In studying the Solar System, we find an important exception to our concept of astronomical objects being so remote that we cannot hope to visit them in the foreseeable future. People have already visited our nearest neighbor in the Solar System, the Moon, and brought back pieces to study in normal Earth-bound laboratories. Unmanned probes have landed on Venus and Mars and have visited all the other planets. Clearly, the opportunity for even limited close-up viewing has had a major impact on our understanding of the Solar System.

However, the study of the Solar System is not simply devoted to sending probes when we feel like it. The spacecraft have followed literally centuries of study by more traditional astronomical methods. By the time the first probe was launched to any planet, astronomers had already developed a picture of what they expected to find. Many of these pictures did not survive the planetary encounters, but they did provide a framework for asking questions, and for deciding what instruments were important to place on the various probes.

We have also had the advantage of having the Earth as an example of a planet to study. It has been possible to develop ideas about planetary surfaces, interiors, atmospheres and magnetospheres by studying the Earth. For that reason, we have devoted one whole chapter of this Part to the Earth, viewed not as our home base, but as just one planet.

In Chapter 10 we saw how stars evolve to the red giant or red supergiant stages, and how low mass stars (less than 5M⊙) lose enough mass to leave behind a white dwarf as the final stellar remnant. We also saw that electron degeneracy pressure can only support a 1.44 M⊙remnant. In this chapter we will see what happens to higher mass stars.

It is important to remember that stars lose mass as they evolve. This mass loss can be through winds, or the ejection of planetary nebulae. (In the next chapter, we will see that stars in close binary systems can transfer mass to a companion.) Though we only have estimates for the total amount of mass loss, it seems likely that massive stars can lose more than half of their mass by the time they pass through the red supergiant phase. A star's evolution will depend on how much mass it starts with, and how much mass it loses along the way.

Supernovae

Core evolution of high mass stars

In the core of a high mass star the buildup of heavier elements continues. If we look at nuclear binding energies (Fig. 9.3) we see that the isotope of iron 56Fe has the highest binding energy per nucleon. This makes it the most stable nucleus. This means that any reaction involving 56Fe, be it fission or fusion, requires an input of energy.

Distribution of galaxies

If we look at the distribution of galaxies, such as that shown in Fig. 18.1, we see that the galaxies are not randomly arranged on the sky. Among the patterns we see distinct groupings, called clusters of galaxies.

Clusters are interesting for a number of reasons. They may provide us with clues on the formation of galaxies themselves. This is especially true if, as many think, cluster-sized objects formed first and then broke into galaxy-sized objects. (The alternative view is that galaxies formed first and then gathered into clusters.) Clusters also pose us with interesting dynamical problems, including a dark matter problem of their own. Finally, when we reach the scale of clusters of galaxies, we are beginning to reach a scale which has some significance in the overall structure of the universe.

The cluster of galaxies to which the Milky Way belongs is called the Local Group. As clusters go, it is not a very rich one. Besides the Milky Way, it contains several irregulars, including our companions, the Large and Small Magellanic Clouds, the spiral galaxies M31 and M33, and a number of dwarf ellipticals. Other nearby clusters are named by the constellation in which they are centered. For example the Virgo, Coma, Hercules and Centaurus clusters are shown in Fig. 18.2.

Cluster dynamics

Just as with clusters of stars, clusters of galaxies may be isolated collections of masses interacting gravitationally. As such, they are interesting systems to understand.

In the outer planets, we find a considerable contrast with the four inner planets. We therefore study them as a group, comparing surfaces, interiors and atmospheres. The relative sizes of the outer planets (and Earth) are shown in Fig. 25.1.

Basic features

Jupiter, shown in Fig. 25.2, is by far the most massive planet in the Solar System. It is 318 times as massive as the Earth, and is a respectable 0.1% as massive as the Sun. (The rest of the planets together only have 129 Earth masses.) Jupiter's density is much lower than that of the inner planets, 1.3 g/cm3 vs. 5.4, 5.3, 5.5 and 3.9 for Mercury, Venus, Earth and Mars, respectively. Its density is only slightly greater than that of liquid water. This suggests that the composition of Jupiter is basically different from that of the inner planets. This is due, in part, to the larger gravity, 2.54 g at the cloud tops. The larger gravity means that the lighter gases have been retained.

