A&B's Astronomy Lab, Fall 2001, No. 6

The Moon, Our Constant Companion

Let's explore the only satellite of the Earth, the Moon.
We will discuss the Moon's orbit, different phases and its formation.
Also, we will take pictures of the Moon.

The Moon

Orbit: 384,400 km from Earth
Diameter: 3476 km
Mass: 7.35e22 kg
The Moon is the only natural satellite of Earth:
It is the second brightest object in the sky after the Sun. As the Moon orbits around the Earth once per month, the angle between the Earth, the Moon and the Sun changes; we see this as the cycle of the Moon's phases. The time between successive new moons is 29.5 days (709 hours), slightly different from the Moon's orbital period (measured against the stars) since the Earth moves a significant distance in its orbit around the Sun in that time. Due to its size and composition, the Moon is sometimes classified as a terrestrial "planet" along with Mercury, Venus, Earth and Mars.

The Moon was first visited by the Soviet spacecraft Luna 2 in 1959. It is the only extraterrestrial body to have been visited by humans. The first landing was on July 20, 1969 (do you remember where you were?); the last was in December 1972. The Moon is also the only body from which samples have been returned to Earth. In the summer of 1994, the Moon was very extensively mapped by the little spacecraft Clementine and again in 1999 by Lunar Prospector.

The gravitational forces between the Earth and the Moon cause some interesting effects.
The most obvious is the tides. The Moon's gravitational attraction is stronger on the side of the Earth nearest to the Moon and weaker on the opposite side. Since the Earth, and particularly the oceans, is not perfectly rigid it is stretched out along the line toward the Moon. From our perspective on the Earth's surface we see two small bulges, one in the direction of the Moon and one directly opposite. The effect is much stronger in the ocean water than in the solid crust so the water bulges are higher. And because the Earth rotates much faster than the Moon moves in its orbit, the bulges move around the Earth about once a day giving two high tides per day. (This is a greatly simplified model; actual tides, especially near the coasts, are much more complicated.)

But the Earth is not completely fluid, either. The Earth's rotation carries the Earth's bulges slightly ahead of the point directly beneath the Moon. This means that the force between the Earth and the Moon is not exactly along the line between their centers producing a torque on the Earth and an accelerating force on the Moon. This causes a net transfer of rotational energy from the Earth to the Moon, slowing down the Earth's rotation by about 1.5 milliseconds/century and raising the Moon into a higher orbit by about 3.8 centimeters per year. (The opposite effect happens to satellites with unusual orbits such as Phobos and Triton).

The asymmetric nature of this gravitational interaction is also responsible for the fact that the Moon rotates synchronously, i.e. it is locked in phase with its orbit so that the same side is always facing toward the Earth. Just as the Earth's rotation is now being slowed by the Moon's influence so in the distant past the Moon's rotation was slowed by the action of the Earth, but in that case the effect was much stronger. When the Moon's rotation rate was slowed to match its orbital period (such that the bulge always faced toward the Earth) there was no longer an off-center torque on the Moon and a stable situation was achieved. The same thing has happened to most of the other satellites in the solar system. Eventually, the Earth's rotation will be slowed to match the Moon's period, too, as is the case with Pluto and Charon.

Actually, the Moon appears to wobble a bit (due to its slightly non-circular orbit) so that a few degrees of the far side can be seen from time to time, but the majority of the far side (left) was completely unknown until the Soviet spacecraft Luna 3 photographed it in 1959. (Note: there is no "dark side" of the Moon; all parts of the Moon get sunlight half the time (except for a few deep craters near the poles). Some uses of the term "dark side" in the past may have referred to the far side as "dark" in the sense of "unknown" (eg "darkest Africa") but even that meaning is no longer valid today!)

The Moon has no atmosphere. But evidence from Clementine suggested that there may be water ice in some deep craters near the Moon's south pole which are permanently shaded. This has now been confirmed by Lunar Prospector. There is apparently ice at the north pole as well. The cost of future lunar exploration just got a lot cheaper! The Moon's crust averages 68 km thick and varies from essentially 0 under Mare Crisium to 107 km north of the crater Korolev on the lunar far side. Below the crust is a mantle and probably a small core (roughly 340 km radius and 2% of the Moon's mass). Unlike the Earth's mantle, however, the Moon's is only partially molten. Curiously, the Moon's center of mass is offset from its geometric center by about 2 km in the direction toward the Earth. Also, the crust is thinner on the near side.

