The Earth's Moon

The Moon is the nearest body to us in the Solar System, and as a consequence of the Apollo missions is the only extra-terrestrial object that has yet been explored directly by humans. As a consequence of that exploration by both manned and unmanned spacecraft, we now know a great deal about our nearest celestial neighbor.

Here is an interactive viewer which displays views of the Moon from the Earth, Sun, night side, above named formations on the lunar surface, or as a map showing day and night (Credit: John Walker).

Intrinsic and Orbital Properties

The mass of the Moon is about 1/80 that of the Earth, and its diameter is about 1/4 that of the Earth. The orbit of the Moon is very nearly circular (eccentricity ~ 0.05) with a mean separation from the Earth of about 384,000 km, which is about 60 Earth radii. The plane of the orbit is tilted about 5 degrees with respect to the ecliptic plane. The Apollo missions to the Moon left devices that can reflect laser light sent to the moon from the Earth. By timing the roundtrip of such light, it is possible to determine the distance to the Moon at any particular time with an uncertainty of only a few centimeters (!).

Since the synodic rotational period of the Moon is 29.5 days, Lunar day and Lunar night are each about 15 Earth days long. During the Lunar night the temperature drops to around -113 degrees Celsius, while during the Lunar day the temperature reaches 100 degrees Celsius. The temperature changes are very rapid since there is no atmosphere or surface water to store heat.

Orbit and Phases

The orbit of the Moon is very nearly circular (eccentricity ~ 0.05) with a mean separation from the Earth of about 384,000 km, which is about 60 Earth radii. The plane of the orbit is tilted about 5 degrees with respect to the ecliptic plane.

Revolution in Orbit

The Moon appears to move completely around the celestial sphere once in about 27.3 days as observed from the Earth. This is called a sidereal month, and reflects the corresponding orbital period of 27.3 days The moon takes 29.5 days to return to the same point on the celestial sphere as referenced to the Sun because of the motion of the Earth around the Sun; this is called a synodic month (Lunar phases as observed from the Earth are correlated with the synodic month). There are effects that cause small fluctuations around this value that we will not discuss. Since the Moon must move Eastward among the constellations enough to go completely around the sky (360 degrees) in 27.3 days, it must move Eastward by 13.2 degrees each day (in contrast, remember that the Sun only appears to move Eastward by about 1 degree per day). Thus, with respect to the background constellations the Moon will be about 13.2 degrees further East each day. Since the celestial sphere appears to turn 1 degree about every 4 minutes, the Moon crosses our celestial meridian about 13.2 x 4 = 52.8 minutes later each day.

Lunar Phases

The Moon appears to go through a complete set of phases as viewed from the Earth because of its motion around the Earth, as illustrated in the following figure.

Phases of the Moon

In this figure, the various positions of the Moon on its orbit are shown (the motion of the Moon on its orbit is assumed to be counter-clockwise). The outer set of figures shows the corresponding phase as viewed from Earth, and the common names for the phases.

Here is an animation of actual lunar phases, and here is a Java applet illustrating the orbit of the moon around the Earth and the corresponding phases of the Moon as viewed from Earth. Notice that you can set this applet to a top view, an Earth view, or both on a split screen, and that you can start and stop the animation with a button. Also, note that in this applet the position of the Sun is shown to the left, whereas in the above figure the view is such that the position of the Sun is to the right.

Perigee and Apogee

The largest separation between the Earth and Moon on its orbit is called apogee and the smallest separation is called perigee. Here is an online Lunar Perigee and Apogee Calculator that will allow you to determine the date, time, and distance of lunar perigees and apogees for a given year (Credit: John Walker).

Rotational Period and Tidal Locking

The Moon has a rotational period of 27.3 days that (except for small fluctuations) exactly coincides with its (sidereal) period for revolution about the Earth. As we will see later, this is no coincidence; it is a consequence of tidal coupling between the Earth and Moon. Because of this tidal locking of the periods for revolution and rotation, the Moon always keeps essentially the same face turned toward the Earth (small fluctuation mean that over a period of time we can actually see about 55% of the Lunar surface from the Earth).

