The Moon

Hopefully during this semester you will get a chance to look at the Moon through one of the telescopes at the campus observatory. Before we talk about the Moon, let's get some numbers out of the way: The equatorial radius of the Earth is 6,378 km, while the Moon has a radius of 1,738 km. The mass of the Earth is 5.97 X 1024 kg, and the mass of the Moon is 7.35 X 1022 kg. The density of the Earth is 5.5 gm/cm3, while the Moon's density is only 3.3 gm/cm3. The average distance from the Earth to the Moon is 384,000 km, and a properly scaled model is shown here:

One glance, and you quickly can see how different the surface of the Moon is from the Earth:

It has a very large number of round "craters", and large flat, dark plains called "Maria" (from the Latin for "seas", Maria is plural, "Mare" is the singular). The origin of most of the lunar features are due to a single process: bombardment of the Moon by large rocks, boulders, asteroids and comets. As the solar system formed, there was an abundance of material left over, most of this was in the form gas and dust, and small "rocks". But there were some large bodies also. Eventually, all of this material ended-up crashing into the Sun, or onto some other planet or moon (note that comets and asteroids, which we will talk about in upcoming classes, are believed to be left over material from the earliest days of the solar system). It is this process that has shaped the surface of the Moon. The Moon has no atmosphere, thus when the Sun is above the horizon, the surface is hot (about 100C, the boiling point of water on Earth), but when the Sun sets it gets very cold (-173C = 100 K)! As shown below, the presence of an atmosphere on Earth traps the heat:

A brief digression on temperature scales. Astronomers (and all scientists) use the "Kelvin" temperature scale system. Because many equations that describe real physical processes (like gas pressure: P = NkT/V) have a "T" in them, if the scale suddenly switches between positive and negative temperatures, the equation would suddenly switch signs--obviously air pressure does not go to negative pressure between +1 F and -1 F, or go to "0" at T = 0 F. So we need a temperature that does not have negative values or a zero that can be encountered in the physical world. The chosen system is "Kelvin". The size of the Kelvin degrees are the same size as those of the Celsius system, which are larger than Farenheit degrees [K = (F + 459.67) x 5/9]. Here is a comparison:

On the Moon, a small fraction (< 10%) of the sunlight is reflected into space, the rest is absorbed by the solid surface, heating it to fairly high temperatures. Note that the Earth has a lot of cloud cover, and it reflects about 40% of the incoming sunlight, keeping us cooler than if all of the sunlight hit the Earth's surface--but it also traps heat in, keeping us warmer at night. Once night falls on the Moon, all of the gained heat is radiated off into space--one of the heat transfer mechanisms we mentioned a few classes ago. Shortly, we will talk how this cold might trap water in the form of ice deposits near the poles.

Because the Moon has no atmosphere, and it does not have active volcanoes or plate tectonics, there are no processes to erase the craters left over from the bombardment phase. Thus, the surface of the Moon reflects the violent history of the early days of our solar system. Note that the Earth probably suffered even greater numbers of craters, but the erosion processes here erased MOST traces of such events (not all, however, see below).

Let's look at a lunar crater more carefully. Here is the lunar crater Copernicus (named after Nicholas):

If you look carefully at this picture, you will see lots of radial features that emanate from the crater ("crater chains"). These smaller pockmarks are from material blasted out of the crater that fell on the surrounding surface creating hundreds of smaller craters. Copernicus is about 93 km across. Note how the surrounding plains have been disturbed by the impact. Near the center of the crater you can see some small mountain peaks. Here is a view taken by the Apollo 17 crew of Copernicus from a different angle than we can see on Earth:

Now we can see the central hills/mountains more clearly. These peaks are about 1 km in height. So how does all of this structure form? Here is the basic process:

As the meteorite impacts the lunar surface it first compresses and heats the surface rocks, this then "rebounds" in a giant explosion that excavates the crater. Some material is ejected outwards forming rays and crater chains. Other material falls back in. Sometimes the central part rebounds and forms a central peak (or complex in the case of Copernicus). Here is the basic structure of craters:

Breccia is a type of rock made from the "cementing" of lots of broken bits of rock together (go here for more on lunar soils). Here is a simple crater (Moltke):