The atmosphere is 85% hydrogen and 15% helium, with a variety of trace constituents. This composition is much closer to that of the Sun than it is to the inner planets. The motions in the atmosphere are affected by the planet's rapid rotation. The period is 9.92 hr at the equator. The rotation period is greater at the poles. The rapid rotation produces a large coriolis force.

Foundations of special relativity

Problems with electromagnetic radiation

The problems that lead to special relativity start with Maxwell's theory of electromagnetic radiation. Maxwell's equations, presented in 1873, allow for the existence of waves of oscillating electric and magnetic fields. All waves known before electromagnetic waves required a medium in which to travel. For example, sound waves can travel through air, but not through a vacuum. There is no obvious medium necessary for the propagation of electromagnetic waves. Physicists postulated a medium that is difficult to detect, called the luminiferous ether, or simply the ether. The ether supposedly fills all of space. Once we have a medium, then we have a reference frame for the motion of the waves. For example, the speed of sound is measured with respect to the air through which it is moving. An observer moving through the medium will detect a different speed for the waves than an observer at rest in the medium.

Einstein's questions about Maxwell's equations involve the appearance of electromagnetic waves to different observers, who are moving at different speeds. Einstein started with the postulate of special relativity, that, the laws of physics, properly stated, should be independent of the velocity of the observer. It may be that the values of certain quantities change with the motion of the observer, but the relationships among the physical quantities do not change.

Einstein examined Maxwell's equations to see if they obeyed this simple rule. His reasoning is illustrated in Fig. 7.1.

The Earth belongs to a group of nine planets, orbiting the Sun, called the Solar System. Each object follows its own orbit about the Sun. All of the planets orbit in the same direction. As large as the Earth seems to us, it is small compared to the distances between objects in the Solar System. This is true of the other planets, even those much larger than the Earth. For all practical purposes, the Solar System is vast emptiness, with a few small island oases.

If we could look at a side view of the Solar System, we would notice that the orbits are not very tilted with respect to that of the Earth. So, in a side view from the outside, the Solar System would look like a very thin disk. We call the plane of the Earth's orbit the ecliptic. The motion of the Earth around the Sun causes the Sun to appear to move against the background of fixed stars. That path is just the projection of the ecliptic onto the sky. The Earth's rotation axis is tilted (by 23.5°) so that the ecliptic does not line up with the Earth's equator.

We begin a brief tour of the Solar System by looking at the planets. A photograph of each planet is shown in Fig. 22.1. It is convenient to divide the planets into two groups, the inner planets and the outer planets. The inner four planets are Mercury, Venus, Earth and Mars. The giant outer planets are Jupiter, Saturn, Uranus and Neptune.

Most of the light we can see from our galaxy appears as a narrow band around the sky. From its appearance, we think that we are in the plane of a disk, and that this disk looks something like the Andromeda galaxy. However, our location within our own galaxy makes its structure very difficult to study. In this part we will see both how we learn about our galaxy and what we have learned about it so far.

Most of the light that we see comes directly from stars. Among all the objects we can see, the stars provide most of the mass. Averaged over the whole galaxy, the gas and dust between the stars – the interstellar medium – contains only about 1% as much mass as the stars themselves. Of the interstellar medium, 99% of the mass is in the form of gas, and 1% of the mass is in the form of dust. However, this small amount of dust is very efficient at blocking light, making optical observations of distant objects difficult.

We expect that stars form out of interstellar material. Since most of the mass of the interstellar material is in the form of gas, it is the gas that will provide the gravitational attraction for the star formation process. In this part, we will first look at the contents of the interstellar medium. We will then look at how stars are born. Finally, we will see how the stars and interstellar medium are arranged in the galaxy as a whole.

We have already seen that the mass of a star is the most important property in determining a star's structure. For a main sequence star the mass determines the size and temperature. The lifetime of a star on the main sequence depends on the available fuel and the rate at which that fuel is being consumed – the luminosity. Both of these quantities depend on the star's mass, so the lifetime on the main sequence also depends on the mass. When the star uses up its basic supply of fuel, its ultimate fate also depends on its mass. In fact, the mass and the initial composition of a star completely determine its structure and evolution. This can be proven mathematically on the basis of the physical equations involved. This result is known as Vogt's theorem.