Lunar Tides

The tides at a given place in the Earth's oceans occur about an hour later each day. Since the Moon passes overhead about an hour later each day, it was long suspected that the Moon was associated with tides. Newton's Law of Gravitation provided a quantitative understanding of that association.

Differential Forces

Consider a water molecule in the ocean. It is attracted gravitationally by the Earth, but it also experiences a much smaller gravitational attraction from the Moon (much smaller because the Moon is much further away and much less massive than the Earth). But this gravitational attraction of the Moon is not limited to the water molecules; in fact, the Moon exerts a gravitational force on every object on and in the Earth. Tides occur because the Earth is a body of finite extent and these forces are not uniform: some parts of the Earth are closer to the Moon than other parts, and since the gravitational force drops off as the inverse square distance, those parts experience a larger gravitational tug from the Moon than parts that are further away.

In this situation, which is illustrated schematically in the adjacent figure, we say that differential forces act on the body (the Earth in this example). The effect of differential forces on a body is to distort the body. The body of the Earth is rather rigid, so such distortion effects are small (but finite). However, the fluid in the Earth's oceans is much more easily deformed and this leads to significant tidal effects.

A Simple Tidal Model

We may illustrate the basic idea with a simple model of a planet completely covered by an ocean of uniform depth, with negligible friction between the ocean and the underlying planet, as illustrated in the adjacent figure. The gravitational attraction of the Moon produces two tidal bulges on opposite sides of the Earth.

Without getting too much into the technical details, there are two bulges because of the differential gravitational forces. The liquid at point A is closer to the Moon and experiences a larger gravitational force than the Earth at point B or the ocean at point C. Because it experiences a larger attraction, it is pulled away from the Earth, toward the Moon, thus producing the bulge on the right side. Loosely, we may think of the bulge on the left side as arising because the Earth is pulled away from the water on that side because the gravitational force exerted by the Moon at point B is larger than that exerted at point C. Then, as our idealized Earth rotates under these bulges, a given point on the surface will experience two high and two low tides for each rotation of the planet.

More Realistic Tidal Models

The realistic situation is considerably more complicated:

1. The Earth and Moon are not static, as depicted in the preceding diagram, but instead are in orbit around the common center of mass for the system.

2. The Earth is not covered with oceans, the oceans have varying depths, and there is substantial friction between the oceans and the Earth.

Spring Tides and Neap Tides

Another complication of a realistic model is that not only the Moon, but other objects in the Solar System, influence the Earth's tides. For most their tidal forces are negligible on Earth, but the differential gravitational force of the Sun does influence our tides to some degree (the effect of the Sun on Earth tides is less than half that of the Moon).

Competition between the Sun and Moon in producing tides.

For example, particularly large tides are experienced in the Earth's oceans when the Sun and the Moon are lined up with the Earth at new and full phases of the Moon. These are called spring tides (the name is not associated with the season of Spring). The amount of enhancement in Earth's tides is about the same whether the Sun and Moon are lined up on opposite sides of the Earth (full Lunar phase) or on the same side (new Lunar phase). Conversely, when the Moon is at first quarter or last quarter phase (meaning that it is located at right angles to the Earth-Sun line), the Sun and Moon interfere with each other in producing tidal bulges and tides are generally weaker; these are called neap tides. The figure shown above illustrates spring and neap tides.

Tidal Coupling and Gravitational Locking

We have introduced tides in terms of the effect of the Moon on the Earth's oceans, but the effect is much more general, and has a number of important consequences that we will discuss further below. For example, as a consequence of tidal interactions with the Moon, the Earth is slowly decreasing its rotational period and eventually the Earth and Moon will have exactly the same rotational period, and these will also exactly equal the orbital period. Thus, billions of years from now the Earth will always keep the same face turned toward the Moon, just as the Moon already always keeps the same face turned toward the Earth.

Tide and Gravitational Locking

We have introduced tides of the Moon's observational characteristics through the effect of the Moon on the Earth's oceans, but the effect is much more general, and has a number of important consequences.

