial precession”) was described by the great Greek astronomer and mathematician, Hipparcos, in the 2nd century B.C., who was based on observations that Babylonian astronomers and astrologists carried out. Hipparcos realized that the position of the stars during equinoxes was slightly different from the ones observed by astronomers in the past, and he calculated that it should move 1° per century (the value given today is 1.38° per century). In the 4th century A.D., this phenomenon was also explained by the astronomer Yu-Xi from the Jin dynasty, in China. In spite of these insights, the answer to why precession occurred remained unknown, and only because of the studies of celestial mechanics by Isaac Newton, it could be understood fully: the precession refers to the forces that the Sun and the Moon cause on Earth, and to Earth being a non-perfect spheroid.
On the other side is nutation, which is a motion overlapping precession. It happens mainly for a gravitational attraction that Earth feels towards the Moon and Sun[2] and, mainly, due to its 5° inclination of the plane in which the Moon orbits the Earth regarding the plane where the Earth orbits the Sun.
To sum up, these two motions are caused by the rotation of the Earth on its axis and its non-perfect sphere shape. In this motion, the Moon creates a small extra distortion because it is not aligned correctly with Earth’s orbit.
Something else about tides
There is a force known as the tidal force, and it occurs since the gravity force gets weaker while things are separated by greater distances. This difference in the distance also makes a difference in the gravitational attraction among two points, making the closer region higher and the opposite region lower. That is the reason why the tidal force “faint” too fast, but is stronger when the distance between the involved bodies is short.
For instance, in the case of the Earth and the Moon, we say that its distance is, on average, 384,000 km. However, that is measured from the Earth’s core to the Moon’s core. If we measure from the surface (without counting the distance between the center and the last mentioned), the Moon is 6700 km closer, whereas who is on the other side of the Moon is 6700 km further regarding the center of the Earth.
As we have seen, both gravity and tidal force decrease according to the distance. For example, if we increase the distance between two objects twice, the gravity force slows down four times, rather the tidal force does the eighth part. If we increase the distance five times between these objects, gravity decreases 25 times, but the tidal force does 125 times!
Then, we can confirm that the gravity force drops with the distance squared, whereas the tidal force does with the distance cubed. For that reason, the region of the Earth that is straight towards the Moon is under more attraction, the regions in the middle are under a “neutral” force, and the further region is under less attraction. For that very reason, high tides occur in the region that directly faces the Moon and, in the opposite-in-diameter part.
It is essential to have in mind that the tidal force is related to gravity, and it is a consequence of gravity acting on sized objects.
1 · The Moon and the Sun seem to be the same size, that is the reason why total and annular eclipses happen. If both Sun and Moon’s sizes are known, can we know at which distance is each from the Earth?
2 · At what distance must be the Moon from the Earth for a total and an annular eclipse to occur? Does it depend on Earth-Sun distance?
Answers
The Earth is an elliptical (almost circular) orbit around the Sun, just like the Moon around the Earth. The maximum and minimum distances from the Earth to the Sun are 147 and 152 million kilometers, respectively, and the Sun has a diameter of 1,391,400 km.
For the Moon, the minimum and maximum distances to the Earth are 356,500 and 406,700 km, and it has a diameter of 3474.2 km.
With these numbers, we can calculate the angular sizes (the apparent size we see in the sky measured in grades) using the following math relation:
Angular size = tangent (diameter / distance)
If we replace the values mentioned above, we find that the angular sizes are: -Maximum size of the Sun (when it is closer) = 32.54 minutes of an arch (0.54°).
Minimum size of the Sun (when it is further) = 31.47 minutes of an arch (0.52°).
Maximum size of the Moon = 33.50 minutes of arch (0.56°).
Minimum size of the Moon = 29.37 minutes of arch (0.49°).
We can see that if the Moon is at a minimum distance from the Earth, it doesn’t matter at what distance is the Earth from the Sun if the conditions form an eclipse are given, the total eclipse is seen. Whereas if the Moon is at its furthest distance from the Earth, a total eclipse would never happen, only annular (and partial), no matter the distance Earth-Sun.
For any other middle point, it is necessary to analyze in detail the relative distances of the three bodies.
3 · How much longer will it take to stop producing eclipses?
In order to never experience an eclipse again, we have to imagine ourselves in the worst possible scenario. Even when the Moon is the closest to Earth, and the Earth the farthest from the Sun, the Moon looks smaller than the Sun.
Let’s suppose that both of them don’t change their sizes, that the orbit of the Earth remains constant, and the Moon is the only one moving away.
In this case, the minimum size of the Sun is 31.47 minutes of arc, and to have no more eclipses the rule is that the Moon, in its maximum size, must be lower than that.
Then: Angular size = 31.47 = 0.54° =
tangent (diameter / distance).
So, how do we know what size the Moon is (diameter)?
At this distance, the Moon won’t be able to eclipse the
Arctangent (0.54°) = 3474.2 kmdistance
0.0091 = 3474.2 kmdistance
0.0091 = 3474.2 kmdistance = 379.530 km
Sun completely!
If we suppose that the Moon will keep moving away 3.8 cm per year as it does today, it would have to pass 715 million years to experience no more a total eclipse of the Sun. It will be right, even when the Moon is to the closest distance to Earth, and the Earth to the furthest distance from the Sun (that is, the Moon being the largest ever possible, and the Sun the tiniest ever possible).
Although, in fact, the process is a little more complicated because as the Moon moves away from the Earth, the tides are slightly weaker, and, as a result, the Moon moves slower away, which would increase the time we have to keep observing total eclipses. However, in that timescale, the Sun would not be the same size, actually, it would grow a little bit, accelerating the effect that the Moon produces when moves away. As a consequence, the change of the Sun size would accelerate the process to leave us without total eclipses in about 500 million years more.