Evolution off the main sequence

Low mass stars

We first look at stars whose mass is less than about 5 M⊙. Eventually a star will reach the point where all the hydrogen in the core has been converted to helium. For a low mass star, the central temperature will not be high enough for the helium to fuse into heavier elements. There is still a lot of hydrogen outside the core, but the temperature is not high enough for nuclear reactions to take place. The core begins to contract, converting gravitational potential energy into kinetic energy, resulting in a heating of the core.

In the preceding chapter, we noted that Lemaitre first pointed out that if the universe is expanding, then there must have been an era in the past when it was much denser than it is now. This hot, dense early era was named the big bang by Fred Hoyle, a steady-state cosmologist, in an attempt to ridicule the theory. The theory survived the ridicule, the name remained, and we now refer to all cosmological models with an evolving universe as ‘big-bang cosmologies’. In this chapter, we will see what we can learn about conditions in the big bang, and what the relationship is between those conditions and the current state of the universe.

The cosmic background radiation

Following the idea that the universe was very hot and dense, George Gamow suggested, in 1946, that when the universe was less than about 200 seconds old, the temperature was greater than one billion kelvin, hot enough for nuclear reactions to take place rapidly. In 1948, Ralph Alpher, Hans Bethe and Gamow showed (in a paper often referred to as the alpha/beta/gamma (for the names of the authors) paper) that these nuclear reactions might be able to explain the current abundance of helium in the universe. (We will discuss the synthesis of the elements in the next section.) In a more thorough analysis of the problem, Alpher and Robert Herman, in a classic paper published in 1948, found that the early universe should have been filled with radiation, and that the remnant of that radiation should still be detectable as a low intensity background of microwaves.

Einstein once said that the most incomprehensible thing about the universe is that it is comprehensible. It is amazing that we can apparently describe the universe with what are very simple theories. We can ask truly fundamental questions of where we have come from and where we are going and expect scientific answers. In this chapter and the next, we will study cosmology, the large-scale structure of the universe. We can learn a great deal using only the physics we have introduced in this book. With the introduction of some more physics, namely elementary particle physics (in Chapter 21), we will see that even more fascinating concepts are within our grasp.

The scale of the universe

When we study the gas in a room, we must deal with it as a collection of molecules. We don't care about the fact that the molecules are made up of atoms or that the atoms are made up of protons, neutrons and electrons; or that the protons and neutrons are made up of other particles. All we care about is how the molecules interact with one another, and how that affects the large-scale properties of the gas. When we study the universe, we also treat it as a gas. The molecules of the gas are galaxies. In the big picture, stars, planets, etc., don't matter. Of course these smaller objects can still contain some hidden clues for us to learn about the larger structure.

The study of astronomy has blossomed in a variety of ways in the last decade of the 20th century. Every part of the electromagnetic spectrum has seen a revolution in observing techniques. While much of this has been on the ground, space-based observing has come into its own, as we are seeing the results of second and third generation spacebased telescopes. These have provided sensitivity and clarity that have revolutionized all subfields in astronomy and created some new ones. These observational developments have been supplemented by massive improvements in computing power, allowing for the processing of large amounts of astronomical data, and the theoretical modeling of the results.

The most amazing aspect of all of this progress is that we can still provide reasonable answers to the naive question, ‘How does it all work?’ As our astronomical horizon expands, we can still use familiar physics to explain the wealth of phenomena. Even when the explanation at the research level requires a complex application of certain physical laws, there is usually still a way of understanding the phenomena based on introductory level physics. Perhaps this is just the realization that the laws of physics are small in number but apply universally. There are a few exceptions, where the astronomical problems help drive back the frontiers of physics, but these can be explained in more familiar terms.

This book is dedicated to the student who would like more out of even a brief study of astronomy than a list of what there is.