Tidal Coupling and Gravitational Locking

Some important consequences of tidal forces in the Solar System include:

1. Tidal forces will distort any body experiencing differential gravitational forces. This will normally occur for bodies of finite extent in gravitational fields because of the strong distance dependence of the gravitational force. Thus, not only the oceans, but the body of the Earth is distorted by the Lunar gravity. However, because the Earth is rigid compared with the oceans, the "tides" in the body of the Earth are much smaller than in the oceans.

2. There is a limiting radius for the orbit of one body around another, inside of which the tidal forces are so large that no large solid objects can exist that are held together only by gravitational forces. This radius is called the Roche Limit. Thus, solid objects put into orbit inside the Roche limit will be torn apart by tidal forces, and conversely, solid objects cannot grow by accreting into larger objects if they orbit inside the Roche limit. A famous example is the rings of Saturn: because they lie inside the Roche limit for Saturn, they cannot be solid objects held together by gravitation and must be composed of many small particles.

   Obviously solid objects can exist inside the Roche limit (for example, spacecraft) but they must be held together by forces other than gravity. This is true of a spacecraft, where chemical forces between the atoms and molecules are much larger than the gravitational forces.

3. The tidal forces are reciprocal. Not only will the Moon induce tides in the body of the Earth and the Earth's oceans, but by the same argument the gravitational field of the Earth will induce differential forces and therefore tides in the body of the Moon. Again, because the body of the Moon is quite rigid these Lunar tides will be very small, but they occur.

4. This reciprocal induction of tides in the body of the Earth and the Moon leads to a complicated coupling of the rotational and orbital motions of the two objects. These tidal forces and associated couplings have the following general effects:

   • The interior of the Earth and Moon are heated by the tides in their bodies, just as a paper clip is heated by constant bending. This effect is very small for the Earth and Moon, but we shall see that it can be dramatic for other objects that experience much larger differential gravitational forces and therefore much larger tidal forces. For example, we shall see that the tidal forces exerted by Jupiter on its moon Io are so large that the solid surface of Io is raised and lowered by hundreds of meters twice in each rotational period. This motion so heats the interior of Io that it is probably mostly molten; as a consequence, Io is covered with active volcanos and is the geologically most active object in the Solar System.

   • The tidal coupling of the orbital and rotational motion tends to synchronize them. In the simplest instance, the period of rotation for the two bodies and the orbital period eventually become exactly equal because of this tidal coupling (and as a result, the size of the orbit is changed in such a way as to conserve angular momentum for the entire system). This is called gravitational (or tidal) locking, because as the two objects revolve around their common center of mass each keeps the same side turned toward the other.

Tidal Coupling in the Earth-Moon System

Thus, the fact that the rotational period of the Moon and the orbital period of the Earth-Moon system are of the same length is not an accident. Presumably this was not always true, but over billions of years the tidal coupling of the Earth and the Moon has led to this synchronization. In the case of the Earth-Moon system the synchronization is not yet complete. The Earth is slowly decreasing its rotational period and eventually the Earth and Moon will have exactly the same rotational period, and these will also exactly equal the orbital period. At the same time, the separation between the Earth and Moon will slowly increase in just such a way as to conserve angular momentum for the entire system.

Thus, billions of years from now the Earth will always keep the same face turned toward the Moon, just as the Moon already always keeps the same face turned toward the Earth. We will encounter other examples of such tidal locking in other pairs of objects in the Solar System.

The Surface

The surface of the Moon has two hemispheres with rather asymmetric properties; as a consequence the nature of the Lunar surface that we can see from the Earth is substantially different from the surface that is always hidden from the Earth.

The Near Side

The face of the Moon turned toward us is termed the near side (image at right). It is divided into light areas called the Lunar Highlands and darker areas called Maria (literally, "seas"; the singular is Mare). The Maria are lower in altitude than the Highlands, but there is no water on the Moon so they are not literally seas (Recent evidence from the Clementine spacecraft suggests that there may be some water on the Moon, contrary to previous assumptions). The dark material filling the Maria is actually dark, solidified lava from earlier periods of Lunar volcanism. Both the Maria and the Highlands exhibit large craters that are the result of meteor impacts. There are many more such impact craters in the Highlands.