There are two primary types of terrain on the Moon: the heavily cratered and very old highlands and the relatively smooth and younger maria. The maria (which comprise about 16% of the Moon's surface) are huge impact craters that were later flooded by molten lava. Most of the surface is covered with regolith, a mixture of fine dust and rocky debris produced by meteor impacts. For some unknown reason, the maria are concentrated on the near side.

Most of the craters on the near side are named for famous figures in the history of science such as Tycho, Copernicus, and Ptolemaeus. Features on the far side have more modern references such as Apollo, Gagarin and Korolev (with a distinctly Russian bias since the first images were obtained by Luna 3). In addition to the familiar features on the near side, the Moon also has the huge craters South Pole-Aitken on the far side which is 2250 km in diameter and 12 km deep making it the the largest impact basin in the solar system and Orientale on the western limb (as seen from Earth; in the center of the image at left) which is a splendid example of a multi-ring crater.

A total of 382 kg of rock samples were returned to the Earth by the Apollo and Luna programs. These provide most of our detailed knowledge of the Moon. They are particularly valuable in that they can be dated. Even today, 20 years after the last Moon landing, scientists still study these precious samples. Most rocks on the surface of the Moon seem to be between 4.6 and 3 billion years old. This is a fortuitous match with the oldest terrestrial rocks which are rarely more than 3 billion years old. Thus the Moon provides evidence about the early history of the Solar System not available on the Earth.

Prior to the study of the Apollo samples, there was no consensus about the origin of the Moon. There were three principal theories: co-accretion which asserted that the Moon and the Earth formed at the same time from the Solar Nebula; fission which asserted that the Moon split off of the Earth; and capture which held that the Moon formed elsewhere and was subsequently captured by the Earth. None of these work very well. But the new and detailed information from the Moon rocks led to the impact theory: that the Earth collided with a very large object (as big as Mars or more) and that the Moon formed from the ejected material. There are still details to be worked out, but the impact theory is now widely accepted.

The Moon has no global magnetic field. But some of its surface rocks exhibit remanent magnetism indicating that there may have been a global magnetic field early in the Moon's history. With no atmosphere and no magnetic field, the Moon's surface is exposed directly to the solar wind. Over its 4 billion year lifetime many hydrogen ions from the solar wind have become embedded in the Moon's regolith. Thus samples of regolith returned by the Apollo missions proved valuable in studies of the solar wind. This lunar hydrogen may also be of use someday as rocket fuel.

The Orbit of the Moon and Eclipses

The word eclipse means to block one? view of something. Look at a light bulb or a window. Now put your hand in front of your face so you cannot see the light or window. You can now say that your hand has eclipsed the light bulb or window. When most things get blocked from our view, we do not use the term eclipse to describe the event. Instead “eclipse” is reserved for special situations like when the sun is blocked by the moon. The term Solar Eclipse is used to describe this special situation. If dark clouds obscure the sun, this is not an eclipse. Having clouds cover the sun will happen many times a year (in some locations, it is the normal weather pattern) and is not that unusual. But the moon covering the sun is unusual. A solar eclipse does not occur during every new moon phase because the orbit of the Moon around the Earth is tilted in respect to the apparent orbit of the Sun.

SOLAR ECLIPSE LUNAR ECLIPSE

Solar eclipses are caused when the Moon gets in front of the Sun as viewed from the surface of the Earth. The Moon can only get in front of the Sun during a new moon phase, which occurs about once a month when the Moon is not visible at all during the night. Scientists identify three types of solar eclipses. The first type is the most common and is called a Partial Solar Eclipse. As the name implies, this is a partial covering of the sun by the moon. The other two types are much rarer and require that you be in the right location to see them. The other types of solar eclipses are called Total and Annular Solar Eclipses. Total Solar Eclipses are as the name implies ? a total eclipse or blocking of the sun by the moon. Annular Eclipses are similar to total eclipses, but the apparent size of the Moon is slightly smaller than the apparent size of the Sun. As a result, a ring of the bright Sun shines all around the Moon. This shape is called an annulus (a fat-flat circle) and hence the name Annular Eclipse.
When the Earth is directly between the Moon and Sun, the shadow of the Earth falls across the face of the Moon causing the Moon to be dark. This is a Lunar Eclipse. When an eclipse of Moon occurs, the moon darkens almost to the point of being invisible. You might think that it would get completely dark since the sun's light has been blocked, but that is not the case. Instead the Moon turns a deep reddish brown color. This is why some people call a total lunar eclipse the “Blood Moon.” Lunar eclipses are caused by the Earth moving in front of the Sun as viewed from the surface of the Moon. The Earth can only move between the Sun and Moon during a full moon phase, which occurs about once a month as the Moon rotates around the Earth. During a full moon phase the Moon is visible at all times during the night (the full moon rises at sunset and sets at sunrise). Lunar eclipses only occur during the Full Moon, when the Moon is furthest from the Sun relative to the Earth.

