This work was created by Dr Jamie Love and Creative Commons Licence licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Eclipses (Part 1)

by Dr Jamie Love Creative Commons Licence 1997 - 2011

Now that you understand an orbit's shape (elliptical) and tilt (inclination) from last month's lesson on orbits, it's an appropriate time to teach you about occulations and eclipses.

There are a lot of planets and moons moving around in the Solar System and all of them follow specific, very predictable orbits. Sometimes one object passes in front of another. You will recall that when one celestial body covers another we call it an occultation. This is a "line-of-sight" effect meaning that an occulation occurs due to the geometry of the two objects and the observer. Clearly, occulations are part of what I call "observational astronomy". These are an astronomical event that has to do with the position of the observer and has nothing to do with the properties of the objects involved (other than their positioning with respect to the observer).

An occulation is an unusual event because it depends upon the "lucky" situation of the two objects (the one occulating and the one being occulated) sharing the same declination (which you learned about in February) and right ascension (which you learned about in January). Think about that for a moment because it bears repeating. Occulation occurs when the two objects have the same RA and declination.

Several months ago I told you how the monthly motion of the Moon causes it to occulate many stars and occasionally the Moon will occulate a planet. The Moon is the largest object in our night sky and it moves so quickly that it is a major "occulater".

Hey, I thought Jupiter was bigger than the Moon?

It is. Lots of planets are bigger than the Moon (and move faster). Notice I used the expression "in our night sky".
In this lesson we will be limiting our attention to how things appear from the face of the Earth "in our night sky". (That's why we use degrees or fractions of a degree to make these measurements.)

You will recall that the Earth-Moon system orbits around a common center of gravity called the barycenter but this point is inside the surface of the Earth so we tend to oversimplify the situation by thinking that the Moon simply goes around the Earth. For the purpose of this lesson, we can live with that simplification. (I just wanted to remind you about the barycenter. )

As the Moon orbits the Earth a very special type of occulation can be visible from our planet.
An eclipse is an occulation involving the Sun. More generally speaking, an eclipse is the blocking of light from any celestial body as it passes behind or through the shadow of another body. With regards to the Earth-Moon-Sun system, there are two kinds of eclipses - solar and lunar.

A solar eclipse happens when the Moon passes in front of the Sun, so a solar eclipse is simply the occulation of the Sun by the Moon. If you remember how the Moon's position determines its phases you will understand that only a New Moon can cause a solar eclipse because you must have a New Moon if the Moon and Sun are to have the same RA. [Right? Think about it.]

A lunar eclipse occurs when the Moon moves into the Earth's shadow, so a lunar eclipse is the occulation of the Sun by the Earth. Some might argue that, technically speaking, this isn't an occulation because you (the observer) are on the Earth and you are seeing the effect of the Earth's occulation of the Sun on the Moon. OK, fine. (I don't care. ) Regardless, if you were on the Moon you would see that during a lunar eclipse the Earth has occulated the Sun. [And, therefore, you would be experiencing a solar eclipse on the Moon. Wouldn't that be exciting?!] This backward way of thinking about lunar eclipses has one important effect on the coordinates of the eclipse. For a lunar eclipse to occur (as seen from Earth) the declinations must be the same (obviously) but the RAs must be exactly 12 hours apart. (That is 180o - on the other side of the sky.) That makes sense when you understand the geometry of a lunar eclipse and keep in mind how RAs are assigned. If you think about it you will realize that a lunar eclipse can only occur during a Full Moon.

Why don't we have a solar eclipse with each New Moon and a lunar eclipse with each Full Moon?

The RAs and declinations must match. These two coordinates must be very precise so let's introduce some new units that you will use here and in the remaining lessons.
You know that a circle is 360 degrees (360o) but degrees are too large for our purpose here. Instead we use small fractions of a degree. Each degree can be divided into 60 equal angles and each of these tiny angles is called a "minute of arc". Minutes of arc, or simply "arc minutes", are designated with a single quote mark like this '. Each arc minute can be further subdivided into 60 extremely tiny angles and each of them is called a" second of arc". Seconds of arc, or simply "arc seconds", are designated with a double quote mark like this ''.
So each degree has 60 arc minutes and 3600 (60 times 60) arc seconds.