Here's another more complex crater (Euler):

Simple craters result from smaller meteorites impacting the Moon, while complex craters are the result of large impacts. In general a meteorite that has a diameter of 1 km will blast a crater that has a diameter of about 20 km. Why such big explosions? Because meteoroids (what a meteor is called before impacting a planet or Moon) are traveling at very high speeds, from 10 to 70 km/s! Compare this to the highest velocity bullets that travel at 1 to 2 km/s. There is a lot of energy in these rocks out there orbiting around the Sun, and the amount of this energy depends on the speed of the collision: Kinetic Energy = 0.5mv2 (one half m-v squared, where m is the mass, and v is the velocity). So, the faster and more massive an object is when it hits, the larger the explosion. Remember the Earth (and Moon) are traveling through space with a high velocity: Sun-Earth distance ("one Astronomical Unit") = 149,600,000 km, so the circumference of the Earth's orbit is 2*pi*149,600,000 = 940,000,000 km. It takes one year to complete an orbit, or 365 x 24 x 60 x 60 = 3.15x107s in a year, so the average velocity of the Earth is 30 km/s! From Kepler's laws we know that all objects near the Earth travel at a similar velocity---it is just their directions that are different. So, you can see that the impact velocities are going to be very high, and the resulting explosions have hundreds or thousands of megatons for even relatively small impactors.

The most dominant features on the Moon, those that are visible without a telescope, are the lunar maria. In this (nearly) full Moon image, the Maria are the large, dark regions:

Here is a close up (below) of one of them, Mare Serenitatis (the Sea of Serenity, it can be located in the full Moon image above--it is the roughly circular dark region above and to the right of center):

As this picture shows, the Maria are quite smooth---almost free of craters. [Mare is the sigular of Maria, so an individual "sea" is called a "mare."] The number of craters a particular region has indicates its age: more craters means that it is older. Why? Well, back when our solar system was young, there was a bunch of junk left over from the formation of the planets. This junk (rock, dust, etc.) was eventually "swept-up" by the planets and the Sun. So, the amount of material floating between the planets declined with time. In the early times, the planets were being bombarded with meteors, but this died off fairly quickly, and fewer, and fewer meteors were left to cause impact craters. Thus, the number of impact craters declined with time. Because maria have few craters, they MUST be younger than the surrounding regions. But, you ask, how is a maria formed? The same way the smaller craters are formed: by impact. But now the impacting body is very large, and it cracks the crust of the Moon and lava from the mantle of the Moon leaks up to the surface and floods the surrounding terrain. Here is a maria impact cartoon:

The cracks in the crust (the red/orange lines in this drawing) show the molten material from inside the Moon making its way to the surface so as to flood the surrounding regions, and to fill in the large hole created by the impact. The bodies responsible for creating Maria are many kilometers in diameter. As the text book notes, a meteor that is 1 km in diameter creates a crater that is 10 to 20 km wide, and 1 km deep. The largest lunar maria are over 1,000 km across! It would take a body about 100 km across to make such a large feature. With the Apollo missions it was possible to actually date the rocks located both within the maria, and outside the maria, in the brighter regions called the "lunar highlands." In the lunar highlands, a region of numerous craters, the rocks were found to be about 4.2 billion years old. The rocks from the maria, however, are somewhat younger: 3.8 billion years old. Obviously, as the solar system aged, the smaller rocks and boulders coagulated into larger bodies, and these larger bodies were "accreted" by the even larger moon-sized and planet-sized objects. Here is another Moon image with the Highlands labeled:

Here is a close-up showing how rough the highlands actually are:

Craters upon craters! There was some trepidation in sending a manned mission into this region due to a fear that the surface would be too rough to safely land, but Apollo 16 targeted the highlands so that we could confirm the hypothesis that the highlands are older.