Total (Solar) Eclipse (above) and Blood Moon (below)

Theories or the Formation of the Earth's Moon

The Big Impact
The giant impact hypothesis exploded in popularity at a conference held in Kailua-Kona, Hawai'i, in 1984, though the fuse had been lit about ten years earlier. Two key papers had been published in 1975, one by William K. Hartmann and Donald Davis (Planetary Sciences Institute in Tucson, Arizona) and the other by Alfred G. W. Cameron and William Ward (Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts). Though they took different approaches to the problem, both suggested that the Moon formed when a huge impactor smashed into the Earth near the end of its construction. To account for the amount of angular momentum in the Earth-Moon system, Cameron estimated that the object would need to be about 10% the mass of Earth, about the size of Mars. (Angular momentum is the measure of motion of objects in curved paths, including both rotation and orbital motion. For the Earth and Moon this means the spin of each planet plus the orbital motion of the Moon around the Earth.) Hartmann approached the problem from the perspective he had gained from studies of the history of lunar impact bombardment. He reasoned that if there were huge impact craters preserved on the Moon that were made by projectiles 150 km across, there must have been other gigantic projectiles, perhaps ten or more times larger. If one hit the Earth, Hartmann and Davis thought, perhaps sufficient material would be lifted into orbit to form the Moon. All four scientists also realized that big impacts fit into the picture of planet formation being painted by physicists studying how planets could have accumulated. Such a monumental impact would cause a large amount of material to be lofted into orbit around the Earth, and the Moon could form from that debris. Cameron's recent research, done partly in collaboration with Robin Canup (Southwest Research Institute, Boulder), indicates that the immense moon-forming impact probably took place when the Earth was only about half constructed. If the Earth is too large, say close to its present size, formation of the Moon requires about twice the amount of angular momentum that the Earth-Moon system has now. An impact of the half-built Earth with an object a little over half its size could have formed the Moon and made the Earth about 2/3 complete. Most intriguing, the recent computer simulations indicate that the projectile hits, but much of it rebounds into a sub-orbital flight to hit the Earth again. The Earth and Moon continue to grow, by other large impacts, but not large enough to form another moon. What a violent beginning to our beautiful blue planet and the shape-changing light globe that decorates the night sky! These pictures are snapshots of the formation of the Moon, as depicted by comuter simulations done by Al Cameron. Blue areas are metallic iron, and red and orange areas are rocky mantles. The growing Earth is the larger of the two objects; the smaller object is the projectile whose impact led to the formation of the Moon. In this simulation, the impactor hits off-centered (frame 1), and heats and deforms both bodies (frame 2). As the event continues, some metallic core (colored blue) is transferred to the Earth, but most remains inside the impactor. The impactor is not completely engulfed by the Earth and pulls away somewhat, as if it bounced off (frames 3-8). All this would have taken only about half an hour. (Changes in apparent size are due to changing the scale of the pictures in order to keep both objects in the field of view.) The impactor now hits the Earth again (frame 9), but this time is incorporated into the Earth (frames 10-12). Its metallic core becomes part of Earth's core. Some rocky material is still left in orbit around the Earth (frames 13-16). The Moon forms from the debris left in orbit, most of which came from the impactor. The accretion of the material into the Moon is not shown in this simulation. Al Cameron notes that there are numerous parameters still to test by computer simulations. He has not yet explored all the possibilities of the ratio of the mass of the growing Earth to that of the impactor, or the total range in angular momentum of the system. Jay Melosh (University of Arizona) points out that the physical properties (called the equation of state) he, Cameron, and others use in impact simulations is far from perfect and might lead to unrealistic results. Cameron agreed, noting that he "considers this game very primitive so far."