Related to this exactness is the fact that we don't live in a flat Solar System. Let's start thinking in three dimensions and this will become clear.
For now, let's limit ourselves to discussing the geometry of a solar eclipse because it will simplify the discussion. We'll return to lunar eclipses later.

Once during each lunar cycle the Sun and Moon will share the same right ascension but they will not necessarily share the same declination. For an occulation to occur both the RA and declinations of the two bodies must be the same. So, let's put the 3rd dimension into our picture.

You will recall that the plane of the Earth's orbit around the Sun is called the ecliptic and there is no reason to expect any other object to orbit in the same plane as the ecliptic. Indeed, all the planets have orbits that are tilted with respect to the ecliptic and (you'll recall from last month's lesson) we call that angle of tilt the orbit's inclination.

The Moon's orbit is inclined to the ecliptic at an angle of 5o 9'. [That's 5 degrees and 9 arc minutes - much less than in my drawings.] That means that most of the time the Moon is not along the ecliptic so most of the time the Moon does not have the same declination as the Sun.

There are only two points in the Moon's orbit when it passes through the ecliptic and we call these points nodes. Most New Moons and Full Moons occur away from a node so there is seldom an eclipse because the declination is wrong.

Therefore, with each lunar cycle we have one chance for a lunar eclipse and one chance for a solar eclipse because the RAs will be correct, however the declinations are usually not the same. On the other hand, with each lunar cycle we have two chances for an eclipse (of one kind or another) because the declination will be correct (at the nodes) but the RAs are usually wrong so these node passages do not produce an astronomical "event".

These images may help you see the complexity of an eclipse's geometry.

Most of the time the Moon passes through a node with its right ascension far from that of the Sun.
We don't even notice it.

Sometimes the RAs during a node passage are close but not close enough.

The RAs and declinations must be within a fraction of a degree or no occulation will occur.
Sometimes the RAs and declinations are very, very close and a part of the Sun is occulated by the Moon.

We call that a partial eclipse. (There's another way to have a partial eclipse and we will get to it shortly.)

When the Moon passes through a node with the same RA as the Sun we might have a proper, total solar eclipse!

However, other conditions must be met.

What other conditions? If the RA and declinations are the same the Moon will cast a shadow on the Earth! Right?

Well, yes, sort of. To fully understand this I have to teach you a little bit about the physics and geometry of shadows.

If the source of the light is very small, what we call a "point source", the shadow produced by an object that blocks that light will have a sharply defined outline. This is the kind of shadow you create when you are making shadow puppets.
To get the sharpest shadow for your puppet use a tiny (but very bright) light. That way you have a "proper shadow" called an umbra.

On the other hand, if the source of light is very large, like the Sun, the shadow will have an umbra surrounded by a penumbra, a dim but not very dark shadow.

Penumbras are a common shadow in astronomy.
When the object occulating the Sun is spherical (like most natural objects in space) the penumbra forms a partial-shadow (dim) cone surrounding the main (dark) cone of the umbra.

Also, when the source of light is large, like the Sun, the shadows are more complicated and you can get different patterns by moving the screen (the object on which the shadow is projected).

For example, if we move the screen farther away, the size of the penumbra continues to grow.

That will probably come as no surprise but you may be surprised to discover that the umbra shrinks until it is a pinpoint.

However, if we continue to move the screen farther way the umbra reappears and grows larger!

The details of this have to do with the way light passes along the edge of the occulating object and I will not go further into it.

So what's this got to do with eclipses?