Close binaries

If the two stars in a binary system are very close to each other, each has the effect of altering the structure of the other star. When this occurs we call the system a close binary system. The surface of a star can be distorted by the stronger gravitational force that the companion exerts on the near side than on the far side. Remember, we said that any effect that depends on variations in the gravitational force from one position to another is called a tidal effect. (A similar situation applies as the Sun and Moon distort the Earth's ocean surface, raising the tides.)

The distortion of stars results in internal dissipation of energy. As a star rotates, different material is incorporated in the bulge. Different layers of material rub against each other, in a fluid friction. This lost energy has to come from somewhere. It comes from both the orbital energy and the rotational energy of the star. As a result, eventually the orbits circularize and the two stars always keep the same sides towards each other. This is the lowest energy arrangement for the system (see Problem 12.1). We say that the spins are synchronized. (The Moon's spin and orbital motion around the Earth are synchronized, and the Moon keeps the same side towards the Earth.)

In certain situations, it is possible for material from one star to be pulled off the surface onto the other star.

Coordinate systems

When we want to locate a star, or any other astronomical object, we only need to specify its direction. We don't need its distance. We therefore need only two coordinates, two angles, to locate an astronomical object. Sometimes, it is convenient to think (as the ancients did) of the stars as being painted on the inside of a sphere, the celestial sphere. Just as we can locate any place on the surface of Earth with two coordinates, latitude and longitude, we need two coordinates to locate an object on the celestial sphere.

We choose coordinate systems for convenience in a particular application. In general, to set up a coordinate system we first identify an equator and then choose coordinates that correspond to latitude and longitude.

A convenient system for any particular observer is the horizon system. The horizon becomes the equivalent of the equator in that system. The angle around the horizon, measured from north, through east, south and west, is the azimuth. The angle above the horizon is called elevation. Instead of elevation, we can use the zenith distance, which is the angle from the zenith (overhead) to the object. From their definitions, we can see that the sum of the zenith distance and the elevation is always 90°. The azimuth ranges from 0° to 360°, and the elevation from −90° to 90° (with negative elevations being below the horizon).

We start our discussion of the planets with the one with which we are most familiar, the Earth. In understanding the processes that are important on the Earth, both now and in the past, we are setting a framework for our understanding of the other planets. Therefore, in this chapter we will develop many of the ideas that should apply to all planets, both in terms of what properties are important and how we measure them.

History of the Earth

Early history

The main steps in the history of the Earth are shown in Fig. 23.2. Somehow, the Earth accreted from the material in the original solar nebula. We will discuss more about the solar nebula in Chapter 27. Enough material collected together so that its own gravitational pull was able to keep most of the material from escaping. As particles fell towards a central core, they were moving closer together, so their gravitational potential energy decreased. This means that their kinetic energy increased. This kinetic energy was then available to heat the forming planet. In addition, heat was provided by the radioactive decay of potassium, thorium and uranium. Such decays led to heating, because the energetic particles – alpha, beta, gamma – were absorbed by the surrounding rock. The relatively massive alpha particles were particularly effective in this heating. The heating resulted in a liquid, or molten, interior.

General relativity is Einstein's theory of gravitation that builds on the geometric concepts of spacetime introduced by special relativity. Einstein was looking for a more fundamental explanation of gravity than the empirical laws of Newton. Besides coming up with a different way of thinking about gravity (in terms of geometry), general relativity makes a series of specific predictions of observable deviations from Newtonian gravitation, especially under strong gravitational fields. These predictions provide a stringent test of Einstein's theory (e.g. Fig. 8.1).

Curved space-time

A central tenet of general relativity is that the presence of a gravitational field alters the rules of geometry in space-time. The effect is to make it seem as if space-time is “curved”. To see what we mean by geometry in a curved space, we look at geometry on the surface of a sphere, as illustrated in Fig. 8.2. The surface is two-dimensional. We need only two coordinates (say latitude and longitude) to locate any point on the surface. However, it is curved into a three-dimensional world, and that curvature can be detected.

To discuss the geometry of a sphere, we must first extend our concept of a straight line. In a plane, the shortest distance between two points is a straight line. On the surface of the sphere it is a great circle. Examples of great circles on the Earth are the equator and the meridians. (A great circle is the intersection of the surface of the sphere with a plane passing through the center of the sphere.)