Accumulating Planets
The cloud from which the Solar System formed was composed of gas and dust. Somehow in that dusty cloud, the Sun formed in the center and the planets formed around it. The inner, rocky planets formed by accretion-they accumulated dust and rocks to become planets. As explained by Robin Canup at the conference, years of studying the physics of planet formation and countless computer simulations reveal three stages in the accretion of the planets. During the first stage, dust grains stuck to each other until objects were large enough to begin to attract material with their gravity fields, producing objects the size of asteroids (up to a few hundred kilometers in diameter). Inside the solar nebula, less than a million years after the sun formed, as depicted by scientist/artist Bill Hartmann. This shows the view in the region where the Earth will form. Small grains of dust are aggregating into planetesimals during stage 1 of planet formation. During the second stage, a period of runaway growth took place, leading to tens of objects much larger than the Moon. Most of the mass of the inner Solar System was contained within these planetary embryos. It may have taken only about a million years from the end of stage 1 to the end of stage 2. During the final stage, these huge objects whacked into each other, creating larger planets, but a smaller number of them. The entire process was dominated by large impacts, making the formation of the Moon by a giant impact a natural consequence of planet formation. Whether a moon forms with each impact depends on the sizes of the two impacting objects and how off-centered an impact is. (Dead centered impacts do not give ejected material enough velocity to allow it to stay in orbit around a growing planet.) Simulations indicate that the third stage took 100 to 200 million years, about the time estimated from isotopic data on rocks from Earth, the Moon, and meteorites.

Assembling the Moon
A giant impact would lead to a ring of very hot debris in orbit around the young Earth. Calculations indicate that the Moon could have formed from that debris in ten years or less! This implies that the Moon would have formed very hot, possibly entirely molten. This scorching initial state is consistent with the idea that the Moon was surrounded by an ocean of magma when it formed. The magma ocean idea has been a central tenet of lunar science for decades, and recent data from the Clementine mission to the Moon finally proved it, as described in "Moonbeams and Elements," an October, 1997 PSRD article. The Moon probably continued to accrete material to it, including some objects up to about half its size. These big impacts could maintain a magma ocean, and scramble any crust that formed. It could also add rock with a composition different from the rest of the Moon, accounting for some unexplained features of the lunar interior. The moon is nearly completely formed in this painting by Bill Hartmann. The existence of a magma ocean on the Moon is also prime evidence against the Moon forming by capture. Calculations show that if the Moon were captured, the process would not heat the Moon very much, certainly not so much that it would be mostly molten.

