The visible Universe contains hundreds of billions of galaxies, each consisting of billions of stars. Recent discoveries of extrasolar planets lead us to believe that a typical galaxy may contain billions of planets (and presumably, asteroids and comets). The planets, stars and galaxies interact on a hierarchy of scales ranging from AU to parsec to megaparsec, experiencing forces arising from gravity, on all scales, and cosmic expansion on the larger scales. The combination of gravitational attraction and cosmic expansion has shaped the visible matter in the Universe into a hierarchy of structures leading to clusters and superclusters of galaxies.

A full description of the interactions that define the large-scale structure of the Universe and its constituent parts requires the application of general relativity on all scales and the introduction of a new force, as embodied in the recently proposed cosmological constant, on the largest scales. In this part, however, we limit ourselves largely to the application of classical (Newtonian) mechanics which is sufficiently accurate to describe the topics covered in this part and has the advantage of being more intuitive and accessible to the reader.

This part begins with a review of the basic elements of classical mechanics, subsequently used to derive Kepler's laws, the Virial theorem and various aspects of orbital motion. The resulting derivations are applied to specific astrophysical problems such as planetary motion, extrasolar planets, binary stars, galaxy rotation curves, dark matter, the large scale structure of the Universe and cosmic expansion.

Geometry is at the heart of Einstein's picture of gravity. The best place to see how gravity as curvature works is in the Solar System, where the predictions must be very close to the description given by Newton. In this familiar arena, we can compare the old and new ways of looking at gravity. In this arena, too, general relativity meets and passes its first two crucial tests: explaining the anomalous advance in the perihelion of the planet Mercury (which we puzzled over in Chapter 5), and predicting that light should be deflected as it passes the Sun by twice the amount that would be calculated from Newtonian gravity (see Chapter 4).

We saw in the last chapter that the equivalence principle tells us that it is not possible to represent gravity just by the curvature of space; the curvature of spacetime must include the curvature of time as well.

Astrophysics strives to describe the Universe through the application of fundamental physics. The Cosmos manifests phenomena in which the physics can appear in its most extreme, and therefore more insightful, forms. Consequently, developing astrophysical concepts from fundamental physics has the potential to achieve two goals: to derive a better understanding of astrophysical phenomena from first principles, and to illuminate the physics from which the astrophysics is developed. To that end, astrophysical topics are grouped, in this book, according to the relevant areas of physics. For example, the derivation of the laws of orbital motion, used in the detection of extrasolar planets, takes place in the classical mechanics part of the book while the derivation of transition rates for the 21 cm neutral hydrogen line, used to probe galaxy kinematics, is performed in the quantum mechanics part. The book could serve as a text for graduate students and as a reference for established researchers.

The content of this book is based on the material used by the author in support of advanced astrophysics courses taught at the University of New Mexico. The intended audience consists of graduate students and senior undergraduates pursuing degrees in physics and/or astrophysics. Perhaps the most directly relevant demographic is the combined Physics and Astronomy departments. These departments tend to emphasize the fundamental physics regardless of the research track pursued by the student. In many cases a separate astrophysics degree is not an option.

One of the most radical changes in the behavior of gravity in going from Newton's theory to Einstein's is that Einstein's gravity has waves. When two stars orbit one another in a binary system, the gravitational field they create is constantly changing, responding to the changes in the positions of the stars. In any theory of gravity that respects special relativity, the information about these changes cannot reach distant experimenters faster than light. In general relativity, these changes in gravity ripple outwards at exactly the speed of light.

These gravitational waves offer a new way of observing astronomical systems whose gravity is changing. They are an attractive form of radiation to observe, because they are not scattered or absorbed by dust or plasma between the radiating system and the Earth: as we saw in Chapter 1, gravity always gets through. Unfortunately, the weakness of gravity, which we also noted in Chapter 1, poses a severe problem. Gravitational waves affect laboratory equipment so little that only recently has it become possible to build instruments sensitive enough to register them.

Gravity is everywhere. No matter where you go, you can't seem to escape it. Pick up a stone and feel its weight. Then carry it inside a building and feel its weight again: there won't be any difference. Take the stone into a car and speed along at 100 miles per hour on a smooth road: again there won't be any noticeable change in the stone's weight. Take the stone into the gondola of a hot-air balloon that is hovering above the Earth. The balloon may be lighter than air, but the stone weighs just as much as before.

1. ▷ Remember, terms in boldface are in the glossary.

This inescapability of gravity makes it different from all other forces of nature. Try taking a portable radio into a metal enclosure, like a car, and see what happens to its ability to pick up radio stations: it gets seriously worse. Radio waves are one aspect of the electromagnetic force, which in other guises gives us static electricity and magnetic fields.

As explained in the preface, I have used high-school mathematics to present some of the material in this book. If you want to know what that means, if you want to learn whether you have the background necessary to do the mathematics, then scan through this introductory material. But remember, it is not necessary to follow all the derivations, particularly the ones in the boxes, if you just want to learn what the main ideas in modern gravity and astronomy are. So if you find your mathematics too old or rusty, then see how you get along without it.

High-school mathematics

The mathematics used is basic numeracy, algebra, and a tiny bit of trigonometry (which you can skip).