Here is a map of where the Apollo missions (green triangles) landed (as well as some unmanned probes. Click here for a bigger image):

[Go here to see recent images of the Apollo 17 landing site taken by a NASA probe.] Speaking of Moon landings, we also get information on the lunar surface, showing it to be very powdery, as can be seen by the amount of dust kicked-up by the rover:

and shown by the footprint:

This is due to the bombardment of the surface by "micrometeorites", very small grains of dust and rock that hit the surface because the Moon has no atmosphere. Over billions of years, this pulverizes the surface. Before we got to the moon there was quite a bit of fear that there could be many meters of this stuff on the surface, and any lunar landers would sink out of sight. But on average there are only a few cm's of this powdery dust.

The Moon has other geological features, including evidence for lava flows, such as this collapsed "lava tube":

Similar features are seen on Earth, here is a lava tube cave:

Somtimes, after crater formation, cracks can develop in the surface due to the cooling of the lava that flowed in:

And, longer versions of these, which are faults, called "graben" can also be seen in the maria:

Faults are also seen on the Earth's surface, like the San Andreas fault pictured below,

but in the case of the Earth, most faults have their origins in tectonic activity--most of those on the Moon are due to fractures caused by impacts, or by the shrinking of the lunar surface.

Two volcanic domes:

While volcanism is an ongoing process on the Earth, most of the evidence shows that nearly all of the volcanism on the Moon ended some 3 or 4 billion years ago. This was shortly after the Moon formed, and was probably due to the inner portion of the Moon still being hot, and some of this leaked to the surface. There is no evidence that the Moon ever had plate tectonics. Interestingly, since the Moon's gravity is about one sixth that of the Earth, the smoothness of the lunar maria imply a rather low viscosity ("runny") for the lunar lava flows, and explosive eruptions (if they were to occur) could eject material to much greater distances than similar events on the Earth. The material from which the Moon is comprised is very water poor, and water (actually steam) is one of the drivers for explosive eruptions on the Earth, like these "composite" volcanoes on the Kamchatka penninsula:

The two main volcano types are composite and shield--Hawaii is a shield volcano, Mt St Helen's is a composite (a go here for more on earthly volcano types). The Moon is almost water-free, thus any volcanic eruptions that occurred were probably less dynamic.

It is interesting to compare lunar craters with some of those on Earth, here is a sample:

The topmost of these three is Berringer ("Meteor") crater (1 km diameter, 170 m deep) in Arizona (near Winslow) that has an age of about 49,000 years. The middle one is Wolfe Creek (0.8 km diameter) in western Australia with an age of about 300,000 years, and the last is Manicouagan (70 km in diameter) in northern Quebec at about 210 million years old (and the oldest easily identified crater on Earth). Thus, like the Moon, the Earth has suffered from meteor/asteroid impacts---it is just our erosion processes (tectonics/weather) that erase the evidence for these impacts.

Composition of the Moon

What is the composition of the Moon? Here is a table comparing the Moon to the Earth:

At first glance, their compositions are completely different. We can see that the Moon is iron-poor, but oxygen rich. Recent space probes (e.g., Clementine) have started mapping the global composition of the Moon (there is renewed interest in the Moon, and even the fledgling Chinese space program is sending probes to the Moon). Here are two maps of the distribution of iron and titanium on the Moon:

If you compare the iron distribution to a picture of the full Moon,

you see that it follows the distribution of maria. Why? Because the maria are comprised of lava that flowed from the interior of the Moon to the surface. Iron is dense, so it naturally drifts towards the center of massive objects ("diffusion"), so there is more of it in the mantle and core of the Moon.

Water on the Moon?

As we have just discussed, the lunar surface is very dry---there is no atmosphere, so that water cannot exist in liquid form. Now, it is possible to have ice on the Moon. Except, we just found out that the surface of the Moon gets very hot during the "day" (remember a lunar day is about two weeks long). Thus, ice could not exist anywhere on the surface that gets direct sunlight. Are there places on the Moon that never see sunlight? Yes! The Moon is covered with impact craters. These craters can be several kilometers deep. Thus, the floors (or parts of the floors) of some craters near the North and South poles of the Moon never see sunlight! These areas are extremely cold, and thus can become a "cold trap." Any molecules of water that happen to be passing by can get frozen to the surface. This is like pulling a beer mug out of the freezer---it instantly gets covered in frost. What is happening is that the water vapor in our atmosphere is freezing to the surface of the mug. If humans ever want to live on the Moon, they will need a source of water. Currently it costs $25,000 to launch one kilogram into Earth orbit. Humans need about 2 liters of water (= 2 kg!) per day. You can guess that even with very efficient recycling, we need lots of water to sustain life on the surface of the Moon. Thus, finding a cheap, local source would help make a Moon base feasible. This was the reason behind the "LCROSS" mission: to crash a big object into the surface of the Moon to see if there was water mixed into the soil (here is a little video on the mission). The mission crashed a projectile into the crater "Cabeus":

