Astronomy
Motions of the Moon: Months and Eclipses
Weblecture
The Motions of the Moon
Lunar Phases, Months, and Eclipses
- Introduction
- A little orientation exercise...
- Lunar Motion and the Moon's Many Months
- Practice with Concepts
- Discussion Questions
- Optional Website Reading
Introduction
After this, because Alyattes refused to surrender the Scythians despite the ongoing pleas of Kytaxares, a war ensued between the Lydians and Medes over a period of some five years. During this time on some occasions the Medes won a battle over the Lydians, while on other occasions the Lydians prevailed over the Medes. They even engaged in a battle by night. While they were still struggling for the upper hand in this war, during a battle begun in the sixth year, it happened that when the fighting had been joined, day suddenly became night. A prediction that this inversion of the day was going to happen, was made publicly by Thales of Miletus in announcements to the Ionian people; he proposed exactly the same period favorable for it as the one in which the omen actually occurred. When the Lydians and Medes alike saw that it had become night in place of day, they broke off the battle and hastened on both sides with even more speed to bring about peace for themselves.
- Herodotus, Histories, Book VII
A little orientation exercise....
To understand the Moon's phases, you (Earth) need to play with a light source (Sun) and another person (Moon). Start by facing the light source and putting your friend between you and the light: this is the "new Moon" position. The other side of the person is lit up, and you see only a side in shadow. Now move the person and turn so that the person is still in front of you and facing you, but the light source is on your right. This is equivalent to the first quarter phase, when the Sun is setting on the western horizon, and the Moon is due south and half-lit on the western (right) side. Now move so that the person is still in front of you and facing you, but the light source is behind you. The full front of the person is lit up (except where your shadow falls on him or her), and the Sun is at "midnight" position. This is equivalent to the full Moon. Finally, move until the light source is on your left and the person is in front of you and facing you. This is third quarter, with the Sun rising in the east but the Moon already high in the sky, and half-lit on the left side.
Notice that throughout this exercise, you never saw the back of the person. For this to happen, the person had to rotate or turn slight as he or she moved around you, making one complete rotation (spin around its own axis) for each complete revolution (trip on orbit around the central body). When the rotation and revolution are related by a simple fraction (here 1:1), we say that the rotation is synchronized. The Moon's relationship to Earth is synchronized at 1:1; Mercury's to the Sun is synchronized is synchronized at 3:2. In contrast, the Earth's rotation:revolution is 365.25:1, a complex relationship.
Lunar Motion and the Moon's Many Months
The Moon's orbit lies in a plane that is tilted just a little from the plane of the Sun's "orbit". Think of the plane of Sun's "orbit" (really the position of the Sun as the Earth moves) as a plate, with the Earth at the center (a small apple) and the Sun on the edge (a light buble). From the apple's (Earth's) point of view, the Sun moves around the edge of the plate once each year. Now put the Moon (a smaller apple) on the plate. It moves around the Earth once a month, sometimes between the Earth and the Sun, sometimes on the other side of the Earth from the Sun.
Phases: The Synodic Month
The Moon itself doesn't emit light; it reflects light from the Sun back to Earth, if it is in the right position to do so, and sometimes Earth's own reflected Sunlight from its darkside back to Earth. Because of the Moon's motion around the Earth, the amount of lighted surface reflecting Sunlight changes over the course of its orbit. When it is between Earth and the Sun, the far side of the Moon is lit up, but we can't see it. When it is opposite the Sun in the sky, the full facing side of the Moon is lit up. So one way to track its position is to consider where it is in the sky relative to the Sun, as seen from Earth.
Each night the Moon moves eastward against the background stars, rises a little later, and a little more of its lit-up face becomes visible from Earth. Eventually it rises at Sunset, on the opposite side of the Earth from the Sun. This is the "full Moon". After this point, the lit-up side of the Moon shrinks, and it rises after midnight. If you get up early, you can see this third-quarter Moon in the morning just before (and sometimes after) dawn.