The Moon
Orbit: 384,400 km from Earth Diameter: 3476 km Mass: 7.35e22 kg	The Moon is the only natural satellite of Earth: It is the second brightest object in the sky after the Sun. As the Moon orbits around the Earth once per month, the angle between the Earth, the Moon and the Sun changes; we see this as the cycle of the Moon's phases. The time between successive new moons is 29.5 days (709 hours), slightly different from the Moon's orbital period (measured against the stars) since the Earth moves a significant distance in its orbit around the Sun in that time. Due to its size and composition, the Moon is sometimes classified as a terrestrial "planet" along with Mercury, Venus, Earth and Mars.
	The Moon was first visited by the Soviet spacecraft Luna 2 in 1959. It is the only extraterrestrial body to have been visited by humans. The first landing was on July 20, 1969 (do you remember where you were?); the last was in December 1972. The Moon is also the only body from which samples have been returned to Earth. In the summer of 1994, the Moon was very extensively mapped by the little spacecraft Clementine and again in 1999 by Lunar Prospector.
The gravitational forces between the Earth and the Moon cause some interesting effects. The most obvious is the tides. The Moon's gravitational attraction is stronger on the side of the Earth nearest to the Moon and weaker on the opposite side. Since the Earth, and particularly the oceans, is not perfectly rigid it is stretched out along the line toward the Moon. From our perspective on the Earth's surface we see two small bulges, one in the direction of the Moon and one directly opposite. The effect is much stronger in the ocean water than in the solid crust so the water bulges are higher. And because the Earth rotates much faster than the Moon moves in its orbit, the bulges move around the Earth about once a day giving two high tides per day. (This is a greatly simplified model; actual tides, especially near the coasts, are much more complicated.)
	But the Earth is not completely fluid, either. The Earth's rotation carries the Earth's bulges slightly ahead of the point directly beneath the Moon. This means that the force between the Earth and the Moon is not exactly along the line between their centers producing a torque on the Earth and an accelerating force on the Moon. This causes a net transfer of rotational energy from the Earth to the Moon, slowing down the Earth's rotation by about 1.5 milliseconds/century and raising the Moon into a higher orbit by about 3.8 centimeters per year. (The opposite effect happens to satellites with unusual orbits such as Phobos and Triton).
The asymmetric nature of this gravitational interaction is also responsible for the fact that the Moon rotates synchronously, i.e. it is locked in phase with its orbit so that the same side is always facing toward the Earth. Just as the Earth's rotation is now being slowed by the Moon's influence so in the distant past the Moon's rotation was slowed by the action of the Earth, but in that case the effect was much stronger. When the Moon's rotation rate was slowed to match its orbital period (such that the bulge always faced toward the Earth) there was no longer an off-center torque on the Moon and a stable situation was achieved. The same thing has happened to most of the other satellites in the solar system. Eventually, the Earth's rotation will be slowed to match the Moon's period, too, as is the case with Pluto and Charon.
	Actually, the Moon appears to wobble a bit (due to its slightly non-circular orbit) so that a few degrees of the far side can be seen from time to time, but the majority of the far side (left) was completely unknown until the Soviet spacecraft Luna 3 photographed it in 1959. (Note: there is no "dark side" of the Moon; all parts of the Moon get sunlight half the time (except for a few deep craters near the poles). Some uses of the term "dark side" in the past may have referred to the far side as "dark" in the sense of "unknown" (eg "darkest Africa") but even that meaning is no longer valid today!)
The Moon has no atmosphere. But evidence from Clementine suggested that there may be water ice in some deep craters near the Moon's south pole which are permanently shaded. This has now been confirmed by Lunar Prospector. There is apparently ice at the north pole as well. The cost of future lunar exploration just got a lot cheaper! The Moon's crust averages 68 km thick and varies from essentially 0 under Mare Crisium to 107 km north of the crater Korolev on the lunar far side. Below the crust is a mantle and probably a small core (roughly 340 km radius and 2% of the Moon's mass). Unlike the Earth's mantle, however, the Moon's is only partially molten. Curiously, the Moon's center of mass is offset from its geometric center by about 2 km in the direction toward the Earth. Also, the crust is thinner on the near side.
	There are two primary types of terrain on the Moon: the heavily cratered and very old highlands and the relatively smooth and younger maria. The maria (which comprise about 16% of the Moon's surface) are huge impact craters that were later flooded by molten lava. Most of the surface is covered with regolith, a mixture of fine dust and rocky debris produced by meteor impacts. For some unknown reason, the maria are concentrated on the near side.
	Most of the craters on the near side are named for famous figures in the history of science such as Tycho, Copernicus, and Ptolemaeus. Features on the far side have more modern references such as Apollo, Gagarin and Korolev (with a distinctly Russian bias since the first images were obtained by Luna 3). In addition to the familiar features on the near side, the Moon also has the huge craters South Pole-Aitken on the far side which is 2250 km in diameter and 12 km deep making it the the largest impact basin in the solar system and Orientale on the western limb (as seen from Earth; in the center of the image at left) which is a splendid example of a multi-ring crater.
	A total of 382 kg of rock samples were returned to the Earth by the Apollo and Luna programs. These provide most of our detailed knowledge of the Moon. They are particularly valuable in that they can be dated. Even today, 20 years after the last Moon landing, scientists still study these precious samples. Most rocks on the surface of the Moon seem to be between 4.6 and 3 billion years old. This is a fortuitous match with the oldest terrestrial rocks which are rarely more than 3 billion years old. Thus the Moon provides evidence about the early history of the Solar System not available on the Earth.
Prior to the study of the Apollo samples, there was no consensus about the origin of the Moon. There were three principal theories: co-accretion which asserted that the Moon and the Earth formed at the same time from the Solar Nebula; fission which asserted that the Moon split off of the Earth; and capture which held that the Moon formed elsewhere and was subsequently captured by the Earth. None of these work very well. But the new and detailed information from the Moon rocks led to the impact theory: that the Earth collided with a very large object (as big as Mars or more) and that the Moon formed from the ejected material. There are still details to be worked out, but the impact theory is now widely accepted. The Moon has no global magnetic field. But some of its surface rocks exhibit remanent magnetism indicating that there may have been a global magnetic field early in the Moon's history. With no atmosphere and no magnetic field, the Moon's surface is exposed directly to the solar wind. Over its 4 billion year lifetime many hydrogen ions from the solar wind have become embedded in the Moon's regolith. Thus samples of regolith returned by the Apollo missions proved valuable in studies of the solar wind. This lunar hydrogen may also be of use someday as rocket fuel.