And here is a sequence of pictures (flipped from previous image) centered on the impact site, showing the tiny little blip that was caused by the impact. Fortunately, this was enough for the instruments on the space craft to detect water (go here for the official press release).

The Formation of the Moon

So, where did the Moon come from? At the time of the Apollo missions, there were four main ideas about the origin of the Moon: 1) the fission hypothesis (Earth was spinning rapidly, and a large chunk broke off), 2) the "capture" hypothesis (the Moon formed elsewhere, and was captured after coming too close to the Earth), 3) the "condensation" hypothesis (the Moon formed in place from material left over from the Earth's formation), or 4) the "giant impactor" hypothesis (a huge body, about the size of Mars, hit the Earth, and the material liberated from the Earth's surface coalesced into the Moon). It is the last idea that is now believed to be correct. New (computer) models for the fission hypothesis show that requires an extremely rapid rotation rate of the Earth, and this is not observed (the Moon would have also ended-up orbiting in the same plane as the Earth's rotation--that is over the equator, tilted by 23.5 o to the Earth's orbit). The lunar rocks also show evidence of tremendous heating. Not possible in the fission model. The capture hypothesis does not work because it is next to impossible to capture such a large body without perfect conditions. The lunar composition (low density of 3.34 gm/cm3) would imply that it had to form out near Mars (which has a density of 3.9 gm/cm3), migrate inwards, and get trapped by the Earth. Here is a table showing how the planets change in density with position in the solar system:

A body coming from outside the Earth's orbit would have way too much energy to get captured by the Earth. The problem with the condensation model was that if the Moon formed from the same material as the Earth, it should have the same overall density and composition. It does not, it has a lower density and is iron-poor. The giant impactor theory gets around all of these problems: the impact of a Mars-sized planet with the Earth would remove mostly crustal/mantle material that is low in iron, this explains the density. Analysis of the Moon rocks shows they have a similar composition to the crust/mantle of Earth:

Finally, the tremendous heating apparent in lunar rocks can be easily explained by the heat of the impact. Here is an artist's view of the impact:

The material blasted from the Earth and from the disrupted impactor during this impact eventually coagulates and forms the Moon (for more on this theory, including new computer models, go here.). So when did this occur? Since the Moon is iron-poor, this tells us that that most of the iron of the Earth had already found (diffused) its way to the core. This indicates that the Moon must have formed well after the Earth. Recent evidence (based on isotopic ratios of Tungsten) suggests that the moon formed somewhere between 60 million years and 100 million years after the Earth formed. One of the outstanding questions is why there is little trace of the impactor---models suggest it should comprise most of the ejected material. But new models suggest that the Earth and proto-moon material were enveloped in a "silicon vapor" cloud/atmosphere, and there was sufficient mixing to drive the final lunar composition to be similar to the Earth's mantle/crust. While the formation of the Moon was violent, not long after formation (a few hundred million years), the Moon became a much quieter place.

As the bombardment phase of the early solar system ended, fewer and fewer impacts were occurring anywhere in the solar system, but some of those that did occur involved large bodies creating the maria, here is a time sequence as described in Fig. 49 of chapter 9:

The rate of cratering of a surface allows us to estimate the age. Here is a plot of the cratering rate that was estimated shortly after the return of the Apollo 12 data:

Because of its small size and low density, the Moon actually cooled very rapidly:

In the early stages, the heavier elements (iron or radioactive species) diffused to the center, and there was probably a liquid core, and a small amount of heating--including that from heavy meteorite bombardment. Within a few hundred million years, the Moon started to solidify. In the early days, the Moon probably had a liquid interior. But now, the Moon is believed to be solid all the way to the core:

Here is a slice through the Earth (left) and Moon (right) showing the (to scale) sizes of the components that comprise the internal structure of the two bodies:

Because the Moon is completely solid, there is very little geological activity on the surface of the Moon. Any volcanoes the Moon had died-out shortly after it formed. To have volcanoes you need a hot, liquid interior. The Moon does not have this, thus the Moon's surface has remained relatively unchanged by geological activity for the last 3.5 billion years. So, as the Moon slowly cooled, it shrank. There has been a bit of buzz about the "incredible shrinking Moon," showing that it was an ongoing process for much of the history of the solar system, and probably stopped about 1 billion years ago. Go here for a recent press release from NASA.

Why doesn't the Moon have an atmosphere? The reason the Moon has no atmosphere is that it the gravity is too weak to hold on to any gases that might have been present during the time when the Moon had volcanic activity. The Moon and Earth are relatively close to the Sun, and the heat of the Sun warms the atmosphere, and it expands. The Moon's gravity is much too weak to hold onto an atmosphere. Thus, without erosion from wind and rain, the Moon's surface does not change (except for--now rare--meteorite impacts).

Tides: The Influence that the Moon Has on Earth

For those who grew up near the Ocean, or have visited a costal region, you are probably aware of "tides." The gravity of the Moon pulls on the Earth:

The oceans, being liquid, respond more easily to this force than solid ground, and a bulge is created that rotates around the Earth twice per day, and the water level on the coast rises and falls:


Astronomical Devices

Some of the images in previous lectures were taken through a telescope (and you will see more in the coming weeks). Telescopes are used to make objects both brighter, and bigger. Before we begin our exploration of the more distant reaches of the Solar System, we need to take a brief excursion to talk about optics and telescopes. As we noted a week or two ago, Galileo is given most of the credit for being the first to use a telescope for astronomical purposes. But glass lenses have been around since at least 1100 AD, and eyeglasses seem to have been developed in the 13th or 14th century. What good is a telescope? First, let's look at something you are familiar with, your eye:

Your eye has a pupil and a lens.

So, how does a lens work? Well, when light encounters the glass, its speed slows down---light travels more slowly in glass then in air, or in empty space. Thus, if light encounters a tilted piece of glass like that shown below:

it is bent. Think of a marching band trying to march in a line and then executing a turn while trying to remain in a line--those on the outside tip of the line have to walk faster while those on the inside edge of the turn are not moving at all. Now picture a marching band that is in a diagonal line formation marching up a football field, but when they get to the 40 yd line they encounter thick mud. The first band members that hit the mud all of a sudden march more slowly, while those in the dry portion of the field keep marching at the same speed until they hit the mud. This causes a slight bending in the line as they go through the mud. So in glass, the bottom portion of the light beam in the figure above hits the glass surface first, slows down first, and this causes a turn in the beam.

In the eye the lens forms the image (upside down!), while the pupil adjusts in size to allow you to let in more light when it is dark, or less light when it is bright. The size of the pupil is what controls how faint of an object you can see. For example, owls have large pupils to allow in more light since they hunt at night. Cats have sensitive eyes, so when it is bright out, their pupil contracts to a very narrow slit (for more on the nature of the human eye, go here.). The size of the lens is the controlling factor for how faint a light source you can see. That's the first important property of telescopes---they "collect light". Looking through a telescope is like replacing your small eye lens with a much bigger lens. The second important property of a telescope is its ability to magnify objects to see finer detail. The amount of detail that you can see depends on the size of your pupil---or the diameter of the lens of a telescope. This is very similar to parallax. The larger the baseline used in a parallax measurement, the smaller angles (finer details) you can measure. The two extreme edges (diameter) of a lens are your "baseline" for creating detailed images. That is why big telescopes are valuable, they collect light, and allow you to magnify an image to see fine detail.

The amount of light a telescope collects depends on its area. For example, the largest dilated human eye pupil has a diameter of about 8 mm. Therefore, it has an area of 50 square mm (π R2!) A one inch telescope, like Galilo had, has an area of (d= 1 inch = 25mm) 490 square mm. Galileo's telescope collected 10X more light than the human eye, allowing him to see stars that were 10X fainter than those visible with the naked eye. The largest telescope (Keck) has a diameter of 10 meters (10,000 mm), it collects 1.5 million times as much light as the human eye.