It is essential to understand scientific notation for numbers, that is how to write numbers in the form 3.2 × 106 and know what the factor 106 means. Scientists use this notation all the time, because otherwise they would be writing out long confusing strings of zeros. The number 3.2 × 106 means 3 200 000, obtained by moving the decimal point in 3.2 six places to the right. Similarly, the number 5.9 × 10−3 is 0.0059, obtained by moving the decimal point three places to the left.

The study of cosmology presents today's physicists with the biggest challenges to their understanding of gravity and of fundamental physics in general. Both on theoretical and on observational grounds, it seems that we will not be able to understand cosmology well until we understand physics better than we do today. But it also seems that cosmology could provide us with the keys to that deeper understanding of physics.

The biggest gap in physics is quantum gravity: we do not yet possess a consistent way of representing gravity as a quantum theory. There is no uncertainty principle in general relativity, no quantization of gravitational effects, no need to use probabilities in making predictions about the outcome of gravitational experiments. This seems inconsistent with the fact that all material systems that create gravity are quantum systems: if we can't say exactly where an electron is, how can we say exactly where its gravitational field is?

The cycle of birth, aging, death, and re-birth of stars dominates the activity of ordinary galaxies like our own Milky Way. The cycle generates the elements of which our own bodies are made, produces spectacular explosions called supernovae, and leaves behind “cinders”: remnants of stars that will usually no longer participate in the cycle. We call these white dwarfs, neutron stars, and black holes.

Governing this cycle is, as everywhere, gravity. An imbalance between gravity and heat in a transparent gas cloud leads to star formation. The long stable life of a star is a robust balance between nuclear energy generation and gravity. This balance is finally lost when the star runs out of nuclear fuel, leading to a quiet death as a white dwarf or to a violent death as a supernova.

We have seen how the Sun's gravity holds the planets in their orbits. The Sun's gravity also holds itself together. Like all stars, the Sun is a seething cauldron, its center a huge continuous hydrogen bomb trying to blow itself apart, restrained only by the immense force of its own gravity. In this chapter, we will see how the Sun has managed to maintain an impressively steady balance for billions of years. In the course of our study, we will learn about how light carries energy and we will build a computer model of the Sun.

Sunburn shows that light comes in packets, called photons

The Sun glows so brightly because it is hot. We can infer just how hot it is from its color. The color and temperature of the Sun are related to each other in just the same way as for hot objects on the Earth.

Black holes. No term evokes the mystery of modern gravity more than this one. The mystery of black holes is more than an invention of popularizers of astronomy and relativity. Black holes were certainly a mystery to Einstein and his contemporaries. Yet today black holes are everywhere: in X-ray binaries, in the centers of galaxies, and of course in books, like this one, on relativity and gravity!

Theorists attacked the problem of understanding black holes, not by using astronomical evidence, but by using lessons they had learned from quantum mechanics. Quantum thinking demanded that physicists ask only questions about things that could be measured, not about what is hidden from experiment. Thus, they can measure that light behaves sometimes as a particle (the photon) and sometimes as a wave, but they find it useless to ask what is a wave–particle.

In the last two chapters we have made a lot of progress in exploring the future and past of the Universe, basically just by using local Newtonian gravity. We argued that the dynamics of an expanding, homogeneous and isotropic cosmology can be calculated from Newtonian gravity, at least if the pressure in the Universe is negligible, because all we need to look at is the local Universe, the part nearest us. The assumption that the Universe is homogeneous guarantees that the rest of the Universe will behave the same as our local region.

1. ▷ The drawing under the text on this page illustrates how complicated three-dimensional solid objects could be. Why is the Universe apparently so simple?

But this line of reasoning has its limitations. Even if we calculate the dynamics of the Universe this way, we don't learn what the distant parts of the Universe will look like in our telescopes. The curvature of space, which is not part of a Newtonian discussion, will affect the paths of photons as they move through the Universe. Moreover, if we want to ask deeper questions about the Universe, such as those we pose in the next chapter, then we should know something more about its the larger-scale structure.

There would be no life as we know it on Earth without the atmosphere. Even life in the oceans would not exist: without the atmosphere's thermal “blanket”, the oceans would freeze. Yet in the beginning, the Earth probably had a very different atmosphere from its present one. The other planets, with their different masses and different distances from the Sun, all have vastly different atmospheres from the Earth's. In the retention of the atmosphere, and in the subsequent evolution of the atmosphere and of life itself, gravity has played a crucial role.

In this chapter, as we look at the role that gravity has played in this story, we shall encounter fundamental ideas about the nature of matter itself: how temperature and pressure can be explained by the random motions of atoms, why there is an absolute zero to the temperature, and even why atoms cannot quite settle down even at absolute zero.

Gravity is the engine that drives the Universe. But it does not work alone, of course. In fact, one of the most satisfying aspects of studying astronomy is that there is a role for essentially every branch of physics when one tries to explain the huge variety of phenomena that the Universe displays. One branch of physics, however, stands out from the rest because of its absolutely central place in helping us to learn about the Universe, and that is the study of the way hot bodies give off light.

Almost all of the information we have from astronomical bodies is carried to us by light, and almost all the light originates as radiation from some sort of hot region. The great breakthrough in physicists' understanding of such thermal radiation was made by the German physicist Max Planck (1858–1947) at the start of the twentieth century. (See Figure 10.2 on page 112.) The story of this breakthrough is the story of physicists' first steps toward quantum theory. It is also the story of the beginnings of a real understanding of the heavens.