The Far Side

The side of the Moon unseen from the Earth is called the far side. One of the discoveries of the first Lunar orbiters is that the far side has a very different appearance than the near side. In particular, there are almost no Maria on the far side, as illustrated in the image shown to the left of a portion of the far side surface. In this figure a number of meteor impact craters are visible.

Cratering Density

The amount of cratering is usually an indication of the age of a geological surface: the more craters, the older the surface, because if the surface is young there hasn't been time for many craters to form. Thus, the Earth has a relatively young surface because it has few craters. This is because the Earth is geologically active, with plate tectonics and erosion having obliterated most craters from an earlier epoch. In contrast the surface of the Moon is much older, with much more cratering. Further, different parts of the surface of the Moon exhibit different amounts of cratering and therefore are of different ages: the maria are younger than the highlands, because they have fewer craters.

The oldest surfaces in the Solar System are characterized by maximal cratering density. This means that one cannot increase the density of craters because there are so many craters that, on average, any new crater that is formed by a meteor impact will obliterate a previous crater, leaving the total number unchanged. Some regions of the moon exhibit near maximal cratering density, indicating that they are very old.

The Lunar Surface Material

The bulk density of the Moon is 3.4 g/cc, which is comparable to that of (volcanic) basaltic lavas on the Earth (however, the bulk density of the Earth is 5.5 g/cc, because of the dense iron/nickel core). The Moon is coverered with a gently rolling layer of powdery soil with scattered rocks that is called the regolith; it is made from debris blasted out of the Lunar craters by the meteor impacts that created them. Each well-preserved Lunar crater is surrounded by a sheet of ejected material called the ejecta blanket.

Geological Composition

One striking difference between the Lunar surface material and that of Earth concerns the most common kinds of rocks. On the Earth, the most common rocks are sedimentary, because of atmospheric and water erosion of the surface. On the Moon there is no atmosphere to speak of and little or no water, and the most common kind of rock is igneous ("fire-formed rocks"). Geologically, the Lunar surface material has the following characteristics:

1. The Maria are mostly composed of dark basalts, which form from rapid cooling of molten rock from massive lava flows.

2. The Highlands rocks are largely Anorthosite, which is a kind of igneous rock that forms when lava cools more slowly than in the case of basalts. This implies that the rocks of the Maria and Highlands cooled at different rates from the molten state and so were formed under different conditions.

3. Breccias, which are fragments of different rocks compacted and welded together by meteor impacts, are found in the Maria and the Highlands, but are more common in the latter.

4. Lunar Soils contain glassy globules not commonly found on the Earth. These are probably formed from the heat and pressure generated by meteor impacts.

Chemical Composition

The Lunar rocks may also be examined according to the chemicals that they contain. Such analysis indicates:

1. They are rich in refractory elements, which are elements such as calcium (Ca), Aluminum (Al), and Titanium (Ti) that form compounds having high melting points.

2. They are poor in the light elements such as hydrogen (H).

3. There is high abundance of elements like Silicon (Si) and Oxygen (O).

Age of Lunar Material

The abundances of radioactive elements in rock samples can be used to tell the age of the rock in a process called Radioactive Dating. When such techniques are applied to the Lunar rock samples, one finds the following:

1. Samples from Mare Imbrium and the Ocean of Storms brought back by Apollo 11 and Apollo 12 are about 3.5 billion years old, which is comparable to the oldest rocks found on the surface of the Earth.

2. The ejecta blanket from the Imbrium Basin (which was formed by a gigantic meteor impact) was returned by Apollo 14 and found to be about 3.9 billion years old.

3. Lunar Highlands rocks returned by Apollo 16 are about 4 billion years old. The oldest Lunar rock found was located by Apollo 17 and appears to be about 4.5 billion years old.

Interior and Geological Activity

Before the Apollo missions we knew almost nothing about the interior of the Moon. The Apollo missions left seismometers on the lunar surface that have allowed us to deduce the general features of the Lunar interior by studying the seismic waves generated by "moonquakes" and occasional meteor impacts.