The Moon's Synchronous Orbit
The Moon not only revolves around the Earth, but rotates once on its axis each revolution. This one orbit-to-one revolution whole number ratio is called a synchronous orbit. It occurs in the case of the Earth and its Moon because tidal forces acting on the Moon have slowed down its rotation since the formation of the Earth-Moon system. The current 1:1 ratio is a "low-energy" configuration which conserves angular momentum in the system. It would take an immense amount of work to shift the current synchronous configuration to one where the Moon spins faster or slower than its revolution period.
As we shall see, synchronous orbits occur in other situations within the solar system.
Position Against the Background Sky: The Sidereal Month
Another way of tracking the Moon's revolution concerns its position relative to the background sky, rather than relative to the Sun. Because the Earth revolves in space around the Sun and carries the Moon with it, the Moon's position against the background stars changes as a different rate than its position relative to the sun. Its sidereal month, counting from the moment it is in position in front of a particular fixed star t the next time it is back in that position, is slightly shorter than the synodic month, just as Earth's sidereal day is slightly shorter than its solar day.
Position Against the Background Sky: The Tropical Month
But any "fixed" star is itself moving in space with "true" motion relative to the stars around it, and to us. So yet another way to determine the Moon's motion against the background sky, which is slightly more accurate, uses the vernal equinox point, rather than stars. This point is of course, moving too, because of precession; in most cases, however, its motion is less than the motion of any star we might use to determine the sidereal month. So if extreme accuracy is required, some astronomers will use a tropical month rather than the sidereal month for calculations of the Moon's motions.
The Moon's Elliptical Orbit: The Anomalistic Month
The Moon's orbit is somewhat elliptical and variable. For example, it ranged from a short axis semi-diameter of 357207 km (221958 miles) to 406603 km (252651 miles) in 2017, but from 356565km (shortest perigee on Jan 1, 2018) to 406459km on Jan 15, 2018. This means that at perigee, it is closer to the Earth by about 49000 km (30700 miles) than at apogee. It appears roughly 14% larger in diameter and about 30% bright than when it is at apogee. The January 1, 2018 perigee coincided with a full moon, making this a "super moon".
It also means we have another way of calculating the lunar month, from perigee to perigee. This is the anomalistic month.
Position Relative to the Ecliptic Plan: The Draconic Month
The plane of the Moon's orbit isn't quite on the plane of the Sun's orbit (think about our plate example); sometimes the Moon is above the plane, and sometimes it is below. The two points at which the Moon's orbit crosses the plane of the Sun's orbit are called nodes. The ascending node is where it crosses from "below" the ecliptic plane (as see from Earth) to above the ecliptic plane. Half a month later, it passes through the descending node as it crosses the ecliptic plane again. The period between two successive passes of the ascending node is the draconitic month.
So, if you are making plans to meet one of your fellow astronomy students in a month, you might need to be a bit more specific!
| Month | Measurement | Length |
|---|---|---|
| Synodic | New moon to new moon | 29.53088 days |
| Sidereal | Star position back to same star position | 27.32166 days |
| Tropical | Vernal equinox position back to same position | 27.32158 days |
| Anomalistic | Perigee to perigee position | 27.55455 days |
| Draconic | Ascending node back to ascending node | 27.21222 days |
Solar Eclipses
For an eclipse to occur, two conditions have to be met; a third governs the kind of solar eclipse that will occur.
- The Moon must be on the line from the Sun to the Earth (on either side of the Earth), at new Moon or full Moon.
- The moon must be at one of its nodes (where the orbit of the Moon crosses the orbit of the Sun), so that it lie directly between the Earth and the Sun
- The Moon's position relative to perigee determines whether the disk of the Moon will be large enough to cover the Sun's face for a solar eclipse, or small enough to fit into the Earth's shadow for a lunar eclipse.
