## Formation and Evolution of the Moon

ror a long time people thought the Moon was a large asteroid that happened into the Earth's orbit and was captured by the Earth's gravity.After careful calculations it was shown that no asteroid captured by the Earth could have exactly the orbit around the Earth that the Moon has. Now scientists have decided that the only way the Moon could have formed with its current rotation and orbital characteristics is if a giant meteorite smashed into the Earth and created a cloud of heated material around the Earth that slowly fell together again to form the outer portions of the Earth and its giant satellite, the Moon. How is this known? Angular momentum is the key.

Angular momentum is a measure of both how fast a rotating object is rotating, and how hard it would be to change its rotation (how much force would be required to slow it down, for example). Figure skating provides the classic example of angular momentum. Imagine a skater spinning in place with his arms out.This skater is rotating, has a mass, is spinning at a particular speed, and his arms measure a length from his center to the tip of his fingers, and so he has some amount of angular momentum. As changes occur to the spinning skater, the amount of angular momentum must stay the same (this is called conservation of angular momentum and is a physical law). Imagine the skater pulls his arms in tightly to his body. The length from the center to the edge of the spinning person has gotten shorter, and so to keep the angular momentum the same the skater's spin speeds up.The skater does nothing but pull his arms in; physics does the rest.

The spinning, orbiting system of the Earth and the Moon has angular momentum, as well. (The angular momentum of the Earth-Moon system

The Earth's tidal bulge is at a small angle to the Moon, forming torques that cause the Earth's rotation to slow and the Moon to recede from the Earth.

 Earth-Moon Tidal Bulge Tidal bulge greatly exaggerated / \ Earth Moon

is 3.5 X 1042 kg/m2sec.) The law of conservation of angular momentum works almost perfectly for the Earth-Moon system, though a small amount of energy is lost in tidal friction, and the total angular momentum in the system has stayed almost the same for the last 4.5 billion years. Though the total angular momentum has stayed the same, as in the case of the skater the spin rate and the distance between the bodies may have changed, and in fact they have.

The tidal bulge of water pulled up from the Earth's surface by the gravitational attraction of the Moon leads the Earth-Moon axis by a small angle a, and the Moon exerts a gravitational torque on the bulge, slowing the Earth's rotation, as shown in the figure here. In its turn, the tidal bulge exerts a torque on the Moon, accelerating the Moon's orbital speed, and causing the Moon to move away from the Earth in order to preserve angular momentum.

There are very thin layers of sandstone or siltstone called tidal rhythmites, one layer of which is created each time the tide goes in and out. If these thin layers (called laminae) are buried and baked into rock over time then it is possible for scientists to count the layers and determine how many lunar months per year there were when that rock was made. If the rock can also be dated absolutely using a radiometric method (see the sidebar "Determining Age from Radioactive Isotopes" on page 76), then the rhythmites can determine how many months there were in a year at a given time in the past.

Based on these and similar analyses, scientists have determined that 2.45 billion years ago, or about half the age of the Earth, a day on Earth was only about 19 hours long. This means that every nineteen hours the Earth rotated and passed through a daylight time and a nighttime. Slowly, in the 4.56 billion years since the Earth first formed, the rotation of the Earth has slowed and days have gotten longer. Days are still getting longer, because of conservation of angular momentum: As the Moon pulls the tides around the Earth, the Earth's rotation is slowed by tidal friction. As the rotation slows, to conserve angular momentum, the Moon moves slightly farther from the Earth.This is the same effect as a skater slowing his spinning by extending his arms. By analyzing the tidal rhythmites and other rocks that also record tides or days scientists have created a record of day length over the past 2.5 billion years. Previously only a few data points were available, and scientists extrapolated the data back to try to determine the day length at the beginning of Earth formation. It was then thought that day length in the early solar system was only about five hours! Now, with more data, it seems that the Earth was never spinning that rapidly (which by the law of conservation of angular momentum, would have required that the Moon be very close to the Earth, the subject of a fantastical short story by Italian writer Italo Calvino). It appears, instead, that the Moon and Earth are moving away from each other increasingly rapidly, and so the lengthening of Earth's days is accelerating.Two and a half billion years ago the rate of recession of the Moon was only one third what it is today, and 620 million years ago it was only two thirds what it is today. By measuring the distance from the Moon to the Earth today by laser ranging (bouncing lasers off mirrors left on the Moon by Apollo astronauts), it is known that the Moon is receding from the Earth at a rate of 1.5 ± 0.03 inches (3.82 ± 0.07 cm) per year!

While this may seem a shocking rate of change in the apparently unchanging Earth-Moon system, it is actually a very old idea. Immanuel Kant, the great philosopher, postulated in 1754 that friction from tides have to slow the Earth's rotation, but as he was a writer and thinker and not a scientist, he did not carry the idea further, and it languished forgotten until the mid-19th century.

Angular momentum is also an important constraint for ideas of how the Moon was made. Whatever model a scientist has for the formation of the Earth-Moon system, that model has to result in an Earth-Moon system with the right amount of angular momentum. The theory of an asteroid being captured into Earth orbit does not produce a system with the correct amount of angular momentum, but the theory of a giant impact does. A giant impactor the size of Mars smashed into the young Earth, it is now believed, and pieces of the pulverized, heated impactor and the outside of the Earth fell back together to form the Moon.

A scientist named Robin Canup, working at Arizona State University, has made a huge computer program to model this process. Her program keeps track of the speed, direction, and temperature of the Earth and the asteroid that hits it, called the Giant Impactor. After the Giant Impactor hits the Earth, the program keeps track of the speed, direction, and temperature of tens of thousands of fragments that fly off the Earth. The energy of the impact is so huge that a large portion of the Earth and all of the Giant Impactor simply melt. The Earth then splashes back into the shape of a ball, and fragments of the Earth and the Giant Impactor fly into orbits around the Earth. Gradually the largest of these orbiting fragments run into each other to form larger planetesimals (meaning "little planets" or planet fragments), the planetesimals collide or are drawn together by gravity to form the Moon. Canup has used her computer model to calculate that the Giant Impactor that hit the Earth would have to have been about the size of Mars. This impact had to be early enough in the formation of the solar system that there were giant impactors orbiting erratically in the inner solar system, not yet in stable orbits of their own. It had to have happened before the oldest known rocks on Earth formed, since the entire outside of the Earth was shocked and liquefied by the giant impact.The oldest known rocks on Earth are about 4 billion years old. The giant impact also had to have happened before the oldest known rocks on the Moon were formed.Thanks to the Apollo missions, which brought back about 1,540 pounds (700 kg) of material from the Moon, scientists have rocks from the Moon that can be dated. The oldest rock dated from the Moon is about 4.4 billion years old.Therefore the formation of the Moon happened after the initial planet formation in the solar system, at 4.56 billion years ago, and before 4.4 billion years ago, when the oldest known Moon rocks formed.