The Moon has an apparent diameter of roughly half a degree of arc.
[Many folks are surprised by that small value. Perhaps you feel the Moon must occulate a larger area of sky but you would be wrong. It's an easy mistake to make because your mind plays tricks with your perception of objects in the sky. Remember, your finger, held at arm's length, will cover about one degree of sky so you can easily hide the Moon behind your outstretched pinky! If you don't believe me, try it. And if you do believe me, try it anyway. That's what observational astronomy is all about!]

Of course, the Moon's orbit is not a perfect circle. It's an ellipse like the orbit of any natural satellite.
The point in the Moon's orbit at which it is farthest from Earth is called apogee. You'll recall that when a planet is farthest from the Sun we say it is at aphelion. The same "ap" applies here but now we are talking about the orbit around the Earth and we think of the Earth as "gee".
[By the way, "one gee" or "1G" is the term used to describe the force of gravity at the Earth's surface. It has nothing to do with the "gee" discussed here but I like to use that trick to remind myself that "gee" refers to the Earth.]
So, apogee is the farthest point from the Earth of any object orbiting the Earth whether it be the Moon or an artificial satellite.

The opposite of apogee is perigee, the point in the orbit at which the Moon or any Earth-orbiting satellite is nearest the Earth.

When the Moon is at apogee it is 406,697 kilometers away from the Earth and it has an apparent diameter of 29'22''. [That's 29 arc minutes and 22 arc seconds and you'll recall that there are 60 arc minutes in one degree of arc and there are 60 arc seconds in an arc minute.] At perigee, the Moon is only 356,410 kilometers away and that difference (of 50,287 kilometers) causes it to have a larger apparent diameter of 33'31''. This variation in the Moon's position and apparent size can have a huge effect on the eclipse.

During a total eclipse of the Sun the umbra forms a cone of shadow that just barely touches the Earth.
This can only occur when the Moon is pretty close to the Earth and it is thus able to block out more of the Sun.
Therefore, the Moon must be near perigee for us to enjoy a total eclipse.

Notice that the eclipse only appears as total on a very limited portion of the globe because the umbra just barely makes it to the Earth's surface. This means that a total eclipse is only at totality, the name for a total occulation, at a very particular location on Earth.

You have to be at the right place at the right time to experience the totality of a total eclipse. Careful calculations of the umbra's cone, along with other information about the Moon's orbit and the Earth's rotation, show that the path of totality can never be more than 272 kilometers wide and totality cannot last longer than 7 minutes and 31 seconds in any one place. Most total eclipses are considerably thinner and shorter than that. People outside the path of totality, but still within the penumbra, will experience a partial eclipse - only a portion of the Sun is hidden. You can go blind if you stare at a partial eclipse. NEVER STARE AT THE SUN, EVEN DURING A PARTIAL ECLIPSE!

What happens if the eclipse occurs near apogee?

Then we have an annular eclipse. Annulus is Latin for "ring" and it's a good name for this type of eclipse because the small disk of the Moon allows a ring of sunlight to shine through around the edge. An annular eclipse can last longer than a total eclipse - up to 12 and a half minutes.
[If you remember Kepler's Laws and understand that annular eclipses only occur during apogee, you will be able to figure out why an annular eclipse could last longer than a total eclipse. What did Kepler tell us about the speed of an object at its farthest point in its elliptical orbit? Give that some thought and you'll see that you are using what you have learned to truly understand more! The wide penumbral shadow, explained below, also causes an annular eclipse to last longer.]

Notice that in this geometry the cone of the umbra has already passed its "pinpoint" and is now expanding. You might think that this new cone would give you complete totality but you would be wrong. The light from the overlapping penumbra ruins the "totalness" so you get a ring.

Annular and partial eclipses are a dull and disappointing event (in my opinion) but a total eclipse is fantastic!

What happens during a total eclipse?

AMAZING THINGS!
To discover what those amazing things are, and to learn more about eclipses, continue on to part 2.




This work was created by Dr Jamie Love and Creative Commons Licence licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.