In August, 2017, the Moon moved into position for a total solar eclipse visible across the entire United States. The left diagram shows the Moon's position relative to the Earth on August 14, one week prior to the eclipse, when the Moon was in third quarter and near the lowest declination below the ecliptic plane.
As the week passed, it moved toward new Moon phase, and also toward the ascending node position, so that on August 21, it lined up precisely, meeting conditions #1 and #2 above.
Because the Moon is moving so quickly in the sky, it crosses the surface of the Sun in just a few hours. From the start to the end of an eclipse takes at most 3 hours, and the longest time the Moon can cover the Sun entirely is about 7 minutes. During this time, however, properly equipped observers can look at the Corona of the Sun—the outer atmosphere that is usually lost in the brighter light from the Sun's surface. The shadow cast by the Moon on the Earth is small, and only people directly in the path of that shadow will see the total eclipse. People near the edges will see the Moon cover only part of the Sun. To everyone else, the Sun will appear normal.
Solar eclipses do not occur every new Moon because the Moon is usually above or below the Sun's orbit. When they do occur, both professional and amateur astronomers may travel halfway across the world to view and record the eclipse and study the Sun's corona and other phenomena visible only during these events.
Lunar eclipse
When the Moon is on the far side of the Earth from the Sun (full Moon) and near a node, it passes through the Earth's shadow. While it doesn't disappear entirely, its surface becomes red and then dark. Because the Earth's shadow is much larger than the Moon's, lunar eclipses occur more frequently than solar eclipses. Also, because the Earth itself is casting the shadow, everyone on the night side of the Earth will see the lunar eclipse.
The Moon moves around Earth, coming close to Earth (perigee) and moving further away (apogee) as it goes around the ellipse. Because the Earth is in motion around the Sun and with respect to the stars, the time it takes the Moon to go around its orbit with respect to the perigee point is not the same as the time it takes to go from new Moon to new Moon, or from one position against the background of stars back to the same position (as observed from Earth). The period between new Moons is called the synodic month, and is somewhat longer than the period between two successive passes of the same star (sidereal phase).
The nodes are in motion around the Earth as the Moon's orbit precesses slowly around the Earth; the Moon is in orbit on that path, and the Earth is in orbit around the Sun. Thus the period between two eclipses is a combination of the lunar month (phase to phase) and the nodal revolution (point to point with respect to the Sun). The pattern of solar and lunar eclipses, called the Saros cycle, repeats every 18 years, 11 1/3 days. This means that if there is a total solar eclipse on a certain day, there will be a total solar eclipse 18 years, 11 days, and 8 hours later.
Other types of conjunctions: Occultations and transits
Any time two moving bodies come together in the sky, we have a conjunction. Often these involve one solar system body moving in front of another, or in front of a bright star. When the Moon or a planet moves in front of small celestial object (not the Sun), the event is called an occultation, because the eclipsing body is larger and completely hides the object. When a planet comes between the Earth and the Sun directly, or a Moon comes between Earth and its planet, the event is a transit, because we can watch the front object move across the rear object's disk.
Eclipses, occultations, and transits are all important events in determining the orbital paths of bodies in the solar system. Aristotle used observations of lunar eclipses and the position of the Sun and Moon in the sky to show not only that Moonlight had to be reflected Sunlight (since Moonlight disappeared when the Earth came between the Moon and Sun), but also that the Earth had to be a sphere, since that was the only shape that could throw a circular shadow on the Moon no matter what the orientation was.
Practice with the Concepts
Discussion Questions
- Why would occultations or transits provide information about the location of an object?
- What would you see happening on Earth if you were on the Moon during a solar eclipse? During a lunar eclipse?
Optional Readings
- The International Astronomical Union has an Eclipse page listing details for lunar and solar eclipses for the next 3 years.
- Notable eclipses are discussed at the Time and Date Solar Eclipses in History site.
- You can also see pictures of the last major total eclipse of the Sun, August 11, 1999, which affected observers from Cornwall, England, to Iran.
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