The Structure of the Interior

Our present picture of the Moon's interior is that it has a crust about 65 km thick, a mantle about 1000 km thick, and a core that is about 500 km in radius. A limited amount of seismic data suggests that the outer core may be molten. There does appear to be some amount of differentiation, but not on the scale of that of the Earth. It has no magnetic field to speak of, but magnetization of Lunar rocks suggests that it may have had a larger one earlier in its history. Although there is a small amount of geological activity on the Moon, it is largely dead geologically (the energy associated with the Earth's seismic activity is about 10^14 times larger than that of the Moon). Most Lunar seismic activity appears to be triggered by tidal forces induced in the Moon by the Earth.

Geological History of the Moon

The weight of the evidence is that the Moon was active geologically in its early history, but the general evidence suggests that the Moon has been essentially dead geologically for more than 3 billion years. Based on that evidence, we believe the chronology of Lunar geology was as follows:

1. The Moon was formed about 4.6 billion years ago; maybe hot or maybe cold. The surface was subjected continuously to an intense meteor bombardment associated with debris left over from the formation of the Solar System.

2. By about 4.4 billion years ago the top 100 km was molten, from original heat of formation and from heat generated by the meteor bombardment.

3. By 4.2 billion years ago the surface was solid again.

4. As the intense meteor bombardment associated with debris left over from the formation of the Solar System continued, most of the craters that we now see on the surface of the Moon were formed by meteor impact.

5. The fracturing and heating of the surface and subsurface by the meteor bombardment led to a period of intense volcanic activity in the period 3.8-3.1 billion years ago. Meanwhile, the meteor bombardment had tapered off because by this time much of the debris of the early Solar System had already been captured by the planets.

6. The lava flows associated with the volcanism filled the low areas and many craters. These flows solidified to become the flat and dark maria, which have little cratering because most of the original craters were covered by lava flows and only a few meteors of significant size have struck the surface since the period of volcanic activity. The regions that were not covered by the lava flows are the present Highlands; thus, they are heavily cratered, and formed from different rocks than the seas.

7. The volcanism stopped about 3.1 billion years ago: the Moon has been largely dead geologically since then except for the occasional meteor impact or small moonquake, and micro-meteorite erosion of the surface.

Theories of formation

An extremely important question is that of how the Moon was formed and came to have its present orbit around the Earth.

Five Serious Theories

Five serious theories have been proposed for the formation of the Moon (not counting the one involving green cheese):

1. The Fission Theory: The Moon was once part of the Earth and somehow separated from the Earth early in the history of the Solar System. The present Pacific Ocean basin is the most popular site for the part of the Earth from which the Moon came.

2. The Capture Theory: The Moon was formed somewhere else, and was later captured by the gravitational field of the Earth.

3. The Condensation Theory: The Moon and the Earth condensed together from the original nebula that formed the Solar System.

4. The Colliding Planetesimals Theory: The interaction of earth-orbiting and Sun-orbiting planetesimals (very large chunks of rocks like asteroids) early in the history of the Solar System led to their breakup. The Moon condensed from this debris.

5. The Ejected Ring Theory: A planetesimal the size of Mars struck the earth, ejecting large volumes of matter. A disk of orbiting material was formed, and this matter eventually condensed to form the Moon in orbit around the Earth.

Constraints from Recent Data

A detailed comparison of the properties of Lunar and Earth rock samples has placed very strong constraints on the possible validity of these hypotheses. For example, if the Moon came from material that once made up the Earth, then Lunar and Terrestrial rocks should be much more similar in composition than if the Moon was formed somewhere else and only later was captured by the Earth.

These analyses indicate that the abundances of elements in Lunar and Terrestrial material are sufficiently different to make it unlikely that the Moon formed directly from the Earth. Generally, work over the last 10 years has essentially ruled out the first two explanations and made the third one rather unlikely. At present the fifth hypothesis, that the Moon was formed from a ring of matter ejected by collision of a large object with the Earth, is the favored hypothesis; however, the question is not completely settled and many details remain to the accounted for.