During the late 17th and early 18th century, telescope technology was quickly improving. As with Galileo's primitive telescope, nearly all the instruments of that time were "refractors". Refractors use lenses to bend the light to a focus where an eyepiece (similar to a little microscope) magnifies the image:

The problem with early refractors was that they used only a single glass lens, and this arrangement could not bring all colors of light to a common focus. Thus, everything you looked at had blue and red images that were not in focus. This is called chromatic abberation:

To counteract chromatic abberation, the first telescopes were made to be very long. Some of these telescopes had small lenses, on the order of 3" in diameter, but were more than 20 feet long (the longest ones approached 75ft)! This made them difficult to use, and discoveries made with them were rather slow in coming. Though, Christiaan Huygens used one of these primitive telescopes to discover Titan, the largest Moon of Saturn, and to figure out the true nature of Saturn's rings (that's why the probe that entered Titan's atmosphere in 2005 was named "Huygens").

It was discovered later that mixing two (or more) types of glass could counteract the chromatic aberration, and all modern telescopes and camera lenses have more than one lens:

One of the major contributions of Isaac Newton was his book on optics entitled Opticks, published in 1704. One of his proposals was to use a curved mirror to focus light to eliminate chromatic aberration. Newton knew that all light, no matter its color, suffers an identical reflection, thus a telescope using a mirror as its objective would eliminate most of the chromatic abberation suffered by refractors. Using mirrors, telescopes could grow in light gathering ability without becoming too large to manage. One of Newton's designs for such a telescope still bears his name:

Besides providing better image quality, telescopes with a single curved mirror were easier to produce than refractors (that have two curved surfaces). They were also cheaper. One of the first people to successfully build and use these types of telescopes was William Herschel (1738 - 1822). A drawing of his largest telescope is shown, below.

Herschel is best known for his discovery of Uranus in 1782, a discovery that would give him a secure future as "astronomer to the king". Herschel also discovered two Moons of Saturn, as well as two Moons around Uranus. He also observed binary stars, and showed that their orbits followed Newton's laws, and thus these laws appeared to be "universal" (that is, they worked everywhere in the Universe the same way as on Earth). Currently, the world's largest telescopes are the 10 m Keck telescopes:

Because it is extremely difficult to make a single piece of glass that is 10 m across and optically perfect, the Keck mirrors are segemented:

The next generation of mammoth telescopes are being planned, like the "Thirty Meter Telescope":

The desire for larger and larger telescopes is due to the need to detect the weak, faint objects found in astronomy. But larger isn't all that we need, going into space allows us to get above the distorting atmosphere. Here is an example:

This is why the Hubble Space Telescope was launched:

But techniques are being developed to allow ground based telescopes to reduce the affects of our atmosphere ("adaptive optics"), where a flexible mirror is used to improve the image.

Most cartoons you see have astronomers looking into eyepieces and making drawings. But just about all astronomy now uses digital detectors like those used in your digital camera:

The only difference is we use better quality detectors, bigger detectors (>60 "megapixels"), and chill them to extremely cold temperatures to get rid of electronic noise. But even with simple webcams, you can get amazing quality--here is comparison between a typical snapshot, and an image made by processing a short movie of Saturn using a webcam at our campus observatory:

Inverse Square Law of Light

Astronomers build bigger and bigger telescopes to collect as much light as possible. This is because the brightness of an object falls off as 1/R2, that is if you double the distance, the object is only 1/4th as bright, because the light spreads out as it travels:

Note that any sphere drawn around a star (or a light bulb in this diagram) intercepts all of the light emitted by the star. The area of a sphere is 4piR2. If you double the radius (R), the area quadruples (22 = 4). The intensity of the light passing through a square centimeter drops as 1/R2. In the figure, the radius of the inner sphere (or hemisphere) is 1, the next one has a radius of 2, and the next one has a radius of 3. The areas of the spheres go as 1, 4, and 9 square units, as is highlighted.