The Orbit of the Moon and Eclipses
The word eclipse means to block one? view of something. Look at a light bulb or a window. Now put your hand in front of your face so you cannot see the light or window. You can now say that your hand has eclipsed the light bulb or window. When most things get blocked from our view, we do not use the term eclipse to describe the event. Instead “eclipse” is reserved for special situations like when the sun is blocked by the moon. The term Solar Eclipse is used to describe this special situation. If dark clouds obscure the sun, this is not an eclipse. Having clouds cover the sun will happen many times a year (in some locations, it is the normal weather pattern) and is not that unusual. But the moon covering the sun is unusual. A solar eclipse does not occur during every new moon phase because the orbit of the Moon around the Earth is tilted in respect to the apparent orbit of the Sun.
SOLAR ECLIPSE	LUNAR ECLIPSE
Solar eclipses are caused when the Moon gets in front of the Sun as viewed from the surface of the Earth. The Moon can only get in front of the Sun during a new moon phase, which occurs about once a month when the Moon is not visible at all during the night. Scientists identify three types of solar eclipses. The first type is the most common and is called a Partial Solar Eclipse. As the name implies, this is a partial covering of the sun by the moon. The other two types are much rarer and require that you be in the right location to see them. The other types of solar eclipses are called Total and Annular Solar Eclipses. Total Solar Eclipses are as the name implies ? a total eclipse or blocking of the sun by the moon. Annular Eclipses are similar to total eclipses, but the apparent size of the Moon is slightly smaller than the apparent size of the Sun. As a result, a ring of the bright Sun shines all around the Moon. This shape is called an annulus (a fat-flat circle) and hence the name Annular Eclipse.	When the Earth is directly between the Moon and Sun, the shadow of the Earth falls across the face of the Moon causing the Moon to be dark. This is a Lunar Eclipse. When an eclipse of Moon occurs, the moon darkens almost to the point of being invisible. You might think that it would get completely dark since the sun's light has been blocked, but that is not the case. Instead the Moon turns a deep reddish brown color. This is why some people call a total lunar eclipse the “Blood Moon.” Lunar eclipses are caused by the Earth moving in front of the Sun as viewed from the surface of the Moon. The Earth can only move between the Sun and Moon during a full moon phase, which occurs about once a month as the Moon rotates around the Earth. During a full moon phase the Moon is visible at all times during the night (the full moon rises at sunset and sets at sunrise). Lunar eclipses only occur during the Full Moon, when the Moon is furthest from the Sun relative to the Earth.
*Total (Solar) Eclipse (above) and Blood Moon (below)*

Theories or the Formation of the Earth's Moon
The Big Impact The giant impact hypothesis exploded in popularity at a conference held in Kailua-Kona, Hawai'i, in 1984, though the fuse had been lit about ten years earlier. Two key papers had been published in 1975, one by William K. Hartmann and Donald Davis (Planetary Sciences Institute in Tucson, Arizona) and the other by Alfred G. W. Cameron and William Ward (Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts). Though they took different approaches to the problem, both suggested that the Moon formed when a huge impactor smashed into the Earth near the end of its construction. To account for the amount of angular momentum in the Earth-Moon system, Cameron estimated that the object would need to be about 10% the mass of Earth, about the size of Mars. (Angular momentum is the measure of motion of objects in curved paths, including both rotation and orbital motion. For the Earth and Moon this means the spin of each planet plus the orbital motion of the Moon around the Earth.) Hartmann approached the problem from the perspective he had gained from studies of the history of lunar impact bombardment. He reasoned that if there were huge impact craters preserved on the Moon that were made by projectiles 150 km across, there must have been other gigantic projectiles, perhaps ten or more times larger. If one hit the Earth, Hartmann and Davis thought, perhaps sufficient material would be lifted into orbit to form the Moon. All four scientists also realized that big impacts fit into the picture of planet formation being painted by physicists studying how planets could have accumulated. Such a monumental impact would cause a large amount of material to be lofted into orbit around the Earth, and the Moon could form from that debris. Cameron's recent research, done partly in collaboration with Robin Canup (Southwest Research Institute, Boulder), indicates that the immense moon-forming impact probably took place when the Earth was only about half constructed. If the Earth is too large, say close to its present size, formation of the Moon requires about twice the amount of angular momentum that the Earth-Moon system has now. An impact of the half-built Earth with an object a little over half its size could have formed the Moon and made the Earth about 2/3 complete. Most intriguing, the recent computer simulations indicate that the projectile hits, but much of it rebounds into a sub-orbital flight to hit the Earth again. The Earth and Moon continue to grow, by other large impacts, but not large enough to form another moon. What a violent beginning to our beautiful blue planet and the shape-changing light globe that decorates the night sky! These pictures are snapshots of the formation of the Moon, as depicted by comuter simulations done by Al Cameron. Blue areas are metallic iron, and red and orange areas are rocky mantles. The growing Earth is the larger of the two objects; the smaller object is the projectile whose impact led to the formation of the Moon. In this simulation, the impactor hits off-centered (frame 1), and heats and deforms both bodies (frame 2). As the event continues, some metallic core (colored blue) is transferred to the Earth, but most remains inside the impactor. The impactor is not completely engulfed by the Earth and pulls away somewhat, as if it bounced off (frames 3-8). All this would have taken only about half an hour. (Changes in apparent size are due to changing the scale of the pictures in order to keep both objects in the field of view.) The impactor now hits the Earth again (frame 9), but this time is incorporated into the Earth (frames 10-12). Its metallic core becomes part of Earth's core. Some rocky material is still left in orbit around the Earth (frames 13-16). The Moon forms from the debris left in orbit, most of which came from the impactor. The accretion of the material into the Moon is not shown in this simulation. Al Cameron notes that there are numerous parameters still to test by computer simulations. He has not yet explored all the possibilities of the ratio of the mass of the growing Earth to that of the impactor, or the total range in angular momentum of the system. Jay Melosh (University of Arizona) points out that the physical properties (called the equation of state) he, Cameron, and others use in impact simulations is far from perfect and might lead to unrealistic results. Cameron agreed, noting that he "considers this game very primitive so far."
Accumulating Planets The cloud from which the Solar System formed was composed of gas and dust. Somehow in that dusty cloud, the Sun formed in the center and the planets formed around it. The inner, rocky planets formed by accretion-they accumulated dust and rocks to become planets. As explained by Robin Canup at the conference, years of studying the physics of planet formation and countless computer simulations reveal three stages in the accretion of the planets. During the first stage, dust grains stuck to each other until objects were large enough to begin to attract material with their gravity fields, producing objects the size of asteroids (up to a few hundred kilometers in diameter). Inside the solar nebula, less than a million years after the sun formed, as depicted by scientist/artist Bill Hartmann. This shows the view in the region where the Earth will form. Small grains of dust are aggregating into planetesimals during stage 1 of planet formation. During the second stage, a period of runaway growth took place, leading to tens of objects much larger than the Moon. Most of the mass of the inner Solar System was contained within these planetary embryos. It may have taken only about a million years from the end of stage 1 to the end of stage 2. During the final stage, these huge objects whacked into each other, creating larger planets, but a smaller number of them. The entire process was dominated by large impacts, making the formation of the Moon by a giant impact a natural consequence of planet formation. Whether a moon forms with each impact depends on the sizes of the two impacting objects and how off-centered an impact is. (Dead centered impacts do not give ejected material enough velocity to allow it to stay in orbit around a growing planet.) Simulations indicate that the third stage took 100 to 200 million years, about the time estimated from isotopic data on rocks from Earth, the Moon, and meteorites.
Assembling the Moon A giant impact would lead to a ring of very hot debris in orbit around the young Earth. Calculations indicate that the Moon could have formed from that debris in ten years or less! This implies that the Moon would have formed very hot, possibly entirely molten. This scorching initial state is consistent with the idea that the Moon was surrounded by an ocean of magma when it formed. The magma ocean idea has been a central tenet of lunar science for decades, and recent data from the Clementine mission to the Moon finally proved it, as described in "Moonbeams and Elements," an October, 1997 PSRD article. The Moon probably continued to accrete material to it, including some objects up to about half its size. These big impacts could maintain a magma ocean, and scramble any crust that formed. It could also add rock with a composition different from the rest of the Moon, accounting for some unexplained features of the lunar interior. The moon is nearly completely formed in this painting by Bill Hartmann. The existence of a magma ocean on the Moon is also prime evidence against the Moon forming by capture. Calculations show that if the Moon were captured, the process would not heat the Moon very much, certainly not so much that it